The standard deviation of a two-asset portfolio (with a risky and a non-risky asset) is equal to:
A) the fraction invested in the risky asset times the standard deviation of the non-risky asset.
B) the fraction invested in the non-risky asset times the standard deviation of the risky asset.
C) the fraction invested in the risky asset times the standard deviation of that asset.
D) the fraction invested in the non-risky asset times the standard deviation of that asset.

Question

Quizplus · Accepted Answer

The standard deviation of a two-asset portfolio is not simply the weighted average of the standard deviations of the individual assets. Rather, it is a function of the correlation between the two assets. The formula for the standard deviation of a two-asset portfolio is:

Standard deviation of portfolio = [(% invested in risky asset) x (standard deviation of risky asset)] + [(% invested in non-risky asset) x (standard deviation of non-risky asset)] + 2 x (% invested in risky asset) x (% invested in non-risky asset) x (correlation coefficient between the two assets) x (standard deviation of risky asset) x (standard deviation of non-risky asset)

If the non-risky asset has a standard deviation of zero, then the formula simplifies to:

Standard deviation of portfolio = (% invested in risky asset) x (standard deviation of risky asset)

Therefore, choice C is the best answer: the standard deviation of a two-asset portfolio is equal to the fraction invested in the risky asset times the standard deviation of that asset.

The Standard Deviation of a Two-Asset Portfolio (With a Risky