Commodity risk premium

[wrongsaidfred]

Hi David,

The term commodity risk premium came up in a question I read. I assumed it was like the equity risk premium or market risk premium (R,market - R, risk free) but instead it said that it was [R, risk free - alpha] where alpha is the total discount rate for the commodity, which in many of the problems that we have done is the CAPM expected rate of return.

I guess what I am really asking is whether or not we can think of the commodity risk premium as a "reward" for taking on more risk then same way we do in the CAPM. And if so, does this reward the commodity holder or the forward holder? I was under the assumption that if the commodity was positively correlated with the stock market alpha would be greater than the risk free rate and if was was negatively correlated with the market it would be less than the risk free rate.

It just does not seem like these two definitions are compatible. Any explanation you could provide would be greatly appreciated.

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Yes, I think this is exactly correct: "can we think of the commodity risk premium as a "reward" for taking on more risk then same way we do in the CAPM" and, under the theory of normal backwardation (i.e., just one theory) that Hull implicitly relies on, better expounded by Kolb, the idea is that the HEDGER is the one who tends to be short the futures contract, the speculator is long, and so the commodity premium is compensation to the speculator (long position) for assuming the price risk. For example, assume

spot = 10,
Rf = 2%
ERP = 4%
commodity beta =1.5,
then discount rate (expected return) of commodity, per CAPM, = 2% + 4%*1.5 = 8%.

The one-year forward, F(0), = 10*exp(2%) = $10.21
The expected future spot price = 10*exp(8%) = $10.833; i.e., $10.833 discounted at 8% equals the current spot.
The long forward expects to profit, in the future, $10.833 - 10.21; this is compensation for bearing the commodity's systemic risk
Similarly, the short forward expects to lose the same: payment for ability to transfer price risk to counterparty

In your terminology, commodity risk premium = 8% - 2% = 6% = commodity beta * common factor = 1.5*4%;
and the long forward expected gain is ln(10.83/10.21) = 6% commodity premium for assuming the price risk

and you can see why it's called thy of normal backwardation: if the commodity has any systematic risk (beta>0), then the forward price is < expected future spot price (definition of normal backwardation!). Why? the long will only bear the commodity risk if he/she can expect a future gain.

Hope that helps, David

 

[wrongsaidfred]

Hi David,

Thank you. It absolutely does help. Just so I have this straight: we calculated our discount rate from CAPM, and then we used the fact that discount rate=growth+dividends (or growth plus lease rate) and in this case, since we did not have any dividends and no explicit lease rate we can say that the growth rate = discount rate = 8% and we can use E(St)=So*e^(g*t). Is this correct?

Also, I might be over thinking this but is this commodity lease rate defined as [Risk free - discount] or [discount - risk free]? I saw it defined as the former, but this would imply a negative risk premium in most cases since the discount rate (if there is positive systematic risk) will be greater than that risk free rate.

Thanks again,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Yes, this is perfectly phrased: "we calculated our discount rate from CAPM, and then we used the fact that discount rate=growth+dividends (or growth plus lease rate) and in this case, since we did not have any dividends and no explicit lease rate we can say that the growth rate = discount rate = 8% and we can use E(St)=So*e^(g*t)."

Keep in mind, CAPM is naive one-factor model so we aren't defending it. It's just Hull's proxy for the risk of the commodity.
But: as total shareholder return (TSR) = capital appreciation(g) + dividends(q), we are assuming the correct discount rate is the E(TSR) and so the discount rate is only equal to the expected growth if there are no dividends.

Re: lease rate: per our other threads, I think that "lease rate" suffers from an ambiguity in the assignments, but in my view, it's positive like a dividend yield is positive, consistent with McDonald's:
lease rate (delta) = discount - growth (g); please note:
discount = growth + lease rate; and it's analogous to TSR = growth + dividends.
So, IMO, the answer is: discount - riskfree rate, and this is only zero if systematic risk is zero (beta = 0). If beta = 0, commodity is theoretically riskless; beta > 0, commodity has systematic risk, and discount > riskfree rate

Thanks, David

 

[wrongsaidfred]

Nice.

Thank you.

Mike