In this workout, we're asked to consider an investor who is thinking about investing in one of two funds. The Stars Fund or the Stripes Fund. We're asked to calculate the Jensen's Alpha and the Sharpe ratio for each fund to help with this investment decision making process. There's also an assumption here of the risk free rate of return being 3.5% and market returns being 9%. We're also given individual information about each fund, starting with the return of the portfolio, the Stars Fund returning 15% and the Stripes 11%. Also, the portfolio standard deviation, 14.5% for Stars and 9% for Stripes, and a portfolio beta, 1.6 for Stars and 1.1 for Stripes. This tells us that the Stars Fund has generated more return but taken more risk to get there. And the Stripes Fund, these two measures, Jensen's Alpha and the Sharp Ratio will help to control for the level of risk that each fund has taken. We also have the risk-free rate of return, 3.5% and market return for each of the two funds being the same. In order to, first of all calculate the Jensen's Alpha measure, we need to initially calculate the return predicted or required by CAPM. So to do that, we need to take the risk-free rate of return and add to it the portfolio beta, multiplied by the difference between the return on the market and the risk-free rate of return. We can see from this that the only factor in relation to the Stars Fund that we're using is its beta. This predicts for us a 12.3% return for the Stars Fund based on its beta. However, the fund itself generated a 15% rate of rate of return in excess of the return required by CAPM, giving us a positive jenssen's alpha number of 2.7.

If we then copy this to the right for the Stripes Fund, we can see that the Stripes Fund had a lower beta and therefore had a lower required return under CAPM. However, it only outperformed its required return under CAPM, the return that CAPM would've predicted by 1.5%. So we'd say here, for these two funds that Stars is the better fund. On a Jensen's alpha basis, it outperformed what CAPM predicted by a higher degree. If we've gone to look at the Sharpe ratio, we can see that the sharp ratio is calculated by taking the return on the portfolio, 15% here for Stars minus the risk-free rate of return of 3.5%, and divide the resultant number by the portfolio risk or standard deviation.

This gives us 0.79 for the Stars Fund and 0.83 for the Stripes Fund. What this is telling us is that the Stripes Fund has generated more return over and above the risk-free rate of return for each unit of risk taken on by the fund using standard deviation as that measure of risk. The higher the Sharpe ratio, the better, the more return we're getting for the risk that's been taken on. And this would indicate that Stripes is the better performing fund on a Sharpe ratio basis. So we're getting a conflicting outcome here between the sharp ratio and Jensen's Alpha, but that is because they use different metrics for risk. The Jensen's alpha metric uses beta as our measure of risk, and beta captures systematic risk only. Whereas the Sharpe ratio uses standard deviation as a measure of risk that captures all of the risk, the total risk faced by that fund. So if we're thinking about this from the investor on a standalone basis where the investor faces all of the risk, then the better metric to use would be the Sharpe ratio and the Stripes Fund would be the better investment. However, if this investment is gonna be held within a portfolio and maybe Unsystematic risk is being diversified away within that portfolio, then the investor is only gonna be facing systematic risk measured by the beta, and as a result, the higher Jensen's Alpha of the Stars Fund would suggest that that was the better investment.