VIEWS: 5 PAGES: 33 CATEGORY: Technology POSTED ON: 12/30/2009 Public Domain
Lecture 16. Tuesday Mar 30th Risk and Diversification Announcements Start reading Chapter Nine (Material from this chapter will be on second midterm) Tuesday Mar 30th Risk and Diversification 2 Uncertainty Uncertainty arises when we do not know and have no way of quantifying the choices or options that we have in front of us Probability Probability Gamble 1 $100 ?% Gamble 4 $? 45% $100 ?% $? 55% Gamble 2 $0 ?% Gamble 5 $? 60% $200 ?% $? 40% Gamble 3 $50 ?% Gamble 6 $10 ? $150 ?% $210 ? Tuesday Mar 30th Risk and Diversification 3 Risk Risk is quantifiable uncertainty. Bring knowledge or information to bear on the situation. Probability Probability Gamble 1 $100 ?% 50% Gamble 4 $? $0 45% $100 ?% 50% $? $200 55% Gamble 2 $0 ?% 50% Gamble 5 $? $0 60% $200 ?% 50% $? $200 40% Gamble 3 $50 ?% 50% Gamble 6 $10 ?% ? 50% $150 ?% 50% $210 ?% ? 50% Tuesday Mar 30th Risk and Diversification 4 There are five “correct #1 (Page 50)(PRS) Class Applicationanswers” and one “wrong To play you pay $100. answer”! Which gamble do you make? Gamble 1 $100 50% Gamble 4 $0 45% $100 50% $200 55% Gamble 2 $0 50% Gamble 5 $0 60% $200 50% $200 40% Gamble 3 $50 50% Gamble 6 $10 50% $150 50% $210 50% Use PRS #7 if don’t know! Tuesday Mar 30th Risk and Diversification 5 Gamble 1 – Expectation Put $100 down, 50% of time get $100 back 50% of time get $100 back. Return is $0 → $100 gets you $100 every time! Risk is zero Tuesday Mar 30th Risk and Diversification 6 Gamble 2 – Expectation Put $100 down 50% of time get $0 back 50% of time get $200 back. Return is $0 → $100 gets you $100 on average! Risk is you might lose $100 every time Tuesday Mar 30th Risk and Diversification 7 Gamble 3 – Expectation Put $100 down 50% of time get $50 back 50% of time get $150 back. Return is $0 → $100 gets you $100 on average! Risk is you might lose $50 every time Tuesday Mar 30th Risk and Diversification 8 Gamble 4 – Expectation Put $100 down 45% of time get $0 back 55% of time get $200 back. Return is $10 → $100 gets you $110 on average! Risk is you might lose $100 every time Tuesday Mar 30th Risk and Diversification 9 Gamble 5 – Expectation Gamble 5 gets you Gamble 4 $0 45% $200, 40% of the $200 55% time Gamble 5 $0 60% Gamble 4 gets you $200, 55% of the $200 40% time Gamble 6 $10 50% Gamble 6 gets you $210, 50% of the $210 50% time. Tuesday Mar 30th Risk and Diversification 10 Gamble 6 – Expectation Put $100 down 50% of time get $10 back 50% of time get $210 back. Return is $10 → $100 gets you $110 on average! Risk is you might lose $90 every time Tuesday Mar 30th Risk and Diversification 11 Your Attitude to Risk If 1 → don’t really like risk If 2 → really like risk If 3 → will take some risk If 4 → want reward for taking risk If 6 → want same reward as in 4, for taking a little less risk Tuesday Mar 30th Risk and Diversification 12 Measurement of Return Tuesday Mar 30th Risk and Diversification 13 Value of Shares 54 days from February 1st 2004 to March 26th 2004 Measurement of Return Bank Of America 5,000.00 4,916.52 