Monte Carlo Hypothesis Testing with The Sharpe Ratio
Nkuliza, Senghor (2012)
Pro gradu -tutkielma
Nkuliza, Senghor
2012
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201209036368
https://urn.fi/URN:NBN:fi-fe201209036368
Tiivistelmä
The purpose of this master thesis was to perform simulations that involve use of
random number while testing hypotheses especially on two samples populations
being compared weather by their means, variances or Sharpe ratios. Specifically,
we simulated some well known distributions by Matlab and check out the accuracy
of an hypothesis testing. Furthermore, we went deeper and check what could happen
once the bootstrapping method as described by Effrons is applied on the simulated
data. In addition to that, one well known RobustSharpe hypothesis testing
stated in the paper of Ledoit and Wolf was applied to measure the statistical significance
performance between two investment founds basing on testing weather
there is a statistically significant difference between their Sharpe Ratios or not.
We collected many literatures about our topic and perform by Matlab many simulated
random numbers as possible to put out our purpose; As results we come out
with a good understanding that testing are not always accurate; for instance while
testing weather two normal distributed random vectors come from the same normal
distribution. The Jacque-Berra test for normality showed that for the normal random
vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal
distribution in contrast 5,3% and 4,3% failed to shown the truth already known;
but when we introduce the bootstrapping methods by Effrons while estimating pvalues
where the hypothesis decision is based, the accuracy of the test was 100%
successful.
From the above results the reports showed that bootstrapping methods while testing
or estimating some statistics should always considered because at most cases
the outcome are accurate and errors are minimized in the computation. Also the
RobustSharpe test which is known to use one of the bootstrapping methods, studentised
one, were applied first on different simulated data including distribution
of many kind and different shape secondly, on real data, Hedge and Mutual funds.
The test performed quite well to agree with the existence of statistical significance
difference between their Sharpe ratios as described in the paper of Ledoit andWolf.
random number while testing hypotheses especially on two samples populations
being compared weather by their means, variances or Sharpe ratios. Specifically,
we simulated some well known distributions by Matlab and check out the accuracy
of an hypothesis testing. Furthermore, we went deeper and check what could happen
once the bootstrapping method as described by Effrons is applied on the simulated
data. In addition to that, one well known RobustSharpe hypothesis testing
stated in the paper of Ledoit and Wolf was applied to measure the statistical significance
performance between two investment founds basing on testing weather
there is a statistically significant difference between their Sharpe Ratios or not.
We collected many literatures about our topic and perform by Matlab many simulated
random numbers as possible to put out our purpose; As results we come out
with a good understanding that testing are not always accurate; for instance while
testing weather two normal distributed random vectors come from the same normal
distribution. The Jacque-Berra test for normality showed that for the normal random
vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal
distribution in contrast 5,3% and 4,3% failed to shown the truth already known;
but when we introduce the bootstrapping methods by Effrons while estimating pvalues
where the hypothesis decision is based, the accuracy of the test was 100%
successful.
From the above results the reports showed that bootstrapping methods while testing
or estimating some statistics should always considered because at most cases
the outcome are accurate and errors are minimized in the computation. Also the
RobustSharpe test which is known to use one of the bootstrapping methods, studentised
one, were applied first on different simulated data including distribution
of many kind and different shape secondly, on real data, Hedge and Mutual funds.
The test performed quite well to agree with the existence of statistical significance
difference between their Sharpe ratios as described in the paper of Ledoit andWolf.