Before distinguishing between different price volatility regimes, it is important to clarify what we mean by volatility and to highlight some conceptual difficulties. It is indisputable that price volatility measures price fluctuations. However, a trader in Chicago will probably give a different assessment of wheat price volatility than a smallholder farmer in Pakistan or a baker in Niger. Whereas they might
volatility? UNU-WIDER Policy Brief.
4 http://www.nigeriasilostransactions.com/background
5 Shane Bryan. 2013. A cacophony of policy responses: Evidence from fourteen
countries during the 2007/08 food price crisis, UNU-WIDER Working Paper.
6 http://www.isdb.org/irj/go/km/docs/documents/IDBDevelopments/Internet/
English/IDB/CM/Publications/IDB _AnnualSymposium/20thSymposium/8- AbdullaAlobaid.pdf
Special features
all be looking at the same estimator to assess volatility, they will very likely focus on prices in different locations or different stages in the value chain. Transmission of price changes is typically neither complete across space and time nor along the value chain. Indeed, movements of the reference wheat prices in Chicago do not necessarily resemble movements of wheat prices in the local market in Pakistan where our farmer sells her/his harvest; and the export price does not automatically move parallel to the flour price, which is relevant for the Niger baker. In addition, the capacity to adjust to price signals typically varies across participants in the wheat market. In contrast to a trader exploiting daily price changes, a farmer cannot easily respond to even weekly or monthly price changes, as adjusting production will take an entire crop season.
Independent from these issues, volatility is usually defined as the “standard deviation of logarithmic returns”, in other words the dispersion of relative changes in prices.8
It is worth noting, however, that other notions of volatility exist, e.g. price volatility as more than 15 percent deviation from the expected price.9 It is key to keep in mind that
the standard deviation is a parameter of a probability distribution. Consequently, not only do we need to define volatility, we also need to agree upon how to infer this parameter, which we do not directly observe, from the price data. There exist various estimators producing potentially different estimates of volatility10 – which one is
the most informative depends on the context.
When comparing volatility metrics, it is vital to pay close attention to their definitions and measurement methods. For example, the International Grains Council bases its Grain and Oilseeds Index’ volatility on non-logarithmic returns, and for the first week of March 2015 its measure ranged from 9.58 percent to 11.56 percent, compared to 4.15 percent to 5.02 percent when the calculations are based on logarithmic returns.11 In addition, agricultural prices are naturally unstable
owing, for example, to the weather. However, whereas sometimes variability can be anticipated which allows market participants to be prepared, it is the unpredictable constituent of price variations, which is problematic.
Different methods to remove the predictable component can produce different volatility estimates.
8 Logarithms stabilize the variance of the series and their properties facilitate
computation.
9 Tsion Taye Assefa et al. 2014. Agro-food chain actors’ perceptions of price
volatility and their management strategies, ULYSSES Policy Briefing.
10 In principle, any function that takes price observations as an input and
produces a positive number as an output can be considered an estimator for volatility. There are infinitely many such estimators, which, naturally, do not all yield equally good results. As an example, a function mapping any arbitrary sample of prices to 0.5 is a poor volatility estimator.
11 http://www.igc.int/en/grainsupdate/igcgoi.aspx.
There are two fundamentally different strategies to estimate volatility: forward-looking and backward-
looking. Exploiting traders’ expectations about volatility as
embodied in option prices offers a forward-looking way to determine volatility. Option prices depend on the volatility of the underlying commodity – inversion of the pricing formula reveals traders’ assumption about it. This is known as “implied volatility”. On the contrary, a backward-looking approach is based on past price observations. Adopting this perspective, a natural first take on volatility is to consider a series of price changes and compute its sample standard deviation. However, when enough price observations are available to obtain a reliable estimate, the variance of the series might change, which is critical to modelling volatility. In case data are available at a higher frequency than the volatility of interest – for example, if the focus is on monthly volatility and we have daily returns at hand – it is thus common to estimate monthly volatility as the sample standard deviation of daily return data for that particular month and adjust it with a scaling factor. This is called realized volatility.12 Time series models present a promising
alternative to assess volatility. In addition to providing an estimate of overall variability, these allow an estimation of time-varying predictable volatility.
Depending on the perspective we take, the price definition varies; price frequency varies; and so does the estimation approach. To illustrate the effect of different frequencies in a simplistic setting, compare the prospect of a farmer who bases decisions on annual price averages with that of a trader dealing with daily prices. The latter has roughly 250 price observations per year and has sufficient grounds to judge whether there has been a regime change in volatility over the past year. For the farmer, in contrast, one more year means only one more observation. Assuming a price of USD 200 and 30 percent annualized volatility, this means that there is an 80 percent chance of the following year’s price falling between USD 136 and USD 294.13 If volatility increased by 10 percent, the lower
and upper price bounds would be USD 131 and USD 305, respectively, again with 80 percent probability. How would the farmer be able to even suspect there has been a 10
12 Some authors use the term “realized volatility” (or “historical volatility”) for
what we refer to as backward-looking, see for example Monika Tothova, 2011, Main Challenges of Price Volatility in Agricultural Commodity Markets In Isabelle Piot-Lepetit and Robert M’Barek (eds), Methods to Analyse Agricultural Commodity Price Volatility, Springer, New York, Dordrecht, Heidelberg, London, 2011.
13 We assume logged prices to follow a random walk. This implies that
Pyear2 = Pyear1 . eε for a normally distributed ε. The lower (upper) bound of
136 (294) is the 10 (90) percent quantile of the lognormal distribution (with zero
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FOOD OUTLOOK MAY 2015
percent increase in volatility in the past year based on one observation? In addition, as the number of observations diminishes and volatility decreases with averaging, changes in volatility will become harder to detect.