Question

Return to question A 12.25-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 1392 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. 1.25 points a. Suppose the yield to maturity on both bonds increases to 9% IWhat will be the actual percentage capital loss on each bond? il. What percentage capital loss would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Answer is complete and correct. Zero Coupon Bond Coupon Bond 10.72 % 11.09 % 10.63 % 11.00 % Predicted loss b. Suppose the yield to maturity on both bonds decreases to 7%. What will be the actual percentage capital gain on each bond? What percentage capital gain would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Answer is not complete Zero-Coupon Band Coupon Bond Actual gain Predicted gain

Answer 1

ke - Microsoft Excel (Product Activation Failed) Add-Ins View - 2x Dr General File Home Insert Page Layout Formulas Data Review % Cut Calibri -11AA = = = Ea Copy Paste Format Painter BIU - D A Clipboard Font Wrap Text Merge Merge & Center - Center SF $ 4:0 .00 :.: Insert Delete Format % % , Number Conditional Format Formatting as Table Styles Cell Styles Σ AutoSum : A Fill Sort & 2 Clear Filter Editing Find & Select Alignment Cells for BR382 BH BI BJ BL BM BN BO BP BQ BR BS BIO 2 381 382 BK ZERO COUPON BOND PAR VALUE YTM MATURITY 12.25 1000 8.00% 383 384 385 386 387 PRICE OF ZERO COUPON BOND 389.55 [=PV(BL383,B0382,,-BL382)] YTM 9.00% PRICE OF ZERO COUPON BOND 347.96 (=PV(BL387,B0382,,-BL382)] 388 389 390 391 ACTUAL LOSS IN ZERO COUPON BOND = -10.68% [=(BM388-BM385)/BM385] COUPON BOND COUPON RATE PAR VALUE PRICE OF COUPON BOND 6.0% MATURITY 1000 YTM 761.51 40 8.0% T=PV(BN394,BN393,-BL393*BL394,-BL394)] 392 393 394 395 396 397 398 399 9.0% YTM PRICE OF COUPON BOND 677.28 [=PV(BL397,BN393,-BL393*BL394,-BL394)] 400 ACTUAL LOSS IN COUPON BOND = -11.06% (=(BM398-BM395)/BM395] 401 beta port future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean YIELD bond portfolio WACC convexity DGM ferences: AZ118 RESI DIV POLICY NAME BOU 120% DIV YIELD Rea 1 + B A .lll + TO 24-11-2019

ke - Microsoft Excel (Product Activation Failed) Add-ins File Home Insert Page Layout Formulas Data Review View - 2x % Cut Calibri 11 A = = = V General A A Wrap Text Merge & Center - BIU - D $ % , :.: Σ AutoSum : A Fill Sort & Find & Clear Filter Select Editing Formatting as Table Styles Styles Font Alignment Number Cells fev BI BJ B K BL BM BN BO BP BQ BR BS BTS PREDICTED LOSS ZERO COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -MODIFIED DURATION*(CHANGE IN YIELD) + 0.5 X CONVEXITY X (CHANGE IN YIELD)^2 PRICE CHANGE(%) = -11.34*(0.01) + 0.5 X 139.2 x (0.01)^2 = -10.64% E Copy Paste Format Painter Clipboard BK417 2 BH 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -12.3*(0.01) + 0.5 X 272.9 x (0.01)^2 = -10.94% ZERO COUPON COUPON BOND BOND ACTUAL LOSS 10.68% 11.06% PREDICTED LOSS 10.64% 10.94% YTM INCREASES PRICE DECREASES SO THERE IS A LOSS, SO ANSWER WILL BE NEGATIVE 418 419 420 421 beta port future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean YIELD bond portfolio WACC DIV YIELD I- convexity DGM ferences: P33 RESI DIV POLICY NAME 20J 120% Rea + DEF * 10 ENG 24-11-2019

ke - Microsoft Excel (Product Activation Failed) Add-Ins File Home Insert Page Layout Formulas Data Review View - 2x % Cut Calibri 11 A = = = V General A A Wrap Text Fat Merge Merge & Center - Center BIU - D E = E Copy Paste Format Painter Clipboard 5 st $ $ % % , , .0 .00 :.: Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles Σ AutoSum : A Fill Sort & Find & Clear Filter Select Editing Font Alignment Number Cells for BL398 вн BI BI BM BN BO BP BQ BR BS BTA Д 381 382 вк I BL ZERO COUPON BOND PAR VALUE YTM MATURITY 12.25 1000 8.00% 383 384 PRICE OF ZERO COUPON BOND 389.55 [=PV(BL383,B0382,,-BL382)] 385 386 387 388 YTM 7.00% PRICE OF ZERO COUPON BOND 436.56 (=PV(BL387,B0382,,-BL382)] 389 390 ACTUAL GAIN IN ZERO COUPON BOND = 12.07% (=(BM388-BM385)/BM385] 391 392 393 394 395 396 COUPON BOND COUPON RATE PAR VALUE PRICE OF COUPON BOND 6.0% MATURITY 1000 YTM 761.51 40 8.0% T=PV(BN394,BN393,-BL393*BL394,-BL394)] 397 7.0% YTM PRICE OF COUPON BOND 866.68 [=PV(BL397,BN393,-BL393*BL394,-BL394)] 398 399 400 401 ACTUAL GAIN IN COUPON BOND = 13.81% (=(BM398-BM395)/BM395] beta port future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean YIELD bond portfolio WACC convexity DGM ferences: BA116 RESI DIV POLICY NAME 20J 120% DIV YIELD Rea + B A .lll + TO 24-11-2019

ke - Microsoft Excel (Product Activation Failed) Add-ins File Home Insert Page Layout Formulas Data Review View - 2x % Cut Calibri Dr General -11AA = = = A E = 5 Wrap Text Fat Merge Merge & Center - Center BI U D st $ $ % % , , .0 .00 :.: Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles Σ AutoSum : A Fill Sort & Find & Clear Filter Select Editing Font Alignment Number Cells Fax BI BJ B K BL BM BN BO BP BQ BR BS BTS E Copy Paste Format Painter Clipboard B0413 2 BH 401 402 403 404 405 406 407 PREDICTED GAIN ZERO COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -MODIFIED DURATION*(CHANGE IN YIELD) + 0.5 X CONVEXITY X (CHANGE IN YIELD)^2 PRICE CHANGE(%) = -11.34*(-0.01) + 0.5 X 139.2 X (-0.01)^2 12.04% 408 COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -12.3*(-0.01) + 0.5 X 272.9 X (-0.01)^2 = 13.66% 409 410 411 412 ZERO COUPON COUPON BOND BOND ACTUAL GAIN 12.07% 13.81% PREDICTED GAIN 12.04% 13.66% 413 414 415 416 417 418 419 420 421 beta port future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean YIELD bond portfolio WACC convexity DGM ferences: BA115 RESI DIV POLICY BO NAME 120% DIV YIELD I- - Rea B A .lll + TO 24-11-2019