Question

A BBB corporate bond portfolio has maturity of Eight years and semiannual. yield to maturity is Five percentage, coupon rate is Eight percentage. The portfolio includes one million bonds.

1.What's the face value of the portfolio.

2.What's the market value of the portfolio.

3.What's the modified and effective duration of the portfolio.

4.If the T-bond futures contract is $98 and whose duration is Four. In order to decrease the portfolio duration to 0, how many contracts needed? Long or short?

Answer 1

1). Assuming a par value of 100, face value of the portfolio will be

par value per bond*number of bonds = 100*1,000,000 = 100,000,000 or 100 million

2). FV (par value) = 100; PMT (semi-annual coupon) = annual coupon rate*par value/2 = 8%*100/2 = 4; N (number of payments) = 8*2 = 12; rate (semi-annual yield) = 5%/2 = 2.5%, solve for PV.

Price per bond = 119.58

Market value of the portfolio = price per bond*number of bonds

= 119.58*1,000,000 = 119,582,504

3). Modified duration = 6.096 years (calculated using MDURATION function in excel.

Effective duration = (P-y - P+y)/(2*P0*change in y) where P-y = price when yield decreases by 1% i.e. yield = 4%; P+y = price when yield increases by 1% i.e. yield = 6%; P0 = current price

Effective duration = (127.16-112.56)/(2*119.58*0.01) = 6.102 years

4). Number of contracts to be sold = (Dt - Di)*MVp/(Df*Pf) where

Dt = effective duration to be achived = 0; Di = initial effective duration = 6.102; MVp = market value of portfolio = 119,582,504 ; Df = effective duration of the fuures contract = 4; Pf = 98*100,000 = 9,800,000 (one T-bond futures has a contract size of 100,000)

Number of contracts = (0-6.102)*119,582,504/(4*9,800,000) = -18.62 or 19 contracts to be shorted