Question

Risky Asset A and Risky Asset B are combined so that the new portfolio consists of 70% Risky Asset A and 30% Risky Asset B. If the expected return and standard deviation of Asset A are 0.08 and 0.16, respectively, and the expected return and standard deviation of Asset B are 0.10 and 0.20, respectively, and the correlation coefficient between the two is 0.25: (13 pts.)

a) What is the expected return of the new portfolio consisting of Assets A & B in these proportions?

b) What is the standard deviation of this portfolio?

c) Assuming a riskless rate of 0.06, what are the proportions of these two securities in their optimal combination of risky assets? What is the expected return of this portfolio combination?

d) Assuming this optimal combination of risky assets is then combined with the riskless asset which has a return of 0.06, what standard deviation would you have to tolerate if you wanted to earn a rate of return of 0.09 from this new portfolio?

e) Again assuming this optimal combination of risky assets is combined with the riskless asset, suppose you have $100,000 to invest and you choose a preferred portfolio consisting of 60% risky assets and 40% riskless assets. Under these parameters, how much of your $100,000 would you need to invest each in Asset A, Asset B, and the riskless asset?

Answer 1

1) When Risk assests A& B are combined to form a portfolio the weights given:

WA=0.70;WB=0.30

E(RA)=0.08,SDA=0.16;E(RB)=0.10,SDB=0.20

(A,B)=0.25

1) E(RP)=E(RA)xWA+E(RB)xWB

E(RP)=0.08x0.70+0.10x0.30=8.60%

2) The optimal portfolio consists of a risk-free asset and an optimal risky asset portfolio. The optimal risky asset portfolio is at the point where the CAL is tangent to the efficient frontier. This portfolio is optimal because the slope of CAL is the highest, which means we achieve the highest returns per additional unit of risk.

WTPA=1-WTPB

WTPB=(E(RB)-Rf)X2A-(E(RA)-Rf)xABAB/((E(RB)-Rf)X2A+(E(RA)-Rf)X2B-(E(RB)-Rf+E(RA)-Rf)ABAB

WTPB=(0.10-0.06)x0.16^2-(0.08-0.06)x0.25x0.16x0.20/(0.1-0.06)x0.16^2+(0.08-0.06)x0.20^2-(0.10-0.06+0.08-0.06)x0.25x0.16x0.20

WTPB=0.642857

WTPA=1-0.642857

WTPA=0.357143

E(Rp)=0.357143x0.08+0.642857x0.1

E(Rp)=9.29%

Expected return of optimal risky portfolio is 8.71%

3) if riskless asset is combined with risky optimal portfolio with expected return of 0.09

then

0.09=0.0929xWR+WRfx0.06

We know

WR=1-WRf

Putting it in above equation:

0.09=0.0929xWR+(1-WR)x.06

WR(0.0871-0.06)=(0.09-0.06)

WR=0.911854

WRf=1-0.911854=0.088146

Standard Deviation=(WR^2xR^2+WRfx0+2xRRfx0xR)^.5

Sd=WRxR

R=(0.642857^2x0.08^2+0.357143^2x0.1^2+2x0.25x0.08x0.1)^0.5

R=0.088997

Putting in earlier equation:

Sd=WRxR

Sd=0.911854x0.088997

Sd=0.081152

d) Under the circumstances where 60% is allocated to A+b, 40% to riskless asset supposeC

then in C I'll invest=0.40*100,000=$40,000

Now again A+B=60,000

Ratio:

A=0.642857

B=0.357143

A=0.642857*60,000=$38,571.42

B=0.357143x60,000=$21,428.58