Fundamentals of Financial Management (Concise 6th Edition)

Chapter 8 Risk and Rates of Return 247

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Calculating beta:

1. Rise-Over-Run. Divide the vertical axis change that results from a given change on the horizontal axis (i.e., the
   change in the stock’s return divided by the changes in the market return). For Stock H, when the market rises from
   –10% to +20%, or by 30%, the stock’s return goes from –30% to +30%, or by 60%. Thus, beta H by the rise-over-run
   method is 60/30 = 2.0. In the same way, we #nd beta A to be 1.0 and beta L to be 0.5. This procedure is easy in our
   example because all of the points lie on a straight line; but if the points were scattered around the trend line, we
   could not calculate an exact beta.


2. Financial Calculator. Financial calculators have a built-in function that can be used to calculate beta. The
   procedure di"ers somewhat from calculator to calculator. See our tutorial on the text’s web site for instructions
   on several calculators.


3. Excel. Excel’s Slope function can be used to calculate betas. Here are the functions for our three stocks:
   BetaH 2.0 =SLOPE(C163:C164,B163:B164)
   BetaA 1.0 =SLOPE(D163:D164,B163:B164)
   BetaL 0.5 =SLOPE(E163:E164,B163:B164)

1

2

3

4

5

10.0%

20.0

-10.0

0.0

5.0

-30.0%

-20.0%

-10.0%

10.0%

20.0%

30.0%

-10.0%^0 10.0% 20.0% 30.0%

Return on Market

High: b = 2.0

Average: b = 1.0

Low: b = 0.5

Return on Stocks

-20.0%

Year rM rH rA rL

10.0%

30.0

-30.0

-10.0

0.0

10.0%

20.0

-10.0

0.0

5.0

10.0%

15.0

0.0

5.0

7.5

Betas: Relative Volatility of Stocks H, A, and L

F I G U R E 8! 7

If a stock whose beta is greater than 1.0 (say 1.5) is added to a bp $ 1.0 portfo-
lio, the portfolio’s beta and consequently its risk will increase. Conversely, if a
stock whose beta is less than 1.0 is added to a bp $ 1.0 portfolio, the portfolio’s beta
and risk will decline. Thus, because a stock’s beta re" ects its contribution to the riskiness
of a portfolio, beta is the theoretically correct measure of the stock’s riskiness.