please use excel with the function illustrated.....

INVESTMENT MANAGEMENT AND PORTFOLIO THEORY Fall 2015 Homework 5 DURATION 1. A Consider a portfolio consisting of the following bonds: Bond Bond A Bond B Bond C No 500 1000 1500 Face value $2,000 $1,000 $1,000 Maturity 2 Years 5 Years 10 Years Coupon 2% 4% 5% Frequency Q S S Yield 1.75% 4.5 % 5.25% a. What is the price of each bond? b. What is the value of the portfolio? c. What is the duration and modified duration of each bond? d. What is the modified duration of the portfolio using the weighted average method? e. What is the duration of the portfolio using numerical method? f. If the yield of the bonds increase by 0.05% determine the value of the portfolio by calculating the new prices of the bonds. g. If the yield of the bonds increase by 0.05% determine the value of the portfolio using duration of the portfolio calculated by weighted average method. h. If the yield of the bonds increase by 0.05% determine the value of the portfolio using duration of the portfolio calculated by numerical method. 2. A portfolio of bonds is valued at $12,750,000. The yield of each bonds falls by 0.025% and the value of portfolio becomes $12,762,500. a. What is the Duration of the portfolio? b. What is the value of the portfolio if the rates increase by 0.03%? 3. Two portfolios of bonds are worth $5,000,000 each. Duration of portfolio A is 2.5 years and duration portfolio B is 4.77 years. c. If you think interest rates will rise, which of the two portfolios will you choose? Why? d. Suppose the rates rise by 0.05% what will be the value of the portfolios? e. If you think interest rates will fall, which of the two portfolios will you choose? Why? f. Suppose the rates fall by 0.03% what will be the value of the portfolios? 1. a. Price of Bond A = $2,009.81 Price of Bond B = $977.83 Price of Bond C = $980.74 b. Value of the portfolio = (500 x 2,0009.81) + (1,000 x 977.83) + (1,500 x 980.74) = $3,453,845 c. Duration of Bond A = 1.97 Duration of Bond B = 4.58 Duration of Bond C = 7.97 d. e. f. 2. g. h. Modified Duration of Bond A = 1.96 Modified Duration of Bond B = 4.47 Modified Duration of Bond C = 7.76 Modified duration of the portfolio = 5.14 Duration of the portfolio = 5.26 New Bond Prices A = $2,007.84 B = $975.65 C = $976.94 Value of portfolio = (500 x 2,007.84) + (1,000 x 975.65) + (1,500 x 976.94) = $3,444,980 Value of portfolio = $3,444,980 Value of portfolio = $3,444,980 a. % change in portfolio value = (12,762,500 - 12,750,000)/12,750,000 = 0.098% Approximate change in the value of portfolio = duration x change in yield x 100 Duration of portfolio = 0.098%/0.025% = 3.92 b. Duration of portfolio = 0.098%/0.03% = 3.27 3. a. If interest rate rises then the value of the bond will fall. The Bond with the lower duration will fall lesser. Thus in case market interest rises we should invest in Portfolio A since it has lower Duration. b. Percentage fall in value of the portfolio A = 2.5 x 0.05 = 0.125% B = 4.77 x 0.05 = 0.2385% Value of portfolio A = 5,000,000 x (1 - 0.001250) = $4,993,750 B = 5,000,000 x (1 - 0.002385) = $4,988,075 c. If interest rate falls then the value of the bond will rise. The Bond with the higher duration will rise higher. Thus in case market interest falls we should invest in Portfolio B since it has higher Duration. d. Percentage rise in value of the portfolio A = 2.5 x 0.03 = 0.075% B = 4.77 x 0.03 = 0.1431% Value of portfolio A = 5,000,000 x (1 + 0.000750) = $5,003,750 B = 5,000,000 x (1 + 0.001431) = $5,007,155 1. a. Price of Bond A = $2,009.81 Price of Bond B = $977.83 Price of Bond C = $980.74 b. Value of the portfolio = (500 x 2,0009.81) + (1,000 x 977.83) + (1,500 x 980.74) = $3,453,845 c. Duration of Bond A = 1.97 Duration of Bond B = 4.58 Duration of Bond C = 7.97 d. e. f. g. h. Modified Duration of Bond A = 1.96 Modified Duration of Bond B = 4.47 Modified Duration of Bond C = 7.76 Modified duration of the portfolio = 5.14 Duration of the portfolio = 5.26 New Bond Prices A = $2,007.84 B = $975.65 C = $976.94 Value of portfolio = (500 x 2,007.84) + (1,000 x 975.65) + (1,500 x 976.94) = $3,444,980 Value of portfolio = $3,444,980 Value of portfolio = $3,444,980 2. a. % change in portfolio value = (12,762,500 - 12,750,000)/12,750,000 = 0.098% Approximate change in the value of portfolio = duration x change in yield x 100 Duration of portfolio = 