Systematic risk (positive beta) implies normal backwardation

[venunair]

Hi David
Regarding Stultz Chapter 2 reading on hedging irrelvance proposition:

I do understand the general concept that as the beta increases the expected return from CAPM increases which then means a higher discount rate is applied. But am not able to make a link from this to normal backwardation. (You state in slide 16 that Systematic risk (positive beta) implies normal backwardation). Could you provide some more explaination on this?

Great videos on foundation 1a and 1b. Looking forward eagerly to the next set

Regards
Venu Nair

 

[David Harper CFA FRM]

Hi Venu,

FWIW, I posted last year a 10-min brief video on exactly this topic @
http://www.bionicturtle.com/learn/article/normal_backwardation_video_market/

(and maybe this question is interesting too:
http://forum.bionicturtle.com/viewthread/1220/)

This is all theory but nonetheless key to Stulz so thanks for highlighting it. I personally prefer Hull's approach to explaining this because he borrows from traditional theory: where the way to look at this is from the perspective of the SPECULATOR who is long the futures contract. If you imagine yourself in the long's shoes, would you go long the forward price if F(0) = expected (Spot @ T)? At F(0) = E(S(t)), you are expecting zero profit! But you are incurring systematic risk. So, that is not enticing to you. Rather, you expect a profit = E(S(t)) - F(0) that is equal to the systematic risk you are bearing. Hence, systematic risk implies F(0) < E(S(t)) to compensate the long for bearing the systematic risk
... on the other side of the trade, it is important to see that the HEDGER who is short the forward has an equal expectation of the same loss! But this is not a problem, this is the expected price of transferring risk, away from the hedger to the speculator (and that is the theory of normal backwardation, basically: that hedgers are, on average, net short with expected losses as the cost of hedging, while speculators are net long with expected profits as compensation for bearing the systemic risk. To restate the fallacy of F(0) = E(St) if systematic risk, then both the long and short are expecting zero profits, yet the short has transferred all systematic risk to the long. )

So, when Stulz says: the company's risk managers cannot add value by reducing systemic risk, his point is that the company would need to short the market to hedge their systemic risk (ie., reduce their beta, say by shorting S&P 1500 index futures) but, according to the theory, this is costly as the short expects a loss. So, this systematic hedge is reducing the expected future cash flow by the expected loss; even though, on the other hand, they are reducing the discount rate.

Another way to look at this, i suppose if we use Stulz rather than Hull is simply: the forward price is not uncertain, it has no risk itself and therefore deserves a riskless rate. But the expected spot price is a function of the commodities systematic risk, such that:
E(St) = S0*exp(capm r), but
F(0) = S0*exp(r)

so if you buy the argument that the forward price deserves a riskless rate (r) because it has no uncertainty itself, then you could accept: if beta = 0, E(St) = F(0), but if beta > 0. then S0*exp(r) < S0*exp(capm r)

Hope that helps, thanks for isolating on the assumption that admittedly i just asserted without foundation...thanks for liking the first 2010 vids!

David

 

[venunair]

Hi David
Thanks a lot for the detailed explaination. THis helps a lot

Applying the same to the MG case study, in the stack and roll trade, MG was in the position of long speculator with the short term futures and was expecting to make a profit of E(S(t)) - F(0) under normal backwardation. Cearly when this shifted to a contago the mtm losses caused the failure (in addition to the accounting rules). Is this the correct interpretation?

Venu

 

[David Harper CFA FRM]

Hi Venu,

There is a difference (which we do explicitly explore in Hull) between:
normal backwardation: F < E(St); I like to think of this as the dynamic that cannot be observed.
backwardation: S0 > F1 > Fn; on the other hand, this is an observable downward sloping futures/forward curve

so "normal backwardation" is doubly theoretical; i.e., we cannot today, at time zero, observe the expected future spot, E(St)
but "backwardation" is simply an inverted forward curve: F1 > F2 > F3

So, in MG case (recent related discussion here @ http://forum.bionicturtle.com/viewthread/929/), IMO, the key is unrelated to E(St) and essentially about the ROLL RETURN on a stack-and-hedge:

if backwardation (inverted), then roll-return is profitable because you go long, say, + 2 months ... then assuming a stable forward curve, imagine marching forward in time 1 month, then your contract is + 1 month. In backwardation, +1 month > + 2 months, and your "roll" (i.e., close out earlier position) must be a gain because the "forward price" is increasing to converge on the spot price.
.... so the key here, IMO, is just to keep in mind that the forward price roughly converges to the spot price as maturity decreases. As contango (not normal contango!) is an upward-sloping curve, given a stable contango, this implies your forward price is dropping to converge on the spot and the roll on your stack hedge is suddenly losing (in the MG case, backwardation gave way to contango because the spot price dropped further than the forward price)

(I agree with the rest of your thought: this shift to contango created roll return LOSSES that were realized/settled immediately. They were hedging offsetting gains but alas MG could not recognize those gains)

hope that helps, David