Stock A has a beta of 1.20 and is farily priced. The riskless rate of return (US Treasury Bills) is 3.2%. The market risk premium is 5.4%. Construct a $100,000 portfolio of stock A and Treasury Bills that will have an expected return of 5.144%. (Rounded to the nearest dollar.)
first let us know the expected return on stock A = risk free rate+ beta *(risk premium)
=>3.2% + 1.20*(5.4%)
=>9.68%.
let the percentage of amount invested in stock A be x..
the percentage involved in treasury bill be (1-x).
weighted average expected return:
=> (x*0.0968) + (1-x)*0.032 =>0.05144.
=>0.0968x +0.032 -0.032x = 0.05144
=>0.0648x=0.01944
=>x = 0.01944/0.0648
=>x=0.30.
percentage of amount invested in stock A = x =0.30
amount to be invested = 100,000*0.30=>$30,000.
amount to be invested in tresury bill =>100,000-30,000=>$70,000.
the portfolio will be like below:
Treasury bill (70%) | 70,000 |
stock A (30%) | 30,000 |
total | 100,000 |
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