Portfolio Theory and Bonds: Solved Questions and Formulas

This text provides solved questions and formulas related to portfolio theory and bonds. It covers topics such as expected returns, standard deviation, bond pricing, yield to maturity, and more. The study material is suitable for finance students and includes subject matter such as course codes, course names, and universities.

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Chapter 25: Portfolio Theory
Question 1
Expected returns of portfolio = Weight of stock A *Expected returns on stock A + Weight of
stock B*Expected returns on stock B = 0.4*14 + 0.6*20 = 17.6%
The standard deviation of a two stock portfolio = √(0.42*0.32+ 0.62*0.52+
2*0.4*0.6*0.2*0.3*0.5) = 34.47%
Question 2
a) Expected returns of portfolio = 0.6*19 + 0.4*3 = 12.6%
Since T bill is considered a risk free asset, hence standard deviation of returns would be zero.
Standard deviation of portfolio = √(0.62*0.292 + 0.42*02+ 2*0.6*0.4*0.29*0) = 17.40%
b) Investment in stock A = 25%*60 = 15%
Investment in stock B = 32% *60 = 19.2%
Investment in stock C = 43% * 60 = 25.8%
Investment in T-bill = 40%
Chapter 5: Bonds
Question 1
The formula for bond price is given below.

In the given case, C = 5% of 1000 = $ 50, i= 9% p.a., n=10 years, M =$ 1,000. Substituting
the given input values, we get
Bond price = [50*(1-(1/1.0910))/0.09] + (1000/1.0910) = $ 743.29
Question 2
The formula for bond price is given below.
In the given case, C = 3% of 1000 = $ 30, i=?. n=5 years, M =$ 1,000, bond price = $1,050.
Substituting the given input values, we get
1050 = [30*(1-(1/(1+i)5)/(i)] + 1000/(1+i)5
Solving the above equation, we get I = 1.94% p.a.
Question 3
The formula for bond price is given below.
In the given case, C = 9% of 1000 = $ 90, i=7%. n=4 years, M =$ 1,000. Substituting the
given input values, we get
Current bond price = [90*(1-(1/(1.07)4)/0.07] + 1000/(1.07)4 = $ 1,067.74
Current yield = (90/1067.74)*100 = 8.43%
Question 4

The formula for bond price is given below.
In the given case, C = 4.5% of 1000 = $ 45, i=2%. n=20 M =$ 1,000.Substituting the given
input values, we get
Current bond price = [45*(1-(1/(1.02)20)/0.02] + 1000/(1.02)20 = $ 1,408.79
Question 5
a) The formula for bond price is given below.
In the given case, C = 12% of 1000 = $ 120, i=?. n=8, M =$ 1,000, Bond Price =$950.
Substituting the given input values, we get
950 = [120*(1-(1/(1+i)8)/(i)] + 1000/(1+i)8
Solving the above, we get I = 13.04%
Hence, the YTM is 13.04%
b) The requisite formula for computing the Yield to Call (YTC) is indicated as shown below.
For the given case, B0= 950, C = 12% of 1000 = $ 120,CP = $1,010, d=4. Substituting the
given input values, we get

950 = (120/2)*(1-(1+(YTC/2))-2*4)/(YTC/2)) + 1010/(1+(YTC/2))2*4
Solving the above, YTC = 13.87%
c) The investors must expect to earn the YTM on the bond as under the current circumstances
it does not seem feasible to recall the bond at a premium to the issue price.
Question 6
a) The formula for bond price is given below.
In the given case, C = 5% of 1000 = $ 50, i=3.5%. n=14, M =$ 1,000. Substituting the given
input values, we get
Current bond price = [50*(1-(1/(1.035)14)/0.035] + 1000/(1.035)14 = $ 1,163.81
b) In the given case, C = 5% of 1000 = $ 50, i=5.5%. n=14, M =$ 1,000.Substituting the
given input values, we get
Current bond price = [50*(1-(1/(1.055)14)/0.055] + 1000/(1.055)14 = $ 952.05
c) If the interest rate after falling to 7% remained there for the remainder of the maturity
period, then the price of the bond would keep on declining as the years progress and
eventually would attain the maturity value at the end of the maturity period.