Question

In: Finance

Consider a 8% coupon bond making annual coupon payments with 4 years until maturity and a...

Consider a 8% coupon bond making annual coupon payments with 4 years until maturity and a yield to maturity of 10%.

  1. What is the modified duration of this bond?
  1. If the market yield increases by 75 basis points, what is the actual percentage change in the bond’s price? [Actual, not approximation]
  1. Given that this bond’s convexity is 14.13, what price would you predict using the duration-with-convexity approximation for this bond at this new yield?
  1. What is the percentage error?

Solutions

Expert Solution

a) Let us Consider the par value of the Bond to be 100

First we need to the find the macaulay duration of the bond

Year (t) Cash flow(CF) PV factor CF* PV (CF* PV)/ Total [(CF* PV)/ Total] * t
1 8 0.909091 7.272727 0.07765 0.0776503
2 8 0.826446 6.61157 0.070591 0.1411824
3 8 0.751315 6.010518 0.064174 0.1925214
4 108 0.683013 73.76545 0.787588 3.1503503
Total 93.66 3.5617044

The macaulay duration is 3.5617

The modified duration = (macaulay duration) / ( 1 + YTM /n ) , where n is the number of coupons per period

= 3.56 / (1 + 1.1)

= 3.2379

Alternatively we can also calculate using MDURATION func in excel

b) The PV of the bond when YTM =10% is 93.66027

Year CF PV factor PV of CF
1 8 0.909091 7.272727
2 8 0.826446 6.61157
3 8 0.751315 6.010518
4 108 0.683013 73.76545
Total 93.66027

The PV of the bond when YTM =10.75% is 91.42253

Year CF PV factor PV of CF
1 8 0.902935 7.223476
2 8 0.815291 6.522326
3 8 0.736154 5.889234
4 108 0.664699 71.7875
Total 91.42253

Hence the actual price change % = (93.66027 - 91.42253)/ 93.66027 * 100 %

= 2.3892 %

The Approximate % decrease in bond price = (The change in yield* the modified duration) * 100%

= -( 0.0075 * 3.2379 ) * 100%

= -2.428 %

c)

Change in price accounting for convexity = Duration effect+Convexity effect

=(-Modifed Duration * ΔYield) + [0.5 * Convexity * (ΔYield)2 ]

=( - 3.2379 * 0.0075) + [ 0.5 * 14.13 * 0.00752 ]

= -0.0238868 or -2.38868  %

d)

Percentage error = (Approx - actual) / actual * 100%

Now, actual price after YTM increase = 91.42253

Approx price  after YTM increase = (1-0.0238868 )* 93.66027

= 91.42302

Hence , % error =( 91.42302 - 91.42253) / 91.42253 *100%

= 0.0005359%


Related Solutions

Consider a 8% coupon bond making annual coupon payments with 4 years until maturity and a...
Consider a 8% coupon bond making annual coupon payments with 4 years until maturity and a yield to maturity of 10%. What is the modified duration of this bond? If the market yield increases by 75 basis points, what is the actual percentage change in the bond’s price? [Actual, not approximation] Given that this bond’s convexity is 14.13, what price would you predict using the duration-with-convexity approximation for this bond at this new yield? What is the percentage error? Please...
A 30-year maturity bond making annual coupon payments with a coupon rate of 8% has duration...
A 30-year maturity bond making annual coupon payments with a coupon rate of 8% has duration of 11.37 years and convexity of 187.81. The bond currently sells at a yield to maturity of 9%. a. Find the price of the bond if its yield to maturity falls to 8%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answers to...
Consider the following bonds Bond Coupon Rate (Annual Payments) Maturity(Years) A 3% 8 B 5% 8...
Consider the following bonds Bond Coupon Rate (Annual Payments) Maturity(Years) A 3% 8 B 5% 8 C 3% 4 D 5% 4 Which of the bonds (A – D) is most sensitive to a 1% increase in interest rates. Which is least sensitive?
Consider a bond with semiannual payments with 10 years to maturity, coupon of 10%, 8% as...
Consider a bond with semiannual payments with 10 years to maturity, coupon of 10%, 8% as Yield to Maturity (YTM),and  face value of 1000, a. Find the price of the bond at t=0. b. Interest rates drop by 1% after 1 year. Find the new Price of the bond. c. Interest rates drop to 0% after two years from time 0. Find the new price. d. Interest rates turn negative to -5% after 3 years from t= 0. Find the new...
Consider a $1,000.00 face value bond with a $55 annual coupon and 10 years until maturity....
Consider a $1,000.00 face value bond with a $55 annual coupon and 10 years until maturity. Calculate the current yield; the coupon rate and the yield to maturity under each of the following: a) The bond is purchased for $940.00 b) The bond is purchased for $1,130.00 c) The bond is purchased for $1,000.00
A 4% annual coupon bond has 5 years remaining until maturity and is priced to yield...
A 4% annual coupon bond has 5 years remaining until maturity and is priced to yield 6%. (a) What is the price per 100 of par? (b) For this bond, estimate the price value of a basis point by first considering an increase in yield and then a decrease in yield.   (c) Now show that for very small price changes, the absolute value of a bond’s price change does not differ much conditional on whether the yield change is a...
8. a) Consider Bond C – a 4% coupon bond that has 10 years to maturity....
8. a) Consider Bond C – a 4% coupon bond that has 10 years to maturity. It makes semi-annual payments and has a YTM of 7%. If interest rates suddenly drop by 2%, what is the percentage change of the bond? What does this problem tell you about the relationship between interest rate and bond price? b) Consider another bond – Bond D, which is a 10% coupon bond. Similar to Bond C, it has 10 years to maturity. It...
Today is T=0. A bond has a 6% coupon rate, annual payments and 8 years until...
Today is T=0. A bond has a 6% coupon rate, annual payments and 8 years until maturity. If the bond sells for $833.9554 what is your capital gain yield between T=6 and T=7.
Today is T=0. A bond has a 6% coupon rate, annual payments and 8 years until...
Today is T=0. A bond has a 6% coupon rate, annual payments and 8 years until maturity. If the bond sells for $8339554 what is your capital gain yield between T=6 and T=7.
A bond has 8 years until maturity, a coupon rate of 8%, and sells for 1,100...
A bond has 8 years until maturity, a coupon rate of 8%, and sells for 1,100 a. If the bond has a yield to maturity of 8% 1 year from now, what will its price be? Price $ b. What will be the rate of return on the bond? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % c. If the inflation rate during...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT