Concurrent Session 4F

"Optimal Growth and Correlation Analysis for PC Insurers"

Last concurrent session...

Dr. Luyang Fu:
Rapid growth is one of the top causes of financial impairment in PC. Growing often means lowering price, looser UW standards, and taking on poorer risks.

"Introduction" slide lists some papers for background reading on the inverse relationship between profitability and growth: Aghion and Stein (2008), Harrington, Danzon, and Epstein (2008), and Ma (2009).

Papers on relationship between policy age and loss ratio: D'Arcy and Doherty (1989; 1990), Cohen (2005), and Wu and Lin (2009).

Papers on optimal growth: D'Arcy and Gorvett (2004) uses a 3-factor econometric model on 14/15 companies. Excluding AIG from the data, he finds that the optimal growth is actually 0%. Including AIG he gets 10%.

Using this model in practice is problematic due to the lack of data and the extreme volatility from removing AIG (parameter risk.) Also the underlying assumptions of the DFA scenarios are iffy. Fu (2012) applies some improvements to the model, but also disadvantages in that it's not stochastic. Equilibrium theory underlies his model. Starts with growth target and % that will be new business to project the combined ratio over a number of years.

Surplus constrains growth, as we know, so there is a limit on the curve. This means that in order to grow faster, CR needs to be lower, and you can draw this "blue line." [KR: see the presentation for formulas. Session is also being recorded.]

Plotting both curves gives you something like the supply and demand curves, yielding the optimal growth. See the Case Study slides for the end results. Note that in the chart of 5-year profits, the column labeled "Year" is supposed to be "Retained Profit." Weight on surplus and the time horizon both make a difference in whether or not growth > 0 is optimal.

Dr. Benedict Escoto (Aon, woot!):
Discussion of correlation/contagion factors. Hierarchical models (Bayes networks) express Y as a function of X. Multivariate distributions with a correlation. Notes that 0 correlation =! independence. Also there are other ways to measure correlation besides the standard Pearson (Cov(X,Y) / SDxSDy.) Copulas (CDF) transform distributions (any monotonic increasing) into a distribution between 0 and 1. Slide 9 shows an interesting example of how even having the perfect underlying distribution can be less effective due to synthesis error. It can work better to use the "wrong" distribution sometimes if it's simpler.

CAT models have traditionally assumed no correlation in severe weather events (non-hurricane.) Tornadoes recently seem to contradict this notion. Traditional model is getting frequency right and severity by layer right, but layer and ground-up CVs are mismatched. Higher layers have more volatility than the traditional model suggests. Using a Gaussian copula [KR: see slides for this formula.] resolves this issue.

Audience question - disconnect between AY CR and CY CR. Does this send false signals about growth?

Luyang: Yes, CY result would be off, particularly if you're under-reserved. It's important to education your executives about the difference between CY and AY.

Luyang's question to Benedict - how often is reinsurance sold in each of these layers versus overall? Does it really matter that we're off on the volatility by layers?

Benedict: Not every reinsurer buys enough layers to solve the problem.

Audience question - how do you parameterize correlations between lines of business?

Benedict: Relatively simple approach. Larger companies with greater diversification in losses are more subject to market risks. We develop a correlation matrix for market risk and layer on top the individual company diversification risk.

End Concurrent Session 4F.