ReAKKT

What do you get for the fund management fees?

2012-01-22T09:03:00.001+01:00

I've recently mentioned that only some small Polish non-benchmark (semi-hedge) funds decoupled from the general market deterioration in 2011.

But how they really compare to the market and how they are correlated between themselves?

From June 2009 till January 2012 Gandalf SFIO virtually didn't change its value:

The annualized return over this period is -0.14%. Meanwhile, WIG20 returned +12.15%.

The main feature of Gandalf SFIO is its low negative correlation with the index.

As for Opera Alfa-Plus, the fund returned +22.8% since inception and +8.62% annualized:

Still that's worse than WIG20 which grew by +31.2%:

In contrast to Gandalf SFIO, the correlation between Opera Alfa-Plus and WIG20 is slightly positive.

It gets quite interesting when you compare performance between the funds:

Opera Alfa-Plus has clearly been better performing than Gandalf SFIO so far, but the funds have been negatively correlated, so the future may change that.

Nevertheless, beating the index (basic buy and hold strategy) is not an easy task. So what do you get for the management fees?

Data: Gandalf SFIO, Opera Alfa-Plus

R source

Distance and dimensions

2012-01-20T08:01:00.001+01:00

Something totally different, today :)

At least as measured by Minkowski distance, distance between three-dimensional objects is inversely proportional to the number of dimensions of the space in which one measures distance.

For example, distance between two randomly selected points may be 150.90 units in R^3, while it drops to 129.86 units, or by 13,94%, in R^96.

So, if one would be able to make shortcuts through some hypothetical additional dimensions, one could travel faster than others moving in plain R^3. The potential gains are not huge, though.

The difference between distances in various R^n spaces decreases quite significantly and around R^20, the incremental gains are usually smaller than 1% per additional dimension:

      dimensions distance    difference   difference%
 [1,]          3 150.9008  1.509008e+02           Inf
 [2,]          4 140.6339 -1.026687e+01 -6.8037222878
 [3,]          5 135.7465 -4.887388e+00 -3.4752557745
 [4,]          6 133.1936 -2.552873e+00 -1.8806176731
 [5,]          7 131.7919 -1.401690e+00 -1.0523697580
 [6,]          8 130.9986 -7.933852e-01 -0.6019982623
 [7,]          9 130.5400 -4.585113e-01 -0.3500124575
 [8,]         10 130.2709 -2.691661e-01 -0.2061942603
 [9,]         11 130.1109 -1.600260e-01 -0.1228409661
[10,]         12 130.0147 -9.616443e-02 -0.0739096136
[11,]         13 129.9564 -5.832922e-02 -0.0448635601
[12,]         14 129.9207 -3.567275e-02 -0.0274497876
[13,]         15 129.8987 -2.197770e-02 -0.0169162448
[14,]         16 129.8851 -1.363012e-02 -0.0104928834
[15,]         17 129.8766 -8.503742e-03 -0.0065471273
[16,]         18 129.8712 -5.334217e-03 -0.0041071429
[17,]         19 129.8679 -3.362549e-03 -0.0025891404
[18,]         20 129.8658 -2.129199e-03 -0.0016395115
[19,]         21 129.8644 -1.353778e-03 -0.0010424441
[20,]         22 129.8635 -8.640018e-04 -0.0006653107

Reconstructing missing observations with R

2012-01-12T10:50:00.002+01:00

I've been playing with reconstruction of missing observations for the last couple of days.

Say you've got a quotations of some equity that miss some data points.

You may want to have them reconstructed for example for pairs trading.

What do you do then?

Chart: example of VAR reconstruction of missing data

I've preliminary tested a number of potential methods from simple mean to Dynamic Linear Models to Random Forest.

Performance varies, but for the moment three reconstruction methods seems to lead the pack: simple mean, some Dynamic Linear Model and Vector Autoregression.

Chart: comparison of various reconstruction methods for one case

Some thoughts on the Polish pension funds

2012-01-12T08:41:00.000+01:00

The Polish (mandatory) pension funds - OFEs - were down in 2011. Average one year performance (as of yesterday) was -3.72%.

Nevertheless, they are on average +192% up over their 13 year period of existence. And that translates into a quite nice +8,6% CAGR.

And - what's important - they have clearly beaten the stock market:

Chart: ING OFE vs WIG20, 1999-2012, stooq.com

However, what's worrying is a very high correlation between all the funds:

Chart: OFE prices 1999-2011

The correlation rank between OFEs keeps between amazingly thin range of 99,51% and 99,97%:

Chart: OFE correlation distribution 1999-2011

Clearly, OFEs are not competitive. For extremely high correlation they are also a potential source of systemic risk.

Source code: http://snipplr.com/view/62513/ofe-correlation-19992011/

WIG20 - S&P500 decoupling

2012-01-11T07:18:00.000+01:00

Chart: WIG20 vs S&P500 futures 5 days, 2012-01-10, stooq.com

The Polish stock market index WIG20 has recently decoupled from the US market index S&P500 quite significantly.

This divergence has lasted for some time now:

Chart: WIG20 vs S&P500 futures 3 months, 2012-01-10, stooq.com

Something will have to correct... But which one?

Or is it just an opportunity for a convergence trade without trying to guess the direction?

Was the yesterday's funny WIG20 action a signal of the future developments?

Questions, questions and more questions... :)

Nevertheless, it's worth keeping in mind that even though Polish and US markets are highly correlated, correlation is not a stable measure. It's much safer to check the spread between the markets based on their cointegration.

Last but not least, S&P500 remains decoupled from the wider risk assets context model.

A WIG20 mystery today

2012-01-10T21:49:00.000+01:00

I'm a little too tired to think clearly and research today (it's nearly 22:00 and I'm awake since 4:50), but I've noticed something funny with WIG20 today:

Chart: WIG20 vs FW20 continous futures, 2012-01-10, stooq.com

It may be connected with Getin - GetBank merger, but I'm not sure...

Nevertheless, WIG20 separated with the most liquid futures by 45 points.

Herd mentality

2012-01-10T20:25:00.001+01:00

2011 was definitelly a bad year for many hedge funds. The Paulson Advantage Plus fund managed by John Paulson who had made a killing during the recent sub prime crisis, lost more than 50% this year.

The Polish "near hedge funds", such as Investor FIZ and Opera FIZ didn't fare much better. But the worst part is their performance this year was highly correlated with the market :(

Chart: Investor FIZ and Opera 3gr vs WIG20; source: stooq.com

Seems one of the better asset management companies in the previous years - IDMSA - unfortunately also employed similar strategy:

Chart: Investor FIZ, Opera FIZ and IDMSA ZZP portfolio vs WIG20

Decoupling was demonstrated by small funds like Opera Alfa-Plus and Gandalf SFIO, but that allowed only for capital preservation instead of accumulation. Opera Alfa-Plus finished the year just 1.24% higher, while Gandalf returned 3.75% (January 4th, 2010 - January 3rd, 2011).

Meanwhile quantitative SuperFund lost -20.2% (SuperFund A SFIO PLN) to conclude its six years of presence on the Polish market more than 22% under the water...

Hedge fund / non-benchmark funds were advertised as market neutral, able to withstand market turbulence. Unfortunately it seems most of them demonstrate unhealthy herd mentality.

Especially when they also have problems with beating the market in good times.

US military expenditures vs GDP

2012-01-06T11:32:00.000+01:00

And now for something completely different, as the Month Python guys would say :)

President Obama visited Pentagon yesterday to announce significant military budget reductions over the next decade. The military expenses should be ~~restricted to $487 billion annually~~ reduced by $487 billion in the coming years.

Taking into consideration, that the United States spent $698 billion for its military in 2010, that translates into ~~an unprecedented cut by 30% and CAGR of -3.5% over 10 years~~ an average cut of 7% annually.

However, the US military budget was close to "just" $500 billion as close as in 2005, before it shoot to the last year's level of nearly $700 billion.

Nevertheless, the announced military cut can possibly have some significant implications to the economy, for:

military expenditures constitute close to 5% of the GDP, and
acted as counter cyclical factor in the most recent recession.

Chart: US military expenditures 1988-2010, billion USD

Chart: US military expenditures as % of GDP, 1988-2010

Chart: growth of US military expenditures vs GDP growth, 1988-2010

WIG20 oversold?

2012-01-04T10:46:00.002+01:00

Chart: "Context model" for WIG20 as of 2012-01-03

Continuing experiments with the "context models" mentioned before, I have prepared a preliminary model for WIG20.

Above you see the visualization of the model result as of 2012-01-03. Seems the Polish market may be oversold versus its "context".

This would correspond pretty well with the "market prediction for 2012" described here.

The time will verify that :)

Shortsightedness and bipolar disorder?

2012-01-01T13:50:00.000+01:00

I've been reading today about the analysts expectations for the performance of the stock market in 2012. Surprised by this year's market turmoil, they expect volatility to remain heightened. They expect either side-bound market or further declines, before later increases. The Q1 should give the definitive answer about the direction of the market in the rest of the year. In total, they are much more worried and divided than last year. And - as I wrote earlier - they are not alone.

Let's compare what the analysts were expecting at the beginning of 2011. The consensus on December 24th, 2011, when WIG20 was at 2768.66, was for the market to raise by 10-15%, most probably after expecting correction to 2500 in 2011Q1, possibly to 3300-3500.

In reality, the WIG20 decreased by 22.15% (from the open of 2754.67 on January 3rd, 2011 to the close of 2144.48 on December 30th, 2011). In the meantime, it reached the peak of 2942.39 (i.e. +6.81% from the beginning of the year (BYD) and +6.27% from December 23rd, 2010) on April 8th to fall to 2018.99 (i.e. -26.70% from the BYD) on September 23rd, 2011.

Since it seems, analysts are usually dead wrong, the best strategy would be to take to opposite view to their current predictions.

Hence, we should either expect the volatility to come down and market to go up (scenario 1) or the market to go up at the beginning of the year, before correcting later (scenario 2).

I both cases, the market should finish the year much higher than it's current level:

Chart: Contrarian to analysts' predictions for WIG20 for 2012

Update 2012-01-04:

Analysts' predictions for S&P500 in 2012:

Morgan Stanley - 1167
HSBC - 1190
Goldman Sachs - 1250
Oppenheimer - 1400
JP Morgan - 1430
Deutsche Bank - 1500
average (Birinyi Associates) - 1334

Other source:

mean: 1363
range: 1167 - 1500

Serendipity or extremes detection

2011-12-31T18:39:00.001+01:00

Chart: Brent oil futures vs "context model"

I've been experimenting with context models for financial assets today, when by serendipity discovered potentially very interesting method for detecting market extremes.

Above you see the chart presenting the price of the Brent oil futures versus some context model.

This was an experiment, since the model was designed to asses prices of some other assets. Brent oil was originally a part of the context. Then I turned the model around.

Nevertheless, the experiment clearly shows that the price of Brent oil extremely diverged from the context in February 2009. Or rather the opposite happened - the context strongly diverged from the Brent.

It would be an interesting indicator for buying context if only I was using this model in 2009...

Hopefully the method will be ready soon for other extremes :)

Zero x2

2011-12-31T11:35:00.002+01:00

S&P500 has just finished the 2011 at 1257.60, nearly perfectly +/-0% from the beginning of the year (1262.82 at the open on January 3rd, 2011, i.e. -0.0041% to be precise).

It also means that the index virtually didn't move from June 1st, 2001, or 10 years and 7 months before, when it closed at 1260.67.

Welcome to the new brave world of ZERO ;)

Source: Google finance

Still. ZERO is better than BEAR MARKET declared by Reuters at the beginning of October this year...

Source: Reuters 2011-10-04

Since the low of 1099.23 on October 3rd, the market rallied 11.15%.

Dot.com 2.0 - opportunity or bubble?

2011-12-17T06:58:00.000+01:00

Zynga Inc. debuted on NASDAQ, yesterday. The company shares felt by -5.00% to $9.50 from the IPO price.

Zynga is the fourth high profile internet company that offered its shares to the public this year - after LinkedIn, Pandora and Groupon.

So what the performance of these companies have been so far? Mixed.

LinkedIn +46.31% from $45 IPO price
Pandora -34.05% from $16
Groupon +15.20% from $20

In total, the portfolio comprising of equally weighted four internet companies bought at IPO would bring +5.61% till yesterday. In the meantime, S&P500 lost -9.22% and NASDAQ -9.49%.

So, do we have a new buying opportunity of a life time or the next dot com bubble?

Commerzbank jumps, but will it last?

2011-12-14T21:38:00.001+01:00

Chart: Commerzbank vs DAX and Deutsche Bank, 2011-12-14, source: stooq.com

Commerzbank's shares jumped by more than 5% today on news of the reactivation of the German bank rescue fund and some increase in the planned purchases of highly discounted hybrid securities by the bank.

