## niedziela, 18 marca 2012

### What is the probability that the market will raise 5% over 25 sessions?

Chart: Probability of at least a +5% change over 25 sessions for WIG20
sampled on the latest 250-1250 sessions

A couple of days ago I wrote a post about differences in return characteristics of various assets.

Now I'd like to take a look on the markets from a little different perspective.

I was asking myself a pretty straightforward question:

What is the probability that the market will raise at least x% over the next n sessions?

The so called "modern portfolio theory" takes expected return of assets constituting the portfolio as one of its three critical parameters (the others are asset correlations and their volatility).

Hence, the people constructing portfolios based on this theory must somehow guess what these parameters will look like in the future.

The problem is, all of these parameters are pretty hard to forecast...

Hence, I decided to explore the first of these parameters - the expected return - and asked the above mentioned question.

On the chart above you can see the probability of a 5% growth of the WIG20 index of the Polish stock exchange over 25 sessions (a month), calculated on the basis of the 25-days samples drawn from the previous 250 to 1250 sessions (1 year - 5 years).

As you can see, the probability fluctuates between 14.38% and 30.46%.

OK, and how it looks from the opposite side, i.e. what is the probability of a 5% decline?

The probability range is pretty similar: 14.24% - 30.68%.

But the shape of the graph is completely different, especially on the left side of the chart:

Chart: Probability of at least a -5% change over 25 sessions for WIG20
sampled on the latest 250-1250 sessions

Even if the overall probability of a +/- x% change seems similar, the specific realization can vary greatly depending on the particular moment in time.