Problem 1
Annual Expected Return = R_{f} + Risk Premium_{A1}*β_{A1 + }Risk Premium_{A2}*β_{A2}
Or 0.19 = 0.06 + Risk Premium_{A1}*1 _{+ }Risk Premium_{A2}*2
Or Risk Premium_{A1}*1 _{+ }Risk Premium_{A2}*2 = 0.13 (i)
Portfolio B:
Annual Expected Return = R_{f} + Risk Premium_{A1}*β_{A1 + }Risk Premium_{A2}*β_{A2}
Or 0.22 = 0.06 + Risk Premium_{A1}*2 _{+ }Risk Premium_{A2}*2
Or Risk Premium_{A1}*2 _{+ }Risk Premium_{A2}*2 = 0.16 (ii)
By equating both the equation, we get:
Risk Premium of F_{1} = 0.03 or 3%
Risk Premium of F_{2} = 0.05 or 5%
Portfolio using Factor 1:
Weight of resulting unit portfolio: 

Weight of Portfolio A 
60% 
Weight of Portfolio B 
0% 
Weight of Riskfree asset 
40% 
= (19%*60%)+(22%*0%)+(6%*40%)
= 13.80%
=(1*60%)+(2*0%)+(0*40%)
= 0.60
Portfolio using Factor 2:
Weight of resulting unit portfolio: 

Weight of Portfolio A 
0% 
Weight of Portfolio B 
70% 
Weight of Riskfree asset 
30% 
= (19%*0%)+(22%*70%)+(6%*30%)
= 17.20%
=(1*0%)+(2*70%)+(0*30%)
= 1.40
Required Return = R_{f} + Risk Premium_{C1}*β_{C1 + }Risk Premium_{C2}*β_{C2}
= 0.06 + (0.03*2) + (0.05*0)
= 0.06 + 0.06 + 0
= 0.12 or 12%
Annual expected return = 16%
Since, actual return is less than annual expected return, hence portfolio is overvalued.
Income = Return on combined portfolio Return on Portfolio C
= 22%  12% = 10%
Weight are given below (in both conditions):
Weight of Portfolio A : 0%
Weight of Portfolio B : 100%
Weight of Portfolio Risk free asset : 0%
Problem 2
A) 
Assets 
Expected Return 
SD 
Correlation with P 
Market beta 

Stock A 
21% 
20% 
95% 
1.14 

Stock B 
34% 
40% 
80% 
3.20 

Portfolio P 
8% 
10% 
100% 
0.60 

TBill 
2% 
0% 
0% 
 

Here, 

Rf = 2% 

Portfolio P 

By using CAPM, calculate Rm: 

RR = Rf + (Rm  Rf)*β 

8% = 2% + (Rm  2%)*0.60 

Rm  2% = 6%/0.60 

Rm  2% = 10% 

Rm = 12% 

Standard Deviation of market portfolio: Systematic Risk of market = SD of portfolio P


B) 
Expected Return of Stock A: 

By using CAPM, calculate RR: 

RR = Rf + (Rm  Rf)*β 

RR = 2% + (12%  2%)*1.90 

RR = 2% + 19% 

RR = 21% 

C) 
Market beta of Stock B: 

Beta = (SD of Stock A/ SD Portfolio P)*Correlation between Stock B and Portfolio P 

Beta = (40%/10%)*0.80 

Beta = 3.20 

D) 
Systematic Risk of Stock B = SD of portfolio*β 

Systematic Risk of Stock B = 10%*3.20 

Systematic Risk of Stock B = 32% 
Problem 3
A) 
Fund 
Expected Return 
SD 
Beta 
(RRsec  Rf)/βsec 
Ranking 
Fund A 
8% 
20% 
0.50 
0.12 
1 

Fund B 
18% 
60% 
2.00 
0.08 
3 

Fund C 
16% 
40% 
1.50 
0.09 
2 

Tbill 
2% 

She should invest in Fund A. 

B) 
Risk Aversion coefficient = 1.50 

Utility score of investment = Rf  0.5*A*SD^2 

= 0.08  0.5*1.50*(0.20)^{2} 

= 0.08  0.03 

= 0.05 or 5% 

Now, to get the expected return of 5%, the proportion of Fund A in portfolio can be calculated as follows: 

Expected return = (RR of Fund A)*(Weight of Fund A) + (RR of Tbill)*(Weight of Tbill) 

Expected return = (0.08*Wa) + (0.02*Wt) 

Expected return = (0.08*Wa) + (0.02*(1Wa)) 

0.05 = 0.08Wa + 0.02  0.02Wa 

0.05 = 0.06Wa +0.02 

0.03 = 0.06Wa 

Wa = 0.03/0.06 

Wa = 0.50 or 50% 

Weight of this fund in his portfolio = 50% 
C)
Calculation of Portfolio Beta 

Fund A 
0.33 
0.5 
0.165 
Fund B 
0.33 
2 
0.66 
Fund C 
0.33 
1.5 
0.495 
1.32 

Calculation of Expected Return 

Fund A 
0.33 
0.08 
0.0264 
Fund B 
0.33 
0.18 
0.0594 
Fund C 
0.33 
0.16 
0.0528 
0.1386 

Basis 
Portfolio 

Alpha 
AR  RR 

Calculation 
0.1386  [0.02+(0.100.02)*1.32] 


0.013 

Remarks 
Underpriced 

Basis 
Portfolio 

Sharpe Ratio 
(RRport  Rf)/βport 

(13.86%2%)/1.32 

0.08985 
Problem 4
Variance of portfolio = + Covariance [Covariance = Beta of stock * Variance of Market]
= + 1*20*20
= 25+400
= 425
Standard deviation of portfolio =
= 20.62%
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