# Risk Adjusted Discount Rate

**Topics:**Net present value, Time value of money, Cash flow

**Pages:**34 (7523 words)

**Published:**January 6, 2011

RUSSELL E. BINGHAM T H E H A R T F O R D FINANCIAL SERVICES G R O U P

Table of Contents

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Subject Abstract 1. Summary 2. Total Return Model 3. After-Tax Discounting 4. Derivation of Risk-Adjusted Discount Rate and Liability Beta Figure l : Baseline Risk / Return Line vs Leverage 5. Liability Beta Figure 2: Equity vs Liability Beta Figure 3: Equity Beta vs Risk-Adjusted Discount Rate (After-Tax) 6. Underwriting Profit Margin Figure 4: Underwriting Profit Margin vs Loss Payout Figure 5: Underwriting Profit Margin vs Investment Yield Figure 6: Underwriting Profit Margin vs Market Risk Premium Figure 7: Underwriting Profit Margin vs Leverage 7. Conclusion Related Background Reference Reading Appendix - Example Exhibit I - Balance Sheet, Income, Cash Flow and Rates of Return Exhibit II - Net Present Value Without Risk Adjustment Exhibit I I I - Net Present Value With Risk Adjustment Exhibit IV - Myers-Cohn "Fair" Premium With After-Tax Discounting

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Abstract

The development of a complete financial structure including balance sheet, income and cash flow statements, coupled with conventional accounting and economic valuation rules, provides the foundation from which risk-adjusted discount rates and liability betas can be determined. Since liability betas cannot be measured directly, a shift in focus is proposed to one based on measures more readily available and better understood, such as cost of capital equity beta, leverage, etc. The risk-adjusted discount rate is shown as a function of these variables based on the developed financial structure and valuation framework.

The liability beta is then shown to follow as a consequence, also to be calculated as a function o f these same variables. The risk-adjusted discount rates that result are less than the risk-free rate and the liability betas are negative to a greater degree than often suggested. Several relationships are demonstrated including: risk / return versus leverage, equity beta versus liability beta, and underwriting profit margin related in turn to loss payout, investment yield, market risk premium, and leverage.

1. Summary

The original Myers-Cohn "model" [ 11 ] presented basic principles of discounted cash flow, with losses risk-adjusted, for use in the determination of a "fair" premium in ratemaking. Determination of the riskadjustment to be used in discounting, a critical model parameter, was based on the liability beta. Unfortunately, determination of liability beta has proven to be both elusive and controversial, since data does not exist to support its direct measurement. As a consequence, arguments in rate hearings

regarding the value of underwriting beta have become influenced more by subjective matters such as one's philosophical view of the role of insurance in society than by concrete facts. The ratemaking focus must be brought back to one based on analytics and supported by financially based, quantifiable assumptions and data. In the end, some means must be established for more rigorously incorporating underwriting risk and variability in the ratemaking process.

While elegant in many respects, what Myers-Cohn first presented was more conceptual than substantive, and it lacked many elements needed to permit its use in a ratemaking environment. Successful

implementation of these concepts in a ratemaking context requires the development of a more complete and sophisticated financial model structure. At a minimum, the means to determine the rate of return implied by a particular rate must be provided. In addition, the present overly subjective practice by

which liability beta is selected in Massachusetts, must give way to a more rigorous and quantifiable one.

The purpose of this paper is to first recap the essential changes which need to be made to the MyersCohn model,...

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