I hope someone can make my dummy go away with this concept that should be simple.
So, I have a bond and I want to use another similar bond futures contract to increase my duration. Lets just say my actual bond is trading at par and the futures contract will settle at 110. The way I understand basis risk is that its the risk my actual bond and the futures bond move in different manners resulting from incorrect duration calculations. correlations and/or the futures was priced wrong. I get that. But why is the basis risk ZERO at expiration? My actual bond may have appreciated while the futures bond is trading at a discount. Yes, I know the price at expiration is known but if I have to buy it at 110 and its only trading at lets say 100 and my actual bond appreciated to 115 then whats the point. My exposure to the upside is now being offset by the very vehicle I was trying to use to leverage that upside.
First, if the underlying bond is trading at par, the only way that the futures contract will settle at 110 is for the effective risk-free rate for the length of the futures contract to be 10%. I realize that you were just grabbing a number out of the air for illustration, but you need to keep that relationship in mind: the price of a futures contract is the spot price of the underlying increased by the risk-free rate for the length of the contract.
The source of basis risk isn’t incorrect duration calculations; markets simply don’t make that sort of mistake. The source of basis risk is that the discount rate that you use to calculate the value of the bond (correctly) may be different from the discount rate that you use to calculate the value of the futures contract (correctly).
For example, suppose that you have a 10-year, zero coupon, $1,000 par bond. The 10-year (annual, effective) spot rate is 6%. The price of that bond today is $558.39 (= $1,000 ÷ 1.0610). If the 2-year (annual, effective) spot rate is 3%, then the price of a 2-year futures contract for that bond is $592.40 (= $558.39 × 1.032).
One year later, suppose that the 9-year (annual, effective) spot rate is 6%, and that the 1-year (annual, effective) spot rate is 2%. Then:
The price of the bond is $591.90 (= $1,000 ÷ 1.069)
The price of a new, 1-year futures contract on that bond (expiring the same day as the original) is $603.74 (= $591.90 × 1.02)
The value of the original futures contract (with one year left till expiration) is $580.79 (= $592.40 ÷ 1.02)
There’s the source of your basis risk: $591.90 − $580.79 (= $11.11).
First, regarding my 10% risk free rate, you’re right I just pulled that for illustration. I would like to invest in a 10% risk free asset though.
Regarding your example, to make sure I got this right. What you are saying is that the basis risk is that the annual effective rate changes in one instrument but not equally in the other (assuming equal durations)? In your example we had a positive gain because the futures yield went down, hence bond price up. Ideally we want two bonds perfectly correlated because when I leverage my duration up using a futures contract I would expect that the bond I own goes up/down by the same percentage in price of the bond as the futures position. Of course the bond I own in your example has a longer duration so it would NOT be -1% to be equal). I need to hope that parts right before moving on.
Regarding my first post on this thread, last comment, when I asked about basis risk being zero at expiration. Is basis risk only risk during the life of the contract? I know you used bonds with different durations for the sake of ease lets pretend the bond and futures had equal durations. At expiration the price of the underlying futures appreciated 2% and the bond I actually own went up 3%. Is the variation in price movement upon expiration not basis risk in itself, or is basis risk only the risk of the 2 moving independently throughout the life of the contract?
I hope I didn’t just make an azz out of myself with all that.
Basis risk is 0 at expiry because the spot price and futures prices converge - otherwise arbitrage would exist. In your original post you contracted to sell the bond at 110. At expiry, for you as the investor, the price of that bond is 110. They converge and again these relationships are bound by arbitrage.
Now if you lift the hedge prior to expiry, the futures and spot may not be the same and thus you have basis risk.
Hope that helped. Also think of it this way (and yes to all you pros I know I’m bending the rules here so don’t beat me up over this illustration).
Take Magicians example. Let’s say you have to fund a liability in 10 years of 1,000. You could buy a 10 year zero at a 6% rate for 588.39. In 10 years the bond will mature and pay you par and you can fully fund the liability (I.e. “No basis risk”)
Let’s say a year down the road, for whatever reason the liability comes due in the amount of the PV of that 1,000 assuming the original discount rate of 6%. Thus the amount needed today to fund it is 591.90. As long as rates didn’t change then your bond you bought last year will be worth 591.90. If rates had changed then you face “basis risk” in the since that your bond will deviate from that 591.90 needed. Same thing with the futures.
I think my mind was on the wrong place last night. I shouldn’t have used bonds as my example but I still want clarification on whatever type of risk I am thinking of. Rather than a bond and treasury futures let’s say I own shares of AAPL and hedge them by selling SP500 futures. Now they won’t be perfectly correlated so throughout the life of the contract AAPL may go up/down and the SP500 may go down/up in different directions. Is this called basis risk as well? Furthermore, upon expiration, the SP500 and AAPL could have and appreciated in different amounts or even gone in opposite directions, potentially. Ideally we want them to move together so is the basis risk only the POTENTIAL to move further apart during the life of the contract or is it also the difference in price changes upon expiration. I how that makes sense.
Or am is this cross hedge risk I’m thinking of?
(FML- thanks for hanging in there with me on this. I know how frustrating it is to be explaining something and the person just won’t grasp it)
This doesn’t hold true in reality right? since you’ll have to adjust the contracts throughout time as interest rates move around? that’s why they introduced delta hedging/adjustment?
I think almostdoneiii is sort of thinking the way I am. I’m thinking that when you have to roll that futures contract over your actual underlying security may have acted completely different than the futures contract making the hedge ineffective
Yes that is a form of basis risk - your AAPL example.
At expiry the spot MUST equal futures price and yes in reality it is pretty damn close because of arbitrage. If not you would short the one that is priced too high and buy the one that is priced too low. Now there is an averaging period for the futures prices at expiry to prevent manipulation - I think it is like average trading price over the final 2 days of trading??? Someone who deals in futures can probably speak more to this. I’m just shooting from the hip here. I thinks it’s beyond the scope of what we need to know though.