Despite today's rally, Commerzbank is still -78% YTD, -79% 1 year and astounding -95% 5 years.

According to Financial Times:

Officials in Berlin are privately sceptical that Commerzbank can keep to its pledge to shore up its capital without using more state funds.

The rescue fund, could allow Commerzbank to get rid of its Eurohypo division. However:

Chintan Joshi, analyst at Nomura, said that transferring bonds to the government at above market value would be a “straight bail-out” and therefore unlikely. “We do believe that a bail-out will come with pain attached ... we do not think Germany can provide a lucrative bail-out to Commerzbank in the current climate,”

Also (Wall Street Journal):

On the downside, selling these assets to the SoFFin would come at the expense of hefty write-offs as they would have to be transferred at lower market values.

And this leads us to (FT again):

Officials in Berlin are privately sceptical that Commerzbank can keep to its pledge to shore up its capital without using more state funds.

While:

Among the measures in the bill are provisions for BaFin, Germany’s financial regulator, to force banks to accept state help if it thinks a bank’s plans to raise capital are insufficient.

According to EBA, Commerzbank need 5.3 billion EUR of fresh capital. It's current market cap is 6.28 billion EUR. It can get some 700 million EUR from the purchases of the hybrid debt. Some more from savings.

Let's assume, the state bail-out will inject "only" 3 billion EUR of the fresh equity. It would mean, that the current shareholders would be diluted by some 66%.

Under such scenario the price of Commerzbank shares can quite easily go under 1 EUR.

More news about Commerzbank: https://pinboard.in/u:mjaniec/t:Commerzbank/

Let's Occupy Wall Street?

2011-12-11T21:06:00.001+01:00

Screenshots from Modern Warfare 3

I wonder whether the Occupy Wall Street movement was inspired by Modern Warfare 3 or the other way around.

Nevertheless, MW3 is definitely my favorite installment is the series so far :)

200 billion EUR without the UK = 170 billion EUR

2011-12-11T09:21:00.001+01:00

At the recent EU summit, politicians declared "up to 200 billion EUR" loans to IMF to strengthen the defense of the Euro.

150 billion EUR should come from the eurozone member countries, and 50 billion EUR from the other EU states.

It's quite easy to find out where these numbers come from: 150 billion EUR / (eurozone GDP / EU GDP) = 202.45 billion EUR.

However, the UK veto changes slightly this calculation.

First some basic statistics (source: Wikipedia):

EU GDP = 12,268,387 million EUR
EU GDP less UK = 10,471,804 million EUR
Eurozone GDP = 9,089,966 million EUR
non-eurozone GDP = 3,178,421 million EUR
non-eurozone GDP less UK = 1,381,838 million EUR

non-eurozone GDP less UK / non-eurozone GDP = 43,48%

Hence, the 50 billion EUR non-eurozone contribution, will most probably be reduced by some 57%:

50 billion EUR * 43.48% = 21.74 billion EUR

Assuming no other country backs off from the plan, we should expect that the IMF loans will total:

150 + 21 = 171 billion EUR

BTW: A Polish newspaper "Gazeta Polska codziennie" suggests the Polish contribution to the IMF loans will equal 100 billion PLN or 22.22 billion EUR. I don't understand where this number comes from. I'd assume, Polish contribution would be equal to 21.74 billion EUR * (Polish GDP / non-eurozone GDP less UK) or 5.57 billion EUR * 4.50 EURPLN = 25.08 billion PLN.

A day at the races

2011-12-09T22:05:00.001+01:00

Fig. S&P500 futures, 2011-12-08 / 09; source: XTB

The S&P500 futures have fallen from 1270 to 1222 yesterday (i.e. -3.8%), to bounce back to around 1250 today (+2,3%).

"The European Union will die - SELL, SELL, SELL!" - suggested reaction to the yesterday's ECB announcement. "The European Union is saved - BUY, BUY, BUY!" - declared investors after the summit.

I have seen quite similar behavior somewhere, some time ago...

Back to Twist

2011-11-21T22:30:00.001+01:00

Chart: S&P500 futures close, 2011-11-21; XTB

After exactly two months, S&P500 has returned today to the level it was just before the Fed announced Operation Twist.

Another failed test of financial data normality

2011-11-20T07:32:00.001+01:00

Chart: Robust non-parametric runs test for tick data for LOTOS, June 2005 - October 2011

Back in May 2010, I presented a preliminary analysis of the probability of consecutive changes and conditional consecutive changes for daily closing prices for S&P500 and EURUSD.

I mentioned then some observed deviations from the random walk model, and postulated further research. I've just had an opportunity to check this behavior on intraday data for a number of stocks listed on the Warsaw Stock Exchange.

I have modified the methodology and changed some assumptions in the test procedure. Above you can see the result of the new test performed on the tick data for Grupa Lotos S.A.

Deviations from the model probability are clearly visible even when a pretty wide confidence band based on the sampled distribution probability is implied to filter out uncertain signals.

It's not HFT on the WSE yet, but...

2011-11-18T16:33:00.001+01:00

Chart: Cumulative ticks per day for WIG20 shares, November 2000 - October 2011

The above chart shows the cumulative number of the ticks per day recorded between mid November 2000 and end of October 2011 for the shares currently constituting WIG20 index (please note that the composition of index was different before September 2011 and some of the share currently traded were not available in the past)

Clearly the frequency of registered quotes hence the trades is raising. Still, it's far from the theoretical maximum.

Let's wait what happens when the Warsaw Stock Exchange introduces a new trading platform next year...

Correlation doesn't mean easy prediction

2011-10-27T19:10:00.002+02:00

Chart: WIG20 futures vs S&P500 futures over 10 years, stooq.com

The Polish and the US stock markets are undeniably connected, which is visible on the above chart, showing performance of the WIG20 futures against the S&P500 futures over 10 years (the realized correlation over the period is 0.7091).

However it doesn't mean that you can use this connection to predict short time price movements - the correlation between previous day change in the S&P500 futures and the current day WIG20 futures change is just 0.1380.

Since for the gaps between the closing on the previous day and the opening on the current you are unable to "catch" the whole daily change of the WIG20, the better value to compare is the change from the opening till close. In this case, the correlation with S&P500 futures changes to -0.1273 (minus).

> fw20c[1:10,]

Date Open High Low Close Volume OpenInt D_Change OC_Change

3 2000-01-05 1827 1839 1807 1811 5172 4694 -0.019683522 -0.0087960985

4 2000-01-06 1802 1849 1784 1848 5220 4801 0.020224794 0.0252068140

5 2000-01-07 1936 1998 1935 1982 5671 4918 0.070002463 0.0234824471

7 2000-01-11 2010 2070 1950 2042 5990 5622 -0.020359404 0.0157949977

8 2000-01-12 2015 2044 2010 2030 4312 5917 -0.005893927 0.0074165977

9 2000-01-13 2110 2148 2093 2135 5174 6033 0.050430854 0.0117786992

10 2000-01-14 2080 2137 2075 2115 5024 5716 -0.009411834 0.0166869188

13 2000-01-19 2035 2044 2005 2036 5719 5936 -0.005388208 0.0004912798

14 2000-01-20 2058 2068 2007 2053 5975 5839 0.008315039 -0.0024324994

15 2000-01-21 2043 2077 2043 2071 3672 6266 0.008729444 0.0136122666

(...)

> esfc[1:10,]

Date Open High Low Close Volume OpenInt D_Change

2 2000-01-04 1467.00 1468.75 1409.50 1411.75 61942 13967 -0.038218999

3 2000-01-05 1411.50 1427.25 1385.00 1413.50 64049 13007 0.001238829

4 2000-01-06 1411.00 1426.25 1395.75 1404.00 73127 13870 -0.006743593

6 2000-01-10 1459.75 1481.00 1455.25 1475.00 60548 15339 0.009879147

7 2000-01-11 1473.75 1475.00 1447.00 1454.25 59343 16080 -0.014167686

8 2000-01-12 1453.50 1459.50 1438.75 1442.00 70097 16982 -0.008459265

9 2000-01-13 1441.50 1466.75 1441.25 1458.50 62509 16832 0.011377471

11 2000-01-18 1478.00 1480.25 1462.00 1469.50 57421 16106 -0.005767616

12 2000-01-19 1468.75 1474.00 1450.25 1472.50 65454 16859 0.002039430

13 2000-01-20 1472.75 1485.00 1448.00 1457.00 57788 18126 -0.010582109

(...)

> cor(esfc$D_Change,fw20c$D_Change)

[1] 0.1380338

> cor(esfc$D_Change,fw20c$OC_Change)

[1] -0.1273032

> cor(fw20c$D_Change,fw20c$OC_Change)

[1] 0.8551321

Source code available here.

Cointegrated drunk and her dog visualized

2011-10-25T22:31:00.002+02:00

Chart: Drunk and Her Dog

I was reading today an article about cointegration, written by Michael P. Murray. It describes a case of a random walking drunk accompanied by an unleashed dog. Occasionally the dog barks or the drunk calls the dog, and they try to get a little closer to each other based on the sounds.

I thought it may be interesting to visualize the process. You can see the result above :)

The drunk and her dog start at the position [0,0]. Their final positions (in this case after 100,000 moves by each) are indicated by the crossings of the green - for the drunk - and blue - for the dog - lines.

There are three parameters to set: the number of steps, the frequency of either dog barking or the drunk calling the dog, and the efficiency of the correction mechanism, i.e. how much they can reduce distance between themselves on each occasion they try to get closer, and how precisely they can set the course toward each other (the angel).

Although trajectories of both the drunk and the dog follow the random walk:

They are highly correlated:

> cor(drunk_path[,1],dog_path[,1])

[1] 0.9951132

> cor(drunk_path[,2],dog_path[,2])

[1] 0.9937595

And the distance between them is a stationary process:

> mean(distance);sd(distance)

[1] 8.948513

[1] 6.242085

You can decrease the correlation of the cointegrated processes by manipulating the frequency of error correction and precision of the correction mechanism - see parameters mentioned above.

Source code available here.

Eat this Berkshire Hathaway ;)

2011-10-07T19:08:00.001+02:00

Chart: Danaher Corp. vs Berkshire Hathaway & S&P500

Since June 1990, stock price of Warren Buffet's Berkshire Hathaway was growing on average by 13.5% annually. As a result Berkshire shares rose by 1435% versus just 218% for S&P500. Pretty good, isn't it?

Yes, but you can find companies that dared significantly better. One of them is Danaher Corporation - a conglomerate of various industrial and technological companies - that grew by 2961% over the same period.

Its performance is equally impressive over a much longer period of nearly 33 years - 37093% in total or 19.3% annually versus 1100% for S&P500.

Highly distorted prices of long term BofA call options

2011-10-02T09:50:00.000+02:00

There is something funny going on with the long term out-of-the-money call options on Bank of America. And its not a typical example of the "volatility smile" ;)

$1.00 calls for December 2013 were trading (lightly) at $0.08 on Friday. According to Black-Scholes formula, a theoretical value of such option is $5.12.

At the same time, $1.00 calls for December 2014, were quoted at $0.36, although there were no transactions.

If you cannot save it, dump it

2011-10-01T23:20:00.001+02:00

Chart: S&P 500 Heatmap 2011-09-30; finviz.com

Nobody was willing to window dress on the last day of September. S&P500 index felt 2.5% on Friday. Futures were down even more - 3.13%. S&P500 is down 7.2% for September and 14.3% for the quarter.

Maybe I'm too optimistic, but I'd assume that at least some money managers decided that if they couldn't improve their quarterly numbers it might be better for them to sink even more to lower the baseline for the next quarter.

Many investors believe that S&P500 currently is at the critical technical level and either it will defend it or sharply go down. Some of the most pessimistic analysts even see the 400 level...

Definitely there are reasons to worry about the prospects of the global economy and hence stock prices. As mentioned in the previous posts, investors are highly divided, which leads to high volatility.

Two key factors affect the markets: dragging crisis in Europe and fears about the economy. Since we shouldn't expect resolutions to these problems soon, the volatility will most probably continue. More panic sell outs are likely.

Nevertheless, I'd not expect the Greek crisis to transform into another Lehman crash, even if Greece defaults. The Greek debt is much smaller than Lehman's assets, it has different characteristic, and the parties involved had plenty of time to prepare.

In the meantime, the economic data are mixed, with weak confidence readings overshadowing some signals of slow improvements.

On October 11th, the Q3 earning season begins. The company earnings may be a little better than expected. Provided that none catastrophic event materializes, there is a chance markets will raise. Although I'd not aim at the 1450 level at the end of the year as some analysts...

Warren Buffett didn't make 20% on August 26th...

2011-09-30T19:02:00.003+02:00

...he potentially made over 63%!

And his investment is asymmetrically depended on the performance of the Bank of America shares. He can gain when shares go up, but doesn't lose when they go down. Unless the bank fails.

How does it works?

