Question

1. Consider a two-stock portfolio.  Which one of the following statements about the expected return and risk is correct of the portfolio is correct?

A). The expected return of the portfolio is less than the weighted average of the returns of the two stocks as long as the correlation between the returns of the two stocks is less than 1, but the standard deviation of the portfolio return equals the weighted average of the standard deviations of the returns of the two stocks

B). The expected return of the portfolio equals the weighted average of the expected returns of the two stocks, but the standard deviation of the portfolio return is less than the weighted average of the standard deviations of the two stock returns as long as the correlation between the returns of the two stocks is less than 1

C). The standard deviation of the portfolio return is greater than the weighted average of the standard deviations of the returns of the two stocks if the correlation between the two stock returns is positive and lower if the correlation is negative

D). The expected return of the portfolio equals the sum of the expected returns of the two stocks and the standard deviation of the portfolio return equals the sum of the standard deviation of the returns of the two stocks

2. An individual can choose between two investments, each of which require a $10,000 investment.   Project A will pay off $8,000 with probability 0.10, $11,000 with probability 0.80, and $13,000 with probability 0.10.  Project B will pay $7,250 with probability 0.20, $11,000 with probability 0.60, and $$14,250 2ith probability 0.20.  Which investment would a risk-averse investor choose and what is the rationale for the choice?

A). Project B because the two projects have the same expected return but Project B provides the largest chance to get the highest return

B). The investor is indifferent since both investments provide the same expected return

C). Project B because the two projects have the same expected return but Project B has the highest standard deviation

D). Project A because the two projects have the same expected return but Project A has the lowest standard deviation

Answer 1

1)

B). The expected return of the portfolio equals the weighted average of the expected returns of the two stocks, but the standard deviation of the portfolio return is less than the weighted average of the standard deviations of the two stock returns as long as the correlation between the returns of the two stocks is less than 1

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

where x and y are the securities

Here, the expected return is a simple weighted average

The standard deviation is the portfolio would be lesser than the weighted average becuase the correlation of stocks returns is less than 1. This is due to diversification benefits.

2) D). Project A because the two projects have the same expected return but Project A has the lowest standard deviation

Expected return = Summation of [Probability*Expected return of the scenario]

Standard deviation = Square root of {Summation of [Probability*(Expected return of the scenario-Expected return)^2]}

A risk-averse investor chooses the portfolio with lower risk (standard deviation) for the same level of expected return. Here, the expected return of both the portfolios are same, however, the risk of portfolio A is lower than that of Portfolio B.