Appendix S: Content Portfolios and Diversification 1188 The expected return on a portfolio is a weighted average of the expected return on the individual id assets; but estimating the risk, or standard deviation of a portfolio, is more complicated. 1189 Portfolio expected rate of return = (fraction of portfolio in first asset * expected rate of return on the first asset) + (fraction of portfolio in the second asset * expected rate of return on the second asset) + etc. Variance for Individual Assets Take N deviations from the average rate of return for asset a and square each of them: (average return a actual return a ) 2 Then average the products. 1190 Stewart C, and Marcus, Alan J. Fundamentals of Corporate Finance, McGraw-Hill Irwin, New York 2004 1191 1
The resulting number is the variance for the asset. The higher the number, the higher the potential risk of the asset. Diversification/ Portfolio In order to find the standard deviation for asset a ( ), σ take a the square root of the variance. The closer is to zero, the closer the expected outcome σ a is to complete certainty. Stewart C, and Marcus, Alan J. Fundamentals of Corporate Finance, McGraw-Hill Irwin, New York 2004 1192 Stewart C, and Marcus, Alan J. Fundamentals of Corporate Finance, McGraw-Hill Irwin, New York 2004 1193 The goal of diversification is to reduce the variances of the portfolio as a whole. In order to estimate the rate at which the two stocks covary, multiply the deviation of asset a by the deviation of asset b in each of N scenarios, and then average the products. 1194 1195 2
(deviation a 1 * deviation b1) + (deviation a2 * deviation b2) N For the covariant coefficient ( ρab ). divide that covariance by the product of the standard deviations of asset A and of asset B. ρ ab = Covariance ( σa * σ b ) 1196 1197 Covariant coefficients range between 1 to 1. Values of 1 indicate perfect negative correlation; i.e. elimination of unique risk. Value of 0 means returns on the two assets vary independently, and 1 indicates perfect positive correlation; a poor portfolio match. If the returns on two assets in a portfolio varied in perfect lockstep, the standard deviation of the portfolio would be the weighted average of the standard deviations of both assets: 1198 1199 3
If the covariance coefficient = 1, let x a = fraction of stock a in the portfolio, x b = fraction of stock b. Standard deviation of portfolio ab =(x a * ) + x b * ). σ a σ b The incremental risk of an asset depends on whether its returns tend to vary with or against the returns of other assets held. If it varies against, then it reduces the overall variability of a portfolio s returns. 1200 1201 The expected value of a given movie may be high enough to justify its production, but its risk may be high enough to deter producers who cannot afford to lose or to diversify. Expected value of any range of outcomes is the sum of the products of the probability * the result 1202 1203 4
Assume a movie costs $10 million to make, may return 10, 5, 4 1, or -2 million (loss). Based on past experience, the probability of it making 10 million in net revenues is.3 The other probabilities are.4,.2,.1 respectively 1204 Expected Value for movie A = (.3*10) + (.4*5) + (2*4) (.2 + (.1 1*-1) 1) = 5.7 1205 Sum of the probabilities of all possible events must equal 100%, because one of them will occur. Now that we have determined probability of all possible outcomes, we multiply the probability of each outcome by the dollar value: 1206 1207 5
The expected value of the project is the sum of probabilities * payoffs. Advantages of Product Variation: Gives studios a better chance of hitting a moving target reduces the risks of concentrating on the wrong market segment generates information on developing market trends 1208 1209 Portfolio rate of return = (fraction of portfolio held in first asset * rate of return on the first asset) + (fraction of portfolio held in the second asset * rate of return on the second asset) But it also increases the number of flops 1210 1211 6
As long as returns on assets are negatively correlated (when one does bad, the other does well) even extremely volatile assets will help to decrease the volatility of an overall portfolio. Portfolios eliminate unique risk and leave the content company only with market risks. 1212 1213 Assume portfolio of movies that include Movie Cost Probability & Return A 10M 30% 10M; 40% 5 M; 20% 4 M; 10% -1M; B 50M 20% -60 M; 20% 50 M; 30% 30 M; 30% 10M; C 100M 35% 200 M; 15% 100 M; 20% 90 M, 30% -2M; D 200M 50% 300M; 25% 250M; 15% 190M; 10% 150M; What is the portfolio s expected value? Expected Value for movie A = (.3*10) + (.4*5) + (2*4) (.2 + (.1 1*-1) 1) = 5.7 1214 1215 7
Expected Value for movie B = (.2*70) + (.2*60) + (.3*40) + (.3*10) = 41 Expected Value for movie C = (.35*200) + (.15*100) + (.2*90) +(.3*2) = 102.4 1216 1217 Expected Value for movie D = (.5*300) + (.25*250) + (.15*190) + (.10*150) = 256 So our expected value for the portfolio is 5.7 + 41 + 102.4 + 256 = 405.1 1218 1219 8
Expected Return for Investment Movie A (5.7-10) \ 10 = -43% Movie B (41-50) \ 50 = -18% Movie C (102.4-100)\100 = 2.4% Movie D (256-200)\200= 28% Overall Portfolio (405.1-360)\360 = 12.5% 1220 The Expected Value of a Film May be high enough to justify its production, but its risk may be high enough to deter producers who cannot afford to lose, or to diversify risk. 1221 Expected Value Threshold Assume: Small studio ss threshold is 90%. Big studio s threshold is 70%. Studio will decide to produce film if it does not exceed threshold of expected value. Realistically they will not know the threshold until production starts. 1222 1223 9
The incremental risk of an asset depends on whether its returns tend to vary with or against the returns of other assets held. If it varies against, then it reduces the overall variability of a portfolio s returns. As long as returns on assets are negatively correlated (when one does badly, the other does well) even extremely volatile assets will help to decrease the volatility of an overall portfolio. 1224 1225 Portfolios thus reduce or eliminate unique risk and leave the investor only with market risks. Variance Take 4 deviations from the average rate of return and square each of them. Then average that. If it s high, variance is high. Now, take the square root: that s the Standard Deviation. 1226 1227 10
The closer the outcome gets to certain, the closer the SD is to zero. 1228 11