2. You want to create a portfolio equally risky as the market, and you have $1,0

ID: 1170473 • Letter: 2

Question

2. You want to create a portfolio equally risky as the market, and you have $1,000,000 to invest. Stock A has an expected return 10%. Stock B has an expected return 12%. Other information is as follows: investment $150,000 $300,000 Beta 0.80 1.20 1.50 Asset Stock A Stock B Stock C Risk-free asset Required: (10Marks/2'Each) (1) What is the beta of risk-free asset? (2) What is the investment of Stock C? (3) What is the investment of risk-free asset? (4) What is the risk-free rate? (5) What is the expected return on the market?

Explanation / Answer

Assume Risk Free Rate=Rf

Market Return=Rm

Expected Return of Stock A=Ra=Rf+Beta(a)*(Rm-Rf)

Ra=10

Beta(a)=0.8

10=Rf+0.8*(Rm-Rf)………..(Equation 1)

Expected Return of Stock B=Rb=Rf+Beta(b)*(Rm-Rf)

Rb=12

Beta(b)=1.2

12=Rf+1.2*(Rm-Rf)………..(Equation 2)

Subtracting Equation (1) from Equation (2):

2=0.4*(Rm-Rf)

(Rm-Rf)=2/0.4=5

10=Rf+0.8*(Rm-Rf)………..(Equation 1)

10=Rf+0.8*5

Rf=10-(0.8*5)=6

Rf=6

Rm-Rf=5

Rm=Rf+5=6+5=11

.(1) Beta of Risk Free Asset=0

Expected return from risk free asset=Rf+Beta*(Rm-Rf)=Rf+0*(Rm-Rf)=Rf

.(4) Risk Free rate=Rf=6%

.(5) Expected return from the market=Rm=11%

Portfolio Beta=Market beta=1

Wa=Weight of Stock A in portfolio=150000/1000000=0.15

Wb=Weight of stock B in portfolio=300000/1000000=0.30

Assume weight of Stock C in portfolio=Wc

Weight of Risk free asset in portfolio=Wf

Portfolio Beta=0.15*0.8+0.3*1.2+Wc*1.5+Wf*0=0.12+0.36+Wc*1,5

Portfolio Beta=1

0.12+0.36+Wc*1.5=1

Wc*1.5=1-0.12-0.36=0.52

Wc=0.52/1.5=0.43333

Wa+Wb+Wc+Wf=1

Wf=1-0.15-0.30-0.43333=0.11667

(2)Investment of Stock C=1000000*Wc=1000000*0.43333= $ 433,333

(3)Investment in risk free asset=1000000*0.11667= $ 116,667

Asset

Investment

Beta

Stock A

$150,000

0.8

StockB

$300,000

1.2

Stock C

$ 433,333

1.5

Risk free asset

$ 116,667

TOTAL

$1,000,000