Biological asset valuation: Risk pricing

William Clark, 1823, “The Mill Yard” from “Ten Views in the Island of Antigua”

This article continues from my basic discussion of biological asset valuation which presented an overview of the financial reporting requirements for biological assets, the fundamental problem of biological asset valuation, and a general solution to the problem (including an example using an Indian sugar cane crop and using NYMEX #11 sugar contract prices to extract market risk-adjusted discount rates and average selling costs):

Biological asset valuation: Basics

What was not covered in the previous article, however, was how to estimate market risk-adjusted discount rates independently of selling costs, which is generally necessary because selling costs are most often unique to the company owning the biological assets.

In this article I will complete the discussion by presenting a method based on modern asset pricing theory for estimating the (fair market) price of biological asset risk. Before continuing, it’s important to recognize that—apparently contrary to the consensus view of the valuation profession—determining an appropriate discount rate for any asset requires direct estimation of risk price(s) using actual market data. This is in contrast to the common approach used by valuation professionals where they make casual, subjective assumptions of what an appropriate risk premium should be based largely on “professional judgment.”

There is, of course, nothing wrong with using professional judgment in asset valuation and, as will be seen, it is quite necessary. But there is a problem with using professional judgment to make subjective assumptions about risk pricing: When estimating risk-adjusted discount rates intended for use in estimating the fair (market) value of an asset, it is how actual traders in actual markets price risks that matters; not what valuation professionals think the risk price should be based on their professional judgment. This might seem a subtle point but its truth should be fairly obvious:

When estimating the fair value of an asset–which is a market value–we are interested in what is in the minds of actual traders; not what is in the minds of valuation professionals.

With this idea firmly fixed in our consciousnesses, we can continue and explore how we can extract estimates of biological asset risk prices from market data and use it to construct fair value risk-adjusted discount rates. So, let’s proceed!


1. Estimation objective and professional judgment

Fundamental biological asset valuation model. Recall the fundamental biological asset (BA) valuation model from my previous article:

In the previous article, I used an example where I was estimating the fair value of a sugar cane crop using NYMEX #11 futures contract price data and an econometric method to infer both the risk-adjusted discount factor and the expected net unit selling price for raw sugar. Because it is not always possible to obtain futures contract price data on agricultural products derived from biological assets, and because it’s generally necessary to estimate the discount rate and expected net selling price separately, this article will focus strictly on estimating risk-adjusted discount rates for biological assets.

Discount rate estimation objective. To keep things as simple as possible, I will again use one of the simplest examples in BA valuation where I will derive an estimated risk-adjusted fair market discount rate appropriate for estimating the value of a sugar cane crop. Arguably (and this is one place where professional judgment comes in), the value of a sugar cane crop is exposed to only one significant risk: raw sugar market price risk. This assumption is based on the idea that such risk is observable through raw sugar futures contract market prices, which aggregate the information and beliefs of sugar producers, traders, and users about raw sugar supply and demand conditions over time. With this assumption, the discount rate estimation objective related to valuing a sugar cane crop can be written as …

It is, of course, true that an individual sugar cane crop—and, hence, its value—might be exposed to a variety of risks other than raw sugar price risk; e.g., an individual crop might be subject to incompetent agricultural management, various weather risks, etc. But under modern asset pricing theory, although the value of an asset depends on all significant risks to which it is exposed, the expected rate of return on an asset depends on only those risks which are actually priced in the market.

Perhaps the simplest way to think about this distinction is to recognize that the expected future cash flows derived from an asset are probability-weighted averages. So, for example, an accurate valuation of a sugar cane crop requires that the expected future cash flows to be derived from the crop are based (perhaps implicitly) on probability weightings to adjust for incompetent management, weather, and other risk factors. But these risks are likely not priced in the markets—largely because they are unobservable to sugar market traders—and, accordingly, do not influence the estimated risk-adjusted expected market rate of return on assets with sugar risk exposures. Rather, such unobservable risks are likely to be diversified in some way.

On the role of professional judgment in valuation. Note that considerations similar to those presented above represent the appropriate role for professional judgment in valuation; not, for example, things like including subjective discount rate premiums based solely on one’s professional judgment. It’s fairly common for valuation professionals to justify such rate premiums by making statements similar to “We can adjust either the expected cash flows by a probability adjustment, or we can instead just adjust the discount rate, to estimate fair value.” based on the idea that, mathematically, one can arrive at an equivalent valuation either way.

