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168 Part Two Risk4% per year (g = .04). Therefore the expected total rate of return is r = 5 + 4 = 9%. We can
find the portfolio’s present value (PV) by plugging these numbers into the constant-growth
dividend-discount model from Chapter 4:PV = DIV 1 /(r − g) = 120/(.09 − .04) = $2,400The required return of 9% of course includes a risk premium. If the risk-free interest rate is
2%, the risk premium is 7%.
Suppose that investors now see the stock market as a safer investment and revise their
required risk premium downward from 7% to 6% and required return from 9% to 8%. The
value of the market portfolio increases toPV = DIV 1 /(r − g) = 120/(.08 − .04) = $3,000The dividend yield falls to 120/3,000 = .04 or 4% and r = 4 + 4 = 8%.
Thus a fall of one percentage point in the risk premium causes a 25% rise in market value,
from $2,400 to $3,000. The total return to investors when this happens, including the 5%
dividend yield on the initial PV of $2,400, is 5 + 25 = 30%. With a 2% interest rate, the risk
premium earned is 30 – 2 = 28%, much greater than was expected.
If and when this 28% risk premium enters our sample of past risk premiums, we may be led
to a double mistake. First, we will overestimate the risk premium that investors required in the
past. Second, we will fail to recognize that investors require a lower expected risk premium
when they look to the future.Dividend Yields and the Risk Premium
Figure 7.4 plots dividend yields in the U.S. starting in 1900. The average is 4.3% over the
entire period. There are sharp fluctuations but also a clear, long-term downward trend. At
the end of 1917, stocks were yielding 9.0%. By the end of 2014, the yield had fallen to 1.9%.
When dividend yields fall, the ratio of price to dividends increases and the returns realized
by investors also increase. (Think back to the previous example, where the dividend yield fell
from 5% to 4% and investors earned a juicy 30% one-year return.) Thus, part of the market
returns and risk premiums over the last century or so can be attributed not just to the growth
in dividends, but also to the higher price that investors are now willing to pay per dollar of
dividends.
Can the price-dividend ratio continue to increase in the future? It can’t keep increasing for-
ever. If the growth in the price-dividend ratio stalls, then average returns and risk premiums
will be lower in the future than in the past, all else equal. Thus there’s a case for adjusting the
historical-average risk premium downward by subtracting that part of past average returns
that came from the upward trend in price-dividend ratios. The adjustment for the U.S. would
subtract about .5%.16, 17
What about the short-run fluctuations in dividend yields and price-dividend ratios? Do
they forecast periods of high or low dividend growth rates? Apparently not: Low dividend
yields do not seem to forecast high dividend growth. Instead a reduction in the dividend yield
seems to herald a reduction in the risk premium that investors can expect over the following
few years. So, when yields are relatively low, companies may be justified in shaving their(^16) See E. Dimson, P. R. Marsh, and M. Staunton, Credit Suisse Global Investment Returns Sourcebook 2014, pp. 29–33.
(^17) There has also been a long-term upward trend in price-earnings ratios. Instead of adjusting for the trend of price-dividend ratios,
one could adjust the historical-average market risk premium by subtracting the average return caused by the trend in price-earnings
ratios. The adjustment would subtract .67%, based on U.S. returns from 1926. See Ibbotson SBBI 2014 Classic Yearbook, Morning-
star, Chicago, p. 157.