The Dividend Investing Resource Center

Letting Dividends Do Their Work

Alpha and Beta

by George L Smyth

Risk and reward are intertwined.  Risk is acceptable if paired with an appropriate reward, and understanding how alpha and beta fit into the calculation is essential for the proper determination of risk.

“Successful investing is about managing risk, not avoiding it.”
Benjamin Graham

I do not bother with lottery tickets.  I can understand purchasing a single ticket for the entertainment value of imagining what one might do with the money were they to win, but from a risk perspective, it makes no mathematical sense.  I have said that lotteries prey on the mathematically challenged, though there is one notable exception of which I am aware.  Simple arithmetic can highlight its futility.

The odds of winning the big prize playing Powerball or Mega Millions are 1 in 292 million and 1 in 303 million, respectively.  While I have heard it said, "someone has to win," I have a way of explaining the unlikelihood of winning.  If you were given an envelope and told to deliver it to someone in the United States without being told who the person was or where they lived, and you happened to give it to the right person, then you would win the lottery.  Otherwise, you would lose.

These are hopeless odds.  When you offer a dollar for a ticket, then the odds of losing that dollar are not worth the investment.  But it is possible to make it mathematically worthwhile.  If the odds are 300 million to 1 against you, and the jackpot is $300 million, then the reward equals the risk.  Of course, in this situation, the fact that it is possible for more than one person to win sullies the calculation. Alas, this article is about dividend stocks, not the lottery, but the basic idea of risk and reward is the same. 

There is a level of risk attached to everything in life, and purchasing a stock always contains some element of risk.  It is tolerable if the reward equals or exceeds the risk.  I think of this each time I see someone shoot their car through an intersection.  Yes, they will possibly arrive at their destination earlier, but does the reward of this possibility of getting to their destination 20 seconds earlier overcome the risk of an accident or that a red light camera may force the driver to pay a fine?

Alpha and beta are terms used to quantify risk in stocks.  Examining the numbers for a stock can better help us determine the appropriate level of this risk.


Beta is a measure of the relative volatility of a stock to the market.  Investopedia notes that it is calculated through regression analysis and defines the formula as, “the covariance of the return of an asset with the return of the benchmark divided by the variance of the return of the benchmark over a certain period."  I will let someone else do the calculation, as Yahoo Finance already has this covered.  We simply need to understand what the value of beta means.  

When a stock has a beta of 1, it means that its movements in price follow that of the market.  As the market moves up, the stock moves up, as the market moves up a lot, the stock moves up a lot.

If a stock’s beta is greater than 1, then it has greater volatility than the market – when the market moves up, the stock moves up, but more.  The higher the number, the greater the volatility.  Conversely, if a stock's beta is less than 1, then it is less volatile than the market.

The value of beta is a multiplicative factor.  One uses it as a multiplier, so a stock with a beta of 2 means that it is twice as volatile as the market (the market goes up, the stock goes up twice as much), and one with a beta of 0.5 means that it is half as volatile (the market goes up, the stock only goes up half as much).  We often use the S&P 500 Index as a proxy for the market, so in this article, I will use them interchangeably.

Beta can also be a negative number, which indicates that the stock moves counter to the market – if the S&P 500 goes up, the stock goes down.  This link offers examples of negative beta stocks.  In such a situation a stock with a beta of -2 indicates that when the S&P 500 goes up, the stock goes down twice as much.

Beta, i.e. volatility, is a shorthand for risk.  Stocks with a beta of 2 or more are considered to be high beta, or very volatile, low beta stocks hover closer to 0.

Beta is often driven by sector.  Utilities are generally immune to the movements of the S&P 500, while the computer and software sector may drive the market’s swings.  One seeking the calm may want to gear themselves toward low beta stocks, whereas those who are willing to deal with volatility may wish to expand to a higher beta value.


Alpha is the percentage difference between a stock’s gain (or loss) and its expectation.  That expectation is often a benchmark, like the S&P 500.  If the S&P 500 goes up 5%, and the stock has increased by 20%, then that yields an alpha of 15 (the difference between 5% and 20%).  Reverse the numbers, and it offers an alpha of -15.  A positive alpha outperforms the market, and a negative alpha underperforms.

It is a positive event when a stock has increased by 25% in a year, and most of us would be glad for that to happen.  However, the S&P 500 returned 30% in 2019.  While 25% may appear to be successful when isolated on its own, it has not performed as well as the market, so this indicates an alpha of -5, or 5% less than its expectation.

Alpha places gains and losses into context.  If a rising tide lifts all boats, then alpha shows how much higher a particular boat might be over others in that rising tide.  It is the difference between looking good because all stocks are looking good, and looking good through actual outperformance.

Using the Two Together

Both alpha and beta are backward-looking.  Attempts to predict the future may be problematic, but the realization of a stock’s historical nature can give the investor an indication of what to expect.  If we understand the volatility of a company and compare its actual fluctuation to that of the market, then we have a better idea as to whether or not the risk has been worth the reward.

For example, consider a hypothetical company that has returned 12% over a specified period, while the S&P 500’s return was 10% over that same period.  The stock outperformed the index, so on the face, this is a positive event.  The real question is whether or not the reward for owning the stock had been worth the risk.

This example stock shows a beta of 1.5, which means that its volatility is 50% higher than that of the market.  As the S&P 500 returned 10%, 50% higher would have brought us a return of 15%.  While this stock outperformed the market, only returning 12% gave us an alpha of -3, which means that the risk had not been worth the reward.

The advantage dividend investors have with this exercise is that when dividends are collected and reinvested, the dividends increase the total return of an investment, and reinvested dividends increase the number of shares.  The ability to do both gives the investor a better chance for success toward a positive alpha.

But Does This Matter?

“Just when I thought I knew all the answers, someone changed the questions.”

The idea of beta and alpha is to have a means of numerically exploring risk and reward.  If one is willing to assume higher risk, then they should receive a higher reward (as well as accept a greater loss).  This is one of the basics of the Capital Asset Pricing Model (CAPM).

The problem is that in the real world, this may not be happening.  In 1972 Merton Miller and Myron Scholes showed that high beta stocks underperformed low beta stocks.  In other words, risky stocks had lower returns than less risky stocks.

Yuval Taylor wrote Why Low Beta Outperforms, which is interesting to the mathematically inclined.  To those who wish to cut to the chase, he shows that there is a negative correlation between beta and alpha, and low beta stocks outperform their high beta equivalents.  The bottom line is that while one should be rewarded for being exposed to higher risk, they may be more greatly rewarded by involving themselves with lower risk.

Finishing Up

High risk should bring high rewards.  Low risk may offer higher rewards.  High beta stocks command that their performance compares favorably to the appropriate benchmark – low beta stocks demand the same.  The use of beta allows one to work within a margin of safety when making a purchase, offering guidance in the issue of risk.

It is problematic that whereas exposure to high risk should result in a high reward, it is possible that a low risk could bring about greater reward.  One should at least understand where the risk lies in their portfolio and take it into account when making decisions.

Other Articles of Interest

6 Myths about 6 Problems with Dividend Investing

Cash Flow for the Dividend Investor

Stock Tips are Bunk



This website is maintained by George L Smyth