Basis

[wrongsaidfred]

Hi David,

I have a couple of quick questions about the discussion on basis in part a of the prodcuts videos.

First, in slide 52, you say that when the basis goes from -10 to -5 it is a weakening of the basis. By this, do you just mean that it was supposed to be zero at the end of the hedge, but because it is now less than zero it would be considered a weakeing of the basis?

Next, from this discussion, it seems like all hedgers expect the basis to decrease to zero. Is this correct?

This market is obviously in cantango. Does the same methodology apply when in normal backwardation?

Finally, the whole idea of "favorable" or "unfavorable" is a little confusing to me. Does this mean that they are better off than they were when they put on the hedge, better off than if they did not hedge at all, etc? It just seems a bit arbitrary.

Thank you,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Good questions that get to the heart of the issue.

The example means to illustrate Hull's key point about basis risk. To understand this is probably to understand the rest, and the key word is unexpectedly: "Note that basis risk can lead to an improvement or a worsening of a hedger's position. Consider a short hedge. If the basis strengthens (i.e., increases) unexpectedly, the hedger's position improves; if the basis weakens (i.e., decreases) unexpectedly, the hedger's position worsens. For a long hedge, the reverse holds. If the basis strengthens unexpectedly, the hedger's position. worsens; if the basis weakens unexpectedly, the hedger's position improves." (Hull p 53)

Basis = Spot price - Futures price.

1. -10 to -5 is an absolute strengthening (increase) in the basis, but the as the hedger (and his/her hedge) planned for convergence to zero basis, it is UNEXPECTED relative weakening (from expected zero to -5).

2. "Next, from this discussion, it seems like all hedgers expect the basis to decrease to zero. Is this correct?"
No. Firstly, Hedgers (and speculators) expect the futures contract to converge to the spot (minus frictions, not exactly but to a "zone of convergence") at MATURITY of the futures contract only; just as any forward curve exhibits backwardation/contango, we expect the basis (S - F) to be non-zero at any other time.
Second, the hedge often does NOT contemplate riding the futures contract to maturity. This is about hedging price (market) risk so the hedge just wants the price movement of the forward to offset the price move of the spot during some timeframe.

3. Yes, applies in contango/backwardation ...

4. Favorable/unfavorable I meant to equal to Hull's "improves" or "weakens:" this refers to the hedger's NET position (keep in mind, the hedge is two positions: underlying spot plus forward contract) GAINS or LOSSES relative to expectations. In a pure hedge, the hedger expects zero gain/loss due to spot price risk. Favorable/improves means hedger profits; e.g., if hedger is long spot and short futures contract (i.e., short hedge), UNEXPECTED basis weakening (i.e., as B = S - F, unexpected weakening implies change in F is greater than change in S), the hedger on the net position is worse (less favorable) than expected.

I hope that helps, David

 

[southeuro]

Hi David, can you explain how the short hedger stands to gain from an unexpected strengthening of the basis? Can we assume that the hedger stands to gain from the relative strengthening of spot versus forward (or the relative drop in forward)? Since he's short, he will be buying at a lower price than he was hoping to? Thanks

 

[David Harper CFA FRM]

Hi southeuro,

The key is expected/unexpected. It looks like the price of March corn futures, F(0,1), is $5.71/bushel.
Say you are a farmer who will sell one bushel next March; you hedge by shorting 1/5,000th of a futures contract (so it's just one bushel we're talking about); you short futures at F(0,1) = 5.71; i.e., promise to sell in one year at $5.71

If you know the basis converges to zero, your hedge is approximately perfect regardless of the future spot:

• If S(march 2013) goes up to 6.0, and F(1,1) converges to 6.0, your net receipt is $5.71 = $6.0 spot sale - $0.29 futures loss,
• If S(march 2013) goes down to 5.0, and F(1,1) converges to 5.0, your net receipt is $5.71 = $5.0 spot sale + $0.71 futures gain

... doesn't matter where S(T) ends up, what makes your net payoff certain is that you can plan for future basis = S(t) - F(t) = constant k (in this case, 0)

But, if in March 2103, the basis unexpected strengthens, you are better off:

• If S(march 2013) goes up to 6.0, but F(1,1) doesn't converge but only to 5.80, your net receipt is $5.91 = $6.0 spot sale - $0.09 futures loss,
• If S(march 2013) goes down to 5.10, but F(1,1) doesn't converge but only to 5.00, your net receipt is $5.81 = $5.1 spot sale + $0.71 futures gain

As b = S(t) - F(t), you can hedge against a predicted future basis, but as a short hedger, your net payoff will be: S(t) + [F(0,1) - F(1,1)]
... you plan will not include unexpected changes to S(t) or F(1,1), which create dispersion around your expected future net payoff.

I hope that helps,

 

[southeuro]

For someone who has no background on these topics and minimum exposure to math (me), it does clarify it REALLY well - thanks David

Hi southeuro,

The key is expected/unexpected. It looks like the price of March corn futures, F(0,1), is $5.71/bushel.
Say you are a farmer who will sell one bushel next March; you hedge by shorting 1/5,000th of a futures contract (so it's just one bushel we're talking about); you short futures at F(0,1) = 5.71; i.e., promise to sell in one year at $5.71

If you know the basis converges to zero, your hedge is approximately perfect regardless of the future spot:

• If S(march 2013) goes up to 6.0, and F(1,1) converges to 6.0, your net receipt is $5.71 = $6.0 spot sale - $0.29 futures loss,
• If S(march 2013) goes down to 5.0, and F(1,1) converges to 5.0, your net receipt is $5.71 = $5.0 spot sale + $0.71 futures gain

... doesn't matter where S(T) ends up, what makes your net payoff certain is that you can plan for future basis = S(t) - F(t) = constant k (in this case, 0)


But, if in March 2103, the basis unexpected strengthens, you are better off:

• If S(march 2013) goes up to 6.0, but F(1,1) doesn't converge but only to 5.80, your net receipt is $5.91 = $6.0 spot sale - $0.09 futures loss,
• If S(march 2013) goes down to 5.10, but F(1,1) doesn't converge but only to 5.00, your net receipt is $5.81 = $5.1 spot sale + $0.71 futures gain

As b = S(t) - F(t), you can hedge against a predicted future basis, but as a short hedger, your net payoff will be: S(t) + [F(0,1) - F(1,1)]

... you plan will not include unexpected changes to S(t) or F(1,1), which create dispersion around your expected future net payoff.

I hope that helps,