A 14. 55-year maturity zero coupon bond selling at a yield to maturity of 7% eff

Question

A 14. 55-year maturity zero coupon bond selling at a yield to maturity of 7% effective annual yield has com e 7 and modified ration in a ea s A year maturity 5% coupon bond making annual coupon payments also selling at a yield to maturity of 7% has nearly identical modified duration-13.96 years-but considerably higher convexity of 338.8 a Suppose the yield to maturit on both bonds increases to 8% What will be the actual percentage cap al oss on each bond? what percentage capital loss would be predicted the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) n Bond Coupon Bond Actual loss Predicted loss b. Suppose he yield o maturity on both bonds decreases to 6 6 What will be he actual percentage capital an on each bond the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) what percentage capita ain would be predicted Zero-Coupon Bond Coupon Bond Actual gain Predicted gain

Explanation / Answer

if Yield changes to 8%

Zero coupon

Price = FV / (1+YTM)n

Price(@ 7%) = 100/(1+0.07)^14.55 = 37.37

Price(@ 8%) = 100/(1+0.08)^14.55 = 32.64

Actual loss = (32.64 - 37.37) / 37.37 = -12.66%

Predicted Price change = (-duration*change in yield) + (0.5*convexity*change in yield2)

Predicted loss = (-13.6*0.01) + (0.5*197.7*0.012) = -12.61%

Coupon Bond

Zero coupon

Price = Coupon*(1 - 1/(1+YTM)n) / YTM

Price(@ 7%) = 5*(1- 1/(1+0.07)^40)/0.07 = 73.34

Price(@ 8%) = 5*(1- 1/(1+0.08)^40)/0.08 = 64.23

Actual loss = (64.23 - 73.34) / 73.34 = -12.42%

Predicted Price change = (-duration*change in yield) + (0.5*convexity*change in yield2)

Predicted loss = (-13.96*0.01) + (0.5*338.8*0.012) = -12.27%

Repeat with 6% rate

if Yield changes to 6%

Zero coupon

Price = FV / (1+YTM)n

Price(@ 7%) = 100/(1+0.07)^14.55 = 37.37

Price(@ 6%) = 100/(1+0.06)^14.55 = 42.84

Actual profit= (42.84 - 37.37) / 37.37 = 14.64%

Predicted Price change = (-duration*change in yield) + (0.5*convexity*change in yield2)

Predicted profit = (-13.6*-0.01) + (0.5*197.7*(-0.01)2) = 14.59%

Coupon Bond

Price = Coupon*(1 - 1/(1+YTM)n) / YTM

Price(@ 7%) = 5*(1- 1/(1+0.07)^40)/0.07 = 73.34

Price(@ 6%) = 5*(1- 1/(1+0.06)^40)/0.06 = 84.95

Actual profit = (84.95 - 73.34) / 73.34 = 15.84%

Predicted Price change = (-duration*change in yield) + (0.5*convexity*change in yield2)

Predicted profit = (-13.96*-0.01) + (0.5*338.8*(-0.01)2) = 15.65%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.