Suppose that consumption growth has lognormal distribution with the possibility of rare disasters:
Here ε is a standard normal random variable, while ν is an independent random variable that has value of either zero (with probability of 98.3%) or ln(0.65) (with probability of 1.7%).
Simulate ε with (at least) 104 random draws from standard normal distribution, and simulate ν with (at least) 104 random draws from standard uniform distribution.
Use the simulated distribution of consumption growth to find the simulated distribution of the pricing kernel for power utility:
Repeat this process for values of γ in the range from 1 to 4, in increments of 0.1 (or less). (You can reuse the same simulated distribution of consumption growth for all values of γ)
Calculate the mean (μM) and standard deviation (σM) of pricing kernel for each value of γ, and plot the volatility ratio (σM/μM) on the vertical axis vs γ on the horizontal axis.
Find the smallest value of γ (in your data) for which σM/μM > 0.4. Explain (in words, without using mathematical equations or formulas) the economic significance of this result.