Selected Data:

Portfolio: total 25 billion: 3b in equities, 22b in bonds.

- $ 3 billion in equitiies has to be converted to cash. Annual Risk free rate: 5%. Time to futures expiration: 5 mths.

Futures price: 1,058. Multiplier: 250.

The number of futures to be sold: (3,000,000,000 (1+.03)^5/12)/25*1,058 = 11,482.71 contracts.

- Adjust $25 billion into 25% stocks and 75% bonds.

Requires selling $3,250,000,000 in bonds and buying stock futures. The target beta is 1 and the futures beta is also 1.

The answer provided is [(beta target - beta portfolio)/beta futures]* Value of portfolio/price of portfolio* multiplier =

[(1-0/1) * 3,250,000,000] /250*1,058 = 12,287.33

My question: in “2.” are we not effectively equitizing cash and since the target and futures beta is the same, how come we are not using the formula of “1” i.e. [3,250,000,000 * (1+.03)^5/12] /250*1,058 = 12,439 contracts.

Thanks.