Question

1. Assume you have a $500,000,000 portfolio: 50% equity with a beta of 1.2, and 50% fixed income, corporate bonds, average credit quality of BBB, duration of 5. You wish to design a portfolio: 75% equity asset allocation, beta 1.6, fixed income 25% asset allocation, duration 3. The available futures are: equity index 2,000, multiplier 250, fixed income Tbond $100,000 par, 97 price, 2 duration. The simulation is that in one day the market appreciates by 1.5% and the interest rates fall by 1%. Provide the correct number of contracts and do a proof.

Answer 1

Answer :

The current allocation of Equity = 500 million $*50% = 250 million $ with a Beta of 1.2

Proposed equity allocation = 500 million $*75% = 375 million $ with a Beta of 1.6

As the proposed value of equity and Beta are higher than present, we need to buy or go long on equity index futures. The Beta of index futures is 1. Value of one contract = 2000*250 = 0.5 million $

Number of index future contracts to be bought to get the proposed allocation = [(375 million *1.6) - (250 million * 1.2)] / 0.5 million = (600 - 300) / 0.5 = 600 Contracts of index futures

The current allocation of fixed income = 500 million $ *50% = 250 million $ with a duration of 5.

Proposed fixed income allocation = 500 million $*25% = 125 million $ with duration of 3 .

As the proposed value of fixed income allocation and duration are lower than present, we need to sell or go short on fixed income T - Bonds future. The duration of T - bonds is 2. Value of one contract of T - Bond = 97/100*100000 = 0.097 million $

numer of T - Bonds to be sold or short to get the proposed allocation = [(250 million *5) - (125 million*3)]/0.097 million = (1250 - 375)/0.097 = Approx 9021 contracts of T -Bonds futures