Asset 1 has an expected return of 10% and a standard deviation of 15% and asset 2 has an expected return of 15% and a standard deviation 25%. Assume the correlation of the two asset returns is pr, =...

Question 1
a. Details Provided:
Particulars Asset 1 Asset 2
Expected Return 10% 15%
Standard Deviation (σ) 15% 25%
Correlation (p12) 0.15
Calculation of Weight for Asset 1
W1 = (σ2
2
- p12. σ1 .σ2) / (σ1
2
+ σ2
2
- 2 p12. σ1 .σ2)
= (25%
2
– 0.15x 15% x 25%) / (15%
2
+ 25%
2
- 2 x 0.15 x 15% x 25%)
= 77.12%
W2 = 100% - 77.12% = 22.88%
b. Expected Return of MVP = W1 x ER1 + W2 x ER2
= (77.12% x 10%) + (22.88% x 15%)
= 11.14%
Variance of Portfolio = (σ1
2
x W1
2
) + (σ2
2
x W2
2
) + 2 x W1 x W2 x σ1

x σ12

x p12
= (15%
2
x 77.12%
2
) + (25%
2
x 22.88%
2
) + 2 x 77.12% x 22.88%x 15% x 25% x 0.15
= 3.36%
Standard Deviation = Square Root of Variance = 18.34%
Question
a. Calculation of annualised yield on bonds:
Particulars Bond 1 Bond 2 Bond 3 Bond 4
Maturity 1 year 2 years 3 years 4 years
Price $970.874 $939.856 $907.640 $874.818
Face Value $1,000 $1,000 $1,000 $1,000
Yield 3% 3.15% 3.28% 3.4%
Yield = (Face Value/Present Value)
1/n
- 1
b. Term Structure of interest rate is the difference in the yield of bonds with different terms and
similar risks. In general, the higher the terms of bonds the higher is the yield.
Liquidity Premium Theory: This theory explains that the bonds with higher maturity has
higher yield. According to this theory, since the duration of the bond is higher which results
in higher risks, thus increasing the yield of such bonds. The increased yield is to compensate
the buyers for the increased risk.
Generally, the term structure is upward sloping but in some situation it might be downward
sloping also. The term structure may be downward sloping if in case the interest rates are
expected to decline in future.
c. Calculation of price and duration of bonds:
Particulars Bond 1 Bond 2
Maturity 2 years 2 years
Annual ytm 5% 5%
Coupon 2% 10%
Price of Bond = Coupon * 1 – (1 + ytm)
-t
+ Face Value
R (1 + Ytm)
t

Price Bond 1 = 20 * 1 – (1.05)
-2
+ 1000
0.05 (1.05)
2

= $944.22
Price Bond 1 = 100 * 1 – (1.05)
-2
+ 1000
0.05 (1.05)
2

= $1092.97
Duration of Bond = ∑Ct(t)/(1+r)
t

∑ Ct(1+r)
t
Duration of Bond 1 = (20*1)/(1.05) + (1020*2)/(1.05)
2

(20)/(1.05) + (1020)/(1.05)
2

= 1.98 years
Duration of Bond 2 = (100*1)/(1.05) + (1100*2)/(1.05)
2

(100)/(1.05) + (1100)/(1.05)
2

= 1.91 years
Bond 1 is more risky as compared to Bond 2 as the coupon rate is low as compared to the
yield to maturity. Yes, the value of duration of the bond confirm this since the duration of
bond 1 is greater than bond 2 which means that bond 1 will take more time to repay the
investor.
d. It is expected that the interest rate will increase more than what the market...