Asked by Louie Allard on Jun 20, 2024
Verified
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.
Two-Asset Portfolio
A financial portfolio consisting of two different assets, aiming to diversify investment risks and returns.
Standard Deviation
A measure of the dispersion or spread of a set of numbers, indicating how much variation exists from the average.
Risky Asset
An investment that holds a degree of uncertainty regarding its returns or principal amount.
- Understand the utility of standard deviation in analyzing risk within portfolios that integrate assets with both negligible and substantial risk factors.
Verified Answer
JB
Jasmine BhangooJun 20, 2024
Final Answer :
C
Explanation :
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.
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.
Learning Objectives
- Understand the utility of standard deviation in analyzing risk within portfolios that integrate assets with both negligible and substantial risk factors.
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