Derive the standard deviation of the returns on a portfolio that is invested in stocks x, y, and z , where twenty percent of the portfolio is invested in stock x and 35 percent is invested in Stock z. State of Economy Probability of State of Economy Rate of Return if State Occurs Stock x Stock y Stock z Boom .04 .17 .09 .09 Normal .81 .08 .06 .08 Recession .15 − .24 .02 − .13 1. 7.72 percent 2. 6.31 percent 3. 7.38 percent 4. 6.49 percent 5. 5.65 percent

Explanation:

So, the variance and standard deviation of each stock is:

sA2 =.20(.01 – .0865)2 + .55(.09 – .0865)2 + .25(.14 – .0865)2

sA2 = .00189

sA = (.00189)1/2

sA = .0435 or 4.35%

sB2 =.20(–.25 – .1275)2 + .55(.15 – .1275)2 + .25(.38 – .1275)2

sB2 = .04472

sB = (.04472)1/2

sB = .2115 or 21.15%

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