The Mathematics of Financial Modelingand Investment Management

3-Milestones Page 86 Wednesday, February 4, 2004 12:47 PM

86 The Mathematics of Financial Modeling and Investment Management

Another facet in this apparent contradiction of the pursuit of active

strategies despite empirical evidence on market efficiency was soon to be

clarified. Agents optimize a risk-return trade-off based on the stochastic

features of price processes. Price processes are not simply random but

exhibit a rich stochastic behavior. The objective of investment analysis

is to reveal this behavior (see Chapters 16 and 19).

CAPITAL ASSET PRICING MODEL: SHARPE, LINTNER, AND

MOSSIN

Absence of arbitrage is a powerful economic principle for establishing

relative pricing. In itself, however, it is not a market equilibrium model.

William Sharpe (in 1964),^16 John Lintner (in 1965),^17 and Jan Mossin

(in 1966),^18 developed a theoretical equilibrium model of market prices

called the Capital Asset Pricing Model (CAPM). As anticipated 60 years

earlier by Walras and Pareto, Sharpe, Lintner, and Mossin developed the

consequences of Markowitz’s portfolio selection into a full-fledged sto-

chastic general equilibrium theory.

Asset pricing models categorize risk factors into two types. The first

type is risk factors that cannot be diversified away via the Markowitz

framework. That is, no matter what the investor does, the investor can-

not eliminate these risk factors. These risk factors are referred to as sys-

tematic risk factors or nondiversifiable risk factors. The second type is

risk factors that can be eliminated via diversification. These risk factors

are unique to the asset and are referred to as unsystematic risk factors

or diversifiable risk factors.

The CAPM has only one systematic risk factor—the risk of the over-

all movement of the market. This risk factor is referred to as “market

risk.” This is the risk associated with holding a portfolio consisting of

all assets, called the “market portfolio.” In the market portfolio, an

asset is held in proportion to its market value. So, for example, if the

total market value of all assets is $X and the market value of asset j is

$Y, then asset j will comprise $Y/$X of the market portfolio.

(^16) William F. Sharpe, “Capital Asset Prices,” Journal of Finance (September 1964),
pp. 425–442.
(^17) John Lintner, “The Valuation of Risk Assets and the Selection of Risky Invest -
ments in Stock Portfolio and Capital Budgets,” Review of Economics and Statistics
(February 1965), pp. 13–37.
(^18) Jan Mossin, “Equilibrium in a Capital Asset Market,” Econometrica (October
1966), pp. 768–783.