What is the Sharpe measure of your resulting complete portfolio in problem 1? En

Question

What is the Sharpe measure of your resulting complete portfolio in problem 1? Enter your answer rounded to two decimal places.

Problem #1: You invest $100,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 13.75% and a standard deviation of 40% and a treasury bill with a rate of return of 3.50%. How much money should be invested in the risky asset to form a portfolio with an expected return of 9%? Be sure to convert your percentage weight in the risky asset to dollars. Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box.

Explanation / Answer

Let Weight of Risky asset be W. If total weight is 1, then weight of Tbill is (1 - W).

Expected return of portfolio = Expected returnRisky x WeightRisky + Expected returnTbill x WeightTbill

or, 9% = 13.75% x W + 3.50% x (1 - W)

or, 9% = 13.75%W + 3.50% - 3.50%W

or, 10.25%W = 5.50%

or, W = 0.53658536585

Amount to be invested in Risky asset = Total investment x WeightRisky = $100,000 x 0.53658536585 = $53,658.54

Sharpe Measure = (ERP - Rf) / SDP

where, ERP = Expected return of portfolio = 9%, Rf = Risk free rate or T-bill rate = 3.50%, SDP = Standard deviation of portfolio

Since this portfolio has one risk free asset, which has zero standard deviation, the standard deviation of portfolio would be -

SDP = Standard Deviation of Risky asset x Weight of Risky asset = 40% x 0.53658536585 = 21.463414634%

Sharpe measure = (9% - 3.50%) / 21.463414634% = 0.25625 or 0.26

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