"investment portfolio" exercise : standard deviation

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Questions 1:

Based on the following historical data, which is closest to the standard deviation for the two-asset portfolio shown in the table?

	Asset A	Asset B	Asset C
Standard deviation	4.7%	7.7%
Portfolio weight	0.4	0.6
Correlation			0.3

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A. 6.5%

B. 5.5%

C. 5.0%

Questions 2:

When considering a portfolio that is optimal for one investor, a second investor with a higher risk aversion would most likely:

A. expect a higher variance for the portfolio.

B. derive a lower utility from the portfolio.

C. have a lower return expectation for the portfolio.

View answer resolution

【Answer to question 1】（B）

【analysis】

The standard deviation of a two asset portfolio is calculated as follows:

The formula is shown in the following figure:

lALPD4d8qVBVjrVgzQHY_472_96

【Answer to question 2】（B）

【analysis】

Utility has two terms: the expected return and a negative term based on the portfolio risk weighted by risk aversion. For an identical portfolio, the investor with a higher risk aversion (A) would calculate a lower utility (U).

U=E(r)-½Aσ

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