s. You are trying to develop a strategy for investing in two different stocks. T

Question

s. You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1000 investment n each stock under four different economic conditians hasthe probability distribution shown to the right Probab ty Econom KCondit on Return on stockx Return on Stock Y Recession 100 03 Slow Growth 150 0.3 Moderate Growth 80 -20 0.3 Fast Growth 150 -100 2. Compute the expected return for stock x and for Stock Y, and compute the standard deviatian for Stock X and for Stock Y. b. Would you invest in stock x or Stock Y? Explain c. Covariance of stock Xand stock Y d. Suppose you wanted to create a portfolio that consists of stock X and stock Y. Suppose 30% of the portfolio is in stock X. Compute the portfolio expected return and portfolio riskl Standard Deviation)

Explanation / Answer

(a)

Expected return for stock X:
E(X)=0.1*(-100)+0.3*(0)+0.3*(80)+3*(150)
             =59
Expected return for stock Y:
E(Y)=0.1*(50)+0.3*(150)+0.3*(-20)+0.3*(-100)
             =14
Standard deviation for stock X:
   Var(X)=E(X2)-E(X)2
   E(X2)=0.1*(-100)2+0.3*(0)2+0.3*(80)2+3*(150)2
                =9670
     E(X)2=(59)2
                  =3481
     Var(X)=9670-3481
                   =6189
       Standard deviation of x=78.670
Standard deviation for stock Y:
   Var(Y)=E(Y2)-E(Y)2
   E(Y2)=0.1*(50)2+0.3*(150)2+0.3*(-20)2+0.3*(-100)2
                =10120
     E(Y)2=(14)2
                  =196
     Var(Y)=10120-196
                   =9924
       Standard deviation of Y=99.6127

(b) stock X gives the investor a lower standard deviation while yielding a higher expected return so the investor should select stock X

(c) Cov(X,Y)=E(XY)-E(X)E(Y)
          E(XY)=0.1*(-100)(50)+0.3*(0)(150)+0.3*(80)(-20)+0.3*(150)(-100)
                       =-5480
            Cov(X,Y)=-5480-59*14
                               =-6306

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