Investors
want more return/less risk
The first assumption is that investors are riskaverse.
They will want to be compensated with higher returns
if they take on greater risk. This leads to a
conclusion that each investor will value certain
investments identically: a lowreturn, lowrisk
asset is just as good as a mediumreturn, mediumrisk
asset, which is just as good as a highreturn,
highrisk asset. Not all investors will be equally
riskaverse, but we predict they will always prefer
more return for the same risk, and less risk for
the same return. Their investment desires (or
utility curves) can be shown graphically:
[chart] xxx / black at 108
An "optimal
portfolio" best matches return and risk.
The second assumption is that, although there
will be many ways to construct portfolios that
combine return and risk, there will be an optimal
portfolio. At some point, you cannot do better.
This analysis begins by constructing a series
of portfolios for which you cannot reconstitute
the portfolios to provide more return with the
same risk, or less risk with the same returns.
That is, there is a "frontier" to the
set of "efficient" portfolio possibilities.
[chart] xxx / black at 108
Is one of these "efficient" portfolios
optimal? The answer is yes  wherever the investor's
investment demand curves touches the portfolio
supply curve. (Or in the language of financial
economists, this is where the "indifference"
curve is tangent to the "efficient frontier.")
[chart] xxx / black at 109
But is there a way to improve this portfolio,
so it satisfies an even higher "utility curve"
 is even more desirable to an investor?
Even more
"optimal" portfolio can be constructed
using riskfree assets.
The third assumption is that you can construct
new portfolios, that lie above the "efficiency
frontier," by adding or subtracting riskfree
assets to the "optimal portfolio."
This can be done in one of two ways:
 Lending at riskfree rates.
You can lend some of the assets in your "optimal"
portfolio and invest these funds in riskfree
assets. Your portfolio now has a different returnrisk
profile. You have increased the proportion of
riskfree assets and decreased the proportion
of risky assets. With this lending, your portfolio's
return and risk decrease along a straight
line  proportional to the riskfree rate and
the "optimal" portfolio rate.
 Borrowing at riskfree rates.
You can borrow funds at riskfree rates (assuming
this possible) and invest these funds in additional
"optimal" assets. This has the effect
of leveraging your portfolio's returnrisk characteristics.
You decrease the proportion of riskfree assets
and increase the proportion of risky assets.
With this borrowing, your return and risk increase
along a straight line  again proportional
to the riskfree rate and the "optimal"
portfolio rate.
See Black at 110.
Risk and
return lie on a straight "capital market
line."
The fourth assumption is that market participants
have homogeneous riskreturn expectations. This
means that the "optimal" portfolio in
terms of combining risk and return is the portfolio
of all securities available in the market,
weighted by their market values. This weighted
portfolio is, by definition, the market portfolio.
As we have seen, it is possible to reconstruct
the riskreturn characteristics of the market
portfolio along a straight line. By lending at
the riskfree rate, you can construct a portfolio
that moves down the line. By borrowing at the
riskfree rate, your portfolio moves up the line.
[Chart Black at 112 ]
The slope of the capital market line represents
the additional return the market assigns to taking
additional risk. Notice that this line lies above
and beyond the regular reward (or rate of return)
assigned to simply waiting  the time value of
a riskfree investment. The capital market line
tells us the amount of additional expected return
that market participants require for assuming
additional risk  or volatility.
Different investors, with different risk preferences,
can create portfolios with different risk profiles.
But they cannot create a portfolio that lies above
the capital market line. If any investment is
offered with returns that the riskadjusted returns
predicted by the capital market line, investors
will seek the investment and its price will rise.
And if its price rises, its returns fall  until
they reach the capital market line!
