XVII. SECURITY PRICING AND SECURITY ANALYSIS IN AN EFFICIENT
MARKET
Consider the following somewhat simplified description of a typical analyst-investor's
actions in making an investment decision. First, he collects the information or "facts" (both
fundamental and technical) about the company and related matters which may affect the
company. Second, he analyzes this information in such a way so as to determine his best
estimate (as of today, time "zero") of the stock price at a future date (time "one"). This best
estimate is the expected stock price at time one which we denote by P (1) . From looking at the
current stock price, P(0), he can estimate an expected return on the stock, Z , which is Z =
P(1)
.
P(0)
However, his analyst's job is not finished. Because he recognizes that his information is not
perfect (i.e., subject to error, unforeseen events which may occur, etc.), he must also give
consideration to the range of possible future prices.
In particular, he must estimate how
dispersed this range is about his best estimate and how likely is a deviation of a certain size from
this estimate. This analysis then gives him an estimate of the deviations of the rate of return from
the expected rate and the likelihood of such deviations. Obviously, the better his information, the
smaller will be the dispersion and the less risky the investment.
Third, armed with his estimates of the expected rate of return and the dispersion, he must
make an investment decision and determine how much of the stock to buy or sell. How much
will depend on how good the risk-return tradeoff on this stock is in comparison with alternative
investments available and on how much money he has to invest (either personally or as a
fiduciary). The higher the expected return and the more money he has (or controls), the more of
the stock he will want to buy. The larger the dispersion (i.e., the less accurate the information
that he has), the smaller the position he will take in the stock.
To see how the current market price of the stock is determined, we look at the
aggregation of all analysts' estimates, and assume that on the average the market is in
equilibrium. I.e., on average, the price will be such that total (desired) demand equals total
supply. Analysts' estimates may differ for two reasons: (1) they may have access to different
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Finance Theory
amounts of information (although presumably public information is available to all); (2) they
may analyze the information differently with regard to its impact on future stock prices.
Nonetheless, each analyst comes to a decision as to how much to buy or sell at a given market
price, P(0). The aggregation of these decisions gives us the total demand for shares of the
company at the price, P(0). Suppose that the price were such that there were more shares
demanded than supplied (i.e., it is too low), then one would expect the price to rise, and vice
versa, if there were more shares available at a given price than were demanded. Hence, the
market price of the stock will reflect a weighted average of the opinions of all analysts. The key
question is: what is the nature of this weighting? Because "votes" in the marketplace are cast
with dollars, the analysts with the biggest impact will be the ones who control the larger amounts
of money, and among these, the ones who have the strongest "opinions" about the stock will be
the most important. Note: the ones with the strongest "opinions" have them because (they
believe that) they have better information (resulting in a smaller dispersion around their best
estimate).
Further, because an analyst who consistently overestimates the accuracy of his
estimates will eventually lose his customers, one would expect that among the analysts who
control large sums, the ones that believe that they have better information, on average, probably
do.
From all this, we conclude that the market price of the stock will reflect the weighted
average of analysts' opinions with heavier weights on the opinions of those analysts with control
of more than the average amount of money and with better than average amounts of information.
Hence, the estimate of "fair" or "intrinsic" value provided by the market price will be more
accurate than the estimate obtained from an average analyst.
Now, suppose that you are an analyst and you find a stock whose market price is low
enough that you consider it a "bargain" (if you never find this situation, then there is no point
being in the analyst business). From the above discussion, there are two possibilities: (1) you do
have a bargain─your estimate is more accurate than the market's. I.e., you have either better than
average information about future events which may affect stock price and/or you do a better than
average job of analyzing information. Or, (2) others have better information than you do or
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Robert C. Merton
process available information better, and your "bargain" is not a bargain.
One's assessment of which it is, depends on how good the other analysts are relative to
oneself. There are important reasons why one would expect the quality of analysts to be high:
(1) the enormous rewards to anyone who can consistently beat the average attract large numbers
of intelligent people to the business; (2) the relative ease of entry into the (analyst) business
implies that competition will force the analysts to get better information and better techniques for
processing this information just to survive; (3) the stock market has been around long enough for
these competitive forces to take effect. Unfortunately, the tendency is to underestimate the
capabilities of other analysts. Ask any analyst if he is better than average, and invariably he
answers "yes." Clearly, this cannot be true for all analysts by the very definition of average. If
the analysts are so good, why aren't most of them rich? Precisely because they compete with
each other, the market price becomes a better and better estimate of "fair value," and it becomes
more difficult to find profit opportunities. To stay ahead, the analyst must develop new ideas
continually. As the limiting case of this process, one would expect that as market prices become
better estimates of "fair value" in the sense of fully reflecting all relevant known information, the
fluctuations of stock prices around the expected "fair return" will be solely the result of
unanticipated events and new information.
Hence, these fluctuations are random and not
forecastable. And it is in this sense that the fluctuations in stock prices can be described by a
random walk.
This also explains why the performance of most "managed" portfolios will be no better
than the performance of an "unmanaged" well-diversified portfolio. In fact, the "unmanaged"
portfolio, because it takes market prices as the best estimate of value, is equivalent to a
"managed" portfolio whose manager is a no-worse-than-average analyst! The investor who buys
such a portfolio is simply "piggy-backing" on the actions taken by active analyst-investors
competing with each other.
This is essentially the story behind the "Random Walk Theory." It does not imply that a
better-than-average analyst cannot make greater than fair returns. It does not imply that all
analysts should quit their jobs, and in fact, its cornerstone is that enough analysts remain and
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Finance Theory
actively compete so that market prices are good estimates of "fair" value. It is only in this way
that the "piggy-backing" by investors can be justified. Further, it does not imply that all investors
should hold "unmanaged" portfolios. If an investor can identify an analyst with above-average
capabilities and is willing to bear the risk of his capabilities, then a "bargain" can be struck so
that both are rewarded for the effort. The theory does imply that to make "extra" profits, one
must have superior techniques which process information in a way not generally known in the
market and that the longer that the market is in existence, the greater the number of participants,
the more difficult it is to make these "extra" profits.
An Example to Illustrate the Efficient Market Concept
Consider a firm in a cyclical business whose earnings are completely predictable but vary
in the following fashion: If the earnings per share this period are $50, then next period's earnings
per share will be $100, and if the earnings per share this period are $100, then next period's
earnings per share will be $50. I.e., if Et
denotes earnings in period t , and if
E0 = $50 then E1 = 100, E 2 = 50, E3 = 100,... or
t
E t +1 = E t + (-1) 50
If the firm pays out all earnings as dividends (Dt = E t ) and if the required return ("fair market
return") is 20% per period, then the correct price per share, St (ex-dividend) is given by
S0 = $386.36, S1 = $363.64, S2 = $386.36, S3 = $363.64,...
St +1 = St + (-1)
t +1
22.72
I.e., the return per dollar from investing in the shares from time 0 to time 1,
Z1 =
D1 + S1 100 + 363.64
=
= 1.20, and from time 1 to time 2,
386.36
S0
Z2 =
D2 + S2 50 + 386.36
=
= 1.20, and so forth.
363.4
S1
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Robert C. Merton
Suppose that investors are myopic and assume that current earnings (and hence, current
dividends) are permanent. I.e., their best guess of future dividends is that they will be equal to
'
current dividends. If St denotes price per share under this belief, then
50
100
D0
D
=
= $250; S1' = 1 =
= $500,
r
r
.2
.2
50
100
D2
D3
=
=
= $250; S3' =
=
= $500,...
r
.2
r
.2
t
'
St' +1 = St + (-1) 250
S0' =
S 2'
or
The return per dollar from investing in the shares from time 0 to time 1 under this pricing is
Z1' =
'
100 + 500
D1 + S1
=
= 2.4 or 140%
'
250
S0
'
and from time 1 to time 2 , Z 2 is
Z 2' =
'
50 + 250
D 2 + S2
=
= 0.6 or - 40%
'
500
S1
and it continues to alternate.
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Finance Theory
Empirical Studies of Capital Market Theory
In Sections IX and X, we developed a theory for the capital markets based on essentially
rational behavior and optimal portfolio selection. Specifically, by applying the mean-variance
model and aggregating demands, we deduced the Capital Asset Pricing model, which provided a
specification for equilibrium expected returns among securities. Based on this model, we
deduced a naive or benchmark portfolio strategy. From our analysis of an efficient speculative
market, we deduced a rationale for random selection of securities or the naive strategy as possible
portfolio strategies. Since these models have important implications for both corporate finance
and financial intermediation, it is most important that empirical testing of the models is
performed. Basically, there are three questions to be answered: (i) How does the "random walk"
theory hold up against the data? (ii) Is the security market line specification a reasonable
description of returns on securities? (iii) How does the performance of the naive strategy
compare with managed portfolio strategies?
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Robert C. Merton
The answer to (i) is simply that a large number of technical trading strategies (filtering,
serial correlation, charting services, volume analysis, etc.) have produced no evidence to refute
the random walk hypothesis. To the extent that any serial correlation in the returns were present,
it was of such small magnitude and "short-lived" nature that no profitable trading was possible.
