Question

This is the third time im submitting this question as no one will answer the 4th question. Part 4) this has not been answered on chegg yet. the response you gave to this was also not to part 4. please answer the very last question in relation to portfolio construction A newly issued bond has the following characteristics: Par value = $1000 Coupon rate = 8% Yield to Maturity = 8% Time to maturity = 15 years Duration = 10 years Calculate modified duration using the information above. If the yield to maturity increases to 8.5%, what will be the change (in dollar amount) in bond price? Identify the direction of change in modified duration if: i. the coupon of the bond is 4%, not 8%. ii. the maturity of the bond is 7 years, not 15 years. How can you construct a portfolio with a duration of 8 years using this bond and a 5 year zero coupon bond?

Answer 1

1. Calculation of Modified Duration:

Modified Duration = Macaulay Duration /(1+YTM)

Modified Duration = 10/(1.08) = 9.25926 or say 9.26

2. Change in the Bond Price.

If YTM increases from 8% to 8.5%

Percentage change in the price of bond = [(-1)(modified duration)(%change in YTM in the terms of basic points)

= [(-1)(9.26 years)(50 basis points)]

= -463 basis point, i.e., there is decrease in 4.63% in price of a bond.

Calculation of 50 basis point is (8.5% - 8%) * 100 ..........ie., 1% = 100 basis points

3. Identify the direction of change in modified duration if: i. the coupon of the bond is 4%, not 8%. ii. the maturity of the bond is 7 years, not 15 years

i. Modified Duration increase when the coupon of the bond was 4% and not 8%

When initerest rates are falling, the early payments' weighs are lower. Also for the payments the weighted average maturity is higher. A low proportion of the bond's total value is tied up in the coupon payments. This implies that the repayment of the par value would require more time.

ii. Since the maturity of the bond is decreased to 7 years and not 15 years. The modified duration will decrease bas on the case.

Lets assume that the yields are higher. Then the distant payments made by bond will have smaller present values and account for lesser share of bond's total value. Hence, the distant payments, receive lesser weights, resulting in smaller duration.

4. Construction of a portfolio with a duration of 8 years using this bond and a five year zero coupon bond.

D_portfolio = (WZero coupon Bond * D_{zero coupon bond} ) + (W_perpetuity * D_perpetuity )

W stands for Weights

D stands for Duration

The portfolio stands for zero coupon bond and perpetuity. Hence, the weight of the perpetuity is (1-W _{zero-coupon bond})

The equation could be rewritten as:

D = (W _{zero-coupon bond} * 5) + (1-W _{zero-coupon bond} ) * 11

By this way the duration of the portfolio should bee 8 years and duration of the zero coupon bond is 5 years.