Chapter 5 Risk and Rate of Return

2 EXPECTED RATE OF RETURN Outcomes Known K μ = E(R) = P 1 K 1 + P 2 K 2 + P 3 K 3 Outcomes Unknown (sample) _ K = ΣK n

3 RISK VARIANCE: σ 2 = P 1 (K 1 - K μ ) 2 + P 2 (K 2 - K μ ) 2 + P 3 (K 3 - K μ ) 2 _ _ _ VARIANCE: S 2 = [(K 1 - K) 2 + (K 2 - K) 2 + (K 3 - K) 2 ]/n-1 STANDARD DEVIATION = SQUARE ROOT OF VARIANCE

4 Example: Mean Return θ P K W K μ =.2(-10) +.2(40) +.2(-5) +.2(35) +.2(15) = 15 W μ =.2(40) +.2(-10) +.2(35) +.2(-5) +.2(15) = 15

5 Example Variance θ P K W(K-K μ ) 2 (W-W μ ) ____________________________________ σ K = √[.2(625) +.2(625) +.2(400) +.2(400) +.2(0)] = ____________________________________ σ W = √[.2(625) +.2(625) +.2(400) +.2(400) +.2(0)] = 20.25

6 Buy Equal Amount of K & W θ P K W (K-K μ ) 2 (W-W μ ) 2.5K+.5W

7 Put 75% in K and 25% in W θ P K W (K-K μ ) 2 (W-K μ ) 2.5K+.5W.75K+.25W

8 CORRELATION PERFECT POSITIVE = +1 PERFECT NEGATIVE = -1 UNCORRELATED = 0

9 Merging 2 Assets into 1 Portfolio Two risky assets become a low-risk portfolio

10 DIVERSIFICATION TOTAL RISK = NONDIVERSIFIABLE RISK + DIVERSIFIABLE RISK TOTAL RISK = SYSTEMATIC RISK + UNSYSTEMATIC RISK TOTAL RISK = MARKET RISK + FIRM RISK

11 Reducing Total Risk by Diversifying

12 Market Risk BETA = INDEX OF HOW SECURITY RETURN MOVES WITH MARKET β > 1, SECURITY IS AGGRESSIVE β < 1, SECURITY IS DEFENSIVE BETA OF PORTFOLIO β p = W 1 β 1 + W 2 β 2 + W 3 β 3

13 Estimating Beta Holding Period Returns – Stock X PeriodPrice(P t - P t-1 )/ P t-1 Return Sep / Aug / Jul / Jun / May / Apr

14 Estimating Beta Holding Period Returns – S&P 500 Period Index (I t - I t-1 )/ I t-1 Return Sep / Aug / Jul / Jun / May / Apr

15 Beta

16 An Example: Sample Returns YEARSTOCK ASTOCK B 1 6%20% –2 – Sum Sum/6 = AR= 8%20%

17 A’s RETURNRETURN DIFFERENCE FROM DIFFERENCE YRTHE AVERAGESQUARED 16%– 8% = –2%(–2%) 2 = 4% 212 – 8 = 4(4) 2 = – 8 = 0(0) 2 = 0 4–2 – 8 = –10(–10) 2 = – 8 = 10(10) 2 = – 8 = –2(-2) 2 = 4 Sum 224% Sum/(6 – 1) = Variance 44.8% Standard deviation =  44.8 = 6.7%

18 Using Average Return and Standard Deviation If the future will resemble the past and the periodic returns are normally distributed: 68% of the returns will fall between AR -  and AR +  95% of the returns will fall between AR - 2  and AR + 2  95% of the returns will fall between AR - 3  and AR + 3 

19 For Asset A 68% of the returns between 1.3% and 14.7% 95% of the returns between -5.4% and 21.4% 99% of the returns between -12.1% and 28.1%

20 Which of these is riskier? Asset AAsset B Avg. Return8% 20% Std. Deviation 6.7% 20%

21 Another view of risk: Coefficient of Variation = Standard deviation Average return It measures risk per unit of return

22 Which is riskier? Asset AAsset B Avg. Return8% 20% Std. Deviation 6.7% 20% Coefficient of Variation

23 Capital Asset Pricing Model Required Rate of Return = R f + Risk Premium Risk Premium = Market Price of Risk + Nondiversifiable risk Risk Premium = (K m – R f )β Required Rate of Return = R f + (K m – R f )β

24 Capital Asset Pricing Model

25 Overvalued and Undervalued

26 Impact of Inflation