Chart: Bank of America, 3M, 2011-09-30; stooq.com

Bank of America is down again today. So far -2.6% at $6.18. That's 11.6% below the price on the day when Warren Buffett invested $5 billion in the company ($6.99), and 16.6% below the strike price of warrants granted to him ($7.14).

Nevertheless, one cannot say that Mr. Buffett is down on his investment.

The Buffett's investment consists of two elements:

preferred shares paying 6% dividend
10 years warrants for 700 million BofA shares with the exercise price of $7.14

Preferred shares are more like a subordinate debt rather than ordinary shares. Their performance is not connected with market fluctuations. As long as BofA don't go bust, they pay a nice dividend and retain their value.

Warrants are equivalent of call options on BofA shares. Based on the historic 10 years BofA volatility of 55% and using 10 year T-bonds yield of 1.83% we can estimate the value of the warrants using Black-Scholes formula. The result is $4.5 per warrant.

Since Bank of America granted 700 million warrants to Mr. Buffett, the potential value of them is about $3.15 billion. $3.15 billion on top of $5 billion investment makes a 63% return.

There are two critical assumptions in this investment, though:

Bank of America does not go bankrupt
Bank of America does not require a substantial government bail-out that wipes out existing shareholders and decimates share price

Even if you assume a high discount rate (say 50%) for calculating the potential value of the preferred shares purchased by Buffett, the total ROI on investment is above 10%.

Waiting for the break out

2011-09-30T11:50:00.001+02:00

Chart: Risk-on / risk-off investor behavior; Bloomberg BRIEF

Thursday's Bloomberg BRIEF describes the recent bipolar investors behavior dubbed "risk-on / risk-off".

Such behavior seems connected with the investors' uncertainty about the prospects of the economy. While many still believe in the recovery, similar number worry about a possible "double-dip".

And the prolonging crisis in Europe does not help...

As a result the distribution of the daily changes of the S&P500 index for the previous 20 sessions seems to resemble the investors assessment of the economy:

Chart: distribution of daily S&P500 changes, 20 days through 2011-09-29

Pretty unusual distribution (BTW: kurtosis of -1.2587 is characteristic to Wigner semicircle distribution) in connection with high volatility makes the market difficult for trend-oriented investors.

But the market won't stay range-bound forever, will it?

Probability of Lotto

2011-09-26T11:15:00.001+02:00

There is currently a noticable accumulation in the Polish Lotto - 50 million PLN or $15.2 mln / 11.3 mln EUR.

Since there are 6 numbers to select from 49, according to the basic probability calculations, the chance that some single ticket will win is 1 to 13,983,816.

Hence, the expected value for a single ticket would be 50 million PLN * 1/13983816 or 3.57 PLN. Seems, someone buying some 13.98 million tickets (each at 3 PLN, which requires an investment of 42 mln PLN) cannot lose, right?

Not exactly.

It may happen there will be more than one winner. Let's suppose, some 10 million tickets will be bought in total by various people. Then, the probabilities of 2, 3, 4 or 5 distinctive winners are as following:

> dbinom(2:5,10e6,1/choose(49,6))

[1] 0.1250688763 0.0298127636 0.0053298679 0.0007622907

In other words, there is a pretty large chance (16.1%), there will be 2 or more wining tickets.

OK, so what is the expected value given the number of tickets bought?

Assuming that between 1 and 50 million tickets will be bought, the expected value decreases from 3.512 to 1.319:

Chart: expected value [PLN] vs number of tickets sold [mln]

For 10 million tickets, the EV is equal to 2.9659, which is below the price of the ticket (3 PLN):

> Nwinners <- 100 # max. simultaneous winners in history - 80
>
> Nbets <- 10e6
>
> Vwin <- 50e6
>
> Wwin <- sum(dbinom(1:Nwinners,Nbets,1/choose(49,6))/sum(dbinom(1:Nwinners,Nbets,1/choose(49,6)))*(Vwin/(1:Nwinners)))
>
> Wwin
[1] 41475080
>
> Wwin/Vwin
[1] 0.8295016
>
> Wwin/choose(49,6)
[1] 2.965934

And there is also a 10% tax on winnings...

UPDATE: On March 30, 1994 there was 80 winning tickets. The probability of such an event is 4.985477*10^-86, even if ALL the Poles would have bought one ticket.

> dbinom(80,38*10^6,1/choose(49,6))
[1] 4.985477e-86

The probability drops to 1.529368*10^-131 with 10 million tickets bought.

Just as a reference, the number of the atoms in the observable universe is estimated at 10^80.

A bigger bubble?

2011-09-25T09:18:00.000+02:00

Do you think gold is a bubble? If yes, what would you say about Apple?

Chart: Apple vs gold, 10 years; stooq.com

Seven

2011-09-23T17:19:00.000+02:00

Over the last nearly three years researches at CERN have been observing some interesting discrepancies in time it takes neutrinos to travel between laboratories in Switzerland and Italy.

The difference is very tiny - just 60.7 ns (equivalent to 17,77 meters at c) on a distance of 731,278 meters which translates into a 0.0000248 difference in the speed of light. In other words, the measured speed of neutrinos is 292,799.3 km/s instead of 292,792 km/s, or 7 kilometers per second larger.

Even though the physicists at CERN spent significant time on verification of their surprising measurements, its too early to declare the result definitive. It definitely requires verification at other laboratories.

But if it is confirmed, this tiny rift can transform into huge hole in the contemporary physics.

BTW: In 2008, researches from Fermilab published results of their MINOS experiment, in which the speed of neutrinos was measured at +0.000051, or 299,807.3 - 15 kilometers per second larger than c. However, the possible error was much higher than in the case of OPERA in CERN.

Kweku Adoboli vs Leo Apotheker ;)

2011-09-23T13:46:00.002+02:00

Kweku Adoboli is a UBS trader accused of losing $2.3 billion in a series of rogue transactions. Since September 15th, when the loss was announced, share price of UBS felt down by 14.62%, decreasing UBS market capitalization by some $6.8 billion.

Foto: Kweku Adoboli; Mirror

Leo Apotheker was the CEO of HP till yesterday. Since September 30th, 2010 when he was appointed, the capitalization of HP felt by 47.17% or by $40.44 billion.

Foto: Leo Apotheker; CBS News

Banks squeezed by regulations

2011-09-22T10:34:00.000+02:00

Moody's downgraded debt of Bank of America, Citibank and Wells Fargo yesterday, saying the banks may not be too big to fail anymore.

In response Bank of America shares plummeted 7.54% to $6.36, below the $6.99 price before Warren Buffett invested $5 billion in the company in August. The price of bank's shares is also nearly 11% below the exercise level of warrants granted to Buffett. Fortunately for Mr. Buffett, part of the short-term impact should be reduced by 6% dividend from preferred shares he owns, and the warrants can be exercised anywhere over the 10 year period.

Nevertheless, Moody's action reflects increasing pressure banks both in the U.S. and Europe are facing from new regulations introduced after the crisis of 2008 - mainly Dodd-Frank and Basel III.

The former was conceived as a way to allow safe unwinding of financial institutions without the need of government bail outs. The later increases capital requirements for banks.

According to Basel III, banks should increase their Tier I capital (i.e. common shares + retained earnings) / Risk Weighted Assets ratio to 4% and additionally create a "capital conservation buffer" of 2.5%.

However, there is a significant problem with with the way of calculating Risk Weighted Assets (RWA) under Basel III. The regulations assign no risk to sovereign debt. As a result, European banks that already at least partially implemented Basel III rules, face a difficult situation connected with their holdings of peripheral eurozone bonds.

More conservative way of calculating capital adequacy is to simply divide bank equity by assets. When you use this formula to compare U.S. banks to their European peers, you get quite a scary picture:

Chart: Equity / Assets ratio for selected banks; data as of 2011-06-30 based on Google Finance

Problems in Europe overshadow Operation Twist

2011-09-21T22:41:00.000+02:00

Chart: S&P500 futures 1 day 2011-09-21; stooq.com

As anticipated, Fed has announced the "Operation Twist" today. The declared scale of the operation is a little larger than anticipated. And as a result markets have sunk by 3%... (still, -2.94% is better than
-6.66% ;)

Early comments point to the wording of the FOMC statement about the "significant downside risks to the economic outlook, including strains in global financial markets" (previously: "downside risks to the economic outlook have increased").

Is it really so strange that FOMC confirms there is a culminating problem in Europe, or is there something more?

Since reading even a pretty short FOMC statement is not so easy when markets are reacting aggressively in the real time, many people probably haven't noticed yet a number of slightly positive changes in the wording:

AUGUST > SEPTEMBER

indicators suggest a deterioration in overall market conditions > indicators point to continuing weakness in overall market conditions
household spending has flattened out > household spending has been increasing at only modest pace
inflation picked up earlier in the year > inflation appears to have moderated since earlier this year
The Committee now expects a somewhat slower pace of recovery over coming quarters > The Committee to expect some pickup in the pace of recovery over coming quarters

It seems, Fed has observed some weak signals of the improvements in the economic conditions. The economy is still very fragile, especially the labor market. There is also a significant risk that - when realized - can have a tremendous impact of financial markets.

Probably what has been missing in the FOMC statement is some kind of declaration that Fed is monitoring the situation and is willing and able to act in case of negative developments. Unless there is nothing Fed can do to mitigate this particular risk and market reaction is correct?

Meanwhile, USDJPY has managed to bounce back from the previously mentioned 76.00 defense level. Will see how long it will last...

Chart: USDJPY & USDEUR 1 day 2011-09-21; stooq.com

Comparing two recent forex interventions

2011-09-21T12:53:00.000+02:00

Chart: USDCHF vs USDJPY 3 months, 2011-09-21

Back in August, Bank of Japan intervened in USDJPY. As a result, the Japanese yen felt by nearly 3%. For a single day...

A few days later, the Swiss National Bank's intervention followed. EURCHF shot up by nearly 6%. Supported by gossip about further actions, the franc continued to weaken for a number of days, till the beginning of September, when the fear of another SNB interventions waned.

Then SNB stroke again and pushed EURCHF by another 9% in one day. Just as declared, the Swiss bank has remained determined to defend the 1.2000 level by all means.

Most recently a new wave of rumors hit the market. Some say, SNB may move the target rate to 1.2500 from 1.2000. It has been enough to push market above 1.2200.

So far, SNB's actions demonstrate that central bank is able to successfully intervene in the forex market if only it plays on the right sight of the market (selling UNLIMITED locally currency as opposite to selling limited foreign reserves) and is determined enough to stick to its pledge.

In the meantime, the Japanese play a strange game. They declare intervention, spend quite substantial amount of money on a single action and... back away.

As a result, USDJPY is more than 8% down since a year ago, when BoJ started its recent wave of the interventions.

Most recently, the decreased volatility in USDJPY suggested that BoJ may be intervening in the market in more subtle and effective way in order to defend the 76.00 line.

As USDJPY has just resumed its march down, and currently is less than 0.5% above the imaginary Maginot Line, the day of the test of the BoJ's resolve is coming...

Stabilizing financial markets through forex

2011-09-19T13:38:00.001+02:00

Have you looked recently on the performance of the EURCHF and USDJPY crosses?

They are basically flat:

Chart: EURCHF vs USDJPY 10 days, 2011-09-19; Stooq.com

Both the Swiss and Japanese currency are starting to resemble the tightly controlled Chinese yuan (renminbi):

Chart: EURCHF, USDJPY and USDCNY, 3 months, 2011-09-19; Stooq.com

As suggested earlier, forex volatility of some crosses may disappear for some time.

Volatility still remains present in the emerging market crosses and... in gold, which has become a hard currency proxy of some kind over the recent years.

However, the latest increase in the activity of central banks, who provide virtually unlimited funds through currency swaps and asymmetric market operations, may lead to the further reduction in overall market volatility. There is not a central bank able to "print' gold though, so nobody can put a floor under the price of gold (see also "Gold - correction or trend change?").

Central banks can directly operate on the forex and - partially - on the fixed income markets. Equities and commodities (with the exception of precious metals) are officially off-limits. Nevertheless, since all the financial markets are interconnected, actions on some markets affect the others.

Currently I still have no clear picture of what may be the long term consequences of the above mentioned central banks activities. Most probably many financial markets - not only forex - will stabilize or start raising for reduced risk. Many correlations will disappear or reverse. Various investment strategies may stop working. But what then?

Gold - correction or trend change?

2011-09-16T08:24:00.000+02:00

While the five central banks decide to cooperate in providing dollar liquidity, gold is falling:

Fig. Gold futures vs USDJPY and USDCHF

Even though historically Q4 was on average positive for gold, September tends to be quite volatile, with significant downside potential.

Gold has been recently positively correlated to safe heaven currencies such as Swiss franc and Japanese yen (both in relation to U.S. dollar), and at the same time negatively correlated to equities.

