1. Consider a contract that pays out $190 in 6 months, $131 in 12 months, $80...

1. Consider a contract that pays out $190 in 6 months, $131 in 12 months, $80 in 18 months, $50 in 2 years. What is this contract's Macaulay duration (in years)? Assume this contract is currently trading at a yield of 5%.

2. Consider an annuity contract that pays out $47 at the end of each of the next four 6-month intervals (payments are to be made 6, 12, 18, and 24 months from today). What is this annuity's Macaulay duration (in years)? Assume this contract is currently trading at a yield of 5%.

3. What is the Macaulay duration in years of a 3% coupon bond with 2 years to maturity and a face value of $100? Assume the bond is trading at a yield of 7%, and that the next coupon payment is to be made exactly 6 months from today.

4. What is the modified duration in years of a 10% coupon bond with 2 years to maturity and a face value of $100? Assume the bond is trading at a yield of 4%, coupons are to be paid semi-annually, and that the next coupon payment is to be made exactly 6 months from today.

Solutions

Expert Solution

The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price. Macaulay duration is frequently used by portfolio managers who use an immunization strategy.

Macaulay duration can be calculated:

Where:

t = respective time period
C = periodic coupon payment
y = periodic yield
n = total number of periods
M = maturity value
Current Bond Price (P) = Present value of cash flow

We get the answer in the periods equal to that of coupon payments. i.e If coupons are semi-annual, the Macaulay duration we get from the above equations is also no. of semi-annual periods. so, in this case, we need to divide the result with 2 in order to convert it into Years.

where n= no. of coupons periods per year

1. Macaulay Duration = 0.975 Years

2. Macaulay Duration = 1.235 Years

3. Macaulay Duration = 1.954 Years

4. Macaulay Duration = 3.738 Half-Years = 1.87 Years

Modified Duration = 1.8325 Years

jeff jeffy answered 1 year ago

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