Hedging-Stultz-Ch.2

[PDEM200]

Hi David,
Could you pls clarify some hedging concepts. The words are not clicking in my head.

1) Given,oil has a positive beta, a short forward would have negative beta (agreed)

2) The hedge of market risk from a negative beta asset has positive value (I thought the the value added is zero based on "hedging irrelevance" property.

3) Entering into a short forward contract for oil must have a negative payoff ( why-what I am missing?)

Thank you

 

[David Harper CFA FRM]

Hi Paul,

Starting with (3), which i find instructive because it relies on "theory of normal backwardation," if oil has beta = 0.5, then:
E[future spot] = spot*EXP[riskfree rate + 0.5*market premium]. However, a forward contract's value =
Forward contract F0 = spot * EXP(riskfree rate); i.e., omitting other carry factors like convenience yield.

such that:
F0 < E [future spot price]

if i am the oil hedger and you are the speculator, if you know oil has systematic risk (beta = 0.5), will you commit to a forward price (F0) = expected future spot? No, you would be assuming risk with expected profit of zero. To assume the beta risk, you *expect* a future profit; i.e., expected future spot - Foward price > 0. Therefore, you the long speculator trade with me the short hedger; my expected payoff is negative! This is appropriate: I have transferred the risk to you, you deserve to get compensation. Under this theory, you provided me liquidity, is cost me a "fee" of the negative expected payoff.

Re (1) I prefer to use the term "position or portfolio beta" versus instrument beta, so in our example the oil always has positive beta, it is just that a short position creates a negative *position* beta:

E[return on short] = -Position * positive oil beta = -negative return% or -negative return$.
So, a bit of a nit, but i think it can lead to a bit of confusion (for example) when we commingle"instrument beta" with "position or portfolio beta"

here, positive oil beta (note: beta is just a type of correlation, so it must be "with respect to something else) mean "oil has positive standardize covariance with the overall market"
but a short forward on oil means: a short position multiplied by a positive beta equals a negative expected return on the position (a negative position beta).

Re (2) I agree with you, I don't understand this either. Unless it means: your underlying is a negative beta asset, so you hedge it with a positive beta instrument? otherwise, i don't agree with it either (agree, i don't think we'd expect the hedge per se to have positive value).

David

 

[tsoo821]

My interpretation of 2) is as follow:

In the very first sentence of the paragraph of Stulz - Chapter2, it has claimed that if efficient market is not true, then arbitrage would happen. Therefore, without the assumption of efficient market, the hedging irrelevance proposition is no longer valid.

I think the author wanna express that the VALUE of the firm would increase if we reduce the systematic risk. This statement standalone is true based on the previous discussion of the book. But, the way of hedging that risk would bring us negative value as well. He further claimed if the discrepency is not balanced, there would be arbitrage opportunity.

I think it is too confusing to use "hedge from a negative beta asset", But anyway, those are just my interpretations. It made me feel more comfortable if I interpret in this way. (I have already spent so much time to comprehend what the author is trying to say...)