Since mid-August, the raise of the yen against dollar has been stopped. In September SNB semi-fixated franc against the euro, simultaneously causing USDCHF to raise.

In the meantime, margin requirements for gold has been increasing.

Basically price of gold has been recently driven by three fundamental factors: fear about global economy, possibility of high inflation and low interest rates. While economy is improving extremely slowly, inflation is haunting emerging markets, and interest rates should remain on low level through 2013, all these factors are probably already discounted in the price of gold. Unless a new fear factor emerges, gold may stagnate. And slow correction may easily turn into disorderly liquidation...

So far, the proposed gold-crude pair trade would be in the positive territory.

Bounce from the exteme oversold conditions

2011-09-15T15:50:00.001+02:00

Deutsche Bank is raising more than 10% today:

Source: Reuters

Seems the relief rally from the extreme oversold conditions has materialized.

The question remains how far it can go...

BTW: I wonder whether this is in any way connected with the flop at UBS ;)

UPDATE:

EOD results:

The coordinated action of the five central banks definitely helped the European banks.

Since the end of last week the cumulative performance is:

BNP Paribas +2,35%
Deutsche Bank +5,17%
Societe Generale +5,07%

What distribution does the stock market follow?

2011-09-13T14:40:00.001+02:00

Fig WIG20 and daily changes

Przemek Biecek's "Na przełaj przez Data Mining z pakietem R" (Across Data Mining with the R package) is a fascinating tutorial for people who would like to quickly implement selected data mining concepts in R.

Today I've browsed though the chapter about analyzing the distributions of daily changes of equity prices and applied it to the WIG20 index of the Warsaw Stock Exchange.

No surprises here :)

> summary(daily_changes)

Min. 1st Qu. Median Mean 3rd Qu. Max.

-0.1416000 -0.0100500 0.0002639 0.0006617 0.0113000 0.1479000

> skewness(daily_changes)

[1] -0.04857761

> kurtosis(daily_changes)

[1] 4.414738

Daily changes do not follow normal distribution:

> mec <- mean(daily_changes)

> sdc <- sd(daily_changes)

> ad.test(daily_changes,pnorm,mec,sdc)

Anderson-Darling GoF Test

data: daily_changes and pnorm

AD = 61.0893, p-value = 1.288e-07

alternative hypothesis: NA

Fig. observed distribution of the daily changes of WIG20 vs fitted normal, Cauchy, Laplace and Stable distributions

Among the tested distributions, the best results can be obtained with stable distribution with the following parameters:

Model:

Stable Distribution

Estimated Parameter(s):

alpha beta gamma delta

1.480000e+00 6.700000e-02 1.101051e-02 6.523883e-05

Fig. Fitting of the stable distribution

> ad.test(daily_changes,pstable,sf_a,sf_b,sf_g,sf_d)

Anderson-Darling GoF Test

data: daily_changes and pstable

AD = 1.361, p-value = 0.2134

alternative hypothesis: NA

Hence, even that we can expect daily changes to remain in the (-5.5%, +5.5) range for more than 95% of the time, sometimes we can get a nasty surprise...

> stabledist::pstable(0.055,sf_a,sf_b,sf_g,sf_d)-stabledist::pstable(-0.055,sf_a,sf_b,sf_g,sf_d) # prob. of (-5.5%, +5.5%)

delta

0.9562193

> stabledist::pstable(-0.1,sf_a,sf_b,sf_g,sf_d) # probability of -10% or less

delta

0.007691719

It is still worth keeping in mind that short term distribution can be highly distorted (see here and here) and affected by the recent volatility.

You can see the complete source code here.

Short term relief?

2011-09-12T21:52:00.001+02:00

BERLIN (Dow Jones) 20:54 CET -- The European Union's current treaty doesn't foresee the possibility of an exit by Greece from the euro zone, German Finance Minister Wolfgang Schaeuble said in an interview with the ZDF public broadcaster Monday.

--German Finance Minister Schaeuble says Greek euro exit not possible due to EU treaty
--Schaeuble says contingency plans for a Greek insolvency are not an actual government plan
--Schaeuble comments come as others in government think loudly about Greek insolvency
--Schaeuble criticized such comments as unsettling markets

How will the financial markets react to that?

Definitely these declarations do not end "the Greek tragedy".

But given the extreme oversold conditions of the European banks, they can initiate at least a short relief rally.

Fig. BNP, DB and SG 1YR performance

This may also help for some time:

FT 2011-09-12 20:20 UK Italy turns to China for help in debt crisis

Italy’s centre-right government is turning to cash-rich China in the hope that Beijing will help rescue it from financial crisis by making “significant” purchases of Italian bonds and investments in strategic companies.

Volatility clustering and characteristic of distribution

2011-09-12T11:01:00.000+02:00

Benoit Mandelbrot observed that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes", what was named volatility clustering.

This behavior is not clearly visible in relation between single day changes, where randomness keeps the picture fuzzy:

Fig. Absolute one day change vs next day absolute change (S&P500)

It becomes more visible when one analyzes relations between cumulative changes over n days (say: 5-10-20-30) and the identical proceeding period:

Fig. Absolute cumulative change over n days against previous n days period (S&P500)

Hence we can assume that the distribution of expected price changes for a given period is not a constant, but depends on the previous volatility.

Volatility clustering is also the basis of the family of ARCH volatility models, used with varying successes in VaR calculation.

So what can be done to improve the performance of volatility modeling?

The end of floating exchange rates is coming?

2011-09-11T18:19:00.000+02:00

During the weekend's G7 finance ministers' meeting, Japan was probing participants about possible new forex intervention and didn't meet with any significant objections.

Japans was trying to stop the strengthening of its currency without success for some time now.

However, the recent action by the Swiss National Bank has suggested a new, potentially more fruitful approach.

With inflation at 0.2% (identical to the Swiss'), Japan shouldn't be worrying about dangers connected with "printing" empty money.

Should we expect then another declaration of providing UNLIMTED funds by one more central bank, soon?

Even more interesting question is, how the other major central banks - such as Fed and ECB - will react to another ultimate intervention.

Many studies in the past concluded that interventions are ineffective.

But take a look on the performance of Chinese yuan (renminbi) versus US dollar over the last five years (blue line in the center of the chart):

It's true that yuan is a controlled currency, which value is basically set by the Chinese central bank, and its availability is limited to foreigners.

The famous Black Wednesday of September 16th, 1992 demonstrated that single central bank is not able to defend the value of currency, especially when operating under certain exchange regime, for limited size of its foreign reserves.

Nevertheless, there are at least two situations when central bank cannot lose:

when it intends to weaken "its" currency - it can simply print ANY amount of money to flood the market
when two central banks agree to cooperate in order to regulate the exchange rate for their currencies - they can provide each other with UNLIMTED funds using swap agreements

In the previous years, we were witnesses to various central banks' decisive actions:

strict regulation of USDCNY by PBofC
swap agreements provided by Fed
establishment of the floor in EURCHF by SNB

In the coming days, we can see ultimate intervention in USDJPY by BoJ.

All these moves give rise to fears about the possibility of "currency wars". Paradoxically, what we can see instead is closer cooperation between central banks and more regulation of the forex market.

Germany and France keep pushing for introduction of the financial transaction tax (Tobin tax), which should cover forex. Most probably it will limit the volume of the currency transactions and possibly reduce volatility.

Being the most liquid of the financial markets, forex is not an easy place for arbitrageurs. Introduction of the new market mechanisms can disturb this balance and create new interesting opportunities.

Extreme oversold conditions nearly reached by European banks

2011-09-11T14:53:00.001+02:00

Fig. Extremes for BNP Paribas

Fig. Extremes for Deutsche Bank

Fig. Extremes for Societe Generale

The most stable condition indicating extreme oversold level for the three banks mentioned before is price deviation from long moving average. Based on the historic data, extreme oversold level is reached at -0.3 for BNP Paribas, -0.4 for Deutsche Bank, and -0.5 for Societe Generale.

The second most indicative signal is the price change over the previous year. The threshold levels are -0.5 for BNP, -0.7 for DB and -1.0 for SG (weak signal).

The current levels of the indicators are:

BNP DB SG

DEV MA -0.383 -0.410 -0.544

REL SD 0.242 0.241 0.364

YOY % -0.618 -0.627 -0.931

It seems that based on the deviation from long MA, all three banks have already reached the extreme oversold level, and their annual price change is close to confirming that.

It doesn't mean, the prices cannot go even lower, especially in a shock situation. The extreme oversold conditions have been calculated using daily data for the last 18-24 years (depending on availability). The present may be totally different from the past, though... (so at least in the case of the French banks it may be worth waiting till Moody's downgrades their debt this week)

High probability trading opportunity in European banking stocks?

2011-09-11T13:49:00.000+02:00

On Friday gossip about the potential Greek default has pushed the stock price of Bank of America to the level they had been before Warren Buffett invested $5B in the company.

The same fear is driving down prices of the European banks. From the beginning of the year, Societe Generale dropped 56.29%, Deutsche Bank 40.17% and BNP Paribas 37.25% (based on the ADRs).

While Bank of America is definitely in the red this year (EPS= -1.65), the fall of the stock prices of the still profitable European banks has actually made them pretty attractive from the P/E perspective (4.05 for SG, 4.62 for BNP and 10.10 for DB).

There is however one critical risk factor that weights heavily on the value of the European banks - the stability of the eurozone. Even if the banks direct exposure to the sovereign debt of the unstable countries may be limited, there still is a significant risk of domino and secondary effects caused by the default of even the smallest eurozone member country.

On the other hand it is hard to imagine German or French government allowing their largest banks to fall...

The previous analysis of the extreme oversold levels for S&P500, may suggest that the prices of the European banks may be close to the levels offering high probability long trading opportunity. The model requires re-calibration for higher volatility of individual stocks. And one needs to assume that the banks will survive the possible shock.

Stay tuned :)

Sterilizing SNB intervention with ECB help?

2011-09-06T15:25:00.000+02:00

Swiss National Bank has announced today it will defend EURCHF at the 1.2000 level at any cost.

It has declared it is prepared to sell UNLIMTED amounts of CHF. This means buying adequate amounts of EUR.

In theory, SNB can print unlimted amount of Swiss francs.

By buying euro, SNB will increase its already substantial foreign reserves. This creates a risk of loss if the value of these reserves decreases. However, by providing the floor for EURCHF exchange rate, SNB can defend the CHF-denominated value of its holdings.

Hence, if EUR strengthens, SNB makes - at least on paper - a profit on its position.

And if EUR weakens, SNB can defend it by buying even more EUR with unlimited funds.

There is a problem with unwinding the position though. The larger the EUR position held by the SNB, the harder it is to sell it without affecting the markets and pushing EURCHF down.

One possibility would be to park accumulated EUR at the ECB, using a swap construction similar to the Dollar Liquity Swap Lines previously provided by Fed.

SNB could swap its EUR with ECB for CHF at the fixed rate of 1.2000, securing the CHF-denominated value of its foreign holdings.

However, banks would need to somehow square the interest differential between CHF and EUR. For example, while CHF LIBOR O/N rate is currently (minus) -0,00333%, EUR LIBOR O/N stands at 0,83438%, meaning that on each one billion of EURCHF, ECB would have to pay roughly 8,4 mln EUR of interest daily.

Unless both banks set the IR for the swap at 0%.

BTW: Can BOJ perform similar intervention?

Crude gold

2011-08-11T03:35:00.001+02:00

Back in July 2008 some hedge funds decided to sell oil short and buy gold.

The strategy proved successful.

It was based on an assumption that oil and gold are closely correlated and 1 ounce of gold is equivalent to 10 barrels of oil.

Such relation held true till the beginning of 2008, when first the oil overshoot gold, and later felt down below the previous parity.

In July 2008, one ounce of gold was enough to buy just between 6 and 7 barrels of oil. In January 2009, more than 20.

Later, gold and oil reach a new equilibrium. The new gold-to-oil ratio stood at 13.7 (1100:80) barrels per ounce and 15.8 (1420:90) at the end of 2009 and 2010 respectively.

Most recently the prices diverged significantly again. As for August 10th, one ounce of gold can buy 22 barrels of oil (1796:82).

Gold is most probably entering the final phase of the bubble. It is hard to predict how far it can go during its ultimate exponential ascent. Meanwhile oil is falling in anticipation of economic slow down.

Clearly both assets are on different dynamic trajectories and the gap can extend even further. However, this divergence will most probably end. And the bigger it is, the stronger reversal can occur.

One leg of the strategy is easily implementable using SPDR Gold Trust ETF which very closely tracks gold futures.

For crude oil you can chose either United States Oil Fund ETF or United States 12 Month Oil Fund ETF. For crude oil futures term structure, it is better to chose the later.

Alternatively one can use futures.

Let's see what will happen...

Shorting Apple against the market

2011-08-10T08:23:00.001+02:00

In June 2010 I suggested a pair trading experiment: Apple short vs Google long. It wouldn't have given positive results.