But this, again, is not the issue; the issue is that expected future cash flows of an asset are potentially sensitivity to a variety of risks, only some of which are priced in the markets. Other risks are either hedged or diversified. Making truly subjective adjustments—either to expected cash flows or discount rates—result in opinions rather than estimates. But it is estimates of market discount rates and expected values that represent the valuation objectives: We are interested in estimating what is in the minds of (fair) market participants; not what’s in the minds of valuation professionals. It is somewhat rare that one would actually be interested in the subjective opinions of valuation professionals unless they have genuine specific expertise with respect to the particular type of asset being valued and markets in which it trades.

2. Example: Risk-adjusted expected market rate of return

Estimated sugar risk sensitivities. Continuing the sugar cane crop fair value estimation example, consider the sensitivities of Cosan Ltd. (NYSE: CZZ) and Mondelez Inc. (NASDAQ: MDLZ) equity market returns with respect to the market returns for The Teucrium Sugar Fund (NYSE: CANE), which is an exchange traded fund that invests in a specific mix of Intercontinental Exchange (ICE) No. 11 Sugar Futures Contracts:

Estimated sensitivities of Cosan Ltd. (CZZ) and Mondelez International Inc. (MDLZ) equity returns to joint sugar price and supply risk (CANE).

The sugar risk sensitivities shown above (1.350 for CZZ, and .2018 for MDLZ) were estimated from publicly-available return data (CZZ, MDLZ, CANE) for the 60 months ended March 2019 using the least absolute deviation estimation method.

CZZ and MDLZ were selected for use in estimating the market price of sugar risk because (i) CZZ is perhaps the largest publicly-traded raw sugar and sugar-based alcohol producer in the world and (ii) MDLZ is one of the largest global users of raw sugar, which it uses in producing confectionery foods. CANE was selected because the fund is designed to track the ICE No. 11 Sugar Futures Contract pool, which represents the global benchmark raw sugar contract and therefore global sugar price risk.

It is (quite) reasonable to suppose that capital markets which are rational over the long-run are likely to price raw sugar risk–as proxied by CANE returns–as a component of CZZ and MDLZ equity returns. (If this does not seem intuitive or reasonable, one might want to consider reading my book “International cost of capital estimation: Methods based on modern asset pricing theory.“)

Optimal risk-minimizing portfolio. Following arbitrage pricing theory developed by the renowned economist Stephen Ross in 1976, it is possible for (and reasonable to assume that) investors participating in these markets form portfolios of CZZ and MDLZ in such a way that the sugar risk to which they are exposed is minimized in expectation. Under this assumption–which is equivalent to the simple assumption that investors prefer greater return for accepting greater risk–the risk-minimizing optimal weights for CZZ and MDLZ have a clear, explicit solution:

Estimated optimal CZZ-MDLZ portfolio weights that minimize aggregate portfolio risk sensitivity to sugar risk.

Substituting the risk sensitivity estimates from above into the above solution, it can be shown that the optimal portfolio weights are a 17.6% short position for CZZ and a 117.6% long position for MDLZ. It can be further shown that it is possible to construct such long and short positions for both CZZ and MDLZ, which is consistent with the reasonableness of the risk-minimizing portfolio assumption discussed above.

No-arbitrage sugar risk pricing. If the sugar risk-minimizing portfolio assumption reasonably holds on average over time (e.g., the 60 month sample period ended March 2019), then it follows that no sugar risk arbitrage opportunities existed on average over time as well. It also follows that the expected historical returns to CZZ and MDLZ contain a sugar risk price component that can be extracted from the historical return data by using the sugar risk sensitivity estimates in the following way:

No-arbitrage prices of optimal CZZ-MDLZ portfolio risk and sugar risk.

In this case, the median monthly returns for CZZ and MDLZ over the 60 month sample period were used as estimates of the historical expected returns, resulting in the following risk pricing estimates:

Estimated market prices of optimized CZZ-MDLZ portfolio and sugar risks.

