3-Milestones Page 87 Wednesday, February 4, 2004 12:47 PM
Milestones in Financial Modeling and Investment Management 87The expected return for an asset i according to the CAPM is equal to
the risk-free rate plus a risk premium. The risk premium is the product of
(1) the sensitivity of the return of asset i to the return of the market port-
folio and (2) the difference between the expected return on the market
portfolio and the risk-free rate. It measures the potential reward for tak-
ing on the risk of the market above what can be earned by investing in an
asset that offers a risk-free rate. Taken together, the risk premium is a
product of the quantity of market risk and the potential compensation of
taking on market risk (as measured by the second component).
The CAPM was highly appealing from the theoretical point of view.
It was the first general-equilibrium model of a market that admitted
testing with econometric tools. A critical challenge to the empirical test-
ing of the CAPM is the identification of the market portfolio.^19THE MULTIFACTOR CAPM: MERTON
The CAPM assumes that the only risk that an investor is concerned with
is uncertainty about the future price of a security. Investors, however,
are usually concerned with other risks that will affect their ability to
consume goods and services in the future. Three examples would be the
risks associated with future labor income, the future relative prices of
consumer goods, and future investment opportunities.
Recognizing these other risks that investors face, in 1976 Robert
Merton extended the CAPM based on consumers deriving their optimal
lifetime consumption when they face these “extra-market” sources of
risk.^20 These extra-market sources of risk are also referred to as “fac-
tors,” hence the model derived by Merton is called a multifactor CAPM.
The multifactor CAPM says that investors want to be compensated
for the risk associated with each source of extra-market risk, in addition
to market risk. In the case of the CAPM, investors hedge the uncertainty
associated with future security prices by diversifying. This is done by
holding the market portfolio. In the multifactor CAPM, in addition to
investing in the market portfolio, investors will also allocate funds to
something equivalent to a mutual fund that hedges a particular extra-
market risk. While not all investors are concerned with the same sources
of extra-market risk, those that are concerned with a specific extra-mar-
ket risk will basically hedge them in the same way.(^19) Richard R. Roll, “A Critique of the Asset Pricing Theory’s Tests,” Journal of Fi-
nancial Economics (March 1977), pp. 129–176.
(^20) Robert C. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometri-
ca (September 1973), pp. 867–888.