As for today, the short position on Apple would return -31%, while going long Google would give +25%. Hence the net would be -6%.

I'm going back to this idea, since Apple's market capitalization has exceeded Exxon's just yesterday:

Source: Meet America's New Largest Publicly Traded Company (If Only For A Few Minutes),

Zero Hedge, 2011-08-09

I think I've made a crucial mistake in my assumptions of the above mentioned experiment. I thought Google would continue bringing innovative solutions that would instigate interest in the company from both users and investors. Unfortunately, except for the launch of Google+ (which outlook is still uncertain, taking into account its defensive nature against Facebook), Google did not bring any significant products to the market in the analyzed period.

Yes, the Google's recent financial results were pretty impressive. But Apple delivered both strong financial results AND hype-prone products. The launch of iPhone 5 is expected for September and this should support the Apple stock price. Especially relatively to the market.

Apple has significantly outperformed the market over the year:

Source: stooq.com

Meanwhile, Google's performance was mixed:

Source: stooq.com

I'm not sure whether Google+ will become success Google would like it to be. I do not know whether Google has any more aces in his sleeve to show over the next 12-24 months. However, there is a high probability that Apple's has overrun the market or is very close to it.

Hence I'd like to propose another experiment: shorting Apple against the market, i.e. Nasdaq futures. Probably the best moment would be on the day of the release of iPhone 5.

But let's check the strategy performance before that day:

S&P500 down 6,66%

2011-08-08T22:28:00.000+02:00

S&P500 index has fallen 6,66% today.

It's 10,99% down from the beginning of the year.

As a result we have a nice waterfall formation on the chart:

Downloading market data from Stooq to R

2011-08-05T15:31:00.000+02:00

Stooq provides multiple market data for free in the CSV format. I often use them in my analyses in R.

However there was a small problem with automatically downloading market data from Stooq.

The CSV files are generated dynamically, so there is no static URL available. The name of the instrument for downloading is passed in cookie.

Therefore, I've written a code that circumvents this limitation:

# http://www.rhinocerus.net/forum/lang-php/662887-how-read-download-attachment-uri.html - inspiration :)

library(RCurl)

getStooqData <- function(asset_code,static_cookie=TRUE) {

data_tmp <- tempfile() # "data.csv"
cookie_tmp <- "cookie.txt"

u1 <- paste("http://stooq.com/q/d/?s=",asset_code,sep="")
u2 <- paste("http://stooq.com/q/d/l/?s=",asset_code,"&i=d",sep="")

if (!static_cookie) {

h <- c(paste("GET ",u1," HTTP/1.0",sep=""),
Accept="image/gif",Accept="image/x-xbitmap",Accept="image/jpeg",Accept="mage/pjpeg",Accept="application/x-shockwave-flash",Accept="application/vnd.ms-excel",Accept="application/msword",Accept="*/*",
'Accept-Language'="pl, en-us;q=0.7",'User-Agent'="Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1;SV1)",'Proxy-Connection'="Keep-Alive")

u1Opts <- curlOptions(header=TRUE,httpheader=h,cookiejar=cookie_tmp)
curlPerform(url=u1,.opts=u1Opts,verbose=TRUE)

h <- c(paste("GET",u2,"HTTP/1.0"),
Accept="image/gif",Accept="image/x-xbitmap",Accept="image/jpeg",Accept="mage/pjpeg",Accept="application/x-shockwave-flash",Accept="application/vnd.ms-excel",Accept="application/msword",Accept="*/*",
'Accept-Language'="pl, en-us;q=0.7",'User-Agent'="Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1;SV1)",'Proxy-Connection'="Keep-Alive")

u2Opts <- curlOptions(header=TRUE,httpheader=h,cookiefile=cookie_tmp)

}

else {

h <- c(paste("GET",u2,"HTTP/1.0"),
Accept="image/gif",Accept="image/x-xbitmap",Accept="image/jpeg",Accept="mage/pjpeg",Accept="application/x-shockwave-flash",Accept="application/vnd.ms-excel",Accept="application/msword",Accept="*/*",
'Accept-Language'="pl, en-us;q=0.7",'User-Agent'="Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1;SV1)",'Proxy-Connection'="Keep-Alive",Cookie=paste("cookie_uu=p;cookie_user=%3F0001dllg000011500d1300%7C",asset_code,sep=""))

u2Opts <- curlOptions(header=TRUE,httpheader=h)

}

reader <- basicTextGatherer()

w <- getURLContent(url=u2,.opts=u2Opts)

write(w,file=data_tmp)

stooq_data <- read.csv(data_tmp)

stooq_data
}

stooq_data <- getStooqData("es.f",static_cookie=TRUE)

In most cases, the function should work with static_cookie set to TRUE. However, a possibility that the cookie will change exists, so I've added some additional code that actually downloads a cookie before downloading the data.

Some improvements with MD2 and S&P500

2011-08-02T16:49:00.002+02:00

Seems, the MD2 trading strategy can SOMETIMES work with S&P500, too:

Fig. MD2 strategy (2 variants) for S&P500, 1000 sessions, no commission

blue line - market

black line - strategy

important assumption: perfect asset divisibility

The results as measured by returns are still unstable, but after some modifications, they improve :)

Results for the first variant:

market = 1345.02 -6.143497 %

strategy = 2041.307 42.44396 %

Results for the second variant:

market = 1345.02 -6.143497 %

strategy = 2301.505 60.60075 %

Still, both the lack of stability and returns are not satisfactory.

No bugs so far

2011-08-01T11:57:00.001+02:00

So far I was unable to identify any serious bugs in the code of previously mentioned strategy.

The strategy seems to work (i.e is able to beat the market) for longer horizons (>500 sessions) for EURUSD and USDJPY.

It does not work for SP500 (UPDATE 2011-08-02: seems it sometimes does...)

Fig. MD2 strategy for USDJPY, 500 sessions

blue line - market

black line - strategy

What's even more interesting, it seems there is not short term relation between the signal used and daily fluctuations of the assets:

Fig. Relationship between MD2 signal and daily changes, EURUSD

Currently I'm working on improving the strategy. I'm also going to test it on high-frequency data.

I wonder where is a bug this time...

2011-07-30T20:00:00.002+02:00

In April 2010 I've started working on a short-term forex trading strategy.

The initial results were amazing, just too good to be true.

Shortly it turned out that there was a bug in the code indeed :)

In the meantime, I had some other things to do, so the work on this promising strategy was stopped for nearly 1,5 years.

Recently I've came back to it.

I think, there still must be a bug somewhere...

Even that the generated strategy results are definitely less stable than before, they are still impressive for most of the tested periods:

Fig. Simulated results of the MD2 forex strategy, EURUSD
blue line - market
black line - strategy

The simulated strategy return for EURUSD over 501 sessions through July 22nd, 2011 is 53,81% vs 0,87% market return.

I'll hunt for bugs tomorrow :)

Insignificance of RSI

2011-07-28T10:39:00.001+02:00

RSI or Relative Strength Indicator is one of the popular technical analysis indicators.

It is assumed that RSI above 70 signals market is overbought, while its level below 30 suggests oversold condition.

Let's take a look at the relation between RSI(14) and historical daily changes of S&P500:

Fig. daily changes versus RSI

It doesn't gets any better at different time scales...

Change of deviation from moving average seems neutral to returns

2011-07-28T10:08:00.000+02:00

Relation between daily deviation from moving average to moving average of deviation seems to have no effect on asset returns:

Fig. daily deviation from moving average / average daily deviation from moving average: deviation from EMA15, EMA5 of deviation, return over next 3 days (15-5-3), EURUSD

Fig. daily deviation from moving average / average daily deviation from moving average, EURUSD 45-25-10

Fig. daily deviation from moving average / average daily deviation from moving average, EURUSD 250-25-5

Returns remain random at moderate deviations from moving average

2011-07-28T09:29:00.001+02:00

It was not possible to spot any significant patterns when analyzing short term (3-10 days) price changes versus deviations from short- and mid-term (5, 10 ,50 ,100 days) moving averages for S&P500, EURUSD and gold futures:

Fig. returns versus deviation from moving average, S&P500

Fig. returns versus deviation from moving average, EURUSD

Fig. returns versus deviation from moving average, gold futures

Long term price deviations indicative for stock indexes, not so much for currencies or commodities

2011-07-28T08:09:00.001+02:00

Fig. long term behavior of S&P500

I've mentioned previously that it seems S&P500 tends to reverse to its mean when an extreme deviation occurs.

The first potential buy signal is generated when price deviates more than 20-30% from the 250 days moving average.

There are two more indicators worth observing for long term signals:

relative standard deviation (SD) - i.e. standard deviation / average
long term nominal change - i.e. change of the price over 250 sessions (more or less one year)

In the case of relative SD, a buy signal is generated when the indicator exceeds 0.3.

Another buy signal emerges when price drops -40% / -50% over a year.

What's interesting, a weak signal also appears when a price increases by 50% over a year. There were very few instances of such a situation, though.

You can observe similar long term relations for other stock indexes, such as WIG20 (Warsaw Stock Exchange, Poland):

Fig. long term behavior of WIG20

The picture is not so obvious for currencies and commodities, though:

Fig. long term behavior of EURUSD

Fig. long term behavior of gold futures

The virtue of patience

2011-07-25T13:33:00.001+02:00

Interesting: over the recent more or less 10 years (5000 sessions), anyone patient enough - i.e. ready to hold his position open over up to 250 sessions - who invested in the S&P500 index, would have lost a maximum of 4,1%, even that the market took a two huge dives in that period:

Legend:

black line - return at the end of 250 days period

blue line - maximum return over a 250 days period

red line - maximum loss over a 250 days period

Of course, he would have to close his position at the right moment... ;)

A trillion dollars opportunity

2011-07-25T07:05:00.003+02:00

Source: "Gorączka gazu", Gazeta Wyborcza, 2011-07-18

The Energy Information Agency estimates technically recoverable shale gas resources in Poland at 5.295 trillion cubic meters (5.295e12 m^3).

Based on the current spot price of the natural gas ($4.3780/MMBtu) in the US where shale gas extraction shook the dynamics of the gas market, this translates into around 841 billion USD of potential revenues.

Given the current global economic situation and the idiosyncrasies of the European gas market this is a rather conservative price estimate (I will return to it later).

1 MMbtu / 1027 Btu/cf = 973.71 cf (cubic feet, feet^3)
(see: http://www.think-energy.net/energy_units.htm)

973.71 cf = 27.572 m^3

1000 m^3 / 27.572 m^3 (1 MMbtu) = 36.2687

1000 m^3 * NG.F = $4.3780 * 36.2687 = $158.784 / 1000 m^3

5.295e12 m^3 * $158.784 / 1000 m^3 = $840 761 280 000

OK, so let's go back to some more pricing analysis.

The average price of the natural gas sold by Gazprom reached $306 at the end of 2010 and is expected to increase to $400 in 2011.

Meanwhile the average natural gas spot price over 10 years in the US was $5.69/Btu or $206.369/1000 m^3.

As the production of shale gas in Europe increases and LNG-based geographical arbitrage equalizes prices among regions, the European prices will come down over time.

Hence the long term average spot price is probably the better estimate of the value of reserves. Then the gas reserves of 5e12 m^3 translate into nearly 1,1 trillion USD.

If only reserves are as large as estimated by EIA...

Simple return to mean as investment signal?

2011-07-24T12:44:00.011+02:00

Financial instruments fluctuate around their means. Sometimes the price of an instrument is above this instrument's mean, and sometimes the other way. Price tend to return to the mean. But can you use this mechanism for buying an selling financial instruments?

Let's check the most simple average-based rule on the S&P500 index over the previous 10,000 sessions.

RULE: buy or short sell the index when the price deviates by X% from its mean.

Test 1: EMA=15, position holding period = 3

Buying at deviation from the mean equal to -0.2 (20%) would bring nearly a 10% gain, but there was just one such situation over the whole period being analyzed:

t= -0.2 n= 1 avg= 0.09904726 min= 0.09904726 max= 0.09904726

Short term deviation doesn't look like a viable signal.

Test 2: EMA=200, position holding period = 3

No signals generated (testing only at 0.X, so 0.35 is not covered):

Large deviation from long term average does not influence short period movements.

Test 3: EMA=200, position holding period = 25

One weak signal: deviation = -0.3 increased probability of positive return. One could expect a 9,6% return, but there is also a risk of a loss of -7,1%.

t= -0.3 u= 13 d= 3 avg= 0.0964092 min= -0.07157303 max= 0.2284035

Test 4: EMA=45, position holding period = 10

Another case with weak signal. This time at deviation = -0.2.

t= -0.2 u= 8 d= 2 avg= 0.05415763 min= -0.02528302 max= 0.1521247

Conclusion: Price deviations from the moving average (mean) "larger" than -0.2 significantly increase probability of an increase in price in the case of S&P500, but such deviations are rare events.

