INVESTMENT ANALYSIS - CAPITAL ASSET PRICING THEORY

Learning Objectives

· Capital market line (CML)

· Capital Asset Pricing Model (CAPM)

· Beta compared to Standard Deviation

· Applying CAPM to security analysis

· Estimating Beta

· Beta - good news and bad news

 

Capital Asset Pricing Model (CAPM)

· Equation that quantifies security risk and defines a risk/return relationship

· Based on the idea that investors accept a higher risk only for a higher return

· Other assumptions are not realistic, but necessary to develop the model

 

Assumptions of the CAPM

· Investors have equal information and perceptions, leading to equal expectations

· Frictionless capital markets

No transaction costs

No taxes

Portfolios may be divided among securities in any proportion for optimization

· Investors are rational and seek to maximize their expected utility functions

· All investment is for the same time period

· All investors can borrow or lend at the risk-free rate

Efficient Frontier and
the Optimal Risky Portfolio

· The efficient frontier is a series of portfolios representing the highest return for a given level of risk or the lowest risk for a given expected return

· Any individual security will lie inside the efficient frontier, but may be a part of portfolios on the efficient frontier

· Choosing the optimal efficient frontier depends on individual preferences for risk and return

· Measuring risk aversion and utility curves still won’t provide an objective portfolio choice

 

Developing the Capital Market Line (CML)

 

ER_p = (X) ER_p1 + (1 - X) RF

SD_P = (X) SD_P1

 

Combinations of risk-free assets and risky portfolios can be used to create portfolios along a line connecting the apex of the efficient frontier and the risk-free rate

 

The Capital Market Line (CML)

· Describes the percentage holdings in the risk free asset and the risky diversified market portfolio, surpassing the efficient frontier except at the point of intersection

· Utility curves may cross the CML, indicating appropriate portfolio selections

· Borrowing-lending line is the CML, divided where it intersects the efficient frontier (point M) with the lending line on the left and borrowing on the right

· Portfolio separation theorem allows investors to separate the decision of selecting the risky portfolio from the investor’s risk preference

 

MARKET PORTFOLIO

The Market Portfolio (point M) must be the only risky portfolio chosen by all risk-averse investors.  Because it is demanded by all investors, it must contain all the securities and other traded assets

 

CAPITAL ASSET PRICING MODEL

· Portfolio M’s risk = Market risk

· Security risk = total risk

· Security risk = Market risk + firm-specific risk

· Portfolio M’s risk = (Security 1’s market risk + Security 2’s market risk + … + Security N’s market risk)

 

RELATIVE RISK

· Relative risk contribution of security i

Total risk contribution of security i divided by Total risk of market portfolio, M

· Known as beta, b, it measures security risk, or volatility relative to the market portfolio

· Beta greater than 1.0 is riskier than the market

 

UNDERSTANDING BETA

· All security beta’s are measured relative to the market portfolio beta, which equals 1.0

· A beta greater than 1.0 means the security contributes more than the average risk to the well-diversified market portfolio

· The value of beta implies something about returns relative to the market

· The index used to approximate the market portfolio can affect the beta estimate

 

RISK RECAP

· Market risk

· Firm-specific risk

· Security’s total risk is market risk plus firm-specific risk

· Relative market risk for a security is its beta

· Security’s total risk is beta plus firm-specific risk

· Beta is the systematic or nondiversifiable risk

· Diversifiable risk is irrelevant in a well diversified portfolio

· Decisions made by total risk (standard deviations) instead of beta ignore the systematic risk and diversifiable risk components of total risk

  

DERIVING THE CAPM

· All risk averse investors will invest in one risky portfolio, M, which must be the market portfolio of all traded securities

· Mmust have the same slope as the CML

· ER_i = RF + Risk premium

· (ER_i - RF) = Risk premium

· The left side is the reward for accepting security risk

 

RISK/RETURN RELATIONSHIPS

· Security systematic risk, beta, can be defined as a ratio to the market return

· ER_i = RF + b_i (ER_M - RF)

· Security market line (SML) shows the risk/return relationship for securities and  a graphical representation of the CAPM

· Equation of a line is  Y = a + bX

a is the y-intercept and b is the slope

· The  y-intercept is the risk-free rate

· The slope is (ER_M - RF)

· The equation of the SML is

ER_i = RF + (ER_M - RF) b_i

 equal to equation for CAPM and similar to CML

 

DIFFERENCES BETWEEN CML AND SML

· Capital market line measures risk by standard deviation, or total risk

· Security market line measures risk by beta to find the security’s risk contribution to portfolio M

· CML graphs only defines efficient portfolios

· SML graphs efficient and nonefficient portfolios

· CML eliminates diversifiable risk for portfolios

· SML includes all portfolios that lie on or below the CML, but only as a part of M, and the relevant risk is the security’s contribution to M’s risk

· Firm specific risk is irrelevant to each, but for different reasons

 CAPM AND SECURITY ANALYSIS

· Value Line provides beta estimates for stocks

· Ibbotson Associates gives an average yield spread between the S&P 500 Index and the U. S. Treasury bill rate

· Negative beta means the security is negatively correlated to the market and can significantly reduce portfolio risk

 · With the equation:                                        

 ER_i = RF + b_i (ER_M - RF)                        

 we can estimate the required return for a security, on an SML graph

· Calculate the predicted return for the security based on today’s price, a predicted price a year from today, and expected dividends in the coming year

Predict a holding period return and compare to the SML expected return

If a security seems likely to have a higher return than its risk level justifies, then it is undervalued  (good investment)

A lower expected return than its risk would justify suggests a security is overvalued (not a good investment)

 ESTIMATING BETA

· A beta estimate measures the changes of a security’s return relative to the market return

· A security characteristic line graphs the relationship between the return on the market portfolio and a security return

· The market model uses linear regression to estimate the relationship between the market return and the security return

 DIFFERENCES BETWEEN THE SML AND SECURITY CHARACTERISTIC LINE

· SML graphs required return against betas of many securities

· Security Characteristic Line measures security returns against the market portfolio’s returns

· The SML has a slope the Expected rate less the risk-free rate, and an intercept of the risk-free rate

· The SCL is used to determine how a security return correlates to a market index return and it can be used to estimate beta, the slope of the SCL

· The SML is used to estimate the required return for a security relative to its risk measured by beta

· The beta value for the SML comes from the slope estimate of the SCL

 Beta: good news/bad news

· The SCL estimates beta and the SML graphs it

· Two issues with beta

How well can we estimate beta ?

How well can we predict the future beta using past beta estimates?

· Research has shown little correlation between a security returns and market portfolio returns

· Historical betas can be better predictors of future betas for large portfolios than it is for individual securities

· The more securities in the portfolio, the better predictor the portfolio beta is

· Other strategies can be more successful than strictly investing in beta based strategies

· Some choose to ignore beta - “Beta is dead”

· Beta isn’t perfect, but risk must be measured in making risk/return decisions

· The assumptions of the CAPM were stringent, and not realistic and will be relaxed in the next chapter in developing a general risk/return relationship