Question

A bond portfolio named VEX comprises four bonds (face value=$1000):

1) 100 semi-annual bond, 5-year maturity, a coupon rate of 4%

2) 200 annual bonds, 30-year maturity, 8% coupon bond.

3) 300 zero-coupon bonds, 10-year maturity.

4) 400 zero-coupon bonds, 20-year maturity.

1. If the required yield (discount rate) is 6% for all bonds per year, what is the market fair value of VEX? What is each bond’s weight in the portfolio?

Answer 1

we need to calculate current market price of each bond to get the market fair value of VEX. we can use financial calculator to calculate current price of bonds with below key strokes:

1) N = semi-annual maturity = 5*2 = 10; FV = face value = $1,000; PMT = semi-annual coupon = $1,000*4%/2 = $20; I/Y = semi-annual required yield = 6%/2 = 3% > CPT = compute > PV = current price = $914.70

2) N = maturity = 30; FV = face value = $1,000; PMT = annual coupon = $1,000*8% = $80; I/Y = annual required yield = 6% > CPT = compute > PV = current price = $1,275.30

3) current price of zero-coupon bond = face value/(1+required return)maturity = $1,000/(1+0.06)10 = $1,000/1.0610 = $1,000/1.7908 = $558.41

4) current price of zero-coupon bond = $1,000/(1+0.06)20 = $1,000/1.0620 = $1,000/3.2071 = $311.81

market fair value of VEX = no. of bond 1*price of bond 1 + no. of bond 2*price of bond 2 + no. of bond 3*price of bond 3 + no. of bond 4*price of bond 4

market fair value of VEX = 100*$914.70 + 200*$1,275.30 + 300*$558.41 + 400*$311.81 = $91,470‬ + $255,060‬ + $167,523 + $124,724‬ = $638,777‬

bond 1's weight in the portfolio = market value of bond (no. of bonds*price of bond)/market value of portfolio = $91,470/$638,777‬ = 0.14

bond 2's weight in the portfolio = $255,060/$638,777 = 0.40

bond 3's weight in the portfolio = $167,523/$638,777 = 0.26

bond 4's weight in the portfolio = $124,724/$638,777 = 0.20