Andrew P. Hofer and Raghu Ramachandran explain why dynamic financial analysis is more useful in allocating insurance assets than matrix-based models.
Surely you have heard or read comments describing companies that have not invested in equities as having “missed the boat” or “acted too timidly.” It is certainly easy, with the benefit of hindsight, to look back on recent market performance and wish one had participated to a greater degree. Yet, we must make an allocation decision today without knowing how the company's assets or liabilities will perform tomorrow.

How much of its portfolio can a given insurance company reasonably allocate to equities or other volatile investments without assuming an unacceptable increase in risk? In this article, we look at the shortcomings of the prevailing matrix-based asset allocation analysis and demonstrate how dynamic financial analysis produces conclusions that are more useful.

As an example of matrix-based asset allocation analysis, Graph 1 shows the effects of adding equities, as represented by the S&P 500 Index, to a fixed income portfolio, represented by the Lehman Aggregate Index. In the graph, portfolio C, with a higher percentage of equities than portfolio B, offers an additional 1.44% in annualised return. For this additional return the portfolio has a 3.58% greater standard deviation on an absolute basis (9.53%-5.95%) or 60.2% (9.53%/5.95%) of additional volatility relative to portfolio B. But, for most of us, these numbers are abstract. How much risk is a “standard deviation?” What effect does the additional portfolio volatility have on the company's bottom line? The matrix method, used by so many, falls short of providing the necessary insight for an informed decision. The results provided by a standard matrix analysis have two shortcomings, especially for an insurance company. First, investment professionals, even asset managers, do not intuitively understand the effect one unit of standard deviation has on the bottom line of the company. For example, we do not know how moving from portfolio B to portfolio C affects the company's financials. What implication does the extra 3.58% of standard deviation have on the company's ability to meet an earnings target? How does it affect the company's surplus or risk based capital (RBC) position? Second, the analysis does not account for incoming or outgoing cash flows. As the example which follows shows, we should not ignore cash flows. They can substantially change the risk and reward characteristics of a portfolio.

A simple example

To illustrate these shortcomings, we will use the following simple example. Suppose we have to choose between two portfolios, 1 and 2. We generated sample quarterly returns for these portfolios for the next two years. (See next page) Portfolio 1 has a return of 6.4% with a standard deviation of 2.8% and portfolio 2 has a return of 8.0% with a standard deviation of 4.2%.

If each portfolio started with $100 in invested assets and had no cash flows, at the end of two years they would have a value of $113.24 and $116.64, respectively. Is the extra amount of return portfolio 2 enjoys worth the extra risk?

What happens if there is a claim or a catastrophe? Let us suppose the company has to pay a claim of $80 at the end of the second quarter. From a total return perspective, this cash flow does not affect the calculation of total return. Thus, the portfolios still have the same return measure.

However, consider the asset value at the end of two years; portfolio 1 now appears more attractive on a reward basis as it has 11% more assets. Of course, insurance liability cash flows vary in terms of both timing and magnitude. Consider what would happen if the claim came in the seventh quarter rather than in the second; now portfolio 2 has 3% more assets at the end of the period.

However, if the claim in the second quarter increased to $100, then portfolio 2 would bankrupt the company! Thus, cash flows can alter how we rank portfolios in terms of reward.

Cash flows should also affect a meaningful risk measure, but as with returns, they do not affect the standard deviation of return calculation. Yet, in our example, large cash outflow early in the projection would bankrupt the company. Thus, the company would want an effective way to assign higher level of risk to this allocation than the measured standard deviation would indicate. Reality is even harsher: this example does not take into account transaction costs, taxation and the inherent variability of reserves.

Most matrix-based analyses do not make allowances for these factors and could lead to conclusions detrimental to the company.

Modeling a solutionDynamic financial analysis (DFA) offers a solution to this problem. With a DFA model, the company would project its financials, both assets and liabilities, under various scenarios. When modeled correctly, the company now has a representative set of balance sheets, income statements and cash flow statements. These statements take into account not only the varying asset and liability cash flows, but also frictional costs, such as taxes and transaction fees.

From these financials, the company can construct risk and reward measures that are more useful. As suggested above, one meaningful reward measure is the terminal value of assets, or surplus. However, the company can construct a variety of measures depending on its financial position or business objectives. For instance, for an over-capitalised company the reward objective would be to minimise the initial surplus without affecting the company's operational capabilities. A captive insurance company might measure as reward the ability to reduce the amount of contributions (premiums) from its shareholder-insureds. While DFA allows you to develop unique reward measures, such measurers are generally easy to construct since everybody wants more assets. The real advantage DFA provides is in its ability to create alternate measures of risk. For example, with probabilistic balance sheets created by the DFA process, the company can calculate the likelihood of ruin. If one portfolio assigns the company a probability of ruin of 6% and another assigns the company a probability of ruin of 8%, then the company has a much better understanding of how the selection of an allocation will affect the company as a going concern. Other possible risk measures include the probability of going below a certain RBC threshold, the probability of missing an earnings target or shareholder dividend, or the probability of requiring an infusion of additional capital from a parent. The advantage of these alternate measures is that they measure risk in terms relevant to the company. A public company might care about missing an earnings target while a private company might wish to avoid breaching a RBC threshold. Thus, the company can make a decision based on factors of concern to them.

Another example
We use the following DFA model to show the effects of asset allocation on a combined asset liability model. We first constructed three liability models. In all three models, we assume the company writes, and has written for the past several years, the same amount of premium every year with a 100% combined ratio. For such a company, the change in reserves will exactly offset the amount of claims; thus, claims should not affect surplus. Of course, liabilities will vary and this variability will affect the surplus.

The first model assumes the liabilities have a short tail; the second uses liabilities that have a long tail. The final model combines these two liabilities in equal amounts. We further assume that in this steady state, all of the models have a 2:1 initial reserve to surplus ratio.

Using the five asset allocations in graph 1 and the steady state liabilities, we performed simple DFA analysis to see how we should invest the surplus of the company. Graph 2 (see next page) displays the results of this analysis. The vertical axis shows the average surplus at the end of 10 years; the horizontal axis shows the standard deviation of the ending surplus.

The “surplus only” line shows the value of the surplus in a model without any liabilities. This line is very similar to the line in graph 1. The other three lines show the effect of variable liabilities on surplus. Both types of liabilities add risk. The combined line has less risk than the individual lines, demonstrating the effects of liability diversification. Notice that in all of these models, an all-bond portfolio still has the least risk and the all-stock portfolio still has the highest risk. However, using the DFA output we redefine the risk measures. In graph 3, we look at the probability that the surplus will fall below zero, i.e., the probability of ruin. Without any liabilities, none of the allocations will bankrupt the company. So the “surplus only” line would lie on the y-axis.

Using probability of ruin as the risk measure, we see that the safest allocation is no longer an all-bond portfolio. Indeed, the safest allocation varies by the liabilities of the company. If we used the standard risk/reward measures then all three models would have identical values — those shown on graph 1. However, the viability of an individual company varies based on its asset allocation.

Conclusion
Of course, a full model would include more asset classes than the Lehman Aggregate and the S&P 500 and a liability model more realistic than the steady state model. Although the examples provided are highly simplified, they show that for an insurance company choosing between different asset allocations is not a matter of looking at total return. The example also highlights how standard deviation of total returns does not accurately capture the enterprise risk for an insurance company. Insurance companies, particularly in this era of over-capitalisation, can benefit from aggressive management of their investments. How much of the portfolio to allocate to higher risk investments must be a company-specific decision.

There are many sources for information on calculating efficient frontiers and selecting optimal portfolios. The reader can consult one of the references. For information on constructing a DFA model, look at, for example, Hodes, et. al., Almagro and Sonlin, Feldblum, Skoda, or the CAS DFA paper.

References
Almagro, Manual and Sonlin, Stephen M., “An Approach to Evaluating Asset Allocation Strategies for Property/Casualty Insurance Companies”, CAS Forum, Spring 1995.

Bodie, Zvi, Kane, Alex, and Marcus, Alan J., Investments 2nd Ed., Irwin, 1993.
Brealey, Richard A. and Myers, Stewart C., Principles of Corporate Finance 4th ed., McGraw Hill, 1991.
Feldblum, Shalom, “Forecasting the Future: Stochastic Simulation and Scenario Testing”, CAS Forum, Spring 1995.
Hodes, Douglas M, Neghaiwi, Tony, Cummins, J. David, Phillips, Richard and Feldblum, Sholom, “The Financial Modeling of Property/Casualty Insurance Companies”, CAS Forum, Spring 1996.
Korn, Ralf, Optimal Portfolios: Stochastic Models for Optimal Investment and Risk Management in Continuous Time, World Scientific, 1997.
Skoda, Susan T., “How DFA Can Help the Property/Casualty Industry”, Actuarial Review, V.24, No.1.
Spaulding, David, Measuring Investment Performance: Calculating and Evaluating Investment Risk and Return, McGraw Hill, 1997.
Association of Investment Management and Research (AIMR), AIMR Performance Presentation Standards Handbook, AIMR, 1997.
CAS Valuation and Financial Analysis Committee, Subcommittee on Dynamic Financial Models, “Dynamic Financial Models of Property/Casualty Insurers,” CAS Forum, Fall 1995, pp. 93-127.

Andrew P. Hofer, managing director, insurance asset management group, Brown Brothers Harriman & Co., New York. Raghu Ramachandran, vice president and senior portfolio strategist, insurance asset management group, Brown Brothers Harriman & Co., New York.Contact on 2121 493 7907 and 212 493 7917, or e-mail at insurance@bbh.com

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