Equity

IRR,.ROE, and PVI/PVE
Ira R o b b i n , P h D , S e n i o r P r i c i n g Actuary, P a r t n e r R e

Abstract:

This paper presents three related measures of the return on a Property-Casualty insurance policy. These measures are based on a hypothetical Single Policy Company model. Accounting rules are applied to project the Income and Equity of the company and the flows of money between the company and its equity investors. These are called Equity Flows. The three measures are: i) the Internal Rate of Return (]RR) on Equity Flows, h) the Return on Equity (ROE), and iii) the Present Value of Income over the Present Value of Equity (PVI/PVE). The IRR is the yield achieved by an equity investor in the Single "Policy Company. The ROE is the Growth Model Calendar Year ROE computed on a book of steadily growing Single PoLicy business. The PVI/PVE is computed by taking present values of the projected Income and Equity of the Single Policy Company. The paper includes new results relating the PVI/PVE and ROE to the IRR. Beyond developing the foundation and theory of these

return measures, the other main goal of the paper is to demonstrate how to use the measures to obtain risksensitive prices. To do this, Surplus during each calendar period is set to a theoretically required amount based on the risk of the venture. The main source of risk arises from uncertainty about the amount and timing of subsequent loss payments. With the IRR and PVI/PVE, the indicated prices are those needed to achieve a fixed target return. The indicated price using the Growth Model is that needed to hit the target return at a specified growth rate. With the Growth Model, one can also compute the premium-to-surplus leverage ratio for the Book of Business when it achieves equilibrium. The ability to relate indicated pricing to a leverage ratio, growth rate, and return is an advantage of Growth Model and could lead to greater acceptance of its results. The paper includes sensitivity analysis