Can we price commodities using CAPM?

Hi Guys,

I just came across a concept written by Schweser CFA Level 2 in 2014 on commodities. The statement made was “because commodities are not capital assets, the use of CAPM to derive a commodity’s expected return is inappropriate”. I just want to better understand this statement. Can anyone shed light on this matter?

My perspective:

CAPM captures the risk premium and rewards the investor with the appropriate amount of reward to justify the risk premium. If we’re able to calculate market risk premium (ie using some form of commodity index), couldn’t we calculate the systematic risk of a particular commodity?

A few thoughts. Go find the assumption list for capm - these are the practically the bill of rights or 10 commandments to portfolio managers who use modern portfolio theory. This assumption list ultimately leads to approaches and treatments of idiosyncratic risk for example that wouldn’t otherwise be possible. This in turn leads to justify certain approaches to the covariance matrix that fit nicely within capm.

With that said, commodity pricing reflects a supply curve of the marginal producer more than anything.

additionally, the ‘market’ index you choose to regress to is everything here. I recommend you go through the exercise and correlate weekly returns of individual commodities to some equity indices… that will tell you about their connection to systematic risk, but look at the R2 and t stats on those results to rule out spurious results. Roll the results over time to look for consistency.

I would not regress oil against a commodity index for example, since energy tends to weight so large.

that said, a multi or single factor model of commodity price is possible to generate - you may need to suspend some capm assumptions, and the result can make sense.

Remember capm looks like a single factor regression, but it is also an assumption set.

I think it has to do with the extremes. A carrot can be consumed and its value wiped off. Or extreme rice scarcity can make its value close to infinite. Such possibilities can’t be modeled by CAPM. Capital assets don’t exhibit such characteristics.

Shortly No. Commodity prices depend on different variables than capital assets. Such as weather, natural exploitation level and so. You should also take into account the storage costs and the convenience yield.


Does it really matter whether commodity prices depend on different variables or whether we need to take into account costs?

From my understanding, the Markowitz theory/CAPM has two components:

Component 1: Human’s utility. We assume that people prefer expected returns and do not like risk (captured by standard deviation). The simplified form doesn’t assume third and fourth orders (Skewness and Kurtosis) as risk metrics.

Component 2: Asset side of things. We assume assets are divisible and what we really need here are expected returns and variance-covariance. We can then create a portfolio of assets, based on a mix of different positions in assets.

Addressing your question: Firstly, it doesn’t matter whether the risk of a company or a risk of an asset is different. As long as we can obtain expected returns and risk (I’ll assume here that the risk metric is standard deviation), we can use the same assumptions that CAPM/Markowitz uses. Secondly, I do not see how commodities would violate the two components listed. If we were to be very pedantic, equities would also violate the ‘divisibility’ property of things. It would be good if you could highlight an aspect that commodities violate that equities do not.

To add, to be honest, from a mathematical/economics standpoint, I don’t see why commodities cannot be modeled using CAPM. From the same derivations of Markowitz to CAPM, I don’t see any step that commodities violate specifically that equities do not.

From a logical viewpoint, I guess I can understand that the fundamental risk is different (ie commodities are more driven by supply and demand). But in this context, equity prices are also driven by supply and demand for the good.

R-square and statistical tests don’t rule out spurious results-- not in the slightest. Consistency over time doesn’t allow for spuriousness to be ruled out, either.

@ theOrange

Research it, prove it and publish a scientific article about this in the Science magazine.

I have never found that someone uses CAPM to value the commodities, but could be wrong. I’ve already explained my point.