 # Synthetic positions: which formula to use

The below 2 questions seem the same to me, how do we know which formula to use for no. of contracts? 1. Reading 27 practice problem 3A: Investment management firm has a client who woule like to temporarily reduce exposure to equities by converting a \$25m equity position to cash for period of four months. Firm plans to create synthetic positon using equity futures contracts. Calculate number of contracts to create cash (i have left out some info here). Contracts = Beta x (money to be invested x (1 + risk-free)^T) / (multiplier x futures price) 2. Reading 27 practice problem 5A Pension fund manager expects to receive cash inflow of \$50m in 3 months and wants to use futures contracts to take a \$17.5m synthetic position in stocks and \$32.5m in bonds today.Calculate no. of stock and futures contracts in order to synthetically take the desired position in stocks. Contracts = [(Beta target - Beta portfolio) / Beta future] x (value portfolio / futures price)

I think you have the first one wrong - it is not beta, it is the value. = V(1+r)^t/qf

They seem to give you r if they want you to use the first one and Betas if they want you to sue the second one.

They key is that with synthetic positions you are hedging the future value, so 3A’s hedged value is \$25mn x (1+rt)^T

5A’s future value in 3 months is \$50mn, so that is the value you are hedging.

Both questions mention the word synthetic, hence why i get confused on which to use?

Same i also get confused in this.

Please get my screen name correct: _ S2000magician _, not Smagician2000.

When creating a synthetic position, you use the future value. If they give you the present value, increase it by the risk-free rate. If they give you the future value, use it as is.

Extend a bit more:

1. Synthetic position in equity or bond if given for their initial value Vo, multiply by (1+rf)^t for equity and (1+i)^t for bond.

2. Use Beta, if the mkt. differs. For the same mkt. (position and synthetic instrument) it does not differ so default is 1.

3. Use Target B if it is mentioned, else it is (1-0)/1 for the whole position

Rest of them are plug and play

Okay so once we have the future value, we then divide it by (multiplier x futures price) to find contracts is that correct? While if we already have futures price (value of the portfolio), we go straight to [(Beta target - Beta portfolio) / Beta future] x (value portfolio / futures price)