Modelling an insurance trigger

Hello,

I am currently working on the analysis of an investment (consisting in bonds, stocks and money market instruments) that has a built-in insurance in case of poor performance. I’d like to hear your views on how to assess the probability of the insurance being triggered.

Case 1: there is a determined asset allocation

In this case, the asset allocation percentages are known and cannot be changed. You have the expected means, variances and correlations among asset classes and you have a rule of minimum 5% of annual performance. How to model the probability of the performance being lower than this? Can the normal distribution of returns be used? Or should I imply the distribution based on past data? If the normal distribution can be used, is it enough to do a kind of downside risk assessment? If not, how can I go about it?

Case 2: asset allocations can vary

In this case, is it enough to repeat the calculations under case 1 for a number of potential asset allocations?

Thank you.

So you’re saying that you have an asset allocation, and if you generate less than 5% in any one year, an insurance provision kicks in to provide [5% - (whatever the portfolio return is)] to make up the difference?

So I’d first look to see what the historical returns distribution looks like and how serious the departures from normality are. You can look at things like skew and kurtosis, just to see how close they are to normal. You probably should be looking at log-returns for these. A Q-Q plot is a nice visiual to see how wacky your tails are.

If you think it’s pretty close to normal, then you might just use the mean and standard deviation to compute the liklihood that your insurance policy will kick in, which is basically the area under the normal curve that is <5% return for your asset allocation. You can also try to figure out what those payments are likely to be as well by computing the expected value, conditional on being below 5%.

If the historical returns are not normal enough, then you have two choices - 1) try to see if a different distribution looks more appropriate and try to fit it to parameters of that distribution, or 2) use the historical distribution itself and see how often you would have had to make the insurance payment. You can try to blend the historical with the normal (or other distribution) to give more weight to one or the other.

You will also want to have some kind of safety factor or stress-test, because really large tail events may not be in your historical sample and you want to see what happens when the sh*t really hits the fan.

What’s the purpose of this modelling exercise? I have a tendency to make things super complicated when all someone really needs is an easy way to put in scenarios and see what the performance of the product would be.

Hello,

bchad and jmh530, thank you for your answers.

The purpose of this modelling exercice is to give the risk/reward profile of the investment for the guarantor where risk is the probability that the insurance will be triggered (and the amount at stake) and the reward is the price of the guarantee.