Question

Part A: Assume the risk–free rate is 3.50%. Using the stock and bond portfolios from problem...

Part A: Assume the risk–free rate is 3.50%. Using the stock and bond portfolios from problem 1, what is the bond weight in the tangency portfolio formed by creating the optimal risky portfolio from this stock and bond portfolio?  Enter your answer rounded to two decimal places

STOCK AND BOND INFO:

You put 70% of your money in a stock portfolio that has an expected return of 14.95% and a standard deviation of 44%. You put the rest of you money in a risky bond portfolio that has an expected return of 4.95% and a standard deviation of 18%. The stock and bond portfolio have a correlation 0.32.

Part B: Using the information from problem 4, what is the Sharpe ratio of the tangency portfolio formed by creating the optimal risky portfolio from this stock and bond portfolio? Enter your answer rounded to two decimal places.

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Homework Answers

Answer #1

Answer) Tengency portfolio weight of asset can be derived by use of following formula

Covariance ( )= . = 0.44 *0.18* 0.32 =0.02534

other values are given in question.

WA = [(0.1495 -0.035)*(0.18^2 ) - ( 0.0495 - 0.035) *0.02534] / [(0.1495 -0.035)*(0.18^2 ) + ( 0.0495 - 0.035) * (0.44^2) -( (0.1495 -0.035) +( 0.0495 - 0.035) ) * 0.02534 ]

WA = 1.029

WB = 1- 1.029 = -0.029.

Answer)

E(r) = WA * rA + WB * rB , where , WA , WB & rA, rB are weight and return from stock and bond respectively

= 0.70* 14.95% + 0.30 * 4.95% = 11.95%.

Answer) Sharpe Ratio = Rp - Rf /

Rp = 1.029 * 14.95% - 0.029* 4.95% =15.24%

= 1.029^2 * 0.44^2 + 0.029^2 * 0.18^2 - 2* 1.029 * 0.029 * 0.02534 =0.2035 =20.35%

Sharpe ratio = (15.24 - 3.50) / 20.35 =0.5769

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