hi all

i am a bit confused with the practice problem 8 of the CFA book.

**the question is as follows** :

a Manager holding 350M of US Equities with beta of 1.1

The manager would like to Create a synthetic cash position by temporarily converting the US equity exposure in the fund into cash for a period of three months.

below are the market information:

**S&P 500 futures** **Treasury bond futures** Quoted futures price 2157 Quoted futures price $105,200 Multiplier $250 Duration 6.20 Beta 0.90 Yield beta 0.95 Maturity of futures 3 months Maturity of futures 3 months **Other US market data** Risk-free rate 0.50% S&P 500 dividend yield 3.00%

**The proposed solution by the CFA book**

The number of S&P 500 futures contracts needed to be sold to execute Strategy 2 is calculated as follows.

Nf=(βT−βSβf)(Sf)

**while i would have thought that**

Nf = 350M x (1+RFR)^0.25/Nq

Can somebody tell me where is the mistake in my reasoning? shouldn’t we always look at the FV of the cash that we are synthesizing?

Thank you