Present-Value Relations
Kevin C.H. Chiang
Fundamental Value
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Cash flow (dividend) pricing models say that
security price/value is the sum of discounted
values of expected cash flows (dividends).
With the assumptions of (1) constant
dividend growth rate, g, and (2) constant
discount rate/expected return rate, R, the
present security price/value, P(t), is given by:
P(t) = D(t+1)/[R – g], where D(t+1) is the
expected dividends in the next period.
Intuitions
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One can rewrite P(t) = D(t+1)/[R – g] as follows:
D(t)/P(t) = [R – g] / [1 + g], where D(t)/P(t) is called
dividend yield.
Now suppose that, holding other factors constant,
stock price, P(t), went down sharply today. What
happened to dividend yield? Dividend yield went
up sharply.
The above equation says that (1) either expected
return/discount rate, R, was revised upward, (2)
dividend growth rate, g, was revised downward, (3)
or a combination of both.
D(t)/P(t) = [R – g] / [1 + g]
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Alternatively, (1) If for some reasons investors do not like to
take risk and demand a higher expected return/discount rate for
investing in stocks, then R goes up; i.e., the RHS of the
equation goes up. To balance the equation, P(t) needs to be
lower. So, stock price drops.
(2) If for some reasons investors believe that the growth rate of
dividends would be lower than expected, then the RHS of the
equation becomes higher. P(t) thus needs to be lower.
(3) If scenarios (1) and (2) happen simultaneously, you can
expect stock price drops “a lot.”
Q: Between scenarios (1) and (2), which is the main driver of
stock prices? Alternatively, should we pay more attention to
discount rate/expected return or dividend growth rate?
Different views at the market level
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Traditionally, researchers looked at this
question/issue at the market level; e.g., S&P 500.
Before 1970s, researchers tended to think
scenario/story (2) is more of the case. That is, S&P
500 drops mainly because dividend growth is
revised downward by the investors.
After 1970s, most researchers changed their minds
and thought story (1) is more close to the truth.
That is, stock price drops because investors
demand higher expected returns.
Why researchers changed their minds?
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They did so because they found a positive relation
between S&P dividend yields and subsequent
(particularly 3-5 years) S&P 500 returns.
That is, when S&P 500 drops (i.e., S&P 500
dividend yield goes up), S&P 500 tend to have
good performance during the next 3-5 years.
This effect is weak and close to none in a short
horizon, say less than 1-2 years.
In contrast, there is no relationship between S&P
500 dividend yields and subsequent S&P 500
dividend growth rates.
If this view is correct
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If you think the view is correct and you are a topdown investor, then you should focus most of your
research on expected return/discount rate.
If the market is believed to be willing to take on more
risk in the near future (i.e., investors will require
lower risk premiums/expected returns on S&P 500),
you can infer from it that S&P 500 dividend yield
would be lower.
Strategy: You should take a long position on S&P
500 because its price will go up to achieve a lower
dividend yield.
A naïve example
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D(t)/P(t) = [R – g] / [1 + g]: Suppose that the current
dividend yield is 4%; that is, the price/dividend ratio
is 25. Then, R – g is roughly 4%.
If for some reasons the market is experiencing a 1%
permanent change in expected return/discount rate,
this would translate into a 25% change in price!
Intuition: a small change in expected return can
leads to a big change in price.
Note that this is an extreme, overstated example. In
the real life, we rarely see a permanent change in
anything.
Alternatively,
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If you believe that the view is correct and the S&P
500 dividend yield is now unusually high, then you
should take a long position on S&P 500.
The positive association between market dividend
yields and the subsequent market returns implies
that current high S&P 500 dividend yield will tend to
lead to higher S&P 500 returns in the long run; e.g.,
next 3-5 years.
Q: suppose that you are a short-term (e.g., 1-6
months) market timer and S&P 500 dividend yield is
now relatively high. What should you do?
Can we really be sure about the
dominant view?
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Although the variation in expected return/discount
rate seems to be the main driver of market prices,
we should be carefully about its robustness.
Recent evidence suggests that the positive
relationship between dividend yield and subsequent
market returns is not robust after the 1990s.
Chiang (2009) documents a positive relationship
between REIT dividend yield and subsequent REIT
dividend growth.
It could be that the dominant view and the alternative
view are both partially responsible for setting prices.
At the individual stock level
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The above discussions focused presentvalue relations at the market level.
For bottom-up investors, present-value
relations at the individual stock level are
more relevant.
It turns out that the present-value relations at
the individual stock level are quite different
from those documented at the market level.
Vuolteenaho (2002, J. of Finance)
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He found that firm-level stock returns are mainly
driven by cash flow (i.e., dividends/earnings growth)
news.
Expected return news are highly correlated across
firms. So, their impacts are observable at the market
level.
In contrast, cash flow news can largely diversified
away at the market level. So, their impacts are not
that observable at the market level.