Reference no: EM132524031

QUESTION NINE a). An investor has funds to invest over one year. He anticipates a 1% increase in the curve in six months. The 6-month and 1-year zero-coupon rates are respectively 3% and 3.2%. He has two different opportunities:

1. he can buy the 1-year, sh 1 million zero-coupon T-bond and hold it until maturity,

2. or he can choose a rollover strategy by buying the 6-month shs 1 million T-bill, holding it until maturity, and buying a new 6-month, shs1 million T-bill in six months, and holding it until maturity.

Required:

i. Calculate the annualized total return rate of these two strategies assuming that the investor's anticipation is correct.

ii. Same question when interest rates decrease by 1% after six months.

b). Consider the following zero-coupon curve:

Maturity (years) Zero-Coupon Rate (%)

1 4.00

2 4.50

3 4.75

4 4.90

5 5.00

i. What is the price of a 5-year bond with a Ksh 1 million face value, which delivers a 5% annual coupon rate? (6 marks)

ii. What is the yield to maturity of this bond? (6 marks)

iii. We suppose that the zero-coupon curve increases instantaneously and uniformly by 0.5%. What is the new price and the new yield to maturity of the bond? What is the impact of this rate increase for the bondholder? (8 marks)

iv. Suppose now that the zero-coupon curve remains stable over time. You hold the bond until maturity. What is the annual return rate of your investment? Why is this rate different from the yield to maturity? (8 marks)

c). You have purchased a bond for Ksh973,020. The bond has a coupon rate of 6.4%, pays interest annually, has a face value of Ksh1 million, 4 years to maturity, and a yield to maturity of 7.2%. The bond's duration is 3.6481 years. You expect that interest rates will fall by .3% later today.

i. Use the modified duration to find the approximate percentage change in the bond's price. Find the new price of the bond from this calculation.

ii. Use your calculator to do the regular present value calculations to find the bond's new price at its new yield to maturity.

iii. What is the amount of the difference between the two answers? Why are your answers different? Explain