Saturday, December 31, 2011

Serendipity or extremes detection

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

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 ;)

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%.

Saturday, December 17, 2011 2.0 - opportunity or bubble?

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?

Wednesday, December 14, 2011

Commerzbank jumps, but will it last?

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

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.

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,”
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.
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:

Sunday, December 11, 2011

Let's Occupy Wall Street?

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

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.

Friday, December 9, 2011

A day at the races

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...

Monday, November 21, 2011

Back to Twist

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.

Sunday, November 20, 2011

Another failed test of financial data normality

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.

Friday, November 18, 2011

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

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...

Thursday, October 27, 2011

Correlation doesn't mean easy prediction

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

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

Tuesday, October 25, 2011

Cointegrated drunk and her dog visualized

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.

Friday, October 7, 2011

Eat this Berkshire Hathaway ;)

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.

Sunday, October 2, 2011

Highly distorted prices of long term BofA call options

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.

Saturday, October 1, 2011

If you cannot save it, dump it

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

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...

Friday, September 30, 2011

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

...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;

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:
  1. Bank of America does not go bankrupt
  2. 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

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?

Monday, September 26, 2011

Probability of Lotto

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.

Sunday, September 25, 2011

A bigger bubble?

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

Chart: Apple vs gold, 10 years;

Friday, September 23, 2011


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 ;)

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

Thursday, September 22, 2011

Banks squeezed by regulations

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

Wednesday, September 21, 2011

Problems in Europe overshadow Operation Twist

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

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

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:


  • 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;

Comparing two recent forex interventions

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...

Monday, September 19, 2011

Stabilizing financial markets through forex

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;

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;

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?

Friday, September 16, 2011

Gold - correction or trend change?

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.

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.

Thursday, September 15, 2011

Bounce from the exteme oversold conditions

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 ;)


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%

Tuesday, September 13, 2011

What distribution does the stock market follow?

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:

 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%)

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

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.

Monday, September 12, 2011

Short term relief?

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

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?

Sunday, September 11, 2011

The end of floating exchange rates is coming?

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:

  1. when it intends to weaken "its" currency - it can simply print ANY amount of money to flood the market
  2. 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:

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.