Suppose that an investor buys a 180-day Australian bank bill with quoted yield 4.2% and sells...

 

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Suppose that an investor buys a 180-day Australian bank bill with quoted yield 4.2% and sells the bill after 30 days when the quoted yield is 4.2% (on a 150-day bill). What is the holding period yield on the bill expressed as a continuously compounded rate? [3 marks] (ii) A company has cash-flows C, C and C3 which are to be paid in one, two and three year's time, respectively. Assume that the continuously-compounded interest rate which applies for all maturities is r. (a) Find the present value, P(r), dP/dr and dP/dr for this sequence of cash-flows in terms of x = Ce, x = C e , x3 = C3 -r. [3 marks] (b) If the company wishes the present value of this sequence of cash-flows to be L and the (Fisher-Weil) duration and convexity to be zero, determine C, C and C3 in terms of L and r. [3 marks] (iii) A company has a liability of $1,771,350.09 which it must pay in exactly 2.0815 years time. It may also invest in the following two bonds: bond B B modified modified duration convexity 1.50 3.80 7.25 maturity present value 3 years $100,000 4 years $50,000 3.00 The interest rate that applies between now and the date the liability is due to be paid is 8.15%, compounded semi-annually. (a) Find the present value and the modified duration of the liability and show that its modified convexity is 4.9608 years; [3 marks] (b) Using the two bonds available, construct a portfolio that matches the liability's present value and hedges the investor's exposure to small parallel shifts in the yield curve to the greatest degree possible. [3 marks] Suppose that an investor buys a 180-day Australian bank bill with quoted yield 4.2% and sells the bill after 30 days when the quoted yield is 4.2% (on a 150-day bill). What is the holding period yield on the bill expressed as a continuously compounded rate? [3 marks] (ii) A company has cash-flows C, C and C3 which are to be paid in one, two and three year's time, respectively. Assume that the continuously-compounded interest rate which applies for all maturities is r. (a) Find the present value, P(r), dP/dr and dP/dr for this sequence of cash-flows in terms of x = Ce, x = C e , x3 = C3 -r. [3 marks] (b) If the company wishes the present value of this sequence of cash-flows to be L and the (Fisher-Weil) duration and convexity to be zero, determine C, C and C3 in terms of L and r. [3 marks] (iii) A company has a liability of $1,771,350.09 which it must pay in exactly 2.0815 years time. It may also invest in the following two bonds: bond B B modified modified duration convexity 1.50 3.80 7.25 maturity present value 3 years $100,000 4 years $50,000 3.00 The interest rate that applies between now and the date the liability is due to be paid is 8.15%, compounded semi-annually. (a) Find the present value and the modified duration of the liability and show that its modified convexity is 4.9608 years; [3 marks] (b) Using the two bonds available, construct a portfolio that matches the liability's present value and hedges the investor's exposure to small parallel shifts in the yield curve to the greatest degree possible. [3 marks]

Answer rating: 100% (QA)

i To calculate the holding period yield on the bill expressed as a continuously compounded rate we can use the formula Holding Period Yield ln1 r ln1 ... View the full answer