Surplus--Concepts, Measures of Return, and Determination

This paper discusses the role of surplus in an insurance company and alternative measurements of rate of return on surplus. The multi-year dimension of surplus and its linkage to liabilities over time is explained, and the concept of a calendar period balance sheet as the sum of underlying accident period balance sheets is introduced. Measures of rates of return on surplus inherent in internal rate of return and net present value discounted cash flow models are explained, and the conditions under which the returns are equivalent are demonstrated. This paper also presents a methodology for determining a benchmark amount of surplus needed to support writings in a line of business in order to control the probability of insolvency. The methodology is based on a consideration of both the magnitude and the variability in underwriting, underwriting cash flows, and interest rates. Keywords: Profit Factor, Rate of Return, Risk, Investment Income