Teori Pasaran Modal dan CAPM Reference: RWJ Chapter 10

1. Teori Pasaran Modal dan CAPM Reference: RWJ Chapter 10

2. Lecture Objectives • Know how to calculate expected returns • Understand portfolio returns, variance and standard deviation • The Efficient Set for Two Assets • The Efficient Set for Many Securities • Diversification: An Example • Riskless Borrowing and Lending • Market Equilibrium • Relationship between Risk and Expected Return (CAPM)

3. Expected Returns • Expected returns are based on the probabilities of possible outcomes • In this context, “expected” means average if the process is repeated many times • The “expected” return does not even have to be a possible return

4. Example: Expected Returns • Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? • State Probability C T • Boom 0.3 0.15 0.25 • Normal 0.5 0.10 0.20 • Recession ??? 0.02 0.01 • RC = • RT =

5. Variance and Standard Deviation • Variance and standard deviation still measure the volatility of returns • Using unequal probabilities for the entire range of possibilities • Weighted average of squared deviations

6. Example: Variance and Standard Deviation • Consider the previous example. What are the variance and standard deviation for each stock? • Stock C • Stock T

7. Another Example : ASSIGNMENT • Consider the following information: • State Probability ABC, Inc. • Boom .25 .15 • Normal .50 .08 • Slowdown .15 .04 • Recession .10 -.03 • What is the expected return? • What is the variance? • What is the standard deviation?

8. Portfolios • A portfolio is a collection of assets • An asset’s risk and return is important in how it affects the risk and return of the portfolio • The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets

9. Example: Portfolio Weights • Suppose you have RM15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? • RM2000 of A • RM3000 of B • RM4000 of C • RM6000 of D

10. Portfolio Expected Returns • The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio • You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities

11. Example: Expected Portfolio Returns • Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? • A: 19.65% • B: 8.96% • C: 9.67% • D: 8.13%

12. Portfolio Variance • Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm • Compute the expected portfolio return using the same formula as for an individual asset • Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

13. Example: Portfolio Variance • Consider the following information • Invest 50% of your money in Asset A • State Probability A B • Boom .4 30% -5% • Bust .6 -10% 25% • What is the expected return and standard deviation for each asset? • What is the expected return and standard deviation for the portfolio? Portfolio

14. Expected (Ex Ante) Return, Variance • Expected Return: E(R) = S (ps x Rs) • Variance: s2 = S {ps x [Rs - E(R)]2} • Standard Deviation = s

15. Return and Risk for Portfolios (2 Assets) • Expected Return of a Portfolio: E(Rp) = XAE(R)A + XB E(R)B • Variance of a Portfolio: sp2 = XA2sA2 + XB2sB2 + 2 XA XB sAB

16. Another Example • Consider the following information • State Probability X Z • Boom .25 15% 10% • Normal .60 10% 9% • Recession .15 5% 10% • What is the expected return and standard deviation for a portfolio with an investment of RM6000 in asset X and RM4000 in asset Y?

17. Calculating Expected Return and Standard Deviation

19. WHAT IS COVARIANCE AND CORRELATION? • Covariance: sAB = S {ps x [Rs,A - E(RA)] x [Rs,B - E(RB)]} • Correlation Coefficient: rAB = sAB / (sAsB) • Variance and Standard Deviation measure the variability of individual stock. • Covariance and Correlation measure how two random variables are related

20. PERFECT POSITIVE CORRELATION Returns • Corr(RA , RB) = 1 A + 0 B - TIME

21. PERFECT POSITIVE CORRELATION RETURNS • Corr(RA , RB) = -1 A + 0 B - TIME

22. ZERO CORRELATION Returns A • Corr(RA , RB) = 0 + 0 B - TIME

23. FROM PREVIOUS EXAMPLE

24. Calculating Covariance and Correlation

25. Covariance: sAB = S {ps x [Rs,A - E(RA)] x [Rs,B - E(RB)]} = • Correlation Coefficient: rAB = sAB / (sAsB) =

26. Two-Security Portfolios with Various Correlations return 100% stocks  = -1.0  = 1.0  = 0.2 100% bonds 

27. Portfolio Risk/Return Two Securities: Correlation Effects • Relationship depends on correlation coefficient • -1.0 <r< +1.0 • The smaller the correlation, the greater the risk reduction potential • If r = +1.0, no risk reduction is possible

28. Portfolio Risk as a Function of the Number of Stocks in the Portfolio In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not.  Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Nondiversifiable risk; Systematic Risk; Market Risk n Thus diversification can eliminate some, but not all of the risk of individual securities.

29. The Efficient Set for Many Securities Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios. return Individual Assets P

30. The Efficient Set for Many Securities Given the opportunity set we can identify the minimum variance portfolio. return minimum variance portfolio Individual Assets P

31. The Efficient Set for Many Securities The section of the opportunity set above the minimum variance portfolio is the efficient frontier. return efficient frontier minimum variance portfolio Individual Assets P

32. Optimal Risky Portfolio with a Risk-Free Asset In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills return 100% stocks rf 100% bonds 

33. Riskless Borrowing and Lending Now investors can allocate their money across the T-bills and a balanced mutual fund CML return 100% stocks Balanced fund rf 100% bonds 

34. Riskless Borrowing and Lending With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope CML return efficient frontier rf P

35. Market Equilibrium With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors. efficient frontier return CML M rf P

36. The Separation Property The Separation Property states that the market portfolio, M, is the same for all investors—they can separate their risk aversion from their choice of the market portfolio. CML return efficient frontier M rf P

37. The Separation Property Investor risk aversion is revealed in their choice of where to stay along the capital allocation line—not in their choice of the line. CML return efficient frontier M rf P

38. Market Equilibrium Just where the investor chooses along the Capital Asset Line depends on his risk tolerance. The big point though is that all investors have the same CML. CML return 100% stocks Balanced fund rf 100% bonds 

39. Market Equilibrium All investors have the same CML because they all have the same optimal risky portfolio given the risk-free rate. CML return 100% stocks Optimal Risky Porfolio rf 100% bonds 

40. The Separation Property The separation property implies that portfolio choice can be separated into two tasks: (1) determine the optimal risky portfolio, and (2) selecting a point on the CML. CML return 100% stocks Optimal Risky Porfolio rf 100% bonds 

41. Optimal Risky Portfolio with a Risk-Free Asset By the way, the optimal risky portfolio depends on the risk-free rate as well as the risky assets. CML1 CML0 return 100% stocks Second Optimal Risky Portfolio First Optimal Risky Portfolio 100% bonds 

42. Definition of Risk When Investors Hold the Market Portfolio • Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security. • Beta measures the responsiveness of a security to movements in the market portfolio.

43. Characteristic Line Slope = bi Estimating b with regression Security Returns Return on market % Ri = ai + biRm + ei

44. The Formula for Beta Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio.

45. Relationship between Risk and Expected Return (CAPM) • Expected Return on the Market: • Expected return on an individual security: Market Risk Premium This applies to individual securities held within well-diversified portfolios.

46. Expected return on a security Risk-free rate Beta of the security Market risk premium = + × • Assume bi = 0, then the expected return is RF. • Assumebi = 1, then Expected Return on an Individual Security • This formula is called the Capital Asset Pricing Model (CAPM)

47. Relationship Between Risk & Expected Return Expected return b 1.0

48. Relationship Between Risk & Expected Return Expected return b 1.5