Question

As the portfolio manager of a mutual fund, invested 70% in Stock X and 30% in Stock Y, what are the expected returns and standard deviations of the stocks? Options:

a) High return, low deviation
b) Low return, high deviation
c) High return, high deviation
d) Low return, low deviation

Answer 1

The expected returns and standard deviations of the stocks are b) Low return, high deviation.

Step-by-step explanation:

The expected return of a portfolio can be calculated using the weighted average of the expected returns of the individual stocks. Given that 70% of the portfolio is invested in Stock X and 30% in Stock Y, and assuming the expected returns for Stock X and Stock Y are represented by E(Rx) and E(Ry) respectively, the expected return of the portfolio (E(Rp)) can be calculated as follows:

E(Rp) = (0.70 E(Rx)) + (0.30 E(Ry))

Similarly, the standard deviation of a portfolio can be calculated using the weighted average of the standard deviations of the individual stocks. Assuming the standard deviations for Stock X and Stock Y are represented by σx and σy respectively, the standard deviation of the portfolio (σp) can be calculated as follows:

σp = √((0.70^2 σx^2) + (0.30^2 σy^2) + (2 0.70 0.30 ρxy σx * σy))

Where ρxy represents the correlation coefficient between Stock X and Stock Y.

Given that the portfolio is invested predominantly in Stock X with a higher expected return but also higher risk (standard deviation), it aligns with option b) - low return, high deviation.

In this case, although Stock X may offer higher potential returns, its higher standard deviation indicates greater volatility and risk, resulting in a lower overall expected return for the portfolio.

Correct option is b) Low return, high deviation.