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Consider the following information on a portfolio of three stocks: state of economy probability of state of economy stock a rate of return stock b rate of return stock c rate of return boom .12 .07 .32 .45 normal .55 .15 .27 .25 bust .33 .16 -.26 -.35 if your portfolio is invested 40 percent each in a and b and 20 percent in c, what is the portfolio's expected return, the variance, and the standard deviation?

User Ironsun
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Final answer:

The expected return of a portfolio is calculated by weighing each investment's returns by the portfolio weight and the probability of different economic states. The variance and standard deviation measure investment risk, with higher values indicating greater risk. In the given portfolio, investment C has the highest expected return but also the highest risk.

Step-by-step explanation:

Expected Portfolio Return Calculation

To calculate the expected return of the portfolio, we need to multiply the rate of return of each investment by the probability of that state of the economy occurring and then by the proportion of the portfolio in that investment. Finally, we sum these values for all states of the economy and all investments in the portfolio.

The expected return for stock A, invested at 40%, is (0.12*0.07 + 0.55*0.15 + 0.33*0.16)*0.4. For stock B, also at 40%, it is (0.12*0.32 + 0.55*0.27 + 0.33*-0.26)*0.4. Stock C, at 20%, has an expected return calculated as (0.12*0.45 + 0.55*0.25 + 0.33*-0.35)*0.2. Add all these up to get the total expected portfolio return.

To find the variance, we calculate the squared differences from the expected return for each state of the economy, weigh them by the probability of each state, and sum these values for all investments based on their portfolio weights. The standard deviation is the square root of the variance, giving a measure of the risk associated with the portfolio's return.

Based on the given rates of return, investment C has the highest expected return but also the highest risk. Therefore, stock C is the riskiest, while stock A and stock B seem to be safer but with lower expected returns.

User Oliver Bestwalter
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