Capital asset pricing model (CAPM)

RISK-RETURN RELATIONSHIP, MODEL SHOWING RISKY AND RISK-FREE ASSET, ARBITRAGE PRICING THEORY

1. CAPITAL ASSET PRICING MODEL (CAPM) PRESENTED BY SIMRAN KAUR

2. CAPITAL ALLOCATION LINE Capital allocation line shows the reward to variability ratio in terms of additional beta Let us denote a risk-free portfolio by F, a risky portfolio by M, and a complete portfolio formed by combining them as C. Further w is the fraction of the overall portfolio invested in M, and the remaining (= 1-w) in F. The expected return of complete portfolio may be calculated as E( + w [ E(  

3. TERMINOLOGY E( Expected rate of return on complete portfolio = Risk-free rate of return W = Fraction of complete portfolio C invested in risky asset M E( = Expected return for risky asset M E( = Risk premium for risky asset E( Expected or required rate of return on asset i  

4. STANDARD DEVIATION OF PORTFOLIO Standard deviation of complete portfolio is given by Where = standard deviation of complete portfolio C w = fraction of complete portfolio C, invested in risky asset M = standard deviation of risky portfolio M  

5. SEPARATION THEOREM A risk-averse investor assigns greater weight to the risk-free asset in his portfolio than an investor with greater risk tolerance. However, both use identical sets of two assets – one risk-free and another risky. This result is called separation theorem.

6. MARKET PORTFOLIO Market portfolio is a theoretical construct credited to Prof. Eugene Fama . It is a huge portfolio that includes all traded assets in exactly the same proportion in which they are supplied in equilibrium. The return on market portfolio is the weighted average of return on all capital assets.

7. CAPITAL MARKET LINE (CML) CML is capital allocation line provided by one-month T-bills as a risk-free asset and a market-index portfolio like Dow Jones, Standard and Poor’s and NYSE, as risky asset It is one of the two elements of CAPM, the other being security market line (SML) CML indicates - Locus of all efficient portfolios; Risk-return relationship and measure of risk for efficient portfolios; Relationship between risk (standard deviation) and expected return for efficient portfolio is linear; Appropriate measure of risk for portfolio is standard deviation of returns on portfolio

8. FUNCTIONS OF CML It depicts risk-return relationship for efficient portfolios available to investors It shows the appropriate measure of risk for an efficient portfolios is the standard deviation of return on portfolio

9. SECURITY MARKET LINE (SML) SML is a graphic depiction of CAPM and describes market price of risk in capital markets E( Expected return = Risk-free return + (Beta * Risk premium of market) On security i = Intercept + (Beta * Slope of SML) Risk premium on security I = Beta * Risk premium of market  

10. CAPITAL ASSET PRICING MODEL (CAPM) CAPM is an equilibrium model of trade-off between expected portfolio return and unavoidable (systematic) risk; the basic theory that links together risk and return of all assets It is a logical and major extension of portfolio theory of Markowitz by William Sharpe, John Linterner and Jan Mossin It provides framework for determining the equilibrium expected return for risky assets

11. IMPLICATIONS OF CAPM Risk-return relationship for an efficient portfolio Risk-return relationship for an individual asset/security Identification of under- and over-valued assets traded in the market Effect of leverage on cost of equity Capital budgeting decisions and cost of capital Risk of firm through diversification of project portfolio

12. ASSUMPTIONS OF CAPM All investors are price-takers. Their number is so large that no single investor can afford prices All investors use the mean-variance portfolio selection model of Markowitz Assets/securities are perfectly divisible All investors plan for one identical holding period Homogeneity of expectation for all investors results in identical efficient frontier and optimal portfolio Investors can lend or borrow at an identical risk-free rate There are no transaction costs and income taxes

13. EXPECTED RETURN IN CAPM Risk-free rate plus a premium for systematic risk based on beta The premium of market portfolio, also referred to as reward, depends on the level of risk-free return and return on market portfolio Information related to the following 3 aspects are needed to apply CAPM: risk-free rate, risk premium on market portfolio and beta

14. RISK-FREE RATE R ate of return available on assets like T-bills, money market funds or bank deposits is taken as proxy for risk-free rate The maturity period of T-bills and bank deposits is taken to be less than one year, usually 364 days Such assets have very low or virtually negligible default risk and interest rate risk

15. RISK-PREMIUM ON MARKET PORTFOLIO It is the difference between the expected return on market portfolio and risk-free rate of return CAPM holds that in equilibrium, the market portfolio is unanimously desirable risky portfolio It contains all securities in exactly the same proportion in which they are supplied, that is, each security is held in proportion to its market value It is an efficient portfolio, which entails neither lending nor borrowing It is proportional to its risk ( and degree of risk aversion of average investor  

16. BETA It measures risk(volatility) of an individual asset relative to market portfolio Assets with beta less than one are called defensive assets Assets with beta greater than one are called aggressive assets Risk free assets have a beta equal to zero Beta is covariance of asset’s return with the market portfolio’s return, divided by variance of market portfolio Beta of a portfolio is the weighted average of betas of assets included in portfolio

17. CAPM EQUATION Where = required rate of return on security j b = coefficient showing relative importance of beta = beta of security j t = coefficient showing relative importance of tax effect = dividend yield on security j  

18. POPULARITY OF CAPM Risk-return trade off – the direct proportional relationship between the two – has a distinct intuitive appeal Transition from Capital Market Line (CML) to Security Market Line (SML) shows that undiversifiable nature of the systematic risk makes it the relevant risk for pricing of securities and portfolios Beta, the measure of systematic risk, is easy to compute and use The model shows that investors are content to put their money in a limited number of portfolios, namely, a risk-free asset like T-bills and a risky asset like a market-index fund

19. PROBLEMS WITH CAPM One of this relates to the maturity of the risk-free asset, namely, interest rate on a short term government security like a T-bill or a long-term rate like that on a treasury bond or an intermediate term-rate like that on a 3 year treasury securities Whether market premium should be the expected or historical Use of an appropriate market index If beta is appropriate risk measure

20. VARIABLES IN CAPM Taxes Inflation Liquidity Market capitalization size Price-earnings and market-to-book value ratios

21. ARBITRAGE PRICING THEORY (APT) APT is based on concept of arbitrage It was developed in 1970 by Ross In the context of pricing of (return from) securities, arbitrage implies finding/availability of two securities which are essentially the same (having different prices/returns) APT has markets equilibrating across securities through arbitrage driving out mispricing Arbitrage will ensure that riskless assets(or securities) provide the same expected return in competitive financial markets

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