 # Basis Risk

Hi, I can’t understand well what “Basis Risk” is. In my comprehension, “Basis Risk” occurs when the ratio “Future Price/Spot price” is not constant due to interest rate changes. In the book it is said that the lower the difference between Future price and Spot price, the lower the basis risk. I don’t catch this. Imagine the Sport price increase with 10% and the future price increase 20% (we are short the future), we are short 10% whatever difference between sport and future was. Thanks in advance, Bern

Where are you seeing this? Your understanding of basis risk seems accurate to me. (although there maybe other sources for basis risk other than interest rate risk, e.g. commodity futures will face basis risk due to quality, location, etc.) Typically the futures will be close to spot as the contract is close to maturity, during that time the basis risk is naturally low; perhaps the text is not articulating time aspect?

Moreover: It is said the basis is at any time: Ft - St Why it is not Ft/St ?

basis is the difference b/t the spot px and the futures px you are going to hedge with. so you are long i dunno… airplane fuel and you want to hedge it out. first off, there’s no maybe perfect hedge so you hedge with crude oil. if both moved together perfectly in time, then great, you lock in your hedge. but if interest rates move or the 2 just don’t move in parity, then you as a hedger face basis risk. maturity date- maybe that’s not perfect either and you need to roll it or it’s too long. maybe there are storage issues, transportation costs, delivery grade issues, location of delivery issues, etc… all of these things can help contribute to the fact that your spot and your future isn’t going to move in perfect parity. this is basis risk. so as you get closer to expiration and the futures px is more or less converging on the spot px (if that’s the right way to say it- on expiration the future becomes the spot), the difference b/t them is going to be less and less and there’s less basis risk as it gets closer to expiration.

But imagine F0 = 10 and S0 = 5. If at time t, Ft = 20 and St =10 => the hedge is still perfect even if F-S is not constant, no ? Your portfolio will increase with 100% and your short future position will decrease with 100%. What am I missing ?

bern Wrote: ------------------------------------------------------- > But imagine F0 = 10 and S0 = 5. > If at time t, Ft = 20 and St =10 => the hedge is > still perfect even if F-S is not constant, no ? > > Your portfolio will increase with 100% and your > short future position will decrease with 100%. > > What am I missing ? Yeah but how many contracts did you use to hedge originally? Because the basis has changed, you would need a different number of optimum contracts to create a perfect hedge at time t. You are thinking in %, not \$ terms.

Imagine I have stocks in Switzerland for 100 CHF => portfolio value is 100* 5 = 500 USD =>sell for 100 CHF of futures contract (eg. 100 contract of 1 CHF) At time t: Portfolio value = 100*10 = 1000 USD Future value = 100 * (20 - 10) = 1000 USD Total = 1000 - 1000 = 0 USD You have right. The basis can’t be Ft/St If the basis were constant: F0 = 10, S0 = 5, Ft = 20, St = 15 At time t: Portfolio value = 100*15 = 1500 USD Future value = 100 * (20 - 10) = 1000 USD Total = 1500 - 1000 = 500 USD To sum up, if perfectly hedged: V*St - V(Ft-F0) = V * S0 … Ft-St = F0-S0 The basis should be constant !

bern Wrote: ------------------------------------------------------- > Imagine I have stocks in Switzerland for 100 CHF > => portfolio value is 100* 5 = 500 USD > =>sell for 100 CHF of futures contract (eg. 100 > contract of 1 CHF) > > At time t: > Portfolio value = 100*10 = 1000 USD > Future value = 100 * (20 - 10) = 1000 USD > Total = 1000 - 1000 = 0 USD > > You have right. The basis can’t be Ft/St > > > If the basis were constant: > F0 = 10, S0 = 5, Ft = 20, St = 15 > > At time t: > Portfolio value = 100*15 = 1500 USD > Future value = 100 * (20 - 10) = 1000 USD > Total = 1500 - 1000 = 500 USD > > > To sum up, if perfectly hedged: > > V*St - V(Ft-F0) = V * S0 > … > Ft-St = F0-S0 > > The basis should be constant ! I’m confused by your example. Beginning portfolio is \$500 or 100 CHF, right? Sold 1 contract (100CHF @ \$5/1CHF I’m assuming?) Lay off the numbers for a minute. I don’t see why you’re trying to challenge the CFA material, where it clearly states that the basis can change, hence basis risk. They use the example of interest rate differentials to illustrate their case. If US risk free rate is 1% and the CHF risk free rate is 4%, will the basis always be 3%? No, because the US can raise rates at will. Swiss government can do the same. What if these were oil futures? Let’s say you need oil barrels in Texas, but the barrels linked to the contract are in Alaksa since there are no counterparties available that have oil in Texas. Or what if you’re an airline that uses jet fuel as an input but there are no jet fuel contracts to hedge, so the closest thing available is oil. Sure seems like there’s some basis risk there. The price of jet fuel could go up even if the price of oil stays the same.

I was not trying to challenge the CFA material, but just saying that I finally understood the point thanks to your previous post (think in terms of \$ and not %). So I showed a proof of my mistake with an example. By saying "The basis should be constant ! " I wanted to say “The basis should be constant if we want not basis risk”

By the way. In the CFAI volume 5 page 302 it is said that a contract with the same maturity as the investment has no basis risk. Do I understand well ? Because, if the basis is not 0 at time 0 and is 0 at time t (Future & Spot converge) there is basis risk, no ?

bern Wrote: ------------------------------------------------------- > By the way. In the CFAI volume 5 page 302 it is > said that a contract with the same maturity as the > investment has no basis risk. > Do I understand well ? Because, if the basis is > not 0 at time 0 and is 0 at time t (Future & Spot > converge) there is basis risk, no ? Basis risk is zero because futures price is expected to converge to spot price at maturity.

At initation, the basis = Ft - S0 At maturity, the basis = 0 => the basis is not constant => there is basis risk, no ?

At initation, the basis = F0 - S0 At maturity, the basis = 0 => the basis is not constant => there is basis risk, no ?

bern First a minor point basis is not F - S but it is S - F More importantly, Futures price is expected to follow an expected path of convergence to spot, i.e the Value of (S0 - F0) is expected to diminish to zero when contract expires. The risk is that the Futures price deviates from this expected path. This risk is important as the Futures position may not be held till expiration. If the basis reduced from (S0 - F0) to 0 exactly along expected path, then there is no basis risk. In other words the expected carry benefit, storage and financing costs experienced are exactly as expected when futures were priced at time 0. Confusing?

This chapter makes me crazy !!! Let’s use an example. F0 = 10, S0 = 5, Ft = St = 15 At time 0: Portfolio = 100 CHF = 500 USD At time t: Portfolio value = 100*15 = 1500 USD Futures value = 100 * (15 - 10) = 500 USD Total = 1500 - 500 = 1000 USD 1000 USD > 500 USD Isn’t it the result of basis risk that the final amount is not the same as the beginning one ?

I think basis risks for bond futures is related to the prices of the CTD bond used to deliver. If your liability is hedged using futures , and the actual CTD that is used for delivery differs from some other supposed bond that is the “Spot” , you have a basis differential even when the maturity is exactly same. Basis can come about due to supply-demand, liquidity , specials etc.