You invest 70% of your money on a stock with expected return of 15% and standard deviation of 22%. The rest of your money is invested in T-bills with expected return of 7%. The expected return and standard deviation of your complete portfolio are a. 12.6% and 15.4%. b. 15% and 22%. c. 7% and 0%. d. 11% and 11%. e. None of the above option is correct.

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5 May, 12:15

You invest 70% of your money on a stock with expected return of 15% and standard deviation of 22%. The rest of your money is invested in T-bills with expected return of 7%. The expected return and standard deviation of your complete portfolio are a. 12.6% and 15.4%. b. 15% and 22%. c. 7% and 0%. d. 11% and 11%. e. None of the above option is correct.

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Mr Kitty · Answer 1

The portfolio return is 12.6% and the portfolio SD is 15.4%. Thus, option a is the correct answer.

Explanation:

The expected return of a portfolio is the weighted average of the individual stock returns that form up the portfolio. Thus, the expected return for a two stock portfolio is,

Return of Portfolio = wA * rA + wB * rB

Where,

w represents the weight of each stock in the portfolio r represents the return of each stock

Portfolio return = 0.7 * 0.15 + 0.3 * 0.07 = 0.126 or 12.6%

The standard deviation of a two stock portfolio containing one risky and one risk free asset is the weight of risky asset in the portfolio multiplied by the standard deviation of the risky asset. The risk free asset has zero standard deviation.

Standard deviation of such a portfolio is,

Portfolio SD = w of risky asset * SD of risky asset

Portfolio SD = 0.7 * 0.22

Portfolio SD = 0.154 or 15.4%