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Calculating the sharpe ratio of a timeseries of asset values

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First of all - what is the sharpe ratio and why is it important ?


Well the Sharpe Ratio - SR for short - is a risk/return measure and that in itself makes it important when talking about finance. It is also a simple number to calculate and explain what it means and that is ... it gives a measure of how much excess return you will get from the extra volatility of holding a risky asset -as compared to a risk-free asset.


The formula for calculating it as follows.


​SR = Rx - Rf/STDEV(Rx)


where 


Rx is the expected return of the asset held

Rf is a nominal risk-free rate of return e.g a US treasury bill

STDEV(x) is the standard deviation of the asset return.


So, lets say we have a timeseries of daily asset values. To calculate the SR, first of all


a) generate a series of daily return performances for the asset

b) get the average of the above  and this will be our expected return (Rx)

c) Pick your risk free rate of return Rf

d) Calculate the STDEV of the daily  returns from (a) above

e) Substract (b) from (c) and divide by (d)



Now, the SR is usually quoted as an annual figure.  In our example we have calculated it based on daily returns so in order to annualise we must multiply our final figure by SQRT(252). Why is this?. Well, its above my maths grade but its do with the fact that asset returns being a Weiner process means that their volatilty scales with the square root of time. We assume there are 252 working days in a year hence the SQRT(252). If we had had monthly returns we would multiply the calculated SR by SQRT(12).


Generally speaking the higher the SR figure the better. A negative SR indicates that our asset generates less return that our risk-free proxy