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Brainstorms by Stephen PhilbrickWhy DFA?
Dynamic Financial Analysis (DFA) is probably the fastest growing area in actuarial science. Yet to some, it seems like a solution in search of a problem. It is easy to show graphs of output and makethe argument that distributions of future results convey more information than point estimates. Yet, at the end of the day, senior management makes decisions. Demonstrating the implications of decisions may fascinate risk-averse actuaries but it provides only incremental value to CEOs who are willing to make decisions with limited information.
DFA will provide more value when it indicates different decisions than those arising from traditional analysis.
One potential example involves the asset allocation between taxable and tax-exempt bonds. In Manny Almagro and Tom Ghezzi's excellent paper on federal income taxes (http://www.casact.org/PUBS/proceed/proceed88/88095.pdf), they illustrate the optimum mix of taxable/tax-exempt bonds under a variety of circumstances. A number of factors affect the mix, but I'll start by illustrating the effect of the underwriting results. Their paper included a specific hypothetical example of a company with $200 million in bonds. They calculated the optimal mix for several possible underwriting results:
Underwriting Gain (Loss) Taxable Bonds Tax-exempt Bonds ($10 Million) $44 million $156 million ($15 Million) $80 million $120 million ($20 Million) $116 million $84 million For those companies with good crystal balls, one could "predict" the underwriting results for the next year, and plan the investment portfolio accordingly. Most companies are not so fortunate as to be able to predict their underwriting results with any certainty. For simplicity, let us assume that this company determines that the underwriting result will be either -$10 million or -$20 million, with equal probability. Thus, the expected underwriting result is -$15 million.
The optimal taxable mix differs for the two results, however. The company would want $44 million in taxable bonds if the underwriting result turns out to be -$10 million, but $116 million if the underwriting result turns out to be -$20 million. While a company can alter its mix during the year based upon emerging experience, shifts of these magnitudes are probably higher than prudent investment policy would suggest. Consequently, the company wishes to select a single taxable mix and hold it throughout the year.
One option is to select the taxable mix associated with the expected underwriting result. In this case, the indicated taxable amount would be $80 million. This amount does not maximize the expected net income given the two possible underwriting results, however (the calculations are beyond the scope of this column). In this simple case, with only two possible underwriting results, we can use an optimizing technique in a spreadsheet to find the best taxable/tax-exempt mix. In realistic situations, however, the underwriting results are represented by a distribution of possibilities. In very special cases, it may be possible to find the best answer analytically. But in general, the interactions are too complex and are not easy to represent analytically.
Even this observation does not provide the complete motivation for DFA analysis. Using dynamic assumptions to solve for the decisions that will lead to the maximum net income is one approach. In a dynamic world, however, risk is important. A particular choice may produce the maximum expected net income, but the risk associated with that choice may be high enough that another choice is preferable. A DFA approach can highlight the risk and return trade-offs.
In summary, DFA provides some value when it can be used to illustrate better the potential results of various decisions, but DFA becomes a critical tool when the optimal strategies in a dynamic framework vary materially from the strategies associated with a static approximation of the world.