_ANDR EE_<sup>_ ́_</sup> _DECEMBER - 2021_ _18_ thus based on the full set of markets, but are essentially derived as a weighted average of the imputed markets with more weight given to markets that are more densely surrounded by other markets where WFP maintains or has maintained price monitoring operations.

Table A4 also summarizes the monthly changes in the price indexes over the entire study period using three simple metrics. First, the monthly returns in the price index are annualized. This gives the average rate at which food prices have inflated at an annual basis across all available time periods. The second column provides a maximum draw-down figure, which is the largest negative percentage price change that occurred from top to bottom over the full time period. Apart from price changes, economists are frequently also interested in price uncertainty. The third column in table A4 contains the annualized standard deviation in monthly price returns, which is the average price volatility over the entire period of study. For example, in Afghanistan prices have increased at an average annual rate of 5 _._ 76%, the largest deflationary event was a measured price move of _−_ 43 _._ 86% from top to bottom, and the average standard deviation with which price changes fluctuated was 8 _._ 69%. The simple aggregation of results highlights that food price inflation is problematic in many FCS countries. Inflation-targeting countries often aim for a positive inflation rate just below 2%. Only 6 out of the 25 analyzed countries meet this criterion for food when measured over the entire study period. Moreover, in 7 countries, active price increases in food have been so strong that they outweighed price uncertainty.

Historical famines have frequently been associated with high price increases that led to speculative purchasing of food as an investment (Gr ́ada, 2007). Investors typically aim for investments in high-return low-volatility assets and often track the performance of investments by focusing on risk-adjusted returns (Markowitz, 1991). A commonly applied metric is the Sharpe ratio, which is the annualized return divided by the annualized standard deviation of returns. The ratio is a _z_ -score type of metric that describes the excess return received for the extra volatility endured when holding an asset. In general, for an asset to be investmentgrade, one likes the ratio to be above 1 so that the price increase outweighs the price uncertainty.<sup>29</sup> The Sharpe ratios can be obtained from table A4 by dividing the first column by the third. It is important to note that this ratio is constructed in hindsight and does not fully characterize all the factors involved with an investment decision, nor does it take into consideration the scarcity of information and the complexity of the market environment during inflation events. Nevertheless, it provides a simple and well-understood way to standardize price changes in a way that allows comparing the significance of price changes across markets associated with different typical volatilities. For example, a 4% inflation surge is more significant if the typical price change over that time period is 1% as opposed to, say, 10%. Contrasting these ratios, highlights that some inflation

> 29As a reference, the average Sharpe ratio of the dollar denominated S&P500 index has been around 1 over the past 25 years, while good performing hedge funds often achieve annual Sharpe ratios of 1 _._ 5.