Question

In: Finance

A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield...

A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield increases by 25 basis points, how much of the price change is due to

convexity of the bond? (Face Value = $1,000)

Solutions

Expert Solution

                  K = Nx2
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2
                   k=1
                  K =10x2
1200 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2
                   k=1
YTM% = 5.39

Period Cash Flow Discounting factor PV Cash Flow Duration Calc Convexity Calc
0 ($1,200.00) =(1+YTM/number of coupon payments in the year)^period =cashflow/discounting factor =PV cashflow*period =duration calc*(1+period)/(1+YTM/N)^2
1             40.00                                                             1.03                    38.95                  38.95                  73.87
2             40.00                                                             1.05                    37.93                  75.86                215.78
3             40.00                                                             1.08                    36.93                110.80                420.24
4             40.00                                                             1.11                    35.96                143.85                682.02
5             40.00                                                             1.14                    35.02                175.10                996.18
6             40.00                                                             1.17                    34.10                204.60              1,358.05
7             40.00                                                             1.20                    33.21                232.44              1,763.21
8             40.00                                                             1.24                    32.33                258.68              2,207.49
9             40.00                                                             1.27                    31.49                283.37              2,686.95
10             40.00                                                             1.30                    30.66                306.60              3,197.87
11             40.00                                                             1.34                    29.86                328.41              3,736.74
12             40.00                                                             1.38                    29.07                348.86              4,300.26
13             40.00                                                             1.41                    28.31                368.01              4,885.31
14             40.00                                                             1.45                    27.57                385.92              5,488.97
15             40.00                                                             1.49                    26.84                402.64              6,108.48
16             40.00                                                             1.53                    26.14                418.21              6,741.27
17             40.00                                                             1.57                    25.45                432.68              7,384.90
18             40.00                                                             1.61                    24.78                446.11              8,037.11
19             40.00                                                             1.66                    24.13                458.54              8,695.78
20       1,040.00                                                             1.70                  611.01            12,220.17          243,331.34
      Total            17,639.80          312,311.80
Convexity =(∑ convexity calc)/(bond price*number of coupon per year^2)
=312311.8/(1200*2^2)
=65.06
Using convexity adjustment
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
0.5*65.06*0.0025^2*1200
=0.24

Related Solutions

A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield...
A three-year old 10-year 8% semi-annual coupon bond is selling at $1,200 today. If the yield increases by 25 basis points, how much of the price change is due to convexity of the bond? (Face Value = $1,000)
Consider a 5- year bond with a semi-annual 10% coupon and a yield to maturity(ytm) of...
Consider a 5- year bond with a semi-annual 10% coupon and a yield to maturity(ytm) of 9.00%. what is the duration of this bond in years?
What is the YTM of a 10 year, 8% semi-annual coupon bond with a price of...
What is the YTM of a 10 year, 8% semi-annual coupon bond with a price of $1220?
Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%....
Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be: A. Higher B. Lower C. The same D. Par
A 12.25-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield)...
A 12.25-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 139.2 and modified duration of 11.34 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration—-12.30 years—but considerably higher convexity of 272.9. a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What...
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield)...
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical duration—11.79 years—but considerably higher convexity of 231.2. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What percentage capital...
A 13.05-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield)...
A 13.05-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 120.2 and modified duration of 11.91 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration—-11.65 years—-but considerably higher convexity of 280.2. a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What...
A 13.05-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield)...
A 13.05-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 157.2 and modified duration of 12.08 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration—-12.30 years—-but considerably higher convexity of 272.9. a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What...
Consider a 4-year bond with 12 percent semi-annual coupon payments and currently priced to yield 10...
Consider a 4-year bond with 12 percent semi-annual coupon payments and currently priced to yield 10 per cent per annum. Calculate duration of the bond.
Suppose you purchase a 10-year, 4% semi-annual coupon bond for 78.681. If the yield remains constant...
Suppose you purchase a 10-year, 4% semi-annual coupon bond for 78.681. If the yield remains constant and you reinvest the coupons you receive at that yield, what will be the value of those coupons when the bond matures in 10 years?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT