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How Diversification
Reduces Risk: Risk of Portfolio (Standard Deviation of
Return)
. (The forgetful can take another look.) There we saw
that as the number of securities in the portfolio approached
sixty, the total risk of the portfolio was reduced to its
systematic level. The conscientious reader will now note that
in the schematic illustration, the number of securities in each
portfolio is sixty. All unsystematic risk has essentially been
washed away: An unexpected weather calamity is balanced
by a favorable exchange rate, and so forth. What remains is
only the systematic risk of each stock in the portfolio, which
is given by its beta. But in these two groups, each of the
stocks has a beta of 1. Hence, a portfolio of Group I
securities and a portfolio of Group II securities will perform
exactly the same with respect to risk (standard deviation),
even though the stocks in Group I display higher total risk
than the stocks in Group II.
The old and the new views now meet head on. Under the
old system of valuation, Group I securities were regarded as
offering a higher return because of their greater risk. The
capital-asset pricing model says there is no greater risk in
holding Group I securities if they are in a diversified
portfolio. Indeed, if the securities of Group I did offer higher
returns, then all rational investors would prefer them over
Group II securities and would attempt to rearrange their
holdings to capture the higher returns from Group I. But by
this very process, they would bid up the prices of Group I
securities and push down the prices of Group II securities
until, with the attainment of equilibrium (when investors no
longer want to switch from security to security), the
portfolios for each group had identical returns, related to the
systematic component of their risk (beta) rather than to their
total risk (including the unsystematic or specific portions).
Because stocks can be combined in portfolios to eliminate
specific risk, only the undiversifiable or systematic risk will
command a risk premium. Investors will not get paid for
bearing risks that can be diversified away. This is the basic
logic behind the capital-asset pricing model.
In a big fat nutshell, the proof of the capital-asset pricing
model (henceforth to be known as CAPM because we
economists love to use letter abbreviations) can be stated as
follows: If investors did get an extra return (a risk premium)
for bearing unsystematic risk, it would turn out that
diversified portfolios made up of stocks with large amounts
of unsystematic risk would give larger returns than equally
risky portfolios of stocks with less unsystematic risk.
Investors would snap at the chance to have these higher
returns, bidding up the prices of stocks with large
unsystematic risk and selling stocks with equivalent betas but
lower unsystematic risk. This process would continue until
the prospective returns of stocks with the same betas were
equalized and no risk premium could be obtained for bearing
unsystematic risk. Any other result would be inconsistent
with the existence of an efficient market.
The key relationship of the theory is shown in the
following diagram. As the systematic risk (beta) of an
individual stock (or portfolio) increases, so does the return an
investor can expect. If an investor’s portfolio has a beta of
zero, as might be the case if all her funds were invested in a
government-guaranteed bank savings certificate (beta would
be zero because the returns from the certificate would not
vary at all with swings in the stock market), the investor
would receive some modest rate of return, which is generally
called the risk-free rate of interest. As the individual takes on
more risk, however, the return should increase. If the investor
holds a portfolio with a beta of 1 (as, for example, holding a
share in a broad stock-market index fund), her return will
equal the general return from common stocks. This return has
over long periods of time exceeded the risk-free rate of
interest, but the investment is a risky one. In certain periods,
the return is much less than the risk-free rate and involves
taking substantial losses. This, is precisely what is meant by
risk.
The diagram shows that a number of different expected
returns are possible simply by adjusting the beta of the
portfolio. For example, suppose the investor put half of her
money in a savings certificate and half in a share of an index
fund representing the broad stock market. In this case, she
would receive a return midway between the risk-free return
and the return from the market, and her portfolio would have
an average beta of 0.5.
*
The CAPM then asserts that to get a
higher average long-run rate of return, you should just
increase the beta of your portfolio. An investor can get a
portfolio with a beta larger than 1 either by buying high-beta
stocks or by purchasing a portfolio with average volatility on
margin (see the diagram below and the table
Illustration of
Portfolio Building)
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