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Problem 6.An investor is considering investing $100,000 in three mutual funds. The firstis a stock fund, the second is a long-term government and corporate bond fund, and the thirdis a T-bill money ma
Problem 6.
An investor is considering investing $100,000 in three mutual funds. The firstis a stock fund, the second is a long-term government and corporate bond fund, and the thirdis a T-bill money market fund that yields a risk-free rate of 5 percent. Returns on the stockfund and the bond fund have a correlation coefficient of 0.1 and the following characteristics:
Expected Return Standard deviation
Stock fund: 17 % 20%
Bond fund : 9% 12%
A: When picking the optimal risky-portfolio, how much will the investor invest in each ofthe risky mutual funds?
B: What is the expected value, standard deviation and the Sharpe ratio of the optimalrisky portfolio?
C: If the investor has a standard utility function over returns and has a risk aversioncoefficient of 3, how much will the investor invest in the risk-free mutual fund?
D: What is the expected value, standard deviation and the Sharpe ratio of the optimalportfolio?
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** ******** is *********** ********* ******* ** three ****** ***** The first is * ***** **** *** ****** is * ********* ********** *** ********* **** **** *** *** third is a ****** money ****** fund **** yields * risk-free rate of * *** cent ******* ** *** ***** fund *** *** **** **** have * correlation coefficient ** ** *** *** ********* *********************************** ************** DeviationStock ************** ************** *** ********* exercises ** *** order *** think *********** but please **** sure *** answer *** ** ********* picking *** ******* *************** how **** **** *** ******** invest in each of *** ***** mutual *********** ** *** ******** ***** ******** ********* *** *** ****** ***** of *** ******* ***** ************* *** ******** *** * ******** utility function **** ******* *** *** * **** aversion coefficient ** * how **** **** *** ******** ****** ** *** risk-free ****** fund?DWhat ** *** ******** ***** ******** ********* and *** ****** ***** ** *** ******* ************************ S ** *** ***** fund **** ** the **** fundA First ** calculate *** ********** ******* ***** **** *** bond **** *** ** ***** ** ** = ************ ** S) * ************* ** S) = *** or ******** proportion of ***** **** ** the ******* ***** ********* ** ** ***** by:-wS * *** **** *** ******** *** ** **** – *** Cov ** ***** ** **** *** ******** * ** **** *** ******** *** ** **** – rf * * **** – *** *** ** ***** = [(17 *** ******** *** ** – ** ********** – ******** * ** *** ** (20)^2 *** (9 – 5 + ** *** ** ******* * ***** *** ********* * **** *** ****** * 1632/2544ws = 064The proportion of **** **** ** the optimal ***** ********* ** ** ***** ****** = 1 – **** = * – ***** * ********** the ******** should invest *** ** the ***** **** *** 36% ** the **** fundB *** ******** ***** ** the ******* ***** portfolio E **** ** ***** by:-E (Rp) * **** **** * **** (rB)E (Rp) * 064*17 + ****** (Rp) * ********** standard ********* ** the optimal risky ********* *** ** ***** ******* * ************* + ********** + ******************** * √(064)^2*20^2 + ************ * 2*064*036*01*20*12σp * √16384 * ****** + ********* * ************ * ********** Sharpe ***** ** *** ******* risky *************** ratio * *** **** *** **** σpSharpe ***** = ***** – 5]/1391Sharpe ratio = *********** *** ******** ***** ** ***** ******** ********* ** ***** *** ****** ***** ** *** ******* risky ********* ** ******* Let * ** *** ********** ** risky ******** * ** (rp) *** **** ************** = ***** – *** ***************** = ********** = ********* *** ********** in risk-free ***** * 1 – y1- * * * *** ******* * ********** the investor ****** ****** -0571 in *** ********* asset D The Expected ***** of *** optimal ********* E **** ** ***** ***** **** * *** (y) * (1-y)*E (y)E **** = ********* * ********** **** * ********** ******** ********* ** the ******* portfolio *** ** ***** ******* * √y^2*σy^2 * ***************** + ************************** = ******************** * ************* * 2*1571*(-0571)*1391*0σp = ********** * * **** * ************* = 2185% The Sharpe ***** ** *** ******* *************** ***** = *** (Rp) *** **** σpSharpe ***** * [1933 *** ************* ***** = 0656 Hence the ******** value ** ****** standard ********* ** ***** *** ****** ***** ** *** optimal portfolio ** **********
