THE CAPITAL ASSET PRICING MODEL (CAPM)

Capital Asset Pricing Model (CAPM)

What is CAPM?
It is an Equilibrium model that underlies all modern financial theory
CAMP was derived using principles of diversification with simplified assumptions
Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

Assumptions
Every financial models have key assumption to ease complexity of real worlds.
Of course there are pros and cons with those assumptions.
CAPM makes a number of assumption,

-Individual investors are price takers
-Single-period investment horizon
-Investments are limited to traded financial assets
-No taxes nor transaction costs
-Information is costless and available to all investors
-Investors are rational mean-variance optimizers
-Homogeneous expectations

Resulting Equilibrium Conditions

All investors will hold the same portfolio for risky assets – market portfolio
Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value
Risk premium on the market depends on the average risk aversion of all market participants
Risk premium on an individual security is a function of its covariance with the market

Figure 7.1 The Efficient Frontier and the Capital Market Line

The Risk Premium of the Market Portfolio

M    =    Market portfolio    
rf    =    Risk free rate    
E(rM) - rf    =    Market risk premium    
E(rM) - rf   / sim =    Market price of risk = Slope of the CAPM

*sim = sigma (std. deviation) of market

Expected Returns On Individual Securities

The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio
Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

Expected Returns On Individual Securities: an Example 

Using the Dell example from previous post:

(E(rm) - rf) / 1 = (E(rd) - rf) / Bd

Rearranging gives us the CAPM’s expected return-beta relationship

E(rd) = rf + Bd [E(rm) - rf)]

Figure 7.2 The Security Market Line and Positive Alpha Stock

SML Relationships

b =     [COV(ri,rm)] / sm2
E(rm) – rf   =     market risk premium
SML = rf + b[E(rm) - rf]





Sample Calculations for SML

E(rm) - rf = .08    rf = .03

bx = 1.25
    E(rx) = .03 + 1.25(.08) = .13 or 13%

by = .6
    e(ry) = .03 + .6(.08) = .078 or 7.8%

Graph of Sample Calculations