Beta is a variable in concept stock problems. It shows the relationship between the rate of return and the market premium rate. The beta value is the slope of the line when this relation is graphed. The procedure to find beta is the same as finding the slope of a line. You can calculate this number if you know the required rate of return, the risk-free rate and the market premium rate.
Note the percentages of all your values and convert them to decimals by moving the decimal place to the left two spaces. For example, if you have a required rate of return of 12 percent, a risk-free rate of 2 percent and a market premium rate of 5 percent, your decimal values are .12, .02 and .05, respectively.
Insert the decimals from Step 1 into the Capital Asset Pricing Model. This formula is as follows: required rate of return = (risk-free rate) + (beta x (market premium rate)). Using the example problem numbers, put the decimals in the proper places: (.12) = (.02) + (beta x (.05))
Subtract the risk-free rate from both sides. In the example problem, this yields: (.12) - (.02) = (.02) - (.02) + (beta x (.05)). The result is (.10) = (beta x (.05)).
Divide both sides by the market premium rate. In the example problem, it looks like this: (.10)/(.05) = (beta x (.05))/ (.05). The result is beta = 2.