Why does both Schweser and CFAI claim that currency future payoff is (Ft-Fo)/Fo. How come it is not mentioned that payoff will happen in the future and you have to discount the payoff by risk free rate?
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Probably the same reason why in options they ignore future value of price you pay for the option…
I think they are more concerned with the nominal payoff in absolute terms, ignoring the time value of money… That is how I look at the lack of present value request… Best regards,
“currency future payoff is (Ft-Fo)/Fo.”? The future payoff is Ft-F0*notional size of contract.
Joey, but payoff will happen in the future, so how come it is not discounted? The payoff of future at expiration would be Fo-Spot * Notional, the payoff of Ft-Fo * Notional is when you want to close position prior to expiration, so there is still time value left…
I guess I don’t understand the question. There’s a payoff and there’s a discounted payoff and both might be useful for different things.
Joey, how is just the payoff useful, if it is not what you would use in real world to make a decision?
I don’t know how it is useful. My wife has 700 pairs of shoes and I don’t know how those are useful either.
Joey is wondering future value of 700 pairs of shoes, kid wants present value of his krona. 
anyway, i think payoff is useful in a sense that we all know replicating portfolios have the same payoff, they therefore should be priced the same based on no-arb. if one asks you why you discount that payoff of currency futures by risk-free rate but not some other rate, you may have to show them what its replicating portfolio payoff is. does it make better sense in “real” world?
rand0m, it does, but do you agree that Ft-Fo should be discounted and CFAI doesnt discount it? I just want to make sure i am understanding futures pricing correctly.
(Ft - Fo)/Fo is a rate of return. Your gain is that number times the notional. Your total value is that number plus one times the notional? Now, how are you setting up the problem? Did you buy at Fo in the past, and Ft is now? In that case, it shows how much your future gained or lost in percentage terms (after subtracting one, of course). No need to discount. Is Fo the price today and Ft the imagined price at expiration? Then of course it is the rate of return from the perspective of someone at time t. If you discount it back to the present, then you will discover that the value is Fo, assuming that Ft is simply determined by covered interest arbitrage. If you have some other model that predicts Ft, then you’ll have something else, and the difference between your prediction (assuming it’s correct) and the covered interest arbitrage price will either be used at its future value for calculations about the future, or you’ll need to discount it back to the present to for calculations about current values (and probably discount more for the risk that your prediction isn’t actually correct).
t0: Going long Future price (strike) Fo time to maturity t So - spot Fo=S*e^(rd-rf)*t - (rd - r domistic rf - r foreign) t1 Short F1 = S1 * e^(rd1-rf1)*(t-t1) To close position i short F1 My future payoff, i buy at Fo and sell at F1 so i will get in the future F1-Fo so my PV = (F1-Fo)*e^rd1(t-t1) So please, explain to me what is “Rate of return” if CFAI clearly closes position and shows how much money you would have if you would hedge your posittion with futures
comp_sci_kid Wrote: ------------------------------------------------------- > rand0m, it does, but do you agree that Ft-Fo > should be discounted and CFAI doesnt discount it? > I just want to make sure i am understanding > futures pricing correctly. if they use the word, payoff, they are talking about futue event to my knowledge. i remember i saw the formula you mentioned when they (cfai and schweser) compute hedged returns of a foreign holding. they decomposed the return into local return and return from the hedge. if we are talking about the same spot, then i dont think the hedged return should be discounted.
rand0m can you please explain why hedge return should not be discounted?
the basic form of return is return = EV(T) / BV(0) -1 this is the best explanation i can give. btw, in your previous note. you said Fo=S*e^(rd-rf)*t - (rd - r domistic rf - r foreign) i can understand the 1st part from IRP, but i got confused with the remaining part. what are they?
OK, I misunderstood the notation. I’ll have to think more about this. But my sense is that the decision to close a position is usually made in the future, and so the value at that time is what the equation is trying to predict. If there is a mismatch between the future expiration and when you are going to need the hedge, then I suppose you might try to predict the FV of the position and then discount back as you are wanting to do. Remember then you’d be subject to basis risk, because the future price wouldn’t have converged to the spot price yet, and interest rates may have changed in ways that shift the premium/discount, so you’d probably need to have to discount further for that risk.
Do you have Hull book? look currency futures in hull, explanation is really good there but lets say you want to price usd/eur future You take 1000 euro, invest at risk free and convert at t1 to euro, t - time to amturity future is dc/fc to - 1000 t1 - 1000 * e^(rf * t) * F Or convert 1000 at stop to dollars and invest to - 1000 * S t1 = 1000 * S *e^ (rd * t) So 1000 *e^(rf * t)* F = 1000 * S *e^(rd * t) or F = S*e^(rd-rf)*t
i am fine with F = S*e^(rd-rf)*t, it’s simply IRP it’s different from Fo=S*e^(rd-rf)*t - (rd - r domistic rf - r foreign) which you posted earlier.
bchadwick Wrote: ------------------------------------------------------- > OK, I misunderstood the notation. I’ll have to > think more about this. But my sense is that the > decision to close a position is usually made in > the future, and so the value at that time is what > the equation is trying to predict. > > If there is a mismatch between the future > expiration and when you are going to need the > hedge, then I suppose you might try to predict the > FV of the position and then discount back as you > are wanting to do. Remember then you’d be subject > to basis risk, because the future price wouldn’t > have converged to the spot price yet, and interest > rates may have changed in ways that shift the > premium/discount. CFAI and Schweser problem is that they omit those subtle points (like clearly Call profit is not Max(S-K,0) - Co, but Co brought to future, as there is always a time value. Some omissions i can understand but others i dont, especially in such complicated scenarios as currency futures