Hi, does anybody understand why when constructing a synthetic stock position with index futures and T-bills, we use T(1+Rfr) in the formula and not T ? nb future contracts= (T(1+ Rfr) / (Future Price * multiplier)) Thanks, Bern
Using T(1+ Rfr) locks in the risk free rate of return, while just using T reduces the beta to zero. If you see the word synthetic, just use this equation, if it just mentions removing the systematic risk of the portfolio for a period of time, use T.
- to create a synthetic stock, you long the future and long T-bills. 2. T(1+Rf) is your cash(T-bill) value at the end of the time horizon. 3. buy the stock/index with your cash at the end of the time horizon.
If you remove the sytematic risk, you should get the Risk free rate ! It sill doesn’t explain why using T instead of T(1+Rfr) is not sufficient…
It would be fine if T is in future value terms…
For a synthetic equity position, sometimes they will throw futures beta (let’s say 1.04) as a trap. Anyone know why we ignore it? I know it’s not in the equation, but what’s the reasoning?
If you are investing in the index it is irrelevant what the beta of the future/index is you already know what you are getting. If you are looking to change beta from say 1.5 to 1.04 then the Beta is relevant. If there was a question that said you wanted to create synthetic equity with a 1.0 beta and the beta of the futures was 1.04 then you would use the normal beta formula.