Question

In: Finance

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.

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 2 years ago

Consider an annuity contract that pays out $45 at the end of each of the next...

Consider an annuity contract that pays out $45 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 6%. Round your answer to 3 decimal places. For example if your answer is 5.5175, then please write down 5.518. Hint: First price this contract, and then calculate its duration...

If $675 is deposited every 6 months for the next 5 years. The account pays 12%...

If $675 is deposited every 6 months for the next 5 years. The account pays 12% per year compounded quarterly. Determine the equivalent future worth at the end of the period?

Consider a forward contract for one share of a stock, with T = 0.5 (6 months)....

Consider a forward contract for one share of a stock, with T = 0.5 (6 months). The current stock price is S0 = 50. We assume that the risk-free interest rate is r = 0.05, and that the stock pays discrete dividends, there being exactly one dividend payment, of size 0.75, between times 0 and T, and the payment happens at time t = 1/3 (4 months). Calculate the price of the forward contract. Show your work. Use two decimal...

Consider a 1000-strike put option and a forward contract on the S&R index with 6 months...

Consider a 1000-strike put option and a forward contract on the S&R index with 6 months to expiration. The current index price is $1000. The put writer receives the premium of $74.20 and the forward price is $1020. The annual interest rate is 4%. a. Verify that the S&R index price at which the profit diagram of the purchased put option intersects the x-axis is $924.32. b. At what price of the S&R index the long put option and the...

Consider a bond that pays a $500 dividend once a quarter. It pays in the months...

Consider a bond that pays a $500 dividend once a quarter. It pays in the months of March, June, September, and December. It promises to do so for 10 years after you purchase it (start in January 2019). You discount the future at rate r=0.005r=0.005 per month. a. How much do you value the asset in January 2019? b. Consider a different asset that pays a lump sum at its expiration date rather than a quarterly dividend of $500 dollars,...

1) Suppose that an Intel single-stock futures contract expires in four months. The stock pays a...

1) Suppose that an Intel single-stock futures contract expires in four months. The stock pays a dividend in two months. We have the following information. Annualized, continuously compounded risk-free interest rate for 2-month period: r = 3.86%. Annualized, continuously compounded risk-free interest rate for 4-month period: r = 4.95%. Current spot price of Intel stock: $30 per share. Dividend per share of $0.24 in two months. What must the futures price equal in order than no arbitrage opportunity exist? 2)...

Sanjeev enters into a contract offering variable consideration. The contract pays him $1,850/month for six months...

Sanjeev enters into a contract offering variable consideration. The contract pays him $1,850/month for six months of continuous consulting services. In addition, there is a 70% chance the contract will pay an additional $3,500 and a 30% chance the contract will pay an additional $1,500, depending on the outcome of the consulting contract. Sanjeev concludes that this contract qualifies for revenue recognition over time. Assume that Sanjeev estimates variable consideration as the most likely amount. After Sanjeev has recognized revenue...

The smith family has a basic health insurance plan that pays 80% of out of hospital...

The smith family has a basic health insurance plan that pays 80% of out of hospital expenses after a deductible of $250 per person. If 3 family members have doctor and prescription drug expenses of $877, $1,659, and $192 respectively, how much will the smith family and the insurance company each pay? How could they benefit from a flexible spending account established through mr.smith's employer? What are the advantages and disadvantages of establishing such an account?

At the end of every 3 months, Judy deposits $100 into an account that pays 6%...

At the end of every 3 months, Judy deposits $100 into an account that pays 6% compounded quarterly. After 4 years she puts the accumulated amount into a certificate of deposit paying 7.5% compounded semi-annually for 1 year. When this certificate matures how much will Judy have accumulated?

1. Consider a forward contract for one share of a stock, with T = 0.5 (6...

1. Consider a forward contract for one share of a stock, with T = 0.5 (6 months). The current stock price is S0 = 50. We assume that the risk-free interest rate is r = 0.05, and that the stock pays discrete dividends, there being exactly one dividend payment, of size 0.75, between times 0 and T, and the payment happens at time t = 1/3 (4 months). Calculate the price of the forward contract. Show your work. Use two...