4. a) Compute the modified duration of a 10% coupon, 4-year corporate bond with a yield...

4. a) Compute the modified duration of a 10% coupon, 4-year corporate bond with a yield to maturity of 8%. b) Using the modified duration, If the market yield drops by 25 basis points, there will be a __________% (increase/decrease) in the bond's price.

Expert Solution

To calculate Modified duration we first need to calculate Macaulay duration:

Lets assume that the par value of the bond is 100 so 10% coupon will be 10
CF in year 4 = coupon +par value = 10+100=110
YTM =8%, we discount all the coupons and principal payments to time 0 using YTM as the discount rate
Next we multiply the PV with t or the corresponding year value
Then we sum all PV x t and PV
We divide the sum of PV x t by sum of PV to get the Macaulay duration
Then we divide it by (1+YTM) to calculate Modified duration. As it is an annual coupon bond, n = 1 in (1+YMT/n) in the formula of modified duration

Year	CF	PV	PV x t
1	10	10/1.08 = 9.259259259	9.259259x1=9.259259
2	10	(10/1.08)² = 8.573388203	8.573388203x2=17.14678
3	10	(10/1.08)³ = 7.93832241	7.93832241x3=23.81497
4	10+100= 110	(110/1.08)⁴ = 80.85328381	80.85328381x4=323.4131
	Sum	9.259259259+8.573388203+7.93832241+80.85328381=106.6242537	9.259259+17.14678+23.81497+323.4131=373.6341
		Macaulay Duration	373.6341/106.6242537 = 3.504213
		Modified Duration	3.504213/(1.08) = 3.244642

Duration states the percentage impact in the price of the bond to a percentage change in the interest rate in the market.
Price of the bond is inversely related to the interest rates. When interest rates rise, price falls and vice versa
if YTM falls by 25bps the price of the bond should increase
We use modified duration to calculate the percentage increase
- 3.244642 of modified duration states that for every 1% change in the interest rate of the bond, the price changes by 3.244642% in the opposite direction.
- 25bps =0.25% or 1/4 %
- So if interest rate falls by 1/4% the price of the bond increases by 3.244642/4 % = 0.812%

jeff jeffy answered 1 year ago

a) Compute the modified duration of a 9% coupon, 4-year corporate bond with a yield to...

a) Compute the modified duration of a 9% coupon, 4-year corporate bond with a yield to maturity of 10%. b) Using the modified duration, If the market yield drops by 25 basis points, there will be a __________% (increase/decrease) in the bond's price.

Compute the Macaulay duration and modified duration of a 6%, 25-year bond selling at a yield...

Compute the Macaulay duration and modified duration of a 6%, 25-year bond selling at a yield of 9%. Coupon frequency and compounding frequency are assumed to be semiannual.

A 4-year 12% coupon bond has a yield of 10%. a) What are its Macaulay Duration,...

A 4-year 12% coupon bond has a yield of 10%. a) What are its Macaulay Duration, Modified duration, and convexity b) What is the actual price change, Modified Duration predicted price change and Modified Duration + convexity predicted change in price for an increase of 50 basis point in the yield. Assume a flat term structure before and after the increase and annual coupons.

The McCauley’s duration of a 5-year zero-coupon bond yielding 4% is ________ years and the modified...

The McCauley’s duration of a 5-year zero-coupon bond yielding 4% is ________ years and the modified duration of a 5-year zero-coupon bond yielding 4% is ________ years.

a. A 10-year 5% coupon bond has a yield of 8% and a duration of 7.85...

a. A 10-year 5% coupon bond has a yield of 8% and a duration of 7.85 years. If the bond yield increases by 60 basis points, what is the percentage change in the bond price? b. Alpha Insurance Company is obligated to make payments of $2 million, $3 million, and $4 million at the end of the next three years, respectively. The market interest rate is 8% per annum. i. Determine the duration of the company’s payment obligations. ii. Suppose...

Calculate the approximate modified duration of a 4-year, 5% coupon, semi-annual bond if yields change by...

Calculate the approximate modified duration of a 4-year, 5% coupon, semi-annual bond if yields change by 50bps. Assume the bond currently sells at 5% yield to maturity (YTM). a) 1.79 b) 3.59 c) 7.17 d) 11.95 e) None of the above

40. Calculate the modified duration of a 10-year 7% semi-annual coupon bond priced at 97.50. a....

40. Calculate the modified duration of a 10-year 7% semi-annual coupon bond priced at 97.50. a. 7.316 b. 7.06 c. 6.88 d. 3.53 e. 3.67

Compute the duration and convexity of a 10-year Treasury bond, with coupon 3% and price 102-13....

Compute the duration and convexity of a 10-year Treasury bond, with coupon 3% and price 102-13. Note: 1. Treasuries are semiannual. 2. The price quote “aaa-bb” means aaa+b/32 dollars. 3. Treasuries are non-callable bonds

Calculate the Macaulay duration for a nine year, 5.75% semiannual coupon bond priced to yield 4%....

Calculate the Macaulay duration for a nine year, 5.75% semiannual coupon bond priced to yield 4%. Can someone calculate this using Excel? Please show the variables.

Question 4. A 12.75-year maturity zero-coupon bond has convexity of 150.3 and modified duration of 11.81...

Question 4. A 12.75-year maturity zero-coupon bond has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond with annual coupon payments has nearly identical modified duration of 11.79 years, but considerably higher convexity of 231.2. Suppose the yield to maturity on both bonds increases by 1%. What percentage change in price of the bonds as predicated by the duration plus convexity model? (6) Repeat part (a), but this time assume that the yield to...

Question