t-test in SPPS / Comparing Portfolios

Question

I’m sure this is an idiotic question, but I’m having difficulty with an assignment and hoping somene can help. I’m not a Stats student but am using SPSS for a research project.

I am comparing 5 Year returns (2012 to 2016) of two Portfolios of stocks.

The portfolios get re balanced every year (from a market Index) , and although at any one time will never share a stock, over the 5 year period a stock may switch portfolios from one year to the next There is nothng random about, Portfolios are rebalanced based on an historic rating. if I was to redo the process, I would get the same results.

My supervisor is recommending compare means by Independent sample t-test, and then to just highlight the limitations. Is there a better way through SPSS to compare Portfolio returns ?

Portfolio A is showing 99% return over the 5 years, Portfolio B is showing 71% Yet the Independent sample t-test is showing no significant difference – is that odd or normal enough ?

Thanks in advance

Answer 1

My supervisor is recommending compare means by Independent sample t-test, and then to just highlight the limitations.

If statistically significant, this test would show that, assuming that both returns are normally distributed and sampled independently, the process of sampling 5 years of returns and comparing them would result in one of them being superior about $p\%$ of the time, where $p$ is the p-value. Is this what you are trying to show? Are the assumptions reasonable? If yes, then your supervisor's strategy is sound.

The portfolios get re balanced every year (from a market Index) , and although at any one time will never share a stock, over the 5 year period a stock may switch portfolios from one year to the next There is nothing random about, Portfolios are rebalanced based on an historic rating. if I was to redo the process, I would get the same results.

You seem to think that this violates the assumption where the data is sampled independently. It doesn't. You described how the population (the returns) is generated, not how it's sampled. For example, you can generate two populations of $1000$ individuals with equal mean and variance, and then sample $100$ individuals from each without violating the test's assumptions.

Portfolio A is showing 99% return over the 5 years, Portfolio B is showing 71% Yet the Independent sample t-test is showing no significant difference – is that odd or normal enough ?

Whether the difference between Portfolios A and B is significant or not depends on the population variance (that is, the volatility). The higher the volatility, the larger the difference must be in order to be deemed statistically significant.