Question

You are evaluating a stock mutual fund that is among your employer’s 401k fund electives. The fund is actively managed and seeks to outperform the S&P 500. Over the past 10 years, the fund returned 10.25% per year and had a beta = 0.8. Over the same period, the S&P 500 returned 10% and the risk-free rate was 3%. A colleague asked your opinion of the fund. Recalling the principles from FINC 561, you inform the colleague that the fund produced positive alpha – meaning that the fund’s manager was able to find under-priced stocks thereby beating the market. Your colleague (who has not taken FINC 561) challenges your assertion stating: “The fund returned 10.25%, barely more than the S&P 500. I wouldn’t call 0.25% meaningful alpha – heck it’s not that much better than a S&P 500 index fund.” Comment on your colleague’s assertion. Do you agree? Why or why not? Explain.

Answer 1

Alpha is a measure of performance of an investment as compared to some suitable benchmark (usually market return)

A positive alpha suggest that the investment as outperformed the comaparable (market in this case). A negative alpha would mean that the investment has under performed.

Also, the amount of beta indicate by how much % does the investment over perform or under perform the market.

Alpha = R - Rf - Beta (Rm - Rf)

Where,

R = Expected return

Rf = Risk free rate

Rm = Market return or Index return

So Alpha = 10.25% - 3% - 0.8(10%-3%)

Alpha = 10.25% - 3% - 5.6%

Alpha = 1.65%

So the fund over performed the S&P500 by 1.65%

I disagree on colleagues assertion based on this