Chapter_4_H_W_Solutions

# Chapter_4_H_W_Soluti - Problem 4.1 The price-yield relationship for any option-free bond is a convex relationship The convex shape of the

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1 Problem 4.1 The price-yield relationship for any option-free bond is a convex relationship. The convex shape of the price–yield relationship implies that for very small changes in the yield required (like 1 basis point), the percentage price change is roughly the same, whether the yield required increases or decreases. However, for large changes in the required yield (like 100 basis points), the percentage price change is not the same for an increase in the required yield as it is for a decrease in the required yield, specifically, the percentage price increase is greater than the percentage price decrease. Problem 4.2 a. @ y = 8%; P B (A) = \$100.00 @ y = 8.01% P B (A) = \$99.9819 b The price value of a basis point = \$100 – \$99.9819 = \$0.0181 per \$100. @ y = 8%; P B (B) = \$104.055 @ y = 8.01% P B (B) = \$104.014 b The price value of a basis point = \$104.055 – \$104.014 = \$\$0.0416 per \$100. Problem 4.2 (Continued) b. Macaulay duration (half years) = = = 3.77509 C. D M (years) = D M (periods) / 2 = 3.77509 / 2 = 1.8875 Modified Duration = 1.8875 / (1.04) = 1.814948 . For Bond B: D M (years) = D M (periods) / 2 = 8.3084 / 2 = 4.1542 Modified Duration = 4.1542 / (1.04) = 3.9944 000 , 1 \$ 04 . 1 ) 040 , 1 (\$ 4 04 . 1 ) 40 (\$ 2 04 . 1 ) 40 (\$ 1 4 2 ) ( + . . . + ) ( + 000 , 1 \$ 09 . 775 , 3 \$ Problem 4.2 (Continued) d. @ y = 8.20% b P B = 99.6379 @ y = 7.80% b P B = 100.3638 Approx. Duration (A) = (100.364 – 99.638)/2(\$100)(0.002) = 1.815 Approx. Duration (B) = (104.891 – 103.228)/2(\$104.055)(0.002) = 3.995 e. Convexity (A) = 4.28

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## This note was uploaded on 04/26/2010 for the course FIN 333 taught by Professor Nasseh during the Spring '10 term at Saint Louis.

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Chapter_4_H_W_Soluti - Problem 4.1 The price-yield relationship for any option-free bond is a convex relationship The convex shape of the

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