Alpha, alpha is gonna be the first risk-adjusted performance measure that we'll look at. And these risk-adjusted measures take away the natural tendency of investors to just focus on returns without considering risk. And of course, it's very important to factor in risk when evaluating a portfolio because after all, widely accepted principle of investment management theory and portfolio theory, and in practice is that investors are risk averse and therefore they will demand additional expected return to compensate them for any additional risk. Therefore, it's not surprising that when we evaluate a portfolio manager's performance, we want to compare returns generated by that portfolio manager with the portfolio's corresponding risk. Now, alpha tries to measure how much of the return generated by the portfolio was due to the portfolio manager's investment decisions. So it measures the excess return of the portfolio over a predetermined benchmark or market index. And investors in mutual funds and ETFs want a high alpha because it signifies to them that the portfolio manager created superior return for every unit of risk that he or she took on. Now, in its simplest form, alpha is simply equal to the portfolio's return, the portfolio's absolute return, minus the benchmark, and that is the simplest calculation for alpha. As a result, if alpha is greater than zero, it means that the portfolio manager outperformed the benchmark, and vice versa. If it's less than zero, it indicates an underperformance. Now, Jensen's Alpha is a different take on alpha in the sense that it uses the CAPM framework in the security market line to form a benchmark to compare to portfolio to. It's also sometimes referred to as ex-post alpha. Now with Jensen's Alpha, the measure is the difference between the portfolio's return and the required return as calculated by the CAPM model. In here you'll see that familiar CAPM formula where the expected return on an investment or a portfolio is equal to the risk-free rate plus beta times the equity market risk premium, or the return on the market minus the risk-free rate. Now, if these two do not equal, alpha is present. And alpha is usually depicted by the Greek symbol for alpha. Now, if we did some simple algebra, we can rearrange the formula that would solve for alpha. So alpha would be equal to the expected return on the portfolio, minus the risk-free rate minus beta times the equity market risk premium. And we interpret Jensen's Alpha in the same way. If that alpha calculation is greater than zero, it indicates an outperformance for the level of risk that the portfolio manager is taking on. If the alpha, however, is less than zero, it would indicate an underperformance. The manager produced less return than the amount of risk inherent in the portfolio would dictate. Now, let's go through an example. Here the return for a fund during the last year was a strong 20%. If the risk-free rate was 6% and the portfolio beta was 1.2 while the return on the market was 10% during the same period, what is the alpha created by the portfolio manager? Well, again, we have the alpha formula here. So if we plug our data points into the formula, we know that the return on the portfolio was 20% minus the risk-free rate of 6% and then minus 1.2 which is beta times the equity market risk premium of 10% minus 6%. And here you can see that the alpha produced by the portfolio manager is equal to 9.2%. Now, it's important to note that the 9.2% is less than the difference in the portfolio minus the return in the market, which was 10%. And that's because the portfolio manager took on more risk than the overall market as indicated by the beta of 1.2. So not only is Jensen's Alpha comparing the return of a portfolio versus the market, but is also comparing the amount of risks taken on versus the broad market.
