Download FM212 MT2014 Problem Set Solutions: Portfolio Risk and Return Calculations and more Exercises Accounting in PDF only on Docsity! FM212 MT2014 Problem Set Solutions Class 5 13. a. Variance measures the total risk of a security and is a measure of stand-alone risk. Total risk has both unique risk and market risk. In a well-diversified portfolio, unique risks tend to cancel each other out and only the market risk is remaining. Beta is a measure of market risk and is useful in the context of a well-diversified portfolio. Beta measures the sensitivity of the security returns to changes in market returns. Market portfolio has a beta of one and is considered the average risk. b. If we hold long positions in both stocks: the correlation coefficient that gives the maximum reduction in risk for a two-stock portfolio is -1. If one stock is sold short and another stock is a long position in the portfolio then a correlation of +1 is actually best to minimize portfolio risk. c. Mean A = 8%, Mean M=16%, Cov(Ra, Rm)=0.0138, Var(Rm)=0.0084, Beta=0.0138/0.0084=1.643. d. Cov(Rb,Rm)= (0.8)(0.20)(0.35) = 0.056, Beta = 0.056/0.04 = 1.4. 14. Expected portfolio return = xA E[RA ] + xB E[R B ] = 12% = 0.12 Let xB = (1 – xA ) xA (0.10) + (1 – xA) (0.15) = 0.12 ⇒ xA = 0.60 and xB = 1 – xA = 0.40 Portfolio variance = xA 2 σA 2 + xB 2 σB 2 +2 (xA xB ρAB σA σB) = (0.60 2 ) (0.20 2 ) + (0.40 2 ) (0.40 2 ) + 2(0.60)(0.40)(0.50)(0.20)(0.40) = 0.0592 Standard deviation = 24.33%0.0592σ == 15. a. In general: Portfolio variance = σP2 = x12σ12 + x22σ22 + 2x1x2ρ12σ1σ2 Thus: σP2 = (0.52)(0.29322)+(0.52)(0.29272)+2(0.5)(0.5)(0.59)(0.2932)(0.2927) σP2 = 0.0682 Standard deviation = σP = 26.12% b. One of these securities, T-bills, has zero risk and, hence, zero standard deviation. Thus: σP2 = (1/3)2(0.29322) +(1/3)2(0.29272)+2(1/3)(1/3)(0.59)(0.2932)(0.2927) σP2 = 0.0303 Standard deviation = σP = 17.41% Another way to think of this portfolio is that it is comprised of one-third T-Bills and two- thirds a portfolio which is half Dell and half Home Depot. Because the risk of T-bills is zero, the portfolio standard deviation is two-thirds of the standard deviation computed in Part (a) above: Standard deviation = (2/3)(26.12%) = 17.41%
