Question

1. The price of a 20-year coupon bond, coupon rate 7% p.a., yield to maturity 6% p.a., face value of $100 is closest to (assuming semi-annual compounding)

Questions 2, 3, 4, 5 and 6 refer to the following information.

A one- year bond with a 5% annual coupon rate has a current market price of $101. A two year bond with 7% annual coupons has a market price of $98. A three-year bond with 9% annual coupons has a market price of $102.  

2. Based on the bootstrapping technique and assuming annual compounding, the one-year spot rate is closest to:

A. 2%

B. 3%

C. 4%

D. 5%

E.   6%

3. Based on the bootstrapping technique and assuming annual compounding, the two-year spot rate is closest to:

           

A. 4%

B. 5%

C. 6%

D. 7%

E.   8%

4. Based on the bootstrapping technique and assuming annual compounding, the three-year spot rate is closest to:

A. 11%

B. 10%

C. 9%

D. 8%

E.   7%

5. Which of the following statements is true?

i. The yield to maturity for the one-year bond is more than 5% pa nominal. ii.      The yield to maturity for the two-year bond is more than 7% pa nominal. iii.      The yield to maturity for the three-year bond is equal to 9% pa nominal.

       iv.     The yield to maturity for the two year bond is less than 8% pa nominal.

A. (i) only

B. (ii) only

C. (i) & (iii)

D. (ii) & (iii)

E.   (ii) & (iii) & (iv)

6. Consider a three year bond paying 8% annual coupons and a face value of $100 that trades at a price of $98. Based on the spot rates calculated in Questions 2,3 and 4, this bond is:

A. Underpriced and the investor should sell the bond and buy it back via appropriate strips in order to make an arbitrage profit

B. Underpriced and the investor should buy the bond and sell the cashflows via the strip market in order to make an arbitrage profit.

C. Overpriced and the investor should sell the bond and buy it back via appropriate strips in order to make an arbitrage profit.

D. Overpriced and the investor should buy the bond and sell the cashflows via the strip market in order to make an arbitrage profit.

E. Fairly priced

Answer 1

1. Bond price = ?

Coupon/ interest rate = 7% semi annually payable

YTM = 6%

Redemption value = 100

We can find the price by following:

(Semi annually interest amount x sum of 40 semi years P.V.F @semi annually YTM) + (Redemption price x P.V.F of 40th semi year )

(3.5x23.1148)+(100x0.3066)

=80.90+30.66

=111.56

2.

101= 105/(1+y)

101+101y = 105

Y= 4/101

Y= 0.03960 or 3.96%

So, answer is 4%

3.

98 = 7/1.04 + 107/(1+y)

98 - 6.73 = 107/(1+y)²

91.27 x (1+y)² = 107

(1+y)² = 1.1723

(1+y) = ?1.1723 = 1.0827

Y = 0.0827 or 8.27%

So, the answer is 8%

4.

102 = 9/1.04 + 9/(1.08)² + 109/(1+y)³

102=8.65+7.72+109/(1+y)³

85.63 = 109/(1+y)³

(1+y)³ = 1.2729

(1+y) = 1.0875

Y = 0.0875 or 8.75%

So we can say that answer is 9%.