Monday, December 05, 2005



Alpha can be a difficult concept to understand. The last newsletter took on the topic and a post from last week rehashed Beta. Beta, as readers should recall, is the volatility of an investment when compared to the volatility of the S&P 500 Index.

Let’s start again with the definition of Alpha:

Alpha is a 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 overperformance or underperformance. (i.e., Alpha of 1, 2, or -.5 or –1)

The basic question that Alpha asks and answers is: did you get more reward or less reward for a given amount of risk? Let’s look at the concept of a “given amount of risk”. To do so, we will spin the Roulette Wheel.

Roulette is a mainstay at most casinos.[i] The Roulette Wheel is a spinning wheel with 64 numbers[ii]. The wheel is spun and then a ball is released. There are holes in the wheel that correspond to the numbers. There are two sets of numbers 1 through 32, with a set in red and a set in green. Your odds of hitting Red 1 or Green 32 are one in 64. 1:64. If you bet on Red 1 and win, you get $35 (Check). So 1 unit of risk gets you $35. But there are other ways to play. Lots of bets, but let’s focus on just as couple.

You can bet on the wheel hitting a Red number or a Green Number. One-half the numbers are Red and one-half are Green. You have a much better chance of winning betting on Red or Green, but your winnings are correspondingly smaller. You have a 1 in 2 chance of guessing Red or Green on each spin of the wheel and the payout is $1, 1:2. For a lower risk bet, you get a lower reward.

When people invest in riskier stocks or bonds, they demand a higher return. They demand a higher return because their chance of earning the expected return is less than it is with a safer investment. This is a logical approach, but it often breaks down. It breaks down for two reasons. First, it is often difficult to determine if you are exposing your investment to more risk than necessary for the expected return. Accurate information and projections are not always available to perform the risk/reward assessment. Second, most investors do not even engage in a thorough risk/reward assessment.


Let’s go back to the Roulette wheel. Remember the bet on a single colored number. One dollar, or one unit of risk, will get us a $64 (Check) reward. And one unit of risk will get us one additional dollar if we make a 1:2 bet on Red or Green. The same kind of risk/reward analysis, using historical data, is what Alpha can tell us. Alpha cannot guarantee future risk/reward, but it does give us historical data that we can use in making projections.

Let’s revisit the Alpha calculation we did in the earlier post. 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 Just follow the Bouncing Ball . . .:

1. 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 Treasury 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.

If we invested in any investment considered to be more risky than the US Treasury Note, like stocks, bonds, nearly anything else and earned less than 4%, we got less reward for taking more risk. But if we invested in nearly anything else and got more than 4%, we might have gotten more reward for less risk. But we won’t know until we do the Alpha calculation.

Let’s follow the analysis and work up 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%. Pretty good. But we still won’t know if Slow and Steady gave us a higher return or a lower return for the amount of risk we incurred until we complete the Alpha calculation.

2. 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, or 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[iii]. 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

3. Beta and Expected Excess Return. Remember Beta is a volatility measurement. We need this figure 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 number is critical. This tells us the return we should have earned on a value stock mutual fund. If Slow and Steady mutual fund exceeded this 2.4% return, then the investor for more reward for less risk. But if our mutual fund lagged this 2.4%, then we got less reward for the risk we took by investing in a Slow and Steady.

4. Alpha. Whew. Finally. And as you have figured out by now, Slow and Steady placekicked the competition and earned us a lot of excess return for the risk we took.

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.


Morningstar is a common source of investment information. Many public libraries have Morningstar services. Your broker or investment planner may also have access to Morningstar services. Also, many mutual funds will post their Alphas and Betas on their websites. But remember, Alpha is only one measurement in the selection of a mutual fund. But it is an important one.


[i] We will use a gambling analogy because it is a good demonstration of “risk and reward”. Gambling is not the same thing as investing, however.
[ii] Except at the casinos, where they add one or two zeroes. These zeroes lower your odds of winning and make sure that the house always wins. This is the best argument one can make against gambling at a casino. It is statistically a game you cannot win.
[iii] The symbol of the ETF for this index is IWD. If we were looking at another type of mutual fund, such as the Afterburner Tech Stock fund, we would compare it with an index of tech stocks.