I reexamined my analysis of the ad hoc exact and approximation methods from the review session today, and here is a screenshot from Excel of this problem:
The fair coin toss involved payoffs of $25 and $100; the expected value of wealth under this coin toss is $62.50, and the standard deviation is half of the dispersion between $25 and $100, or $37.50. Applying the “exact” method, we get a risk premium of $6.25. In calculating the risk premium under the Arrow-Pratt (approximation) method, I incorrectly calculated variance as 75^2 = 5,625. Since variance is actually 37.5^2 = 1,406.25, the Arrow-Pratt equation produces a risk premium of $5.63, not $22.50. I knew that right away that one of the model inputs had to be wrong, and it was the variance input, which was 4x the actual variance of the coin toss.
Finance 4335