Return series comparison

[Volatility]

Hi.

Here's my problem, probably an easy one for some of you....

I have 2 return series, each with 26 returns, that is 14-days returns. So both series is one year.

If i want to test if the annual risk-adjusted return (annual return/annual stddev) of time serie 1 is significantly higher than time serie 2, how do i proceed?

If that is not possible, how can i test if the annual stddev of time serie 1 is significantly lower than time series 2?

Regards

Pierre Eric

 

[Muting]

Hi.

Here's my problem, probably an easy one for some of you....

I have 2 return series, each with 26 returns, that is 14-days returns. So both series is one year.

If i want to test if the annual risk-adjusted return (annual return/annual stddev) of time serie 1 is significantly higher than time serie 2, how do i proceed?

If that is not possible, how can i test if the annual stddev of time serie 1 is significantly lower than time series 2?

Regards

Pierre Eric

Hi,

You can use one series to minus the other series. Then you can test the P-value of the new series to find out whether its mean is not equal to 0 with certain significance.

 

[Volatility]

Thanks fo your answer, but then i will just test if the returns in serie 1 is significantly higher than the other.... thats not my problem....

 

[Muting]

Thanks fo your answer, but then i will just test if the returns in serie 1 is significantly higher than the other.... thats not my problem....

When we test whether one returns series is significant higher to the other, we compare the difference between each element in each series. The new series is about difference between the two returns. If the mean of the difference is significantly larger or smaller than 0, we can say they are different.

 

[Volatility]

I understand what you are saying...
just say both of them have the same mean, but one has 2 times higher stdev. It has to be a way to proove that one has significantly lower standard deviation....?

regards.-.

 

[Muting]

I understand what you are saying...
just say both of them have the same mean, but one has 2 times higher stdev. It has to be a way to proove that one has significantly lower standard deviation....?

regards.-.

I am a little confused. You say you want to compare the risk-adjusted return, whcih is return divided by stdev, if they have different stdev, you will get different risk-adjusted return.

 

[Volatility]

I'll try again....
the mean is almost the same on both series, but the risk adjusted return is quite different.
Then the standard deviation has to be quite different too. How can i test if the standard deviation is significantly different?

 

[Yuriy]

Try using an F-Test with Ho: volatilities are equal and Ha: volatilities are not equal, this would give you a two-tail test

The null and alternative are
Ho: (\sigma_{1}=\sigma_{2}) and Ha: (\sigma_{1}\neq\sigma_{2})

The test statistic is then
(F = s^{2}_{1}/s^{2}_{2}),
where (s^{2}_{1}) and (s^{2}_{2}) are your sample variances.

After you calculate your test statistic, compare it to table values and reject the null if
either
(F < F_{(1-\alpha/2,n1-1,n2-1)})
or
(F > F_{(\alpha/2,n1-1,n2-1)})
n1 and n2 are your sample sizes, and you pick your own (\alpha).

 

[Volatility]

Thank you very much, exactly what i was looking for...

Just another quick one: As long as the Sharpe Ratio or risk adjusted return is so widely used as a performance measurement, how do they check if one performance is significantly better ?
Or is is just common to compare the sharpe ratio values?

 

[Yuriy]

Statistical tests rely on some distributional assumptions. For example, the above comparison of volatilities was based on the fact that (F = s^{2}_{1}/s^{2}_{2}) follows an F distribution (at least approximately). I'm not sure what distribution the statistic to measure the difference in Sharpe Ratios follows. I'm not even sure how to construct it should it be the difference or the quotient of the ratios