Hi All, Would you be able to let me know how to integrate the CDF to get the table in the examiner's report? Thanks in advance for your help!
To check for second-order stochastic domination you need to calculate the integrals for the cumulative probability functions, each of which is a step function. When the distributions of returns is discrete, as is the case here, you can instead simply add up the figures used to check first-order dominance. This is equivalent to integration provided you use return intervals of equal length. So, here, as the intervals are not of equal length (some are 2% and some 3%), you need to include intermediate steps, of say, 1% in length. Although, it turns out that in this case, just summing with unequal lengths would have fortuitously led to the correct conclusion. The examiner's report calculates the integral (summation) by multiplying the width of the intervals by the heights of the CDF. In practice it is far far easier to rewrite the table with equal increments and just sum the resulting CDF directly. Hope that helps.
