(1) Calculate the expected return for the two assets given below. State Rec Norm Exp Asset A Pi) 0.25 0.50 0.25 7 XO) 0.04 0.10 0.16 Ex) Asset B PO 0.25 0.50 0.25 TO 1.05 State Rec Norm Exp 32 404 40 .10.18 XO) 0.16 0.10 -0.04 E(x) . (2) Calculate the standard deviation and coefficient of variationfor for the two assets given above E(X) Stato Rec Norm Exp Asset A P(1) 0.25 0.50 0.25 XO) 0.04 0.10 0.16 . 10 10 xlor XO-EX) (XO) - E(X)/2 XO-EX)/2 POL 04. LES1036 255,000 1-1=0 .: 1.006)2.0036 .0056.25 QUOS SO=Tv=J. Variance 0.0018 Std. Dev. 0.0 424 (round 4) C.V. 42.440 (V-so 0.0424 x 100 = 42.4% XO-EX) (XO-EX2 (XO) - E(X)/2*PD) 16-06.01.1942.0064.64.646.25*40C + SAT, bosu .10.06 0.676.000.0004. X.50-2002+ 23.01990194% 23.0036 05 Variance 0654 Std. Dev. (round 4) C.v. 41.367 Asset B P(0) 0.25 0.50 0.25 State Rec Norm Exp E(X) .0% XO) 0.16 0.10 -0.04 colo 19161 (3) Assume a 50%-50% weighting and compute the expected return of the portfolio. Portfolio PO W(b) PC 0.50 State Rec Norm Exp 0.25 0.50 0.25 wa) 0.50 0.50 0.50 Xa 0.040 0.100 0.160 X(b) 0.1600 0.1000 -0.0400 'Som W(a)X(a)-W(b)X(b) "O .Sxoy+.5X.16.02.080..16.2590 1.5x.lt.5.1 Lost Ost. I ES 1-3.167.5X204.98-2023,2.66.750 E(p) 09 0.50 0.50 (4) Alternative method of computing the E(p). ) Asset A B WO) 0.50 0.50 .08 E() WOED 16.55.05 05.5.04 .09 Risk Retur. Example Caicos (5) Assume a 50%-50% weighting and compute the standard deviation of the portfolio Xp) E) Portfolio PO 0.25 0.50 0.25 State Rec Norm Exp Xp-pXp-p 2 XipE Variance Std. Dev. C.V. (6) An alternative method of computing sigmalp)? Siuma WUE Asset A B WO 0.50 0.50 fround 4) (round 4) E() (7) Explain your observations (8) Caluciate the Covariance between assets A and B. Covariance Product of Deviations PO) Prodact of Deiations X( ao) Xib).E(b) State |Rec Norm Exp PU) 0.25 0.50 0.25 Covariance (8) Caluclate the correlation between assets A and B. Cov sigma(a) sigma(b) rfa,b) (round 4) Dr. Basciano Page 2 FINC 4421 Risk Retur. Example Calculations (9) A formula aproach for solving for the standard deviation of a two asset portfolio Variance{p) - Way2 Var(a) + Wyby 2*Var(b) + 2W(a)W(b)Cov(a,b) Sigma(p) - square root of above Prior Example: 0.50000 Wa) Vara) W(b) Varb) Cov(a,b) 0.50000 Varp) Sigma(p) (10) What would happen with changes in the asset weighting to the risk and return of the portfolio? EB) 0.000 E(b) 0.000 Ep2 Sigma) Wib) ) Sismara Wa) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 W(b) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Wia) 0.70 0.69 0.68 0.67 0.66 0.65 0.64 0.63 0.62 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 (11) A formula approach to solving for the minimum variance portfolio. W(a) [Var(b) - cov(a,b)]/[Var(a) + Var(b) - 2cov(a,b)] Example: Var A Var B Cova.b) Wa) (1) Calculate the expected return for the two assets given below. State Rec Norm Exp Asset A Pi) 0.25 0.50 0.25 7 XO) 0.04 0.10 0.16 Ex) Asset B PO 0.25 0.50 0.25 TO 1.05 State Rec Norm Exp 32 404 40 .10.18 XO) 0.16 0.10 -0.04 E(x) . (2) Calculate the standard deviation and coefficient of variationfor for the two assets given above E(X) Stato Rec Norm Exp Asset A P(1) 0.25 0.50 0.25 XO) 0.04 0.10 0.16 . 10 10 xlor XO-EX) (XO) - E(X)/2 XO-EX)/2 POL 04. LES1036 255,000 1-1=0 .: 1.006)2.0036 .0056.25 QUOS SO=Tv=J. Variance 0.0018 Std. Dev. 0.0 424 (round 4) C.V. 42.440 (V-so 0.0424 x 100 = 42.4% XO-EX) (XO-EX2 (XO) - E(X)/2*PD) 16-06.01.1942.0064.64.646.25*40C + SAT, bosu .10.06 0.676.000.0004. X.50-2002+ 23.01990194% 23.0036 05 Variance 0654 Std. Dev. (round 4) C.v. 41.367 Asset B P(0) 0.25 0.50 0.25 State Rec Norm Exp E(X) .0% XO) 0.16 0.10 -0.04 colo 19161 (3) Assume a 50%-50% weighting and compute the expected return of the portfolio. Portfolio PO W(b) PC 0.50 State Rec Norm Exp 0.25 0.50 0.25 wa) 0.50 0.50 0.50 Xa 0.040 0.100 0.160 X(b) 0.1600 0.1000 -0.0400 'Som W(a)X(a)-W(b)X(b) "O .Sxoy+.5X.16.02.080..16.2590 1.5x.lt.5.1 Lost Ost. I ES 1-3.167.5X204.98-2023,2.66.750 E(p) 09 0.50 0.50 (4) Alternative method of computing the E(p). ) Asset A B WO) 0.50 0.50 .08 E() WOED 16.55.05 05.5.04 .09 Risk Retur. Example Caicos (5) Assume a 50%-50% weighting and compute the standard deviation of the portfolio Xp) E) Portfolio PO 0.25 0.50 0.25 State Rec Norm Exp Xp-pXp-p 2 XipE Variance Std. Dev. C.V. (6) An alternative method of computing sigmalp)? Siuma WUE Asset A B WO 0.50 0.50 fround 4) (round 4) E() (7) Explain your observations (8) Caluciate the Covariance between assets A and B. Covariance Product of Deviations PO) Prodact of Deiations X( ao) Xib).E(b) State |Rec Norm Exp PU) 0.25 0.50 0.25 Covariance (8) Caluclate the correlation between assets A and B. Cov sigma(a) sigma(b) rfa,b) (round 4) Dr. Basciano Page 2 FINC 4421 Risk Retur. Example Calculations (9) A formula aproach for solving for the standard deviation of a two asset portfolio Variance{p) - Way2 Var(a) + Wyby 2*Var(b) + 2W(a)W(b)Cov(a,b) Sigma(p) - square root of above Prior Example: 0.50000 Wa) Vara) W(b) Varb) Cov(a,b) 0.50000 Varp) Sigma(p) (10) What would happen with changes in the asset weighting to the risk and return of the portfolio? EB) 0.000 E(b) 0.000 Ep2 Sigma) Wib) ) Sismara Wa) 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 W(b) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Wia) 0.70 0.69 0.68 0.67 0.66 0.65 0.64 0.63 0.62 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 (11) A formula approach to solving for the minimum variance portfolio. W(a) [Var(b) - cov(a,b)]/[Var(a) + Var(b) - 2cov(a,b)] Example: Var A Var B Cova.b) Wa)