Capital Asset Pricing Model

CAPITAL ASSET PRICING MODEL

INTRODUCTION 

The Capital Asset Pricing Model (CAPM) is a model developed in an attempt to explain variation in yield rates on various types of investments

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CAPM is based on the idea that investors demand additional expected return (called the risk premium) if they are asked to accept additional risk

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The CAPM model says that this expected return that these investors would demand is equal to the rate on a risk-free security plus a risk premium

INTRODUCTION 

The model was the work of financial economist (and, later, Nobel laureate in economics) William Sharpe, set out in his 1970 book "Portfolio Theory And Capital Markets"

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His model starts with the idea that individual investment contains two types of risk:  Systematic Risk (or Market risk)  Unsystematic Risk (or Specific risk)

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CAPM considers only systematic risk and assumes that unsystematic risk can be eliminated by diversification

DIVERSIFICATION 

A risk management technique that mixes a wide variety of investments within a portfolio

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The rationale behind this technique contends that a portfolio of different kinds of investments will, on average, yield higher returns and pose a lower risk than any individual investment found within the portfolio

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This only works for unsystematic risks

ASSUMPTIONS The Capital Asset Pricing Model is valid within a special set of assumptions:

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Markets are in equilibrium./There are no market imperfections(perfect Market) There are many investors who behave competitively (price takers). Information is available to all such as covariance , variances, mean rates of return of stocks All investors have equal access to all securities There are no taxes or transaction costs. No commissions.

Continue….    

All investors have identical opinions about expected returns, volatilities and correlations of available investments. Risk-averse rational investor. Investors have homogenous expectations (beliefs) about asset returns There exists a risk free asset and investors may borrow or lend unlimited amounts of this asset at a constant rate: the risk free rate.Unlimited borrowing and lending are available at the risk-free rate.

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There is a definite number of assets and their quantities are fixed within the one period world All assets are perfectly divisible and priced in a perfectly competitive marked All investors are looking ahead over the same (one period) planning horizon.

Formula 

When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor's net exposure is just the systematic risk of the market portfolio.

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Systematic risk can be measured using beta

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According to CAPM, the expected return of a stock equals the risk-free rate plus the portfolio's beta multiplied by the expected excess return of the market portfolio.

CAPM Formulation of CAPM is given by:

where: rk- yield rate on a specific security k rf- risk-free rate of interest rp- yield rate on the market portfolio bk- a measure of systematic risk for security k

Q- if the risk-free rate is 3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%,than calculate Expected rate of return.

Ans. The stock is expected to return E(R) – (3%+2(10%-3%)) =17%

For example Q- suppose a stock has a beta of 0.8. The market has an expected annual return of 0.12 (that is 12%) and the riskfree rate is .02 (2%). Then the stock has an expected oneyear return of

Ans. E(rk) = .02 +.8[.12 – .02] = 0.10

CAPITAL ASSET PRICING MODEL Three Linear Relationships

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Capital Market Line: linear risk-return trade-off for all investment portfolios

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Security Market Line: linear risk-return trade-off for individual stocks

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Security Characteristic Line: linear relation between the return on individual securities and the overall market at every point in time

CAPITAL ASSET PRICING MODEL Three Linear Relationships

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Capital Market Line: linear risk-return trade-off for all investment portfolios

E(R) M Rf s = market s

Standard Deviation (total portfolio risk)

Security Market Line (SML) 

Security Market Line: linear risk-return trade-off for individual stocks

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Systematic Risk: return volatility tied to overall market; also called non diversifiable risk

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Unsystematic Risk: return volatility tied specifically to an individual company; also called diversifiable risk

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Beta: sensitivity of a security’s returns to the systematic market risk factor

CAPITAL ASSET PRICING MODEL Three Linear Relationships

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Security Market Line: linear risk-return trade-off for all individual stocks -

E(R) M Rf b=1

Systematic Risk

Figure 13.5

The BETA Factor

Security characteristic line

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Security characteristic line (SCL) indicates the performance of a particular security or portfolio against that of the market portfolio at every point in time.

Empirical Implications of CAPM 

Optimal portfolio choice depends on market risk-return trade-offs and individual investors’ differences in risk preferences.

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Relation between expected return and risk is linear for all portfolios and individual assets.

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Expected rate of return is risk-free rate plus relative risk (ßp) times market risk premium.

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 High

beta portfolios earn high risk premiums.

 Low

beta portfolios earn low risk premiums.

Stock price b measures relevant risk for all securities.

Application of CAPM 

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CAPM can test Efficient Market Hypothesis To estimate the three key elements needed to apply the CAPM: for the risk-free rate, an estimate of beta, and an market risk premium. For valuation of risky assets For estimating required rate of return of risky projects. To estimate the required premium to compensate for Systematic risk. To predict future required rate of return in perfect market conditions.