The estimated market risk prices are interpreted as follows:

To obtain the estimated risk prices (i.e., the monthly risk-adjusted expected market rates of return to risks), the median of historical CZZ and MDLZ returns is used as a measure of central tendency that is less influenced by individual monthly returns that are unusual and, so, is arguably a more accurate estimate of the historical expectations of sugar market traders than is the mean. Implicit in this estimation method is the rational expectations hypothesis, which suggests that traders actual expectations are consistent with estimated expectations on average across time and market conditions; or, more simply, that traders expectations are correct on average. (Professional judgment has again been used here in selecting the estimation method; but the source data is from the market, not from a valuation professional’s mind.)

There is an additional caveat with respect to the above estimates, which I also address in detail in my book: It’s quite possible that market prices of risks are not stable over time, so it would usually be important to conduct statistical tests of variability of the estimates over time. But I will avoid that here for simplicity ( … get the book if you’re interested in this!).

Risk-adjusted discount rate for sugar risk exposure. Based on the above estimate of the market price of sugar risk, we can now derive the appropriate risk-adjusted discount rate for the sugar cane crop. Because the fundamental cost of money is based on the risk-free rate, which generally differs depending on the investment horizon (cf. yield curve), it is necessary to determine the appropriate maturity horizon to select the appropriate risk-free rate.

For the sake of example, I will assume that we are estimating the value of a sugar cane crop at 31 March 2019, which is expected to mature and be processed into raw sugar on or about 1 January 2020. In this case, the expected sale of the agricultural product (raw sugar) from the biological asset (sugar cane) and related cash flow would occur about 9 months from the valuation date. Perhaps one of the few essentially risk-free asset classes in the world (other than, arguably, currency) are inflation-indexed debt securities issued by governments who control global reserve currencies. So for this example I will (use professional judgment and) select the observable 9 month yield-to-maturity on US Treasury inflation-indexed securities at 29 March 2018 (termed “TIPS”) of 0.246% as the risk-free component of the discount rate.

Combining the risk-free rate with the annualized estimate of the market price of sugar risk–and the assumption that the sugar cane crop has a sensitivity of 1 to raw sugar risk–the estimated risk-adjusted discount rate for a 9 month crop maturity is …

Risk-adjusted discount rate for a sugar cane crop with a 9 month crop maturity.

… annnnnd, subject to the appropriateness of the assumptions and professional judgments discussed above, we are done! Q.E.D.

3. CAPM-based methods and some conclusions

On the prevalence of CAPM-based methods. It is worthwhile to stop and think about how valuation professionals commonly use an alternative method to the no-arbitrage method presented above: a method based on the Capital Asset Pricing Model (CAPM), which is the only such other method actually based on modern asset pricing theory. Based on my experience, valuation professionals typically determine discount rates using a method based on CAPM, but then make ad hoc adjustments to the rates based on their professional judgment. When I’ve discussed the method presented in Section 2 above with such valuation professionals, the most common response is something like “Well, your method might be right or it might be wrong; and, after all, we are only giving our opinion on fair value anyway. So, unless you can show us our CAPM-based method is wrong, I’ll just continue with our existing method; thank you very much!” Relatedly, I’ve had a well-known valuation industry leader tell me “The method you presented is too complex to apply in practice.” (and that’s a direct quote … from someone very important in the valuation profession).

Notice that the combination of asserting that “fair value is just an opinion” and “… unless you can show us our CAPM method is wrong …” are a prime example of Bertrand Russell’s Teapot Analogy, where the burden of proof of showing their ultimately subjective (and, therefore, unobservable) opinions and methods are jointly incorrect falls on an independent observer, which is an impossibility. This is a bit subtle, so I will defer a more complete discussion of this for a future article.

In any case, the valuation profession continues to use CAPM-based methods despite the consensus view of well-known finance researchers who have studied CAPM rigorously for decades:

The [original] version of the CAPM … has never been an empirical success. In the early empirical work, the Black (1972) version of the model, which can accommodate a flatter tradeoff of average return for market beta, has some success. But in the late 1970s, research begins to uncover variables like size, various price ratios and momentum that add to the explanation of average returns provided by beta. The problems are serious enough to invalidate most applications of CAPM. (Fama and French, 2006, p. 43)

In short, CAPM has been repeatedly and consistently rejected by actual capital market data. (I show examples of this in my book.) In particular, the empirical research shows that capital assets are sensitive to substantially more risk factors than implied by the CAPM, which–by the way–is intuitive to anyone involved in finance.

