Pricing + Valuation of Forwards and Futures

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rohit.nerurkar

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This might be a dumb question but I’m getting really hung up on Reading 48 on the Futures contract. I feel like I understood the forwards reading pretty well but I’m struggling to understand why many of the pricing and valuation formulas are different for futures. Shouldn’t they be the same formulas with adding new wrinkles like the mark to market feature and conversion factor?
 
The main difference on the valuation comes from the Marked to Market.
With a forward contract, because it is not marked to market the long end or short end will accumulate value throughout the contract; while a future contract will have no value once the future has been marked to market. You can value a futures contract immediately prior to marking to market where the value would be: current futures price (based on the current spot) - previous marked to market. However, once the marked-to-market occurs, you’re value is now zero (where your margin account has accounted for any changes in pricing).
From a pricing standpoint, if you’re using Schweser Notes the pricing may seem different but in actuality its similar. I know that schweser was using the formula of (So- PVD)(1+Rf) for forward pricing and (So)(1+Rf) - FVD for futures. While these look different, they are similar and should yield same pricing. However, in the future chapter we are also accounting for net cost, which I do not believe was discussed much in the forward contract chapter. Hopefully this helps.
 
Thank you! I think this helps a lot.
One part that I was really getting stuck on was in the CFA books theres a few questions that ask you to find the futures price in terms of the two specifications of the dividend yield. Is this just asking you to do it from using the FV and then from using the PV?
 
Oh yeah - finding the future price based on yield can be quite tricky and this is more specifically talking about an equity index future.
So there are a couple different equations that are related to yield and they can get quite confusion.
The first one is pretty straight forward and should be similar to calculations we’ve had previously and the only calculation that Schweser provides for Equity Index futures
1) FP = So x e ^ (Continuously Compounded Risk Free Rate - Contiounsly compounded dividend yield)(T)
you could also show this for a discrete dividend yield as
FP = (So - PV(Dividend)) (1+r)^T
However, CFAI continues this discussion with two additional calcuations of no-arbitrage future pricing based on the stock index being discounted at dividend yield and compounded at risk free rate. They are basically showing different formulas, based on underlying assumptions of the DDM and using subsitution, to find the future price.
2) FP = (So / (1+δ)^T) (1+r)^T
where
1 / (1+δ)^T = 1 - (FV / So (1+r)^T)
so (1+δ)^T = 1 / (1 - (FV / So (1+r)^T))
and the final variation is
3) FP = SO(1- δ*)(1+r)T
where δ* = PV / SO OR = (FV/(1+r)T)/SO
Basically showing multiple ways to skin a cat, hopefully this helps. I know that those 4-5 pages within the CFAI book contain a lot of equations and it takes a while to deterime what they are actually trying to tell us.
 
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