want more return/less risk
The first assumption is that investors are risk-averse.
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 low-return, low-risk
asset is just as good as a medium-return, medium-risk
asset, which is just as good as a high-return,
high-risk asset. Not all investors will be equally
risk-averse, 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
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?
"optimal" portfolio can be constructed
using risk-free assets.
The third assumption is that you can construct
new portfolios, that lie above the "efficiency
frontier," by adding or subtracting risk-free
assets to the "optimal portfolio."
This can be done in one of two ways:
- Lending at risk-free rates.
You can lend some of the assets in your "optimal"
portfolio and invest these funds in risk-free
assets. Your portfolio now has a different return-risk
profile. You have increased the proportion of
risk-free 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 risk-free rate and
the "optimal" portfolio rate.
- Borrowing at risk-free rates.
You can borrow funds at risk-free rates (assuming
this possible) and invest these funds in additional
"optimal" assets. This has the effect
of leveraging your portfolio's return-risk characteristics.
You decrease the proportion of risk-free assets
and increase the proportion of risky assets.
With this borrowing, your return and risk increase
along a straight line -- again proportional
to the risk-free rate and the "optimal"
See Black at 110.
return lie on a straight "capital market
The fourth assumption is that market participants
have homogeneous risk-return 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 risk-return characteristics of the market
portfolio along a straight line. By lending at
the risk-free rate, you can construct a portfolio
that moves down the line. By borrowing at the
risk-free 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 risk-free 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 risk-adjusted 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!