Introduction to Corporate Finance

7: Risk, Return and the Capital Asset Pricing Model

Outcome Probability Oroton return Return — 10% (Return — 10%)^2

Recession 20% –30% –40% 1,600%^2

Expansion 70% 15% 5% 25%^2

Boom 10% 55% 45% 2,025%^2

Variance = (0.20)(1,600%^2 ) + (0.70)(25%^2 ) + (0.10)(2,025%^2 ) = 540%^2

Standarddeviation 540% 23. 2 %

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The analyst can apply the same model to any share with returns tied to the business cycle. For

example, purchases of Coca-Cola do not vary over the business cycle as much as car purchases do,

so Coca-Cola Amatil shares should be less sensitive to economic conditions than are Oroton’s shares.

Perhaps when the economy is booming, Coca-Cola Amatil shareholders earn 36%. Under normal

economic conditions, Coca-Cola Amatil shares earn 12%, but during an economic slump, the return

on Coca-Cola Amatil shares equals –15%. Maintaining the same assumptions about the probabilities of

recession, expansion and boom, estimates of Coca-Cola Amatil’s expected return, variance and standard

deviation can be constructed as follows:

Outcome Probability Coca-Cola Amatil return Return — 9% (Return — 9%)^2

Recession 20% –15% –24% 576%^2

Expansion 70% 12% 3% 9%^2

Boom 10% 36% 27% 729%^2

Variance = (0.20)(576%^2 ) + (0.70)(9%^2 ) + (0.10)(729%^2 ) = 194.4%^2

Standarddeviation 194. 4 13.9%

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But the probabilistic approach has its own drawbacks. To calculate expected returns for Oroton

and Coca-Cola Amatil, we started with a simplifying assumption that only three possible outcomes or

scenarios were possible. Clearly, the range of potential outcomes is much broader than this. Similarly,

we assumed that we knew the probability of each scenario in advance. Where did those probabilities

come from? Analysts can draw from historical experience, for example, by estimating the probability of

a recession by studying past recession frequencies. If history shows that recessions occur in roughly one

year out of every five, then 20% might be a reasonable estimate of the probability of a future recession;

then again, it might be well off the mark. In any case, the probabilistic approach involves a high degree

of subjectivity. It requires analysts to specify possible future outcomes for share returns and to attach a

probability to each outcome. Once again, these assumptions about possible states of the economy can be

somewhat naïve if the assumptions are based on historical data.

7-1c THE RISK-BASED APPROACH

A third approach to estimate an asset’s expected return is more theoretically sound, and is used in

practice by most corporate finance professionals. It requires an analyst to first measure the risk of

the asset, then translate that risk measure into an expected return estimate. This approach involves

Expected return = (0.20)(-15%) + (0.70)(12%) + (0.10)(36%) = 9%