2 Scenarios If market return is 5 percent stock's expected return is -2 percent If market return is 25 percent expected return is 38 percent What is its beta?

Answer 1

The beta is the relationship of a stock's expected return to the broad market's return. A "high beta" stock will have a beta over 1.00, and thus move up more than the market when the market is advancing, and decline more than the market when the market is declining. A "low beta" stock will decline less than the market, or advance less than the market, depending.

The problem with beta is that it assumes a linear relationship, and what you describe here clearly is not. Your stock falls when the market rises a little, and rises more than the market when the market is advancing. To calculate beta, you should look at a longer term analysis of your stock and the market -- say, weekly observations over a year. Most betas are calculated using this length of data. But check formulas -- many different ones are out there.

Also remember that beta is only one measure of a stock's performance. Alpha is the performance of a stock that cannot be explained by its beta and the broad market movement. And of course, all of this is a "hypothesis" of market behavior which is useful in understanding broad actions, but very weak in predicting individual stock behavior.