Modifying asset allocation

Selected Data:

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

  1. $ 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.

  1. 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.


first one is a case of synthetic cash creation from equity.

2nd one is selling a bond futures position and getting to a equity futures position…(there is no synthetic involved here).

But in 2 are we not selling bond futures to get cash and then converting this cash to equity? If yes, then should not (1) kick in?

no it would not … since you are getting the bond into cash immediately and then using that cash to buy the stock futures and not sometime in the future point.

in (1) you are doing that in a few months time…