# Basis risk

Scweser book 4, page 218 “In our example in LOS 41.a, the PERCENTAGE change in the spot and futures exchange rates were deliberately constructed to be the same (i.e interest rates maintained the same relationship, so the basis didn’t change). Had the basis changed, the value of the hedge would have increase or decreased. That is, the gain on the futures contract could have been more or less than the translation loss on the principal. The investor must be aware of basis risk any time a futures hedge will be lifted prior to the futures maturity date. To aviod basis risk, the investor would have to match the maturity of the futures contract with the intended holding period.” I thought I had this down, but now I am not so sure. It is my understanding that they futures price must converge to the spot at expriation. Based on what they say above though that would lead to basis risk though IF your hedge was lifted at expiration. As long as the futures price at time zero is different than the spot at time zero then you will get different percentage returns to the future and spot assuming the converge at time T (expiration). In the example in the book it appears that the future did NOT expire when the hedge was lifted, but I am trying to reconcile what they are saying above. In one sentence they say if the percentage return to the spot and future is the same then you DON’T have basis risk. They then say, if you want to avoid basis risk set the maturity of the future to the intended holding period. Based on what I wrote above, as the future converges to the spot this should guarentee the percentage returns are different. I am sure I am missing something easy. Can someone help me out here?

I actually think I have it now, but would still like to hear other’s opinions.

I am having some issues trying to understand just what you are asking. But let me give it a shot. At the time of maturity, future price HAS TO EQUAL the spot price, this has to happen as futures are converted into the underlying. During the life of a futures contract however, its price can fluctuate in differing amounts relative to the underlying asset. This fluctuation between the price of the future and spot is the basis risk, if you instantaneously sold out of the future and spot prior to the maturity of the future you could be subject to some pricing difference between the two. This is similar to what we have seen in Credit Default Swaps and underlying straight debt. As financing has become more difficult to source CDS has started to trade rich to the underlying as people have been able to buy CDS with greater ease then the underlying. At Maturity of the Bond, the yield on both CDS and the bond will be equal but if you close out of the position prior to maturity there currently would be a price difference. (i.e. basis risk)

Let me try with an example: Scenario 1 Future with expiration at investment maturity (time T) At time zero: Spot= 50 Future exp at time T= 50.48 At time T: Spot=55 Future exp at time T=55 “The investor must be aware of basis risk any time a futures hedge will be lifted prior to the futures maturity date. To aviod basis risk, the investor would have to match the maturity of the futures contract with the intended holding period.” In #1 the maturity is equal to the holding period so this sentence says there is no basis risk. Scenario 2 Future with expiration later then investment maturity (time T+x) At time zero: Spot= 50 Future exp at time T+x= 50.48 At time T: Spot=55 Future exp at time T+x=55.53 In #2 the percentage move for the spot and the future are exactly the same at 10%. Which the say is a condition for no basis risk. “In our example in LOS 41.a, the PERCENTAGE change in the spot and futures exchange rates were deliberately constructed to be the same (i.e interest rates maintained the same relationship, so the basis didn’t change). Had the basis changed, the value of the hedge would have increase or decreased. That is, the gain on the futures contract could have been more or less than the translation loss on the principal.” I can’t reconcile the two. My guess is the I have the pricing of the futures wrong at time zero.

mwvt9 Wrote: >Scenario 1 > At time zero: > Spot= 50 > Future exp at time T= 50.48 > > At time T: > Spot=55 > Future exp at time T=55 Risk can be fully hedged in scenario 1. > Scenario 2 Future with expiration later then > investment maturity (time T+x) > > At time zero: > Spot= 50 > Future exp at time T+x= 50.48 > > At time T: > Spot=55 > Future exp at time T+x=55.53 The problem here is that Futures price can be 51 or 63, because only at expiration the futures price is equal to the spot price. does that help? “Had the basis > changed, the value of the hedge would have > increase or decreased. That is, the gain on the > futures contract could have been more or less than > the translation loss on the principal.” > I can’t reconcile the two. My guess is the I have > the pricing of the futures wrong at time zero.

and i guess if it was 51 or 63, then there would be basis risk of either 51-55 = -4 or 63-55 = 8…???

