# currency hedging the principal

When currency hedging the Principal, the return of futures is given as: -(Ft - F0)/F0. I dont get this. If I sold a futures contract, wouldnt the payoff at time t be determined by the actual spot rate at time t. In other words, why is the formula not: -(St - F0)/F0 Thanks.

OK here’s why: whenever the hedge is lifted prior to the maturity date of futures, there is a basis risk and it should use the futures rate on that date.

I thought the formula was -(Ft - F0)/S0.

needhelp Wrote: ------------------------------------------------------- > When currency hedging the Principal, the return of > futures is given as: > > -(Ft - F0)/F0. > > I dont get this. If I sold a futures contract, > wouldnt the payoff at time t be determined by the > actual spot rate at time t. In other words, why is > the formula not: > > -(St - F0)/F0 > > Thanks. I made the same mistake as you did. the way to correct this is to realize that futures is mark-to-market. this market is futures market, not the spot market.

CFAAtlanta Wrote: ------------------------------------------------------- > I thought the formula was -(Ft - F0)/S0. very interesting that Schweser uses F0 in the denominator and CFAI uses S0. It makes me nervous about schweser.

cfa text is a little confusing: 1. you are right, you would usually use F0 in the denominator 2. but cfa uses S0 just because of mathematics: see below you have the profit of your portfolio (final minus initial, in your own currency terms) plus your profit in the futures position, and that profit (or loss) in the futures position is equal to the amount to hedge (V0) times the change in the futures (your Ft - F0) you divide all of that by the initial portfolio value (V0 x S0) to get the rate of return when you are hedged all they do is separate the second part of the equation = the futures. As you have V0 both in the numerator (V0 times the change in the futures) and in the denominator (V0 x S0), they take it out V0 and you end with only S0 in the denominator so it is not exactly that they use S0 in de denominator “per se”, is just the result of an ecuation

probalby b/c they are assuming that Fo=So at T 0.

wow, just seen what I wrote… my english is quite bad… hope it doesn´t sound very confusing… hala_madrid Wrote: ------------------------------------------------------- > cfa text is a little confusing: > > 1. you are right, you would usually use F0 in the > denominator > > 2. but cfa uses S0 just because of mathematics: > see below > > you have the profit of your portfolio (final minus > initial, in your own currency terms) plus your > profit in the futures position, and that profit > (or loss) in the futures position is equal to the > amount to hedge (V0) times the change in the > futures (your Ft - F0) > > you divide all of that by the initial portfolio > value (V0 x S0) to get the rate of return when you > are hedged > > all they do is separate the second part of the > equation = the futures. As you have V0 both in the > numerator (V0 times the change in the futures) and > in the denominator (V0 x S0), they take it out V0 > and you end with only S0 in the denominator > > so it is not exactly that they use S0 in de > denominator “per se”, is just the result of an > ecuation Well explained. But even the CFAI text is slightly unclear in this respect as they call (Ft-F0)/S0 the return on the sale of futures contracts. I remember thinking about this when I went through the reading. Someone should ask Schweser for their usage.

I think it’s just an error and it should be (Ft - f0)/f0. What does S0 have to do with your return in the futures contract? > you divide all of that by the initial portfolio > value (V0 x S0) to get the rate of return when you > are hedged is a bogus step

Schweser uses F0 on p113, but S0 on p129 (in the answer to Q2). I believe CFAI uses S0 all along (in the text and in the solutions the end of chapter problems). Did anybody inquire with Schweser on this topic?

Possibly So = Fo at Time 0

That would make sense, but it’s not the case in Schweser/CFAI examples bigwilly Wrote: ------------------------------------------------------- > Possibly So = Fo at Time 0 C’mon now. Unless you are usinng different notation than everyone else, S0 is the price of the underlier at time 0 and F0 is the price of the futures. They are very rarely the same.

C’mon JD. Some examples in the book will state that assume the futures price is the spot price at initiation…I didnt write the book This has been discussed, again the PV ofcourse wont be F1-F0/F0, as it is the Payoff that needs to be discounted back

Sort of related question, at maturity of the future, does Ft=St?

if St and Ft are on the same underlier then yes, otherwise there would be arb

Let’s say yes which is essentially true.

At expiration, theoretically they should be equal…however in the real world that isn’t really true, but for testing purposes it is true.