You currently have $100,000 invested in a portfolio that has an expected return

Question

You currently have $100,000 invested in a portfolio that has an expected return of 10% and a volatility of 10%. Suppose the risk-free rate is 5%, and there is another portfolio has an expected return of 24% and a volatility of 13%.

a. What portfolio has a higherhigher expected return than your portfolio but with the same volatility?
The portfolio should be composed of $_____ in the other portfolio, and $_____ in the risk-free investment (round to the nearest dollar). What is your expected return? _____%

b. What portfolio has a lowerlower volatility than your portfolio but with the same expected return?
You should invest $_____ in the other portfolio and $_____ in the risk-free investment, lowering your volitility to _____%.

You currently have $100,000 invested in a portfolio that has an expected return of 10% and a volatility of 10%. Suppose the risk-free rate is 5%, and there is another portfolio has an expected return of 24% and a volatility of 13%.

a. What portfolio has a higherhigher expected return than your portfolio but with the same volatility?
The portfolio should be composed of $_____ in the other portfolio, and $_____ in the risk-free investment (round to the nearest dollar). What is your expected return? _____%

b. What portfolio has a lowerlower volatility than your portfolio but with the same expected return?
You should invest $_____ in the other portfolio and $_____ in the risk-free investment, lowering your volitility to _____%.

Explanation / Answer

a) Here the investment amount = $100,000

E(Rp) = rf + x(E(R2) - rf) = 5 + x(24- 5)

ratio of standard deviation is taken as

S.D(portfolio 1) = x(S.D(portfolio 2)) ( ratio of the standard deviation can give the weights of the assets)

in order to maintain 10 % volatility for portfolio 1

10 = x(13)

x = 10/13

So we should invest $ 76,923.076 in the second portfolio

and the remaining 23,076.92 in the risk free asset

substitute x in this formula

E(Rp2) = rf + x(E(R2) - rf) = 5 + x(24- 5)

and the expected return from the formula 19.615 %

b) E(Rp1) = rf + x(E(R2) - rf)

10 = 5+ x(24-5)

here x = 26.315 %

Now we should invest $ 26,315 in the first portfolio

and $ 73,685 in the risk free asset

the volatility lowered to (use the formula x = SD1/SD2)

0.26315 = SD1/ 0.13;

SD1 = 0.0342 = 3.42%

The volatility lowered to 3.42 %

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