Question

A 13.05-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 1572 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%. 1. What will be the actual percentage capital loss on each bond? ii. 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 but not entirely correct. Zero-Coupon Bond Coupon Bond 11.33 % 7.92 % % 11.29 % 10.94 % Actual loss 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 complete but not entirely correct. Zero-Coupon Bond Coupon Bond 12.91 % 8.87 % 12.87 % 13.66 % Actual gain Predicted gain

Answer 1

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©vo a ax ENG 01:13 23-03-2020 ... o X BK402 Formula Bar BL BJ BK BL BM BN BO BP Formu Du BR BSA 381 382 ZERO COUPON BOND PAR VALUE YTM MATURITY 13.05 1000 8.00% 383 384 385 PRICE OF ZERO COUPON BOND 366.29 [=PV(BL383,80382,,-BL382)] 386 9.00% 387 388 389 YTM PRICE OF ZERO COUPON BOND 324.78 [=PV(BL387,80382,,-BL382)] 390 ACTUAL GAIN IN ZERO COUPON BOND = -11.33% [=(BM388-BM385)/BM385] COUPON BOND COUPON RATE PAR VALUE PRICE OF COUPON BOND 6.0% MATURITY 1000 YTM 761.51 40 8.00% [=PV(BN394,BN393,-BL393*BL394,-BL394)] 391 392 393 394 395 396 397 398 399 400 9.00% YTM PRICE OF COUPON BOND 677.28 [=PV(BL397,BN393,-BL393* BL394,-BL394)] ACTUAL GAIN IN COUPON BOND = -11.06% (=(BM398-BM395)/BM395] 401 402 403 404 1 ... UTILITY, SHARPE, beta coNvexity DGM beta | port future INDEX INTL CAP BUD SANDRINE LEASING PORTFOLO Q | DIR right clean YIELD bond portfolio ... :

© vol dx 2 ENG 01:13 23-03-2020 ... o X BJ418 BI BJ BK BL BM BN BO BP BQ BR BS . 401 402 PREDICTED GAIN 403 404 ZERO COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -MODIFIED DURATION*(CHANGE IN YIELD) + 0.5 X CONVEXITY X (CHANGE IN YIELD)^2 PRICE CHANGE(%) = -12.08*(0.01) + 0.5 X 157.2 X (0.01)^2 = -11.29% COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -12.30*(0.01) + 0.5 X 272.9 x (0.01)^2 = -10.94% ZERO COUPON BOND 11.33% 11.29% COUPON BOND 11.06% 10.94% ACTUAL GAIN PREDICTED GAIN 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 ... UTILITY, SHARPE, beta coNvexity DGM beta port future INDEX INTL CAP BUD SANDRINE LEASING PORTFOLOQ DIR right clean YIELD bond portfolio ... +

© vol dx 2 ENG 01:13 23-03-2020 ... o X BK417 BI BJ BK BL BM BN BO BP BQ BR BSA ZERO COUPON BOND PAR VALUE YTM MATURITY 13.05 1000 8.00% 2 416 417 418 419 420 421 422 423 424 425 426 427 428 PRICE OF ZERO COUPON BOND 366.29 (=PV(BL421,B0420,,-BL420)] 7.00% YTM PRICE OF ZERO COUPON BOND 413.56 [=PV(BL425,80420,,-BL420)] ACTUAL GAIN IN ZERO COUPON BOND = 12.91% (=(BM388-BM385)/BM385] 429 430 COUPON BOND 431 COUPON RATE 6.0% MATURITY 1000 YTM 761.51 40 8.00% PAR VALUE PRICE OF COUPON BOND (=PV(BN432,BN431,-BL431*BL432,-BL432)] 7.00% 432 433 434 435 436 437 438 439 YTM PRICE OF COUPON BOND 866.68 (=PV(BL435,8N431,-BL431*BL432,-BL432)] ACTUAL GAIN IN COUPON BOND = 13.81% [=(BM398-BM395)/BM395] ... UTILITY, SHARPE, beta coNvexity DGM beta port future INDEX INTL CAP BUD SANDRINE LEASING PORTFOLOQ DIR right clean YIELD bond portfolio ... •

01:14 ' vol dx 2 ENG , 23-03-2020 26 ... o X : x fix BI BI BK BL BM BN BO BP BQ BR BS BK461 - 439 440 441 PREDICTED GAIN 442 ZERO COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -MODIFIED DURATION*(CHANGE IN YIELD) + 0.5 X CONVEXITY X (CHANGE IN YIELD)^2 PRICE CHANGE(%) = -12.08*(-0.01) + 0.5 X 157.2 X (-0.01)^2 = 12.87% COUPON BOND (CONVEXITY RULE) PRICE CHANGE(%) = -12.30*(-0.01) + 0.5 X 272.9 X (-0.01)^2 = 13.66% ZERO COUPON BOND 12.91% 12.87% COUPON BOND 13.81% 13.66% ACTUAL GAIN PREDICTED GAIN 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 ... UTILITY, SHARPE, beta coNvexity DGM beta port future INDEX INTL CAP BUD SANDRINE LEASING PORTFOLOQ DIR right clean YIELD bond portfolio ... +