UPDATE 1:

Additional test: 35000+ quotations, MA=200, holding period = 25.

Both "strong" and "weak" signal has been generated. Average expected return at each deviation added to the chart:

UPDATE 2:

It is getting to start getting more interesting when we consider long moving averages and long expected position holding period. Under such conditions, both the soft and hard signals give pretty solid expected gains with limited loss potential.

Test: EMA=250, holding period=250

soft signal:

t= -0.2 u= 178 d= 3 avg= 0.2415313 min= -0.1348127 max= 0.5206657

hard signal:

t= -0.3 n= 29 avg= 0.3260642 min= 0.1503819 max= 0.5206657

Test: EMA=100, holding period=250

t= -0.2 n= 41 avg= 0.2482144 min= 0.04344005 max= 0.5206657

UPDATE 3:

Measuring price deviation from moving average in terms of standard deviations makes the picture more messy:

Test: SMA=250, holding period=250, deviation in terms of standard deviations:

Google Prediction API v1.2 for R

2011-05-30T09:50:00.001+02:00

Google has recently made available a new version (v1.2) of Google Prediction API. (see announcement from Google I/O 2011).

Hence the previously available implementation of Google Prediction API for R has stopped working :(

I've spent some time and adapted it to new version of the API as well as made some small extensions and modification for Windows/R 2.13.0.

You can find the source code and R package at: http://code.google.com/p/r-google-prediction-api-v12/

Sample usage of the package:

# install package
install.packages("googlepredictionapi_0.12.tar.gz", repos=NULL, type="source")
 
library(rjson)
library(RCurl)
library(googlepredictionapi)
 #--- initialize
 # turn off SSL check - see: http://code.google.com/p/r-google-analytics/issues/detail?id=1#c5 & http://www.omegahat.org/RCurl/FAQ.html
options(RCurlOptions = list(capath = system.file("CurlSSL", "cacert.pem", package = "RCurl"), ssl.verifypeer = FALSE))
 # put your own email, password and API key below
myEmail <- "***"
myPassword <- "***"
myAPIkey <- "***"
 # put path to python.exe on your computer and path do gsutil directory
myPython <- "c:/Python27/python.exe"
myGSUtilPath <- "c:/gsutil/"
 
myVerbose <- FALSE
 #--- work
 # upload local CVS file to Google Storage and initiate training; local file must be in R working directory
my.model <- PredictionApiTrain(data="./language_id_pl.txt",remote.file="gs://prediction_example/prediction_models/languages")
 # alternative: initiate training of a model already uploaded to Google Storage
my.model <- PredictionApiTrain(data="gs://prediction_example/prediction_models/languages",tillDone=FALSE) # tillDone - repeat checking till model is trained
 # check whether model is trained; if tillDone=TRUE was set above, there is no need for that
result <- PredictionApiCheckTrainingStatus("prediction_example","prediction_models/languages",verbose=TRUE)
 # you can adapt the result returned by PredictionApiCheckTrainingStatus to 'predictionapimodel' class used in predictions
my.model <- WrapModel(result)
 
summary(my.model)
 # check new data against model (I have added some Polish-language texts to the Google Prediction API 'Hello World' example)
predict(my.model,"'Prezydent Obama spotkał się z parlamentarzystami'")
 # please note, this package returns all labels and scores for a given data in a format:
# [1] "Polish"   "French"   "Spanish"  "English"  "0.36195"  "0.26396"  "0.260067" "0.114022"
 # some other prediction request
predict(my.model,"'This is a test'")
 # list objects in a Google Storage bucket
PredictionApiListObjects("prediction_example","prediction_models/languages",verbose=TRUE)

Testing LSA in R

2011-05-15T15:26:00.000+02:00

Latent Semantic Analysis (LSA) is a technique used in text mining for identifying concepts in documents.

It can be used, among others, for querying documents for concepts related to specified keywords, or estimating similarities between groups of terms (such as phrases).

Since there is a package implementing LSA in R available, I've decided to put it to a very simple test in the two areas mentioned above:

1. LSA-based search

> q <- fold_in(query("sushi hamster", rownames(myNewMatrix)),myLSAspace)
>
> qd <- 0
> for (i in 1:ncol(myNewMatrix)) {
+
+ qd[i] <- cosine(as.vector(q),as.vector(myNewMatrix[,i]))
+
+ }
>
> cor(q,myNewMatrix,method="spearman")
D1 D2 D3 D4
SUSHI HAMSTER -0.5882353 1 -0.7647059 -0.5882353
>
> qd
[1] 0.05031141 0.99187467 -0.22654816 0.22207399

2. phrases similarity

> ComparePhrases <- function(p1, p2) {
+
+ q1 <- fold_in(query(p1, rownames(myNewMatrix)),myLSAspace)
+ q2 <- fold_in(query(p2, rownames(myNewMatrix)),myLSAspace)
+
+ cosine(as.vector(q1),as.vector(q2))
+
+ }
>
> ComparePhrases("cat dog","monster dog")
[,1]
[1,] 0.995967
>
> ComparePhrases("sushi hamster","monster dog")
[,1]
[1,] -0.1948665

The complete source code is available here.

TextRank implementation in R

2011-05-11T01:27:00.000+02:00

TextRank is a graph algorithm for keywords extraction and summarization based on PageRank developed by Larry Page from Google.

You can read the description of the algorithm and its evaluation in the paper "Text Rank: Bringing Order into Texts" by Rada Mihalcea and Paul Tarau.

I have made a quick and dirty implementation of TextRank in R (http://www.r-project.org/) for keywords extraction only.

My implementation has two differences to the algorithm presented in the above mentioned paper:

it calculates weights of the edges based on the number of instances when two nodes are connected (it is not used in the calculation of ranks though)
it allows circular references, where a node has an edge to itself (used in the calculation)

I have used three R libraries to speed up implementation:

tm (text mining) for preprocessing text to be analyzed
openNLP for part of speach tagging
graph for constructing graphs

I'd like to emphasize once more that this is a really quick and dirty implementation.

Please find source code here.

Is software the real bottleneck?

2011-04-23T21:48:00.000+02:00

"The real bottleneck is software. Creating software can be done only the old-fashioned way. A human—sitting quietly in a chair with a pencil, paper, and laptop—is going to have to write the codes, line for line, that make these imaginary worlds come to life. One can mass-produce hardware and increase its power by piling on more and more chips, but you cannot mass-produce the brain."
Michio Kaku "The Physics of the Future"

It's true that currently all the software is created in the old fashioned way - i.e written by humans. However, the whole idea of artificial intelligence and singularity is closely connected with changing that.

The goal is to allow machines (or rather software powering them) to improve themselves by analyzing and changing the initial code written by people.

It is about machine learning and machine adaptation (you should replace software for machine in both cases).

As software code becomes even longer and more complex, another software layers piling upon themselves, hardware gets more powerful allowing implementation of more advanced algorithms, the number of connections in various kinds of networks grows, people will have increasing problem with keeping pace with all these changes.

They will have to allow software to modify itself. And the bottleneck mentioned by Michio Kaku should disappear at the dawn of singularity...

Deviations from normal distribution depending on sample size

2011-04-21T22:59:00.001+02:00

It's obvious when you visualize it :)

Depending on the number of observations in the sample (N), the perceived distribution (black) may look quite different from what you'd expect from the random sample generation based on the normal distribution (red).

Source available here.

One more comparison for binomial distribution:

I would have forgotten if not Google! ;)

2011-04-21T06:27:00.000+02:00

It's this day of the year. And I would have forgotten if not Google ;)

Another sign of how many information are gathered and processed by the company.

Analyzing search keyphrases similarities with different methods

2011-04-17T08:39:00.005+02:00

Have you ever wondered what kind of similar keyphrases people use when searching for something and how do they compare?
I have :)

Using a subset of keyphrases used by visitors of inlevel.com (some 550 items), I wrote a simple R program that tries to assign potentially similar phrases to each of the keyphrases used.

I employed three methods for this task:

Levenshtein distance - see source code here
length of longest common substring (LCS) - source code of my implementation here
phrases starting with base phrase - very rude implementation available here

Check the small selection of the results of this exercise:

You can download all the results here.

As you will notice, each of the method gives different results. None single set of the results is definitively better than the others. Combining them in some way seems the most interesting solution.

Correcting spelling mistakes before analyzing dependencies seems important for improving results. Some other methods can be added as well.

First steps in text mining with R

2010-12-24T13:37:00.000+01:00

Everyone is preparing for Christmas Eve's Dinner. No one is calling, little email. Looks like a perfect time to start researching text mining in R :)

The problem I'm trying to solve:

extract keywords from multiple texts
try to summarize texts > sentence extraction
group and relate products based on their descriptions > classification / clustering
add relevant information to text based on similar / related text

I've started with tm package.

http://text-analysis.googlecode.com/files/Text_Mining_Infrastructure_in_R.pdf
http://cran.r-project.org/web/packages/tm/vignettes/tm.pdf - introduction to tm package
http://cran.r-project.org/doc/Rnews/Rnews_2008-2.pdf - introduction to text mining in R
http://epub.wu.ac.at/1923/1/document.pdf - text mining in R and its applications

Then I've jumped to TextRank algorithm for keywords & sentence extraction. Seems, TextRank is not present in tm, but there is Java source code available so should be possible to call it from R.

Will need to compare TextRank to KEA. The later is implemented for R in RKEA.

Looks promising.

Extracting content from web pages for text mining

2010-11-28T20:28:00.000+01:00

For the last three days I was looking for ways and tools to extract content (text) and data (for example emails, but that's just a beginning) from web pages.

The best tool I've found so far is Web Harvest: http://web-harvest.sourceforge.net/

Definitely it's not easy too use (it took me nearly a day to understand how exactly did it work), but looks the most powerful among the tools I've evaluated.

I've started with modifying the example of the simple site crawler, to make it more flexible and make it collect all emails found on a specified web site.

Source of my version of site crawler/email collector is available here: http://www.mediafire.com/?c5cjndslu90c8eo

Then, I've written a simple configuration file to collect email addresses from first 100 links returned by Google search for some specified key phrase.

Source code is available here: http://www.mediafire.com/?jkwu6bbs6ef7ohd

Now, I'm moving to the topic I've had in my mind, when I started working on this project - i.e. extracting text content from web pages and analyzing it.

First step: researching topic: Michael J. Giarlo "A Comparative Analysis of Keyword Extraction Techniques"

Real test of USDJPY intervention may come on Tuesday, after FOMC decision

2010-09-18T18:00:00.001+02:00

On September 15th, BoJ intervened on the forex. USDJPY jumped 3,3%, to the level from the end of August. Can this action stop the strenghtening of Japanese yen?

Source: Stooq

An interesting study on Japanese forex interventions in 1990s was prepared by Takatoshi Ito from Institute of Economic Research, Hitotsubashi University.

The amount of money used by the Bank of Japan for the intervention should be disclosed on November 8th on the page dedicated to Foreign Exchange Intervention Operations maintained by the Ministry of Finance in Japan: http://www.mof.go.jp/english/e1c021.htm
The amount of the intervention is estimated at 1 trillion JPY (11,7 billion USD).

The first test of the effectiveness of the intervention may come on Tuesday, September 21st, when FOMC announces its interest rate decision and possibly further plans for quantitative easing.

Finanace and distributed computing does not mix?

2010-09-18T13:16:00.001+02:00

Browsing through the list of distributing computing projects on Wikipedia, I've found just two financial projects - MoneyBee and GStock.

The first of them - MoneyBee - was conceived as a way to forecast stock markets using neural networks. It was launched in September 2000. According to the information on the MoneyBee's website, the project failed and is suspended.

Fig. MoneyBee Screensaver

Source: Moneybee - example of distributed computing

GStock launched in 2006 and is still operational. It uses technical analysis to generate buy and sell signals for over 4000 stocks. According to information on the project's website, the signals given by the system were correct in 2 out of 3 instances.

Fig. Exemplary GStock chart with generated signals for Google Inc. over 1 year period

Source: http://www.gstock.com/stock-picks/GOOG-Google-Inc.html

Sources:

Gold price far from record in EUR and CHF terms - future uncertain

2010-09-17T22:39:00.002+02:00

Fig. Gold in USD, EUR and CHF, 1 year, 2010-09-17

Source: Stooq

Depending on the currency in which you price gold, it has reached the new height in absolute terms (USD), is correcting after a strong fall in July (EUR), or stabilizing after it (CHF).

Based on your choice of currency, you may try to predict the future performance of the gold price. And it's not clear at all.

Lyxor ETF WIG20 - the first ETF coming to Warsaw Stock Exchange

2010-09-03T08:45:00.001+02:00

Lyxor Asset Management, a division of Societe Generale Group, plans to launch the first Polish ETF (Exchange Traded Fund) in September.

