Saturday, November 05, 2005



Some readers may have heard the term “Beta” in reference to mutual fund performance. Perhaps a few of you have even heard the term “Alpha”. These concepts are key to assessing risk and reward for a particular investment. Ideally, investors who take on more risk should get a greater reward. That is why one expects a small capitalization technology stock to have a higher return than the stock of a large-cap food company. The odds of small tech company generating positive returns are less than that of an established consumer non-durable company generating positive returns. But many investors do not effectively balance the risk/reward equation. This post will help you bring things back into alignment.


The interplay of risk and reward must be understood by investors. Without this understanding, you are at a substantial disadvantage to the market and your returns will, over the long term, lag the market. In this post we will look at Beta and Alpha. In another post we may take a run at R-squared or standard deviation. For all you squares and deviants out there.

Risk is a concept that could fill many file server discs. Many books have been written just on the concept, history, and quantification of “risk”. A good definition of investment risk is:

“The chance that an investment's actual return will be different than expected. This includes the possibility of losing some or all of the original investment.”

This definition comes from And there are many types of market risk. But for this post we will look at risk that the Author will vaguely define as “market-adjusted risk”. We will consider, using Beta and Alpha, how a particular investment performs considering the quantified risk we are taking owning such investment.


Beta is a measure of a stock’s volatility. Volatility is the tendency of an investment to swing in price over a period of time. A stock that goes up and down by 10% is more volatile than a stock that only swings 1 to 2% in the same period. Usually volatility is measured against a benchmark. In the case of Beta, the Beta of an individual stock or mutual fund is compared against the overall volatility of the S & P 500 index. The S & P 500 Index is assigned a Beta of 1. So if you own an S&P 500 Index mutual fund, its Beta should be darn close to 1.


Let’s take a look at a couple of examples that are common in mutual fund investing. We will look at two funds, one a “conservative” value oriented mutual fund called the “Slow and Steady Value Stock Mutual Fund”. The other is an aggressive small capitalization tech stock mutual fund called “Afterburner Tech Stock Fund”.

If the Slow and Steady Value Stock Mutual Fund has a beta of .8, that means that the mutual fund is only 80% as volatile as the S&P 500. This fund historically only moves 80% in value in comparison to the S&P 500. So it the S&P was up 5% for the past year, Slow and Steady would be expected to be up 4% (5 * 80% = 4). However, if the S&P was down 7.21%, then Slow and Steady would have only fallen by 5.77%.

Afterburner Tech Stock Fund has a beta of 1.25. This means that this mutual fund is 25% more volatile than the S& P 500. So if the S&P 500 rises by 9%, then Afterburner would be expected to be 11.25%. But if the S&P nosedives by 13.3%, then Afterburner will sink by 16.625%.

Beta has limits, however. Beta tells you the historical volatility of an investment, and is useful for examining expected returns in light of historical results. But to get an idea of whether you are getting more reward than risk, or more risk than reward, we must plug Alpha into the equation.


Alpha is not too difficult to explain, but it is a little complex to calculate. But to really understand Alpha, readers will need to know how it is calculated. We will start with the definition, in English not Geek:

Alpha is the risk-adjusted return on an investment. Alpha demonstrates whether your investment outperformed or underperformed a risk-related benchmark. If you outperformed the benchmark, then you got more reward for a given amount of risk. If the investment underperformed the benchmark, then you took on extra risk to get less reward. Alpha is measured in percent of over performance or underperformance. (i.e., Alpha of 1, 2, or -.5 or –1)

Let’s do an Alpha calculation to sort all of this out. For this calculation we will use the Slow and Steady Value Mutual Fund. Last year, the Slow and Steady fund returned 10%. And in doing this calculation we will bring in a couple of other financial concepts. You won’t need a calculator, but a beverage of choice may be advisable.

Risk-free rate of return. One of the first things you need to know to calculate Alpha is the risk free rate of return. This is not hard to calculate, however. The risk-free rate of return is the interest rate paid on a US Treasury note. Why the Treasure Note? They are considered risk-free because they are guaranteed by the “Full Faith and Credit” of the US government. So let’s say that a 6-month Treasury note is paying 4%. So the risk-free rate of return is 4%

Let’s follow the analysis and work up the basis for the Alpha equation at each step. Slow and Steady returned 10% last year. The risk-free rate of return was 4%.

10% (Slow and Steady Return- 4% (Risk free rate of return) = 6%. Slow and Steady exceeded the risk-free rate of return by 6%. Whether that is a good or a poor return will require some more analysis, however.

Excess Return. In a good year for the stock market, many stocks and most indices will have a higher return than the risk-free rate of return, the interest paid on a Treasury Note. Slow and Steady had an excess return of 6%. However, the excess return has to be considered in light of a benchmark for similar investments. Slow and Steady is a value stock mutual fund. For a comparison with an index of comparable stocks, we will compare it with the Russell 1000 Value Index[i]. This is an index of large capitalization value stocks. Last year this index returned 7%. So the benchmark excess return for large cap value stocks is:

7% (Large value stock benchmark)-4% (Risk free rate of return) = 3%

Beta and Expected Excess Return
. Remember Beta is a volatility measurement. We need it to compare our risks with our returns. The excess risk we would expect for a our large value fund is calculated as follows:

Beta * Excess Return for Benchmark = Expected Risk-Adjusted Return

.8 (Beta for Slow and Steady) * 3% (Excess Return for large value index) = 2.4%

So the expected excess return for Slow and Steady is 2.4%. This is the excess return that the benchmark value fund index generated.

Alpha. Whew. Finally. Remember that Alpha demonstrates whether your investment outperformed or underperformed a risk-related benchmark. In this case, Slow and Steady drop-kicked the benchmark.

6% (Slow and Steady’s Excess Return) – 2.4% (Expected Excess Return) = 3.6% Slow and Steady has an Alpha of 3.6%. This means you got a return of 3.6% above and beyond the return you should have expected given the risk that you took (as measured by Beta) for investing in Slow and Steady. You should send the Fund Manager a Christmas Card and a Chia pet.

Few people actually calculate Alphas. One good source for Alpha calculations is Morningstar, a service for mutual fund investors. Morningstar calculates Alphas for mutual funds. This is a premium service, but it may be available at your local library if your library subscribes to Morningstar. And while we are on the topic of investments, if you live in a medium-sized town or a large city, your library may provide these services free of charge.

Alpha, as a stock measure of risk-adjusted return, is more problematic. An individual stock is more difficult to compare to a broad benchmark. But if you are a mutual fund investor, Alpha is a concept that you need to consider in fund selection and retention. Remember, however, Alpha is an historical calculation, and past performance is not guarantee of future results.


IMPORANT DISCLAIMER: This post is offered for informational purposes only. Sources of information provided are believed to be reliable, but are not guaranteed to be complete or without error. Opinions and suggestions are provided with the understanding that readers acting on information contained herein assume all risks involved. The Author may or may not buy or sell securities discussed in this post.

[i] The symbol of the ETF (Exchange-Traded Fund) for this index is IWD.