Other studies of brokerage house and general service recommendations, dividend announcements
and earning reports have shown no evidence of providing trading profits. "Dart throwing" or
more careful random selection of portfolios provide no evidence against the random walk
hypothesis.
In the study of managed portfolio performance, both the random walk hypothesis and the
asset pricing model are implicitly tested.
Returns on the "Market"
NYSE index:
value-weighted index of all stocks on the New York Stock Exchange
≈80% in market value of all securities)
S&P index:
Standard & Poors 500-stock index including the largest companies (in
1965 representing ≈80% of market value of NYSE stocks)
Random Selection of Stocks (Fisher & Lorie): Equally-weighted portfolio of all stocks on
the New York Stock Exchange 1926-1965.
Average Return (1-year): including dividends, no taxes, or commissions
Years
Average Annual Return
(Arithmetic Average)
Standard Deviation
(Annual)
1926-1945
17.8%
41.2%
1946-1965
15.1%
19.8%
1926-1965
16.5%
32.3%
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Finance Theory
"Market" (in this sense) was much more volatile in the pre-war versus post-war period.
Average Compound Return: including dividends, no taxes, but including purchase commissions:
Years
Average Compound Return
(Geometric Average)
1926-1945
6.3%
1946-1965
12.6%
1926-1965
9.3%
All Stocks on the New York Stock Exchange: Value-Weighted
Cowles (1871-1937): Average Compound Return: 6.6%
Since the Fisher Lorie results for average performance of randomly selected portfolios is as good
as managed portfolios on average over the same period, this is additional evidence in favor of the
Random Walk.
319
Simulated Rate of Return Experience for Successful Market Timing*
Monthy Forecasts: P = Probability of Correct Forecast
January 1927 – December 1978
Per Month
P=1.0
P=.90
Market Timing
P=.75
P=.60
P=.50
NYSE
Stocks
Average Rate of Return
2.58%
2.17%
1.56%
0.94%
0.53%
0.85%
Standard Deviation
3.82%
3.98%
4.13%
4.19%
4.18%
5.89%
Highest Return
38.55%
38.27%
37.61%
36.41%
35.12%
38.55%
Lowest Return
-0.06%
-17.05%
-22.02%
-24.52%
-25.64%
-29.12%
2.51%
2.10%
1.47%
0.85%
0.44%
0.68%
Average Compound Return
Growth of $1,000
$5,362,212,000
$418,902,144
$9,146,722
$199,718
$15,602
$67,527
Average Annual
Compound Return
34.65%
28.32%
19.14%
10.69%
5.41%
8.47%
*Buy the market when the forecast is for stocks to do better than bonds.
Buy bonds when the forecast is for bonds to do better than stocks.
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Robert C. Merton
Average Annual Compound Return on the Market (value-weighted, including reinvesting
dividends, no commissions, or taxes) (Scholes)
Years
Total:
10 Years:
5 Years:
1953-1972
1953-1962
1963-1972
1953-1957
1958-1962
1963-1967
1968-1972
NYSE
Average
Return
Avg. Excess
Return
S&P
Average
Return
Avg. Excess
Return
11.98%
13.11%
10.86%
12.25%
13.99%
14.53%
7.31%
7.57%
10.00%
5.15%
9.45%
10.52%
9.70%
0.71%
11.63%
13.38%
9.90%
13.50%
13.26%
12.34%
7.52%
7.22%
10.25%
4.19%
10.70%
9.79%
7.50%
0.92%
Jensen Performance of Mutual Funds Study 1945-1964
Testing 115 Funds ability to Forecast (relative to Security Market Line):
Model Specification:
Z j (t) = R(t) + β j[ ZM (t) - R(t)] + α j (t)
Test:
~ (t) = R(t) + β [ ~ (t) - R(t)] + (t) + ~ (t)
αj
εj
Zj
j ZM
E(~ε j (t)) = 0; Cov(~ε j (t), ~ε i (t - k)) = 0 i, j = 1,
k = 1,2,...
Assumes: β j is stationary. Suppose not:
~
~
β j (t) = β j + U j (t)
estimated
~ ,~ ) > 0
) < βj
if you can forecast the market, then Cov ( U
which would imply E(β j
j ZM
and biases tests in favor of superior performance (i.e., larger α j ).
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Robert C. Merton
115 Funds Studied. Returns net of all costs including management fees.
76 funds had measured α j < 0
39 funds had measured α j ≥ 0
Average α = – .011
= – 1.1%
The statistical significance of the positive α j were no more than would have been expected by
chance when the true α j = average α .
