Assume that in recent years both expected inflation and the market risk premium (rM − rRF) have declined. Assume also that all stocks have positive betas. Which of the following would be most likely to have occurred as a result of these changes? a. The required returns on all stocks have fallen by the same amount. b. The average required return on the market, rM, has remained constant, but the required returns have fallen for stocks that have betas greater than 1.0. c. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas. d. Required returns have increased for stocks with betas greater than 1.0 but have declined for stocks with betas less than 1.0. e. The required returns on all stocks have fallen, but the decline has been greater for stocks with lower betas.

c. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.

Explanation:

The Capital Asset Pricing Model formula can be applied to this question.

The formula is,

Er = rF + b( rM - rF)

Where

Er is the required return

rF is the risk free rate

b is beta

rM - rF is the market premium.

Now looking at that formula, you can tell that if market premium falls, the required return would fall as well.

However, for stocks with larger betas, they would drop more spectacularly because they would be coming from higher values to lower.

Take a stock with beta 4 vs one with beta 5 for instance.  

Assume that Market premium went from 6% to 3% and a risk free rate of 3%.

Beta 5 stock

When market premium is 6,

= 3% + 5 (6%)

= 33%

When market premium is 3,

= 3% + 5(3%)

= 18%

Beta 4 stock

When market premium is 6

= 3% + 4 (6%)

= 27%

When market premium is 3

= 3% + 4 (3%)

= 15%

Notice how the stock with beta 5 fell by 15% while the stock with beta 4 fell by 12%.

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