Using Beta to Select Stocks and Manage Risk

By Thomas Stridsman

©2001, Reprinted with permission of Active Trader magazine (www.activetradermag.com)

Basically, there are two types of risks to consider when trading the stock market. The first risk, called beta, reflects to what degree a stock moves in conjunction with the overall market (typically measured by a market index). The second risk, called alpha, is associated only with a specific stock (or industry group).

Beta is a measure of how much and in what direction (in percentage terms) a specific stock is likely to fluctuate given a specific move in its market index (e.g., American Express vis-à-vis the Dow Jones Industrial Average). Beta can be either positive or negative. A positive beta means the stock in question is likely to move in the same direction as the overall market; a negative beta means the stock is more likely to move in the opposite direction as the overall market.

A beta of 1 or -1 indicates the stock is likely to move just as much as the market, with the sign of beta indicating the direction of the move in relation to the index. A stock’s beta in relation to the overall market is similar to an option’s delta in relation to its underlying stock.

While there is no way to get around alpha, beta can be lowered through proper diversification or be used to select stocks to trade. For example, many long-term investors try to lower the overall beta of their portfolios by combining their stocks in such a way that the beta of one stock cancels out the beta of another. Others try to combine their investments so the overall portfolio mimics the general market, which by definition has a beta of 1.

Beta for traders

But combining stocks in an investment portfolio is not the focus here; rather, we need to consider how beta can give you a statistical edge in your trading. Depending on your assumptions of general market direction, you should trade different stocks under different circumstances, based on their beta values.

If a stock has a beta higher than 1, it’s an indication the stock is more volatile than its index — that is, it tends to move more than 1 percent for a 1-percent move in the index. The same is true of stocks with betas lower than -1. Similarly, if a stock has a beta between -1 and 1, it’s an indication the stock is less volatile than the index.

To get a feel for how much a stock is likely to fluctuate, simply multiply its beta with the expected move of the index. For example, if a stock has a beta of +1.8 it can be expected to fluctuate 1.8 percent for every 1-percent move in the index, and in the same direction as the index. Therefore, if you believe the market is poised for a 5-percent up move, you can expect a stock with a beta of 1.8 to rally 9 percent (5 x 1.8).

If, on the other hand, the market is expected to decline 5 percent, you can expect a stock with a beta of -1.8 to rally 9 percent. If your strategy is designed to trade in the direction of the overall market, the higher the beta of the stock you’re trading, the better off you will be, provided you forecasted the general direction of the market correctly.

Using beta to select stocks

Following the simple principle just outlined, long-side traders should buy stocks with high positive betas if they believe the index will trade higher, and buy stocks with high negative betas (less than -1) if they expect the index to trade lower. If you like to short, sell stocks with a high positive beta if you expect the market to decline, and short stocks with high negative betas if you believe the market will rally.

However, if you trade high-beta stocks (above 1 or below -1) you stand to lose more when you’re wrong than if you trade low-beta stocks (between -1 and 1). A stock with a beta of +0.5, for example, is likely to rise only 2.5 percent when the overall market rises by five percent.

For those who trade several stocks simultaneously, the betas of the different stocks can be combined into a composite beta for all open trades. For example, over a large number of trades, a trader who always goes long in a stock with a beta of 1.2 will only break even if he also takes simultaneous long positions of the same size in a stock with a beta of -1.2. This is because when one stock is likely to zig in the same direction as the index, the other stock is likely to zag in the opposite direction by the same amount.

This suggests you need to vary the size of each trade in accordance with the beta of the stock so the dollar profits and losses will be equal between different stocks. For example, assume two stocks are both trading at $100, but one has a beta of 1 and the other a beta of 2. If you expect the index to go up 5 percent over the next few days, all else being equal, you should invest twice as much in the 1-beta stock as in the 2-beta stock to achieve an equal risk-reward relationship.

These principles will only hold true over a long period of time and a large number of trades (provided the betas of the stocks don’t change over time). Also, the longer the trades last, the more likely they are to behave as beta indicated. For each trade, the result is unknowable and also largely dependent on the alpha of each stock. All the beta value gives you is an indication of what is likely to happen — a slight statistical edge. See “Calculating beta” (right) for specific instructions on calculating and charting beta.

Practical trading implications

To get a feel for which stocks are better than others for this type of analysis, compare a stock’s estimated beta to its actual performance over a specific time period. (This analysis assumes the general market direction could be estimated correctly.)

Figure 5 (below) shows such a comparison over 12-month periods for American Express (AXP). The green line shows how the stock actually performed. The red line shows how AXP would have been expected to perform (given a correct forecast of the index) multiplied by the one-year beta at the time. As you can see, for the last six years or so, these lines have moved pretty much in tandem, meaning that, based on its beta, American Express would have provided very few or no surprises, given the trader was in tune with the overall market.

To round things off, let’s look at a few possible market scenarios and what types of stocks to trade, given a trader’s inclination to take some risk in an effort to achieve the best possible statistical edge.

A. If you firmly believe the index will go up:

B. If you firmly believe the index will go down:

1. Buy stocks with high negative beta values;
2. and/or go short stocks with high positive beta values.

C. If you’re only moderately sure the index will go up:

1. Buy stocks with low positive beta values;
2. and/or go short stocks with low negative beta values;
3. or buy a stock with a high positive beta and buy a stock with a low negative beta;
4. or buy a stock with a high positive beta and go short a stock with a low positive beta;
5. or go short a stock with a high negative beta and buy a stock with a low negative beta;
6. or go short a stock with a high negative beta and go short a stock with a low positive beta;

D. If you’re only moderately sure the index will go down:

1. Buy stocks with low negative beta values;
2. and/or go short stocks with low positive beta values;
3. or buy a stock with a high negative beta and buy a stock with a low positive beta.
4. or buy a stock with a high negative beta and go short a stock with low negative beta;
5. or go short a stock with a high positive beta and buy a stock with a low positive beta;
6. or go short a stock with a high positive beta and go short a stock with a low negative beta.

All trading alternatives within each scenario are ranked based on the assumption the trader prefers to go long rather than short, and that he wishes to keep track of as few positions as possible. In scenarios A and C, alternative 2, and scenarios B and D, alternative 1, the trader will make money if the stock moves against the general direction of the market as indicated by the negative beta value of the selected stock.

Scenarios C and D, alternatives 3 to 6, require you to place several orders in a spread trade. On average and over several trades, this approach will let you make a little money if you’re right and also limit losses if you’re wrong, because a part of the profit or loss in the highbeta stock will be canceled out by a move in the wrong direction by the lowbeta stock.

Remember, however, there are no guarantees. Beta is nothing but an estimate that can provide a slight statistical edge, based on historical price data likely to change over time. There also are other risks to consider, such as the alpha and how accurately the index can be forecasted. When it comes to spread trading, you also should consider the amount invested in each stock, as a large enough investment in a low-beta stock will be just as risky or profitable for your bottom line as a small investment in a high-beta stock.