Consider a portfolio 15,000,000 portfolio with a weighted duration of 7.5. Next, suppose that
the portfolio manager wants to completely isolated the portfolio from changes in interest
rates. Suppose the mangers is considering the 10-year note futures (107:8) contract and the
30-year note futures (98:16)contract. Which contract is preferable? How many contracts
would used? Is it a long or a short position.
Duration of the 10-year futures contract
step 1 = calculate the implicit YTM = 5.062619
step 2 = calculate duration = 7.755618
Duration of the 30-year futures contract
step 1 = calculate the implicit YTM = 6.10942
step 2 = calculate duration = 14.14241
The 30-year futures would be preferred, since the duration of the 10-year contract is close to
the duration of the portfolio
Number of contracts so that the duration of the combined portfolio (cash and futures) is zero
n = -(duration of portfolio x value of portfolio / duration of futures x price of futures contract)
= -80.7594 which round to = -81
Consider a bond portfolio with $250,000,000 in assets. It is composed of approximately 60% U.S.
government securities (Treasury and agency securities) and 40% in a broadly diversified portfolio
of corporate bonds. Suppose that the manager wants to increase the exposure to corporate
bonds using derivatives, and the Lehman Aggregate Bond futures contract will be used to gain
this exposure. Show what will be done and the structure of the portfolio when it is completed.
Note that the government "sleeve" has the duration characteristics of the 10-year Treasury
note, and the 10-year Treasury futures contract is 106:8. The Lehman Agg Bond index contract is
1122.5
250000000 = 0.6*250000000-Treasury 10-year futures +0.4*250000000+ Lehman agg futures
nominal size of the Treasury futures = 250,000,000*.05 = $12,500,000
nominal size of the Lehman agg futures = 250,000,000*.05 = $12,500,000
Treasury futures contract price = 100,000*1.0625 = 106250
Lehman Bond Agg contract price = 100*1122.5 = 112250
number of Treasury futures contracts = 118 short
number of Lehman Bond Agg futures = 111 long
Basis risk: (1) the government bond "sleeve" and the 10-year Treasury note futures is a cross
hedge, since the movement in the agency securities and the Treasury securities may diverge. (2)
the corporate bond "sleeve" and the Lehman Agg Bond futures is also a cross hedge if the
exposure with the bond sleeve differs from the exposure within the Lehman Agg Bond Index