In order to create a synthetic stock index using cash, the number of future contracts that needs to be bought is determined by [T-held(1+Rf)^t]/Pf*multiplier.
Why do we use T-held(1+Rf)^t rather than just T-held?
Can someone please clarify? Thanks.
This gets back to the discussion about synthetic equity in this thread (the discussion you described as interesting): http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91328468.
Because you won’t get ownership of the stock index until the future, you have to purchase an amount that corresponds to the amount your cash (T-bills) will be worth in the future, which is today’s amount of cash grown at the risk-free rate.
yeah i agree with s2000magician perfectly. rmber the pricing mechanism of futures contract from level 2 guy. the value of the cash held grown to the maturity/ expiration date by the risk free rate is simply equal to the futures price times the number of contracts and a multiplier. so solving for number of contracts to trade today will give you the outcome you are refering to.
hope it clear to you.
Thanks. Got it.
Do you know why don’t we use (1+Rf) in the formula used when changing allocation between equity and bonds?
Because unlike cash, neither stocks nor (long-term) bonds are assumed always to grow at the risk-free rate: their values fluctuate.
The index futures used for synthetic positions don’t cover the risk-free returns. (Futures earn equity less risk-free)
Equity/bond returns include the risk-free returns. (alpha measures equity less risk-free).
http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91328468
Check Item #6. S2000’s example.