Question

The risk-free rate is 2%. Portfolio A has an expected return of 10% and a standard deviation of 18%. You currently have XA = 48% of your wealth invested in Portfolio A and the rest invested in the risk-free asset. You have decided to use Portfolio B (which has an expected return of 12% and a standard deviation of 21%). instead of Portfolio A but wish to have the same overall expected return as before. You will thus now allocate XB% of your total wealth to Portfolio B (note XB may differ from XA) and the rest to the risk-free asset. What is the overall standard deviation you will face in your complete portfolio (considering you will invest in both Portfolio B and the risk-free)? Enter the standard deviation in decimal form and rounded accurately to four decimal places (e.g., 20.456% should be entered as 0.2046 and not any other way).

Answer 1

Portfolio return is equal to weighted average return

Current Portfolio return = 10*48% + 2*52% = 5.84%

Let weight of portfolio B be x

5.84% = 12%*x + 2%*(1-x)

5.84% = 12%x + 2% - 2%x

x = 0.384

i.e. 38.40%

Portfolio standard deviation with one risky asset and one risk free asset = Weight of risky asset*Standard deviation of risky asset as standard deviation of risk free asset is equal to 0.

Hence, overall standard deviation = 21%*0.3840 = 8.064%

i.e. 0.08064

i.e. 0.0806