0.098%/0.025% = 3.92 b. Duration of portfolio = 0.098%/0.03% = 3.27 3. a. If interest rate rises then the value of the bond will fall. The Bond with the lower duration will fall lesser. Thus in case market interest rises we should invest in Portfolio A since it has lower Duration. b. Percentage fall in value of the portfolio A = 2.5 x 0.05 = 0.125% B = 4.77 x 0.05 = 0.2385% Value of portfolio A = 5,000,000 x (1 - 0.001250) = $4,993,750 B = 5,000,000 x (1 - 0.002385) = $4,988,075 c. If interest rate falls then the value of the bond will rise. The Bond with the higher duration will rise higher. Thus in case market interest falls we should invest in Portfolio B since it has higher Duration. d. Percentage rise in value of the portfolio A = 2.5 x 0.03 = 0.075% B = 4.77 x 0.03 = 0.1431% Value of portfolio A = 5,000,000 x (1 + 0.000750) = $5,003,750 B = 5,000,000 x (1 + 0.001431) = $5,007,155 1. a. Price of Bond A = $2,009.81 Price of Bond B = $977.83 Price of Bond C = $980.74 b. Value of the portfolio = (500 x 2,0009.81) + (1,000 x 977.83) + (1,500 x 980.74) = $3,453,845 c. Duration of Bond A = 1.97 Duration of Bond B = 4.58 Duration of Bond C = 7.97 d. e. f. 2. g. h. Modified Duration of Bond A = 1.96 Modified Duration of Bond B = 4.47 Modified Duration of Bond C = 7.76 Modified duration of the portfolio = 5.14 Duration of the portfolio = 5.26 New Bond Prices A = $2,007.84 B = $975.65 C = $976.94 Value of portfolio = (500 x 2,007.84) + (1,000 x 975.65) + (1,500 x 976.94) = $3,444,980 Value of portfolio = $3,444,980 Value of portfolio = $3,444,980 a. % change in portfolio value = (12,762,500 - 12,750,000)/12,750,000 = 0.098% Approximate change in the value of portfolio = duration x change in yield x 100 Duration of portfolio = 0.098%/0.025% = 3.92 b. Duration of portfolio = 0.098%/0.03% = 3.27 3. a. If interest rate rises then the value of the bond will fall. The Bond with the lower duration will fall lesser. Thus in case market interest rises we should invest in Portfolio A since it has lower Duration. b. Percentage fall in value of the portfolio A = 2.5 x 0.05 = 0.125% B = 4.77 x 0.05 = 0.2385% Value of portfolio A = 5,000,000 x (1 - 0.001250) = $4,993,750 B = 5,000,000 x (1 - 0.002385) = $4,988,075 c. If interest rate falls then the value of the bond will rise. The Bond with the higher duration will rise higher. Thus in case market interest falls we should invest in Portfolio B since it has higher Duration. d. Percentage rise in value of the portfolio A = 2.5 x 0.03 = 0.075% B = 4.77 x 0.03 = 0.1431% Value of portfolio A = 5,000,000 x (1 + 0.000750) = $5,003,750 B = 5,000,000 x (1 + 0.001431) = $5,007,155 1. a. Price of Bond A = $2,009.81 Price of Bond B = $977.83 Price of Bond C = $980.74 b. Value of the portfolio = (500 x 2,0009.81) + (1,000 x 977.83) + (1,500 x 980.74) = $3,453,845 c. Duration of Bond A = 1.97 Duration of Bond B = 4.58 Duration of Bond C = 7.97 d. e. f. g. h. Modified Duration of Bond A = 1.96 Modified Duration of Bond B = 4.47 Modified Duration of Bond C = 7.76 Modified duration of the portfolio = 5.14 Duration of the portfolio = 5.26 New Bond Prices A = $2,007.84 B = $975.65 C = $976.94 Value of portfolio = (500 x 2,007.84) + (1,000 x 975.65) + (1,500 x 976.94) = $3,444,980 Value of portfolio = $3,444,980 Value of portfolio = $3,444,980 2. a. % change in portfolio value = (12,762,500 - 12,750,000)/12,750,000 = 0.098% Approximate change in the value of portfolio = duration x change in yield x 100 Duration of portfolio = 0.098%/0.025% = 3.92 b. Duration of portfolio = 0.098%/0.03% = 3.27 3. a. If interest rate rises then the value of the bond will fall. The Bond with the lower duration will fall lesser. Thus in case market interest rises we should invest in Portfolio A since it has lower Duration. b. Percentage fall in value of the portfolio A = 2.5 x 0.05 = 0.125% B = 4.77 x 0.05 = 0.2385% Value of portfolio A = 5,000,000 x (1 - 0.001250) = $4,993,750 B = 5,000,000 x (1 - 0.002385) = $4,988,075 c. If interest rate falls then the value of the bond will rise. The Bond with the higher duration will rise higher. Thus in case market interest falls we should invest in Portfolio B since it has higher Duration. d. Percentage rise in value of the portfolio A = 2.5 x 0.03 = 0.075% B = 4.77 x 0.03 = 0.1431% Value of portfolio A = 5,000,000 x (1 + 0.000750) = $5,003,750 B = 5,000,000 x (1 + 0.001431) = $5,007,155