An example of a CAPM-based estimate. To see the issues a bit more clearly consider an example of trying to apply CAPM to estimating the risk-adjusted market discount rate for sugar risk. Südzucker AG (FWB: SZU) is the largest sugar producer in Europe and its monthly equity returns have a substantially perfect correlation (a sensitivity substantially equal to 1) with global sugar risk:

SZU sugar risk sensitivity: 1.043 using least absolute deviation estimation method (1.009 using least squares estimation method)

Given this empirical result, it’s reasonable to suppose that we could easily use SZU equity returns to develop a CAPM-based estimate of the market discount rate appropriate for estimating the value of a sugar cane crop.

To see why the risk sensitivity equal to 1 would be important in this respect, consider the hypothetical condition where SZU equity returns were a perfect proxy for sugar risk pricing; i.e., with a risk sensitivity of exactly 1.000 to sugar risk. Under this condition, it seems as if the appropriate market price of sugar risk would be easy to extract from market data:

The market price of sugar risk for the 60 months ended March 2019 is negative (based on the median of SZU equity returns for the 60 month period)?

But, as shown, it turns out that it’s not that easy: (i) SZU returns have been negative over the 60 month period ended March 2019, and (ii) it’s not at all clear which risk-free rate to use in the calculation; e.g., there are a number of different inflation-indexed government debt yields from different countries and currencies over a range of different maturities from which to choose. So, there is no clear solution to the seemingly simple sugar risk price estimation problem; even with a perfect proxy for sugar price risk.

So, what about using CAPM to estimate a risk-adjusted discount rate to price sugar risk and value a sugar cane crop? After all, CAPM is used by most valuation professionals who, in essence, regard it as the only fundamental theory which can be used to develop risk-adjusted discount rates. Using the exact same approach that I’ve seen valuation professionals use many dozens (or perhaps hundreds) of times, I will (i) hypothetically select SZU as a “comparable asset” in terms of risks to the sugar cane crop because it has a sensitivity to sugar risk substantially equal to 1, and (ii) as is common in valuation practice I will use the S&P 500 Index ETF (NASDAQ: SPY) as a proxy for the capital market portfolio, which is suggested by CAPM to aggregate all significant risks priced in the capital markets.

After estimating the sensitivity of SZU to SPY of .912 using the least absolute deviations estimation method, and both the mean and median of the SPY returns as estimates of the expected return on the capital market, CAPM-based estimates of discount rates for the sugar cane crop are …

Conclusions. So, which is the best risk-adjusted discount rate for estimating the fair value of the sugar cane crop? The no-arbitrage estimate of 9.53%, or one of the CAPM-based estimates of either 10.55% or 16.70%? Consider the following:

  • CAPM relies on implausible–and largely untestable–assumptions about the way investors form beliefs and expectations, and the way capital markets aggregate risk information.
  • Leading finance researchers have a consensus view that CAPM theory is inconsistent with decades of empirical research results.
  • CAPM-based estimates of the risk-adjusted discount rate for sugar risk are not estimates of the market price of sugar risk; they depend on an assumption that a “comparable asset” has a CAPM-based expected return to aggregated capital market risk that is equivalent to the market price of sugar risk (?!).
  • The no-arbitrage method estimate is a direct estimate of sugar price risk, subject to two plausible and testable assumptions.

So, esteemed reader, which estimate is better: the one directly estimated based on a minimum of plausible and testable assumptions, or the one based on (quite a few) implausible and largely untestable assumptions, which–by the way–has been shown repeatedly over the last 40+ years to be inconsistent with capital market data?

My view is that, in one of these two cases, the estimate doesn’t quite represent an estimate of a fair market price of sugar risk … or even a estimate of a market risk price at all. And I think we can all agree that would be problematic, no?

São Paulo

Caveats.  Please note: (i) views presented above are my own and do not reflect those of others; (ii) like anyone, I’m not infallible and am responsible for any errors; (iii) I greatly appreciate being informed of any significant errors in facts, logic, or inferences and am happy to give credit to anyone doing so; (iv) the above article is subject to revision and correction; and, (v) the article cannot be construed as investment or financial advice and is intended merely for educational purposes.  MMc