Using Returns Gross of Management Fees
55 funds had measured α j < 0
60 funds had measured α j ≥ 0
Average α = – .004
= –0.4%
Statistical significance of the positive α j were no more than would have been expected by
change when the true α j = 0.
Conclusions: Funds taken as a whole do not show evidence of superior forecasting capability;
and, of course, do not show evidence of sufficient superior forecasting to cover costs.
What about individual funds? Even if funds as a whole do not show evidence of superior
forecasting, what about the overtime performance of particular funds? Is it true that funds with
observed positive α j in the past tend to have positive α j in the future? Jensen & Black studied
the 115 funds for the years 1955-1964 computing the realized α j for each year (a total of 10 ×
115 = 1150 observations). The differential returns were computed gross of management fees.
The results were
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Finance Theory
Number of Successive
Years of Observed
Positive "α"
Number of Times
Observed
Percent of Cases
Followed by Another
Positive "α"
1
574
50.4%
2
312
52.0%
3
161
53.4%
4
79
55.8%
Conclusion: It appears that funds that did well in the past show little evidence of continuing to
do so.
Jensen also found that there was no significant evidence of serial correlation in the return
series in support of the Random Walk Hypothesis.
With respect to providing efficient (or well-diversified) portfolios, on average, Jensen
found that 85% of the variance of the funds' returns were due to market movements. I.e.,
σp ≈ (1.085) σM βp = 1.085 ρpM σp or ρpM ≈
1
= .9216
1.085
Further, on the whole, funds tended to keep about the same level of βp or σp through time.
Overall Summary
1. Over the last forty years, randomly selected portfolios have returns greater than or equal
to randomly selected managed portfolios.
2. Most mutual funds are reasonably well diversified (i.e., have reasonably low nonsystematic risk).
3. On average, funds did not perform, before expenses, any better than a naive strategy
portfolio with the same beta.
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Robert C. Merton
4. On average, funds did worse, after expenses, than the naive strategy portfolio with the
same beta.
5. Few, if any, individual funds showed any consistent performance superior to the naive
strategy over time.
6. Most funds spend too much money trying to forecast returns on stocks: either explicitly
in analyst salaries and support and implicitly through brokerage commissions and spreads
through excess turnover.
Investment prescription: Since these results did not include sales commissions on "load" funds
which run from 1½ - 8½%, clearly one should buy "no load" funds (with no sales commissions).
To achieve an efficient investment strategy, choose a mix of a few well-diversified, no load
funds. Select funds with the lowest costs (management fees and turnover).
(ii)
Testing the Capital Asset Pricing Model
(Miller and Scholes; Black-Jensen-Scholes)
The capital asset pricing model specifies that
E( Z j) = R + β j [E( ZM ) - R] and E( ZM) > R.
I.e., investors are risk-averse; expected excess return on a security is proportional to its beta; it is
dependent only on beta; is linear in beta.
The Black-Jensen-Scholes paper is one of the most sophisticated tests of the capital asset
pricing model. Using monthly returns from 1931-1965 on 600-1100 securities, they found the
following:
1. The expected return on the market is greater than the riskless rate ( ZM > R).
2. Expected return on individual securities (portfolios) is an increasing function of its beta
and the excess returns are linear in beta.
3. Expected return depends on beta.
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Finance Theory
4. The empirical Security Market Line is too "flat." I.e., the returns on "low beta" (β < 1)
stocks were higher than predicted by the Capital Asset Pricing Model and the returns on
"high beta" (β > 1) stocks were lower than predicted by the Capital Asset Pricing Model.
Results 1-3 are consistent with the capital asset pricing model, result 4 is not, and has
been the cause for much concern as well as new research in this area. To analyze this problem,
BJS constructed a "zero-beta" portfolio by combining stocks only (so it has variance), and this
portfolio had realized returns significantly greater than the riskless rate. I.e., Z0-β > R where Z0-β
is the expected return on the minimum-variance, zero-beta portfolio constructed from stocks.
The specification that they fit was Z j - R = β j( Z M - R) + γ(β j)( Z 0-β - R) ,
where γ(1) = 0 and
dγ
< 0.
dβ
While there are many possible theoretical and empirical explanations for this finding, such
analyses are beyond the level of this course. It is evident that the simple form of the Capital
Asset Pricing Model as a means for estimating expected returns on individual securities is not
sufficient; however, the main results implied by that model (1-3) do seem to describe returns and,
as a good approximation, its specification is not unreasonable.
325