only 6% of cattle and 11% of horses in all three _aimags_ . Sheep morality rates are used as the proxy to make BIP and DRP payments when cattle and horses fall below 3,000 in any _soum._

# **Box 5. Data credibility**

<mark>The limited fluctuation credibility approach assumes that the random mortality for a particular</mark> _<mark>soum</mark>_ <mark>-species follows a Poisson process in each year. We want to be sure that the observed mortality for a particular</mark> _<mark>soum</mark>_ <mark>-species-year,</mark> _<mark>M</mark>_ <mark>, is within</mark> _<mark>c</mark>_ <mark>% of the true expected mortality,</mark> _<mark>m</mark>_ <mark>, with probability (1-</mark> _<mark>a</mark>_ <mark>)%:</mark> Prob <mark>[</mark> 1( − _c_ ) _m_ ≤ _M_ ≤ 1( + _c_ ) _m_ <mark>]</mark> = 1 − _a_ .

<mark>Applying the central limit theorem, one can show that the expected mortality for</mark> _<mark>soum</mark>_ <mark>-species-</mark> year _m_ has to be greater than _Z a c_ 2 , where _Z a_ is the (a/2)th percentile of the normal <mark>distribution.</mark> <mark>The average mortality for</mark> _<mark>soum</mark>_ <mark>-species is 4.8% or above in 90% of</mark> _<mark>soums</mark>_ <mark>. We would like to be very sure (99% sure) that the mortality rate estimate is within 1 percentage point of the true value,</mark> 2 i.e., c=21% (=1%/0.048). Given a=1% and c=21%, we have _Z a c_ = 151. The minimum <mark>number of animals is thus 3,146=151/0.048, which is rounded at 3,000.</mark> <mark>The species in a</mark> _<mark>soum</mark>_ <mark>with less than 3,000 animals are considered to have low data and thus cannot be used to make indemnity payments because of their low credibility. This threshold excludes cattle in 17</mark> _<mark>soums</mark>_ <mark>and horses in 19</mark> _<mark>soums</mark>_ <mark>, out of 57</mark> _<mark>soums</mark>_ <mark>. This represents 6% of cattle and 11% and horses in all three selected</mark> _<mark>aimags</mark>_ <mark>. Source: Authors, from AFSC (2004).</mark> The premium rates of the BIP product are calculated for each of the 59 _soums_ in the three pilot _aimags_ and for each species (cattle, sheep, goats and horses). The steps in the ratemaking procedure are detailed in Box 6. The weighted average premium rates, and the minimum and maximum premiums rates, by _aimag_ and species, are listed in Table 5. Bayankhongor is the riskier _aimag_ in this mezzanine layer of risk, with average premium rates and the minimum and maximum rates higher than those in the other _aimags_ , for all four species.

# **Box 6. BIP ratemaking procedure**

<mark>The main steps in setting the premium rates for the BIP program are the following.</mark> <mark>First, the expected value of mortality rates exceeding 7% is computed for each</mark> _<mark>soum</mark>_ <mark>-species.</mark> <mark>Second, each</mark> _<mark>aimag</mark>_ <mark>is divided into 3 risk zones using a pure premium rate for the commingled species (i.e., the</mark> _<mark>soum</mark>_ <mark>of all deaths of all species divided by the</mark> _<mark>soum</mark>_ <mark>of all animals for all species).</mark> <mark>Third, the expected BIP payoff, i.e., mortality rates between 7% and 25%-30%, is computed for</mark> _<mark>soum</mark>_ <mark>-species and zone-species.</mark> <mark>Fourth, as a means of smoothing the premium rates out within a risk zone, the pure premium for a</mark> _<mark>soum</mark>_ <mark>-species is then defined as the simple average between the expected BIP payoff for the</mark> _<mark>soum</mark>_ <mark>-species and the expected BIP payoff for the zone-species, with the corresponding zone of the given</mark> _<mark>soum</mark>_ <mark>.</mark> <mark>Fifth, in order to account for the most extreme events in the region, a catastrophe load is added to the above pure premium. This catastrophe load is the simple average between the expected DRP payoff for the zone-species and the expected DRP payoff for the</mark> _<mark>aimag</mark>_ <mark>-species, with the</mark> 22