1. Security Analysis & Portfolio Management “Capital Asset Pricing Model " By B.Pani M.Com,LLB,FCA,FICWA,ACS,DISA,MBA 9731397829 bpani2001@yahoo.co.in

2. Beta (β) Beta is the relative measure of systematic risk. It measures the sensitivity of the return of the security vis-à-vis the market return. β = Cov(X,Y)/ Var(X) where X = Return on the market Y= Return on individual security It can also be calculated by the following formulae β = (NΣX*Y -ΣX*ΣY ) /( NΣX 2 - (ΣX) 2 ) where N = number of observation.

3. Interpretation of beta β > 1 --------------------------- Aggressive Securities β< 1----------------------------- Defensive securities Explain why the beta of the market is 1

4. Illustration: Calculation of Beta Calculate beta and identify whether security X is an aggressive or a defensive security.

5. Risk Break - Up Total Risk of a security = σ 2 Systematic Risk of a security = β 2 σ 2 m where β = Beta of an individual security σ 2 m = Variance of the market portfolio Write the formulae of Unsystematic risk

6. Other risk calculations Semi-variance or downside risk Semi-variance is defined in analogy to variance, but using only returns below the mean. If the returns are symmetric – i.e., the return is equally likely to be x percent above and below the mean- the semi-variance is exactly one-half of the variance. One approach defines downside risk as the square root of the semi-variance.

8. Beta is a statistical variable and should be considered with its statistical significance (R square value of the regression Using beta as a measure of relative risk has its own limitations. Most analysis consider only the magnitude of beta. line). Higher R square value implies higher correlation and a stronger relationship between returns of the asset and benchmark index.R square correlation If beta is a result of regression of one stock against the market where it is quoted, betas from different countries are not comparable. Staple stocks are thought to be less affected by cycles and usually have lower beta. Procter & Gamble, which makes soap, is a classic example. Other similar ones are Philip Morris (tobacco) and Johnson & Johnson (Health & Consumer Goods). Utility stocks are thought to be less cyclical and have lower beta as well, for similar reasons.Procter & GamblePhilip MorrisJohnson & Johnson 'Tech' stocks typically have higher beta. An example is the dot-com bubble; although tech did very well in the late 1990s, it also cratered in the early 2000s, worse than the overall market.dot-com bubble

9. Target Semi-variance A generalized semi-variance that focuses on returns below a target instead of just below the mean.

10. Beta,  variation in asset/portfolio return relative to return of market portfolio –mkt. portfolio = mkt. index -- S&P 500 or NYSE index  = % change in asset return % change in market return

11. interpreting  if  –asset is risk free if  –asset return = market return if  –asset is riskier than market index   – asset is less risky than market index

12. 12 PORTFOLIO RISK CALCULATING PORTFOLIO RISK –Portfolio Risk: DEFINITION: a measure that estimates the extent to which the actual outcome is likely to diverge from the expected outcome

13. 13 PORTFOLIO RISK CALCULATING PORTFOLIO RISK 2 Security case where  = the covariance of returns between security1 and security2.It measures the degree to which the two securities vary together.It is product of the correlation coefficient and the two standard deviation. Securitysecurity1security2 Security 1 w12  w1w2  Security 2 w2w1  w22 

14. 14 PORTFOLIO RISK CALCULATING PORTFOLIO RISK IN CASE OF n SECURITIES –Portfolio Risk : where  ij = the covariance of returns between security i and security j

15. 15 PORTFOLIO RISK CALCULATING PORTFOLIO RISK –Portfolio Risk: COVARIANCE –DEFINITION: a measure of the relationship between two random variables –possible values: »positive: variables move together »zero: no relationship »negative: variables move in opposite directions

16. 16 PORTFOLIO RISK CORRELATION COEFFICIENT where

17. Asset Pricing Models CAPM –Capital Asset Pricing Model –1964, Sharpe, Linter –quantifies the risk/return tradeoff

18. assume investors choose risky and risk-free asset no transactions costs, taxes same expectations, time horizon risk averse investors

19. implication expected return is a function of –beta –risk free return –market return

20. or is the portfolio risk premium where is the market risk premium

21. so if  portfolio exp. return is larger than exp. market return riskier portfolio has larger exp. Return Portfolio with larger beta will have larger expected return > >

22. so if  portfolio exp. return is smaller than exp. market return less risky portfolio has smaller exp. return < <

23. so if  portfolio exp. return is same than exp. market return equal risk portfolio means equal exp. return = =

24. so if  portfolio exp. return is equal to risk free return = 0 =

25. example R m = 10%, R f = 3%,  = 2.5

26. CAPM tells us size of risk/return tradeoff CAPM tells use the price of risk

27. Testing the CAPM CAPM overpredicts returns –return under CAPM > actual return relationship between β and return? –some studies it is positive –some recent studies argue no relationship (1992 Fama & French)

28. other factors important in determining returns –January effect –firm size effect –day-of-the-week effect –ratio of book value to market value

29. January Effect A general increase in stock prices during the month of January. This rally is generally attributed to an increase in buying, which follows the drop in price that typically happens in December when investors, seeking to create tax losses to offset capital gains, prompt a sell-off.

30. day-of-the-week effect The weekend effect (also known as the Monday effect, the day-of-the-week effect or the Monday seasonal) refers to the tendency of stocks to exhibit relatively large returns on Fridays compared to those on Mondays. This is a particularly puzzling anomaly because, as Monday returns span three days, if anything, one would expect returns on a Monday to be higher than returns for other days of the week due to the longer period and the greater risk.

31. CAPM’s Answers Specifically: Total risk = systematic risk + unsystematic risk CAPM says: (1)Unsystematic risk can be diversified away. Since there is no free lunch, if there is something you bear but can be avoided by diversifying at NO cost, the market will not reward the holder of unsystematic risk at all. (2)Systematic risk cannot be diversified away without cost. In other words, investors need to be compensated by a certain risk premium for bearing systematic risk.

32. Pictorial Result of CAPM E(R i ) E(R M ) RfRf Security Market Line  [COV(R i, R M )/Var(R M )]   = 1.0 slope = [E(R M ) - R f ] = Eqm. Price of risk

33. Use of CAPM For valuation of risky assets For estimating required rate of return of risky projects