Lyxor ETF WIG20 will track movements of 20 biggest Polish stocks included in the main index of the Warsaw Stock Exchange - WIG20.

Key parameters:

quoted on the WSE
price = WIG20 * 1/10
0,5% annual management fee
selling short?

Introduction of this ETF may allow implementation of some arbitrage strategies using either stocks or index futures. Especially if ETF's tracking error will be noticeable, what can happen in times of higher volatility.

see presentation about the ETF: www.lyxoretf.pl/fileadmin/user_upload/ETF/PL/Brochures/LYXOR_ETF_WIG20.pdf

more information: www.lyxoretf.pl

Comparing states of economies of US, EU and China with SENSEnews

2010-09-02T22:26:00.005+02:00

I've just started a trial with semantic news service SENSEnews.

As the first test, I've generated charts visualizing six months information flows about the US, EU and Chinese economies.

I've added some additional queries about performance of euro or probability of bubble forming in Chine to the default set of queries predefined in the system.

As an example, I'm showing below results generated by SENSEnews for the query about possible bubble in China:

Is there a bubble in China?

boobdex

$LVS Just because there is a bubble in China, means Asians want to game even more to make back the money they lost

Twitter - Sep, 02 12:03 (EST)

delete

China's Property Market in 'Very Big Bubble,' StarRock Says

Property bubbles exist in some of Chinas large cities, the Peoples Daily reported Aug. 23, citing Ba Shusong, deputy head of the financial institute of the State Councils Development Research Center. He said there is no evidence of a nationwide property bubble in China. China, which hasnt raised interest rates since December 2007, may start increasing borrowing costs from the fourth quarter because of accelerating inflation, large wage increases and loose liquidity conditions, RBC Capital Markets said after the release of July inflation data on Aug. 11. The inflation rate accelerated to 3.3 percent in July, the fastest pace in 21 months, pushed up by floods that destroyed crops. The government is still studying property tax and plans to introduce property tax reform, Xinhua News Agency reported Aug. 24, citing Xu Lin, director of the finance department at the National Development and Reform Commission.

BusinessWeek - Sep, 02 10:01 (EST)

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S&P warn that real estate bubble is lurking in China

Asharp pickup in real state prices in China is a key risk to the nation's economic growth and is leading to a classic bubble situation, according to Standard & Poor's. It is forecasting that prices will rise 10.3% this year to an unsustainable level and they will need to come down if they are not to affect economic performance. 'The property market looks darn good, it's been going up, and this is a classic bubble. Prices are rising to an unsustainable level,' said David Wyss, chief economist at S&P. The property sector contributes about 20% to the Chinese economy through real estate investments and related industries, according to Citic Bank International. Since April, China has restricted pre-sales by developers and curbed loans for third home purchases to try to cool the market after excess liquidity stemming from record credit growth last year buoyed demand. But property prices are showing signs of slowing. They have gone up 10.3% from a year earlier in July, the slowest pace in six months.

Arendator.ru - Sep, 02 08:16 (EST)

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7Steps2Wealth

China's Property Market in 'Very Big Bubble,' StarRock Says: 2 (Bloomberg) -- China's property market is in a "ver... http://bit.ly/9e2V3Z

Twitter - Sep, 02 04:42 (EST)

delete

chooze2move

S&P warn that real estate bubble is lurking in China | Asia | News http://goo.gl/3QAz

Twitter - Sep, 02 00:30 (EST)

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S&P warn that real estate bubble is lurking in China

:: Analysts warn that flat property lending outlook in UK could result in real estate double dip :: The price of detached properties in the UK have risen the most in past year, report says :: :: UK property market prices falling as downward trend kicks in, latest figures show :: Cuba approves 99 year leases for foreign property investors :: Singapore govt introduces new measures to cool real estate market :: Regulations for all new built property in Wales could add up to 10% to costs, consultants warn :: US real estate foreclosures fall marginally but mortgage delinquencies increase to bring more gloom

Property Wire - Sep, 01 13:14 (EST)

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10 Things You Need To Know Before The Opening Bell (AAPL, BKC, SPY, GLD)

Gus Lubin | Sep. 1, 2010, 7:26 AM | 916 | 1 A A A x Email Article From To Email Sent! You have successfully emailed the post. Good morning. Here's what you need to know: Asian markets were mostly positive in overnight trading, with the Nikkei recovering 1.17%. European markets are all higher in early trading, and U.S. futures point to a higher opening. See overnight action in charts > ADP Employment numbers come out at 8:15 AM. Forecasts expect 13K added jobs, after 42K added in July. Follow the action at Money Game > ISM Manufacturing data comes out at 10 AM, with analysts expecting a decline to 52.9 from 55.5. Also watch the EIA petroleum data at 10 AM. Recent economic data has been neutral-to-weak. Check out the gritty details behind the Philly Fed number > The surge in gold reached $1,254, approaching record highs . The yen rise also continues as investors fear global deterioration. See how to know if gold is a bubble > China announced plans for new regulations to curb still-soaring home prices.

Business Insider - Sep, 01 12:20 (EST)

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10 Things You Need To Know Before The Opening Bell (AAPL, BKC, SPY, GLD)

Gus Lubin | Sep. 1, 2010, 7:26 AM | 847 | 1 A A A x Email Article From To Email Sent! You have successfully emailed the post. Good morning. Here's what you need to know: Asian markets were mostly positive in overnight trading, with the Nikkei recovering 1.17%. European markets are all higher in early trading, and U.S. futures point to a higher opening. See overnight action in charts > ADP Employment numbers come out at 8:15 AM. Forecasts expect 13K added jobs, after 42K added in July. Follow the action at Money Game > ISM Manufacturing data comes out at 10 AM, with analysts expecting a decline to 52.9 from 55.5. Also watch the EIA petroleum data at 10 AM. Recent economic data has been neutral-to-weak. Check out the gritty details behind the Philly Fed number > The surge in gold reached $1,254, approaching record highs . The yen rise also continues as investors fear global deterioration. See how to know if gold is a bubble > China announced plans for new regulations to curb still-soaring home prices.

Clusterstock - Sep, 01 12:17 (EST)

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10 Things You Need To Know Before The Opening Bell (AAPL, BKC, SPY, GLD)

Good morning. Here's what you need to know: Asian markets were mostly positive in overnight trading, with the Nikkei recovering 1.17%. European markets are all higher in early trading, and U.S. futures point to a higher opening. See overnight action in charts > ADP Employment numbers come out at 8:15 AM. Forecasts expect 13K added jobs, after 42K added in July. Follow the action at Money Game > ISM Manufacturing data comes out at 10 AM, with analysts expecting a decline to 52.9 from 55.5. Also watch the EIA petroleum data at 10 AM. Recent economic data has been neutral-to-weak. Check out the gritty details behind the Philly Fed number > The surge in gold reached $1,254, approaching record highs . The yen rise also continues as investors fear global deterioration. See how to know if gold is a bubble > China announced plans for new regulations to curb still-soaring home prices. Fear of a property bubble outweighed positive economic data, as the Shanghai Composite whipsawed and ended down 0.60%.

Business Insider - Sep, 01 11:46 (EST)

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ceacom

S&P warn that real estate bubble is lurking in China | Asia | News http://bit.ly/anOPvi

Twitter - Sep, 01 07:43 (EST)

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Different frequency fft waves for S&P500

2010-08-26T08:26:00.001+02:00

I've added a graph showing fft (Fast Fourier Transform) based waves of different number of frequencies:

What Fourier says about S&P500?

2010-08-26T00:16:00.001+02:00

Based on the Fourier-based extrapolation of the current trend of S&P500, the stock market will raise or fall :)

I've implemented extrapolation of trend based on Fourier analysis, and - as you can see below - depending on the range of data used for calculations, S&P500 will raise or fall:

Fig 1. Fourier extrapolation of S&P500 based on 100 daily quotations

Fig. 2 Fourier extrapolation of S&P500 based on 400 daily quotations

In both cases, Quinn-Fernandes algorithm for frequency estimation was used and 20 harmonics matched.

I adapted MQL5 (MetaStock) code of Extrapolator indicator written by qpwr. Thanks a lot!

(the code is not yet optimized for R)

Download source code (R).

Best correlation trajectory match for EURUSD

2010-08-23T22:40:00.000+02:00

Another test of correlation-based matching of trajectories. This time EURUSD.

Best match with correlation of 0.9295 was found at the beginning of 1980 (red line):

In addition to the best match, two second best correlation matches were added (green lines).

Even though, based on the best correlation match (and one of the others) you might expect pretty significant growth, one of the presented second best matches suggests continued correction.

The next step would be to verify whether such matching has any sense at all :)

Download source code (R) and data.

S&P500 - current trajectory similar to situation from 1959/1960

2010-08-23T14:55:00.000+02:00

If one believes in market repeating itself, one could say that the current situation is the most similar to one from the break of 1959/1960:

The correlation between the current and 1959/1960's periods is 0.9292. If market goes the same way as in the past, we should expect a small market increase of around 0,5% over the next 10 days.

The time will tell :)

Simple perfect arbitrage opportunities on forex

2010-08-22T22:58:00.005+02:00

Forex is the most liquid of the financial markets. Therefore it is deemed totally deprived from simple arbitrage opportunities.

However, it turns out that one can find - although rarely - perfect arbitrage opportunities even on the most liquid currency crosses.

For example, I've analyzed intraday data (with 10 mins. frequency) for EURJPY, USDJPY and EURUSD for the period of March 2nd, 2009 - August 20th, 2010. That gives some 54,700 datapoints for each of the crosses.

I defined a perfect arbitrage opportunity for these three crosses, as a situation when difference between EURJPY and USDJPY*EURUSD exceeds 0.1 yen. Then one would be able to sell short EURJPY and at the same time buy USDJPY together with EURUSD (or vice versa) and produce risk free return after adjusting for total spread of 0.1 yen.

In that period I've found 25 instances (out of 54,703 quotations, or 0,0457%) when arbitrage opportunity appeared:

Nevertheless, some of them were substantial - the largest giving 1,31% risk free return!

Visualization of the difference between EURJPY and USDJPY*EURUSD shows, that the arbitrage gap is very rare phenomenon indeed:

The difference between crosses is concentrated in a very narrow range that hardly ever creates arbitrage opportunities. Still, the distribution has very long tails (or at least one of them):

The situation changes a little when you take a look at some less liquid crosses - for example EURPLN vs USDPLN*EURUSD.

The number of arbitrage opportunities increases noticeably (to 6,42% of all analyzed quotations), as well as the rate of potential risk free return (note: total spread set at 0.105 zł):

The difference between base cross (EURPLN) and its equivalent pair (USDPLN*EURUSD) becomes much more volatile:

However the distribution of differences looks much more "normal":

Clearly, there still exist perfect simple arbitrage opportunities on forex. It's possible to exploit them using algorithmic trading. They are rare and often they generate low individual returns. But they are risk free.

Data source: stooq.com

Download source code (R) and data

The coming black boxes inside business organizations

2010-08-22T01:23:00.002+02:00

Google has recently made available a set of tools for analyzing data using machine learning techniques called Google Prediction API.

As you can read in the recent article in MIT Technology Review:

For example, a bank or credit-card company wanting to use machine learning to build systems that make decisions based on historical transactions is unlikely to have the specialized staff and necessary infrastructure for what is a computationally intensive approach. [...]

Google's black box (...) contains a whole suite of different algorithms. When data is uploaded, all of the algorithms are automatically applied to find out which works best for a particular job, and the best algorithm is then used to handle any new information submitted. [...]

Google does, however, get (...) information [about effectiveness of various techniques] that it can use to improve its machine-learning algorithms. "We don't look at users' data, but we do see the same metrics on prediction quality that they do, to help us improve the service," says Green. The engineers running Prediction API will know if a particular algorithm is rarely used, or if a new one needs to be added to the mix to better process certain types of data.

Source: Tom Simonite "Google Offers Cloud-Based Learning Engine", Technology Review, 2010-08-20

As machine learning and other pattern-recognition technologies become more available and effective, companies will use them more often.

We can learn some lessons from the investment area, where algorithmic trading has already overtaken human discretion at least in terms of number of transactions executed on the US stock exchanges.It's true that quite often trading algorithms are still quite simple, but they are getting better as Moore's law increases the computing power available for them. It seems inevitable that one day algorithmic trading will dominate the investment industry, and human investors will share the fate of chess master Garry Kasparov defeated by IBM's Deep Blue.

Similarly, proliferation of quantitative methods in business may lead to some interesting results. First, managers will be often and often required to know these new technology-enabled methods. Second, the decision making processes, starting with operational aspects, may slowly morph into hardly penetrable black boxes, processing increasing amounts of information generated and gathered by business organizations.

