_positive_ .<sup>6</sup> Under this approach, the crop business profitability is determined by the downside risk characteristics of the specified crop. If the crop yield is lower than the production costs, the survivability of the crop business activity will depend on the farmer’s ability to absorb this income shock. The viability of the crop business thus relies on the farmer’s financial reserves or external capital to cover the unexpected operating losses, which is the minimum amount of capital required to ensure the continuity of the business after the occurrence of an adverse production shock. The relationship between the crop yield risk characteristics and the minimum capital requirements is illustrated in Box 1.

# **Box 1.  Crop yield losses and minimum capital requirements**

Data on cocoa and banana yields from 1961 to 2002 in a South American country are used for the sake of illustration. Data are first detrended using a polynomial procedure. First order serial correlation is tested and the hypothesis of serial correlation is rejected. The figure below shows the variability of these two crops expressed in percentage of the average (adjusted) crop yields, which are estimated at 168.89 kg/ha for cocoa and 23.42 mt/ha for banana. Cocoa yields are more variable than banana yields and exposed to higher extremes.

# **Variability of banana and cocoa, in percentage of average yields.**

<!-- Start of picture text --> 200.00%<br>180.00%<br>160.00%<br>140.00%<br>120.00%<br>100.00%<br>80.00%<br>60.00%<br>40.00%<br>20.00%<br>0.00%<br>year<br>banana cocoa<br>196119631965196719691971197319751977197919811983198519871989199119931995199719992001<br><!-- End of picture text --> The cumulative distribution functions (CDF) of the operating losses are simulated for different levels of average operating profit margin. The downside risk is measured by the Value at risk (VaR) which summarizes the worst loss over a target horizon with a given level of confidence. Formally, this is a specified quantile of the CDF of the operating losses. For example, VaR(5%) is the worst operating loss in a 95% confidence interval. It determines the minimum capital required to absorb potential losses and thus ensures the viability of the crop business following the occurrence of a loss. The higher the average operating profit margin is, the lower are the potential losses and thus the minimum business capital requirements.

The table below presents the minimum capital requirements for two different crops depending on the farmer’s average operating profit margin. It shows that the reserves required for cocoa production are much larger that those required for banana production, as a consequence of the greater (downside) variability of the cocoa yields. When the average operating profit margin is 5%, the amount of capital needed to absorb unexpected production shocks with a 95% confidence interval is equal to 58.2% of the average yield for cocoa and 19.7% for bananas. When the average operating profit margin is 20%, the amount of capital is 46.2% and 2.9% for cocoa production and banana production, respectively.

> 6 Formally, operating loss= max[1( −α) _~~y~~_ − _y_ 0,], where _~~y~~_ is the average crop yield, _y_ is the actual yield and α is the average operating profit margin. Operating loss is thus equal to negative operating profit margin.

6