Portfolio theorytangential to rfSwhere rfSitself is tangential to EE. Investors whose preferences are
similar to those of individual X (who is the least risk-averse of the three) would choose
to borrow at rate rf, so that an amount even greater than their wealth can be invested
in risky securities.
Note that two of our investors will achieve a higher level of utility (a higher level of
expected return for a given level of risk, or lower level of risk for a given level of
expected return) through the existence of the risk-free borrowing/lending oppor-
tunity. Compare point P with point Q (where individual Z would invest without the
opportunity to lend – see Figure 7.6), or point T with point V (where individual X
would invest without the opportunity to borrow) in Figure 7.7. For the third investor
the position is unchanged. Only investors who happen to have preferences that cause
their highest level of utility to be tangential with rfSat M will be unaffected by the
existence of the risk-free borrowing/lending opportunity, and this seems likely to be
a very small minority. Every other investor will be better off.Two-fund separation
The result of this is what is known as two-fund separation. Irrespective of the personal
preferences of individuals they will all choose to invest their wealth in some com-
bination of the portfolio Mand the risk-free asset. This state of affairs is somewhat
analogous to Fisher separation, which we met in Chapter 2. Fisher separation implies
that irrespective of personal preferences as regards investment and consumption, all
investors will concur about the optimum level of real investment provided that a
borrowing/lending opportunity exists. Two-fund separation means that all investors
will concur on the same portfolio of risky securities (portfolio M) if a risk-free
borrowing/lending opportunity exists.What is portfolio M?
The foregoing raises the questions: what is this portfolio in which we all want to
invest, and what securities does it contain?
Let us attack these questions from the other direction. What happens to a security
that does not form part of portfolio M? If we all want portfolio M, the prices of secur-
ities excluded from it will be zero. Any commodity that no one wants has a zero price
(in a free market, at least). This means that there would be securities, with expectations
of returns, that we can buy for nothing. Obviously this position would be too good to
be true. Capital market efficiency, which we know at least broadly to exist, demands
that such anomalies just could not occur in real life; such zero-priced or merely under-
priced securities would offer superior returns for their risk and would enhance the
portfolio M. Thus they would be bought until their price, relative to the prices of secur-
ities generally, was a reasonable one. The only logical conclusion from this is that the
portfolio Mstrictly must contain a proportion of all securities on the market, in other
words, it is the market portfolio.
More strictly still, since the capital market for securities is not a self-contained,
sealed entity, the market portfolio should contain a proportion of all capital assets in
existence. It is possible, and often practical, to sell securities and use the proceeds to
invest in (for instance) gold, land, a painting, or some vintage wine, and thus such
assets must be regarded as possible substitutes for securities, and logically they must
form part of the market portfolio.‘
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