sbmfj Wrote: ------------------------------------------------------- > and i guess if it was 51 or 63, then there would > be basis risk of either 51-55 = -4 or 63-55 = > 8…??? correct

maratikus Wrote: ------------------------------------------------------- > mwvt9 Wrote: > >Scenario 1 > > At time zero: > > Spot= 50 > > Future exp at time T= 50.48 > > > > At time T: > > Spot=55 > > Future exp at time T=55 > > Risk can be fully hedged in scenario 1. > > > Scenario 2 Future with expiration later then > > investment maturity (time T+x) > > > > At time zero: > > Spot= 50 > > Future exp at time T+x= 50.48 > > > > At time T: > > Spot=55 > > Future exp at time T+x=55.53 > > The problem here is that Futures price can be 51 > or 63, because only at expiration the futures > price is equal to the spot price. does that help? > I understand that, but in their example they say there is no basis risk with the numbers I used because the spot and futures prices move by the same percentage amount. I don’t get this.

“In our example in LOS 41.a, the PERCENTAGE change in the spot and futures exchange rates were deliberately constructed to be the same (i.e interest rates maintained the same relationship, so the basis didn’t change).” I think the confusion has to do with the fact that “interest rates maintained the same relationship” does not mean that “interest rates did not change”. Basically, they say that they constructed the problem so that (%change in spot) = (%change in futures price). In order for that to happen, interest rates need to change around in the interim, but they don’t bother to tell you what exactly they did to maintain the relationship. However, if you have \$X amount of Futures to hedge \$Y amount of spot, then the hedge should work fine if \$X and \$Y change by the same percent.

Would you agree that at initiation of a futures contract with a maturity equal to your holding period, that you take on basis risk at beginning of the contract, but know at contract maturity you will have none? And, for the example in LOS 401a, you took on basis risk at initiation, but since the futures price relative to the spot didn’t change, your amount of basis risk didn’t change (which is really what you are worried about)? There is still one thing that gets me though. The return on the futures contract in the example above (call this future 1) directly offset the movement of the spot (perfect hedge I think), but the futures price didn’t equal the spot at expiration. IF I had went long a future with expiration at maturity(future 2) it would have closed at the spot, so it’s return would have been different from future 1. I believe my flaw in thinking comes from not knowing the price of future 2 and initiation and maybe the two futures would have the same percentage return after all. Am I way off base?

I think it’s a semantic thing. If you are planning to hold to expiration, you really don’t have any basis risk, because you know the prices will converge. On the other hand, if there’s a chance that you might have to exit the future before expiration, then you won’t know for sure how different the spot price and future price is, and that’s basis risk. In practice, the issue is usually that it can be hard to get the futures expiration date to line up exactly with when you want to access your money. As far as the “one more thing” that you brought up, I just don’t have enough context about the problem to really see what you’re getting at.

I understand if you don’t want to go any further with this…but if you do: The one more thing- Let’s saying my investment in the foreign asset returns 10% and the foreign currency depreciates 5%. In the example that you don’t have enough information on, the futures contract appreciates by 5% (future 1) to directly offset the loss in the currency even though the term of the contract wasn’t the same as the holding period of the investment (even though spot and futures prices are different). They have the same percentage return as you discussed above. But, if I instead used a future that matured at the time the holding period was up it would be (future 2) priced at the current spot at that time (the spot price at exp is given in the problem). So in order for the outcome to be the same future 2 would have to have a 5% appreciation also, right? This is not possible unless the futures prices are different at invitation from each contract (future 1 and 2). I was assuming they were the same at initiation (which is dumb). IRP would dictate different futures prices just based on the time differences and rates used. I am looking for confirmation that this is where the error in my thinking is really. If neither of them really suffered from basis risk in the end then the returns on the two different hedges would have to be equal right? They should both be perfect hedges.

I think you are correct in your statement and getting a little mixed up with two separate concepts, basis risk which is just the risk that the change in the price of the future is diferent than the price of the undelying, and the fact that the spot= future price at expiration (which can be used at expiration), the fact that at expiration spot =future it does not mean that there was not basis risk if maturities were at diferent periods given that at acquisition time the prices could have been diferent