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# Capital Asset Pricing Model

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Capital Asset Pricing Model (CAPM)

A model that describes the relationship between risk and expected return. The general idea behind CAPM is that investors need to be compensated in two ways: time value of money & risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk gauge (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).

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### Capital Asset Pricing Model

1. 1. Capital Asset Pricing Model(CAPM)<br />is the expected return on the capital asset <br />is the risk-free rate of interest such as interest arising from government bonds <br />(the beta) is the sensitivity of the expected excess asset returns to the expected excess market returns  <br />                                                      , <br />is the expected return of the market <br />E[Ri] = RF + βi(RM – RF)<br />
2. 2. Risk and Return<br />Find the expected return for Company A and B.<br />Find the standard deviation for Company A and B.<br />
3. 3. Find Expected Return<br />
4. 4. Find Standard Deviation<br />=3.8%<br />
5. 5. Portfolio Risk and the unseen egg smasher<br />Market<br />Your Portfolio<br />
6. 6. Lessons from unseen egg smasher<br />1. Assets are not held in isolation; rather, they are held as parts of portfolios.<br />2. Assets are priced according to their value in a portfolio.<br />3. Investors are concerned about how the portfolio of stocks perform--not individual stocks.<br />
7. 7. Risk and Return<br />Expected return for Sun Tan Company = 12%<br />Expected return for Umbrella Company = 12%<br />Standard deviation for Sun Tan Company = 17.15%<br />Standard deviation for Umbrella Company = 17.15%<br />Find the expected return and standard deviation for a portfolio which invests half its money in the Sun Tan and half its money in Umbrella Company.<br />
8. 8. Portfolio Risk and Return<br />
9. 9. Portfolio Risk and Return<br />
10. 10. Lessons from Bikini-clad Boracay Beach<br />1. Combining securities into portfolios reduces risk.<br />2. How? A portion of a stock’s variability in return is canceled (washed out) by complementary variations in the return of other securities<br />3. However, since to some extent stock prices (and returns) tend to move in tandem, not all variability can be ‘stamped out’ through diversification.<br /> or<br /> Even investors holding diversified portfolios have exposure to the risk inherent in the overall performance of the stock market.<br />4. Hence, <br /> Total Risk = unsystematic + systematic<br /> diversifiable non-diversifiable<br /> firm specific/idiosyncratic market<br /> residual risk aggregate<br />
11. 11. Portfolio Choice<br />Standard<br />Deviation<br />
12. 12. Risk and Return<br />2<br />ρ = - 1<br />ρ= 1<br />1<br />Standard<br />Deviation<br />
13. 13. Variability of Returns Compared with Size of Portfolio<br />Average annual <br />standard deviation (%)<br />49% -<br />24% -<br />19% -<br />Unsystematic or diversifiable/idiosyncratic<br />risk (related to firm-specific events)<br />Total Risk<br />Systematic or non-diversifiable <br />Risk/aggregate (result of general market <br />influences)<br />Number of stocks<br />in portfolio<br />1 10 20 25<br />
14. 14. Risk & Return<br />X<br />X X<br />X XX<br />X XXX<br />RF--<br />
15. 15. Risk & Return<br />Lending Borrowing<br />X<br />RM --<br />X X<br />X XX<br />X XXX<br />RF--<br />
16. 16. Security Market Line: Risk/ReturnTrade-Off with CAPM<br />SML<br />RF--<br />β<br />
17. 17. Security Market Line: E[Ri] = RF + βi(RM – RF)<br />SML<br />RM --<br />RF--<br />β<br />| |<br />1 2<br />
18. 18. CAPM<br />Provides a convenient measure of systematic risk of the volatility of an asset relative to the markets volatility.<br /> Gauges the tendency of a security’s return to move in tandem with the overall market’s return.<br /> Average systematic risk<br />High systematic risk, more volatile than the market<br /> Low systematic risk, less volatile than the market<br />
19. 19. 2006 Betas:<br />Betas for a Five-year Period(1987-1992)<br />
20. 20. The SML and WACC<br />SML<br />= 8%<br />Incorrect<br />acceptance<br />B<br />16% --<br />14% --<br />7% --<br />15% --<br />A<br />WACC = 15%<br />Incorrect<br />rejection<br />Beta<br />If a firm uses its WACC to make accept/reject decisions for all types of projects, it will have a tendency toward incorrectly accepting risky projects and incorrectly rejecting less risky projects.<br />
21. 21. The SML and the Subjective Approach<br />SML<br />20% --<br />14% --<br />10% --<br />7% --<br />High risk<br />(+6%)<br />WACC =<br />Moderate risk<br />(+0%)<br />Low risk<br />(-4%)<br />Beta<br />With the subjective approach, the firm places projects into one of several risk classes. The discount rate used to value the project is then determined by adding (for high risk) or subtracting (for low risk) an adjustment factor to or from the firm’s WACC.<br />
22. 22. Finding Beta for Three Companies: High, Average, and Low Risk & Market<br />
23. 23. The Concept of Beta (cont.)<br />Stock H, High Risk: β = 1.5<br />30 --<br />20 --<br />10 --<br /> 0<br />Stock A, Average Risk: β = 1.0<br />Stock L, Low Risk: β = 0.5<br />| |<br />| | |<br />-20 -10<br /> 10 20 30<br />-10 --<br />-20 --<br />
24. 24. Summary of Relationship Between Risk and Return<br />
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