When exactly do we use this formula?
N = [V * (1 + RFR)n] / Futures price * multiplier
That formula is used when turning cash into equity using futures. That’s the first step in a multi-step process.
[N = [V * (1 + RFR)n] / (Futures price * multiplier)] tells you how many unrounded futures you can close on at the expiration of the contract. You’re investing cash today at the risk free rate [V * (1 + RFR)n] and using the proceeds at expiration to settle the futures (Futures price * multiplier).
After that you discount back the rounded number of futures * price to get the amount of cash needed today to buy the rounded number of contracts.
Then you may also have to make an adjustment for the dividend yield to calculate the effective number of shares purchased. Just do a few examples and it should click.
But what confuses me is knowing when it is used over the formula (B target - B p) / B futures * (stock value / futures price). I think there’s an EOC on this topic where inputs for both formulas were provided but the formula used is the one that adjusts the beta to the target beta.
The first equation is turning cash into equity without directing buying shares (high transaction costs).
The formula with beta is used for rebalancing a portfolio between stocks/bonds and adjusting the overall beta to a target beta.
If you understand the concept why risk free rate has to do with it, it makes knowing which formula to use very simple.
If have 10K in cash and you want to invest in equities synthetically using futures… you have two approaches:
-
Invest the full 10K into futures
-
Invest in a bond earning Rf for time T, and simultaneously invest ino futures with the assumption that you will have 10K * (1+Rf)t , because when the bond matures you can use that money plus the intersect to pay for the futures maturity.
Which sounds like it will make more money, method 1 or method 2.
The other formula with beta has nothing to do with the two approaches… its just a rebalancing technique.