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

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Business

Rodrigo Bond

3 October, 00:26

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

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Sofia Ruiz · Answer 1

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%