Originally posted at: blog.inlevel.com

According to today's breaking news, S&P500 will raise or fall :)

2010-08-16T21:03:00.000+02:00

Two consequitive news found at finance.google.com today:

1,200 target reachable for the S&P 500 index

China Post - 16 hours ago

The recent economic reports have shown that the economic recovery is petering out, prompting a few economists to consider the possibility of the economy falling into recession. Robert Shiller ...

Why the S&P 500 Stock Index May Fall Below 1,000

DailyFinance - Aug 15, 2010

The S&P 500 made one sharp move down this year from 1,200 in late April to just about 1,000 in the first week in July. The index may be heading below 1,000 in the next month from the 1,079 where ...

Current index level: 1077.

PQ7: two tubulent years, +107,60%

2010-07-13T10:01:00.002+02:00

Fig. PQ7 net results (after transaction fees and taxes) for 2 years between mid July 2008 and mid July 2010

Final result after 2 years: +107,60% (approx. 37% annulized)

It has been two years since I've started a proprietary trading experiment called PQ7.

Its goal was to test some hypotheses regarding financial markets and... survive :)

It so happened that the PQ7 experiment coincided with one of the most volatile periods in the history of modern financial markets, what is reflected in performance of the strategy.

I have learned a lot during this period. I know now what I more of less do not know :)

The experiment will continue for the next 12-18 months with modified - hopefully less volatile - trading strategy.

More updates to come.

Cyclical analysis of gold prices

2010-07-10T16:37:00.005+02:00

Some investors believe that it is a good time for buying more gold now, for Q4 is usually positive for gold.

This believe is based, among other, on the assumption jewelery demand increases at the end of the year.

Indeed, if you take a look at the average monthly returns over the last 41 years (1969-2010), price of gold was increasing in September, November and December:

Fig. Average monthly changes

Both Q3 and Q4 were on average positive for gold, and stronger then Q1 and Q2:

Fig. Average daily changes in particular quarters

However if you take a closer look at the distribution of monthly changes, the pictures gets less clearer. September was historically a very volatile month, and while average returns for 3 out of 4 months in Q4 were usually positive, the probability of loss was still substantial:

Fig. Distribution of monthly changes

The randomness of changes is even more visible, when you combine two consecutive months - now average bi-monthly returns are very close to zero.

Fig. Distribution of bi-monthly changes

And still more when you analyze daily data - here you can see that daily changes oscillate around zero each month, without a clear tendency:

Fig. Distribution of daily changes in particular months

You can also take a closer look at the distribution of changes in potentially the most beneficial months, such as September and November - in the former positive average return was generated by infrequent high results, and in the later the distribution is rather symmetrical with some outliers on the negative side:

Fig. Histogram of changes in September

Fig. Histogram of changes in November

Hence, based on the available historic data I cannot agree that the probability of gain from investing in gold now and holding it till the end of the year is significantly higher then making a loss on such an investment.

I just can't see a visible cyclical / seasonal pattern in gold prices. But maybe somebody else can and would correct me?

To see daily chart of gold futures prices go to: http://www.wolframalpha.com/input/?i=gold&a=*C.gold-_*Commodity-

You can also find my bookmarks for articles about gold at: http://delicious.com/reakkt/gold

Reorganizacja BP w ramach przepisów upadłościowych może być mniejszym złem

2010-06-28T12:40:00.004+02:00

View the full BP chart at Wikinvest

Od początku bieżącego roku, akcje BP plc spadły o około 50%. Kapitalizacja spółki obniżyła się do 85 mld USD. Tymczasem szacunki kosztów związanych z wyciekiem ropy w Zatoce Meksykańskiej sięgają 100 mld USD. BP zgodziło się na wpłacenie na rachunek powierniczy 20 mld USD (przy rocznym zysku netto w ostatnich 3 latach w przedziale 16,8-21,7 mld USD), istotnie zmniejszając swoją płynność finansową. Przy niemożliwych do oszacowania ostatecznych kosztach kryzysu, coraz bardziej prawdopodobnym rozwiązaniem wydaje się bankructwo BP, co przynajmniej według amerykańskich przepisów (Chapter 11 - reorganizacja przy ochronie przed wierzycielami), pozwoliłoby na ograniczenie ryzyka firmy i... umożliwiło jej przetrwanie. Wywołałoby to jednak zdarzenie kredytowe, mające znaczenie dla długu firmy oraz instrumentów pochodnych związanych z ryzykiem kredytowym BP.

W połowie czerwca spread na CDS-ach dotyczących rocznego długu skoczył do ponad 1000 bps, czyli 10 punktów procentowych, przy równoczesnej czasowej utracie płynności rynku. 10% spread oznaczał, że ubezpieczenie każdych 10 mln USD długu spółki kosztowało rocznie 1 mln USD. Spready na inne okresy również gwałtownie wzrosły i utrzymują się na alarmującym poziomie (>500 bps). Agencje ratingowe obniżyły rating długu firmy, w przypadku Fitch niemal do poziomu obligacji śmieciowych (S&P: A, Moody's: Aa2, Fitch: BBB).

Według sprawozdania rocznego BP na koniec 2009 r., długoterminowy dług spółki wynosił 28,7 mld USD. To jednak nie dług spółki może stanowić największe zagrożenie. Znacznie groźniejsze mogą być różnorodne instrumenty pochodne związane z ryzykiem kredytowym firmy.

Jak wynika z noty analitycznej opublikowanej 21. czerwca br. przez agencję Moody's, około 18% wszystkich obserwowanych przez agencję CSO (Collateralized Synthetic Obligations, czyli instrumentów pochodnych opartych na ubezpieczeniach na dług CDS; więcej na temat konstrukcji CDS można przeczytać w ["CDS guide: new structures. CDSs as building blocks", credit ,2003-04"]) zawiera ekspozycje na ryzyko kredytowe BP i spółki związane.

Pozornie niewielka ekspozycja zawarta w tych CSO (2% dla BP, ok. 3,5% dla wszystkich spółek związanych z obecnym kryzysem naftowym) może paradoksalnie być przyczyną większych kłopotów.

Po pierwsze - związane z BP dłużne instrumenty pochodne stanowią część ogromnego rynku derywatyw kredytowych (BIS oszacował nominalną wartość CDS-ów na koniec 2009 r. na 32,7 billionów USD). W przypadku wymuszonej zdarzeniem kredytowym likwidacji "zarażonych" ryzykiem BP CSO, może dojść do wyprzedaży części aktywów związanych z pozostałymi firmami zapakowanymi w ten sam instrument. Zazwyczaj dotyka to najpierw najbardziej płynne aktywa. Dodatkowym skutkiem byłby silny skok kosztów długu firm zapakowanych w "skażone" derywatywy.

Po drugie - ukryta w złożonych i nieprzejrzystych instrumentach pochodnych ekspozycja na BP stanowi istotny element niepewności, dotyczący tego, kto i ile będzie musiał zapłacić w przypadku bankructwa BP. I czym sfinansuje swoje zobowiązania?

Kolejnym obszarem ryzyka jest rola BP w handlu instrumentami pochodnymi związanymi z energią, walutami i stopami procentowymi. BP jest prawdopodobnie największym podmiotem zaangażowanym w handel pierwszymi z tych instrumentów. Na koniec 2009 r. bilans spółki wykazywał łącznie ponad 17 mld USD w finansowych instrumentach pochodnych (mniej więcej po połowie w aktywach i pasywach). Bez znajomości struktury pozycji zawartych przez firmę, nie da się jednak oszacować skutków ewentualnego bankructwa firmy dla rynku instrumentów pochodnych. Zabezpieczanie tych pozycji przez przeciwne strony kontraktów zawartych z BP (w tym prawdopodobnie duże banki inwestycyjne) niemal na pewno podniesie zmienność na rynku, szczególnie w zakresie notowań energii.

Ostatnim elementem, który trzeba uwzględnić w analizie, są różnego rodzaju formalne i nieformalne gwarancje udzielone przez BP swoim kontrahentom i partnerom - np. związane z realizacją zobowiązań umownych. Likwidacja firmy doprowadziłaby do zerwania misternej i rozległej sieci powiązań między firmą i gospodarką. Skutki takiego zdarzenia są nieobliczalne i mogłoby ono dosłownie wstrzymać na pewien czas światową gospodarkę - np. w rezultacie odcięcia klientów BP od dostaw surowców niezbędnych do prowadzenia działalności. Z tego punktu widzenia, bezpieczniejszym rozwiązaniem wydaje się reorganizacja firmy pod ochroną przepisów upadłościowych. A to - o czym była mowa wcześniej - prowadzi do szoku na rynku instrumentów związanych z długiem. Może to jednak być mniejsze zło, a rynek finansowy można przynajmniej czasowo uspokoić kolejnym zastrzykiem płynności.

Źródła:

"BP and Counterparty Risk", Wall Street Pit, 2010-06-26

http://wallstreetpit.com/33059-bp-and-counterparty-risk

"BP Bankruptcy in U.K. Is Obama’s Worst Nightmare: Caroline Baum"

Bloomberg, 2010-06-24

http://www.bloomberg.com/news/2010-06-25/bp-bankruptcy-in-u-k-is-obama-s-worst-nightmare-caroline-baum.html

"BP Default Swaps Rise on Concerns Storm May Disrupt Oil Cleanup", Bloomberg Businessweek, 2010-06-22

http://www.businessweek.com/news/2010-06-22/bp-default-swaps-rise-on-concerns-storm-may-disrupt-oil-cleanup.html

"Death by (collateralised) BP association", FT Alphaville, 2010-06-22

http://ftalphaville.ft.com/blog/2010/06/22/267496/death-by-collateralised-bp-association/

"BP's Bankruptcy Would Impair 117 (18% Of Total) Collateralized Synthetic Obligations, Lead To Pervasive Losses", zerohedge, 2010-06-21

http://www.zerohedge.com/article/bps-bankruptcy-would-impair-117-18-total-collateralized-synthetic-obligations-lead-pervasive

"A Bankrupt BP - Worse For The Financial World Than Lehman Brothers?", Oil Price.com, 2010-06-22

http://oilprice.com/Energy/Energy-General/A-Bankrupt-BP-Worse-For-The-Financial-World-Than-Lehman-Brothers.html

"Has BP Sprung A Counterparty Risk Leak?", zerohedge, 2010-06-09

http://www.zerohedge.com/article/has-bp-sprung-counterparty-risk-leak

"CDS guide: new structures. CDSs as building blocks", credit ,2003-04

http://db.riskwaters.com/public/showPage.html?page=11387

Link: notowania opcji 2012-01 BP

Thanks to quantitive easing we will get more beautiful money! ;)

2010-06-18T19:35:00.003+02:00

Thanks to the quantitative easing there is much more money. And now they're going to be beautiful - the new $100 note will have a cool 3D stripe! ;)

More info: http://www.newmoney.gov/newmoney/default.aspx

Correlation between S&P500 and the US economy

2010-06-16T18:10:00.002+02:00

As I've written in my previous post, there was not any straightforward correlation between annual S&P500 returns and GDP nor FFR.

However, when you compare one year's market return to the product of the next year's GDP and FFR (actually 1+FFR), the correlation jumps to 0.61.

GDP*(1+FFR) can be interpreted as the sum of the economic growth and risk free rate in a given time.

Hence we can assume that stock market is predicting future economic situation and future risk free rate. And it's doing it pretty well :)

Nevertheless, due to high volatility, even that market predictions of the future economy state were pretty good, returns produced by the market were only marginally better than the risk free rates as expressed by FFR.

XLS file: http://www.mediafire.com/?mmmyummkzry

Where is the risk premium II?

2010-06-15T10:09:00.004+02:00

In the recent 55 years between 1955 and 2009, the average effective Fed Funds Rate was 5,52%. In the same period, the average annual return of S&P500 index reached 6,40% - that's a difference of just 88 pp!

Meanwhile, in the recent 34years between 1976 and 2009, the average yield of Moody's AAA bonds was 8,36% vs 7,63% returned by S&P500. The Fed Funds Rate averaged 6,13%. Even that the risk premium for S&P500 was a little higher - 151 pp - than in the first analyzed period, it was below the premium on AAA bonds!

It is also worth mentioning that no straight correlations between GDP, Fed Funds Rate and GDP existed

correlation GDP Fed Funds Rate
S&P500 -0.0383 -0.0689
GDP -0.0627

GDP vs Fed Funds Rate vs S&P500 [%] (1955-2009)

XLS file: http://www.mediafire.com/?yonzywyzizj

Data sources: FFR & AAA - Federal Reserve, GDP - BEA, S&P500 - Stooq

Note: the previous post, "Where is the risk premium?" was temporarily removed for revision and update.

Starting playing with signal analysis for modeling returns

2010-06-14T01:22:00.001+02:00

I'm starting to test applications of trigonometric functions for modeling returns.

Below a nice graph from Wolfram Alpha:

source: http://www.wolframalpha.com/input/?i=sin(x)%2Bsin(x*x%2Bx),+from+0+to+20