11.9 Returns and Standard Deviations Consider the following information: State of Economy Probability of SE Rate of Return if State Occurs. Stock A Stock B Stock C Boom .20 .24 .45 .33 Good .35 .09 .10 .15 Poor .40 .03 -.10 -.05 Bust .05 -.05 -.25 -.09 Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? What is the variance of this portfolio? The standard deviation?
11.9 Returns and Standard Deviations Consider the following information:
State of Economy Probability of SE
Stock A Stock B Stock C
Boom .20 .24 .45 .33
Good .35 .09 .10 .15
Poor .40 .03 -.10 -.05
Bust .05 -.05 -.25 -.09
- Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio?
- What is the variance of this portfolio? The standard deviation?
30 % is invested in stock A
40 % is invested in stock B
30 % is invested in stock C
expected return for portfolio will be
=[probability A * rate of return A] + [probability B * rate of return B] + [probability C * rate of return C]
expected return for boom = [0.30 * 0.24] +[0.4 *0.45] +[0.30 *0.33]
= 0.072 +0.18 +0.099
= 0.351
expected return for good = [0.30 * 0.09] +[0.4 *0.10] +[0.30 *0.15]
= 0.027 +0.04+0.045
= 0.112
expected return for poor = [0.30 * 0.03] +[0.4 *(-0.10)] +[0.30 *(-0.05)]
= 0.009 -0.04-0.015
= -0.025
expected return for bust = [0.30 * (-0.05)] +[0.4 *(-0.25)] +[0.30 *(-0.09)]
=- 0.015-0.10-0.027
= - 0.142
expected return of the portfolio = [0.20 *0.351] +[0.35*0.112] + [0.40*-0.025] +[0.05*- 0.142]
= 0.0702+0.0392-0.01-0.0071
= 0.0923
expected return of the portfolio = 9.23%
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