Bank One 5,000.00 5,290.41 Tuesday Mar 30th Risk and Diversification 14 Measurement of Return Value of Shares 54 days from February 1st 2004 to March 26th 2004 Bank Of America 5,000.00 4,916.52 Bank One 5,000.00 5,290.41 Formula 8.1 R W = [End Value - Start Value] / Start Value R BoA = [4,916.52 - 5,000.00] / 5,000.00 = - 0.016696 R ONE = [5,290.41 - 5,000.00] / 5,000.00 = + 0.058082 Tuesday Mar 30th Risk and Diversification 15 Measurement of Return Value of Shares Dividend 54 days from Feb 1 2004 to Mar 26 2004 Bank Of America 5,000.00 4,916.52 No Dividend in Period March 10 Dividend of 44.8 cents per share Bank One 5,000.00 5,290.41 on 98.44 shares. Total Dividend $44.10 Formula 8.1 (with dividends) End Value for Bank One = Value of Share + Value of Dividend Paid R W = [End Value - Start Value] / Start Value R ONE = [(5,290.41+44.10) - 5,000.00] / 5,000.00 = + 0.066902 Tuesday Mar 30th Risk and Diversification 16 Measurement of Return Value of Shares Dividend 54 days from Feb 1 2004 to Mar 26 2004 Bank Of America 5,000.00 4,916.52 No Dividend in Period March 10 Dividend of 44.8 cents per share Bank One 5,000.00 5,290.41 on 98.44 shares. Total Dividend $44.10 Simple Annualized Return = Periodic Return * Periods in Year R BoA = - 0.016696 * 365 54 = - 0.11285 or - 11.285% R ONE = + 0.066902 * 365 = 0.4522 or 45.22% 54 Tuesday Mar 30th Risk and Diversification 17 Measurement of Return 1 Asset Assume we can calculate the return for a share under several different economic scenarios (states of nature) that occur with know probability… For example: Good Economy Prob=.35 R=25% Tuesday Mar 30th Risk and Diversification 18 Measurement of Return 1 Asset E ( R ) = ∑ i =1,n R i * Prob i Economy Probi Returni i Boom Prob1 R1 1 Good Prob2 R2 2 Fair Prob3 R3 3 Recession Prob4 R4 4 Depression Prob5 R5 5 Tuesday Mar 30th Risk and Diversification 19 Measurement of Return 1 Asset E ( R ) = ∑ i =1,n R i * Prob i Economy Probi Returni i Boom 0.20 0.28 1 Good 0.25 0.25 2 Fair 0.30 0.15 3 Recession 0.20 0.08 4 Depression 0.05 -0.05 5 Tuesday Mar 30th Risk and Diversification 20 Measurement of Return 1 Asset i Econ Probi Ri 1 B 0.20 * 0.28 = 0.0560 2 G 0.25 * 0.25 = 0.0625 3 F 0.30 * 0.15 = 0.0450 4 R 0.20 * 0.08 = 0.0160 5 D 0.05 * -0.05 = -.0025 Sum = 0.1770 Tuesday Mar 30th Risk and Diversification 21 Expected Returns of Gambles 1 and 4 E ( R ) = ∑ R * Prob i =1, n i i Probability Probability Gamble 1 $100 50% Gamble 4 $0 45% $100 50% $200 55% $100 to play, so E(R ) = ($100-$100)*.50 + ($100- 1 $100)*.50 = 0 a return of 0% E(R ) = ($0-$100)*.45 + ($200- 4 $100)*.55 = $10 a return of 10% Tuesday Mar 30th Risk and Diversification 22 Measurement of Risk σ ( Ri − E ( R ) ) 2 = ∑ i =1,n 2 * Prob i Finance uses the variance in the return over the different scenarios as a measure the riskiness of the asset. Tuesday Mar 30th Risk and Diversification 23 Variance of Returns on Gambles σ = ∑ ( R i − E ( R ) ) * Prob 2 1 and 4 2 i =1, n i σ = ( R1− E ( R ) ) * Prob + ( R 2 − E ( R ) ) * Prob 2 2 2 1 1 2 σ = ( 0−0 ) * 0.50 + ( 0−0 ) * 0.50 = 0 2 2 2 1 Return Probability Probability Gamble 1 0% 50% Gamble 4 -100% 45% E(R1)= 0% 0% 50% E(R2) = 10% 100% 55% ( R1− E ( R ) ) * Prob + ( R 2− E ( R ) ) * Prob 2 2 σ 2 2 = 1 2 ( −1.0−0.10 ) * 0.45 + (1.0−0.10 ) * 0.55 2 2 σ 2 2 = σ = ( −1.10 ) * 0.45 + ( 0.90 ) * 0.55 = .99 2 2 2 2 Tuesday Mar 30th Risk and Diversification 24 Expected Returns and Variances of Gambles σ = σ 2 = ∑ ( Ri − E( R ) ) * Prob i =1, n 2 i Gamble E(R) VAR StDev 1 0.00 0.00 0.000 2 0.00 1.00 1.000 3 0.00 0.25 0.500 4 0.10 0.99 0.995 5 -0.20 0.96 0.980 6 0.10 1.00 1.000 Tuesday Mar 30th Risk and Diversification 25 PRS Q – Which 2 Gambles might it be “sensible” to take?? 1 for 1 and 2 6 for 1 and 3 2 for 2 and 3 7 for 1 and 4 3 for 3 and 4 8 for 1 and 5 4 for 4 and 5 9 for 1 and 6 5 for 5 and 6 Tuesday Mar 30th Risk and Diversification 26 Return 2 Projects (or Assets) i Econ George RGi Probi RKi Kramer 1 Recession 0.000 = 0.00 * 0.2 * 0.00 = 0.000 2 Slow 0.018 = 0.06 * 0.3 * 0.05 = 0.015 Growth 3 Moderate 0.032 = 0.08 * 0.4 * 0.10 = 0.040 Growth 4 Prosperity 0.010 = 0.10 * 0.1 * 0.15 = 0.015 0.060 = Sum Sum = 0.070 Course Notes Page 53 Tuesday Mar 30th Risk and Diversification 27 Course Notes Page 53 George Kramer Variance 2 Projects (or Assets) i Ec [RGi -E(RG)]^2 RGi - Probi RKi - [RKi -E(RK)]^2 * Probi E(RG) E(RK) * Probi 1 R 0.00072 0.00 - 0.2 0.00 - 0.00098 0.06 0.07 2 SG 0.00000 0.06 - 0.3 0.05 - 0.00012 0.06 0.07 3 MG 0.00016 0.08 - 0.4 0.10 - 0.00036 0.06 0.07 4 P 0.00016 0.10 - 0.1 0.15 - 0.00064 0.06 0.07 0.00104 = VAR VAR = 0.00210 Tuesday Mar 30th Risk and Diversification 28 Covariance 2 Projects (or Assets) σ xy = ∑ i =1,n (R xi − E ( R x) )(R yi −E ( R )) * Prob y i i Ec RGi -E(RG) RKi -E(RK) Probi Probability Weighted Product 1 R 0.00 -0.06 * 0.00 - 0.07 * 0.2 = 0.00084 2 SG 0.06 -0.06 * 0.05 - 0.07 * 0.3 = 0.00000 3 MG 0.08 -0.06 * 0.10 - 0.07 * 0.4 = 0.00024 4 P 0.10 -0.06 * 0.15 - 0.07 * 0.1 = 0.00032 COV = 0.00140 George Kramer Tuesday Mar 30th Risk and Diversification 29 Correlation 2 Projects (or Assets) Correlation = ρ = σ GK σ Gσ K GK ρ GK = 0.0014 ( 0.032249*0.045826) ρ GK = 0.0014 0.001477842674 = 0.9473 George Kramer Geo / Kra E(R) 0.06 0.07 Variance 0.00104 0.00210 St. Dev. 0.032249 0.045826 Covariance 0.00140 Correlation 0.9473 Tuesday Mar 30th Risk and Diversification 30 Historical Relationship Risk/Return (Notes page 51) Investment Average Low High Standard Return Deviation Treasury Bills 3.8% 1% 15% 3.3% Treasury Bonds 5.4% -9% 31% 5.8% Large Common 12.7% -44% 54% 20.3% Stock Small Common 17.7% -50% 143% 34.1% Stock Tuesday Mar 30th Risk and Diversification 31 Current Relationship Risk / Return Spread is percentage above the “risk free rate” paid. 100 basis points = 1 percent. Tuesday Mar 30th Risk and Diversification 32 Articles from The Economist Links on the Course Web Site “News” Page to 5 articles: Australian Economy. House Price Inflation. Investment Research. Separation of Traders from Analysts. US Monetary Policy. About Interest Rates. Warren Buffet. About Risk/Reward Tradeoff. Appetite for Risk. About Risk. Tuesday Mar 30th Risk and Diversification 33