Return attribution analysis of the UK insurance portfolios

We examine the attribution of premium growth rates for the five main insurance sectors of the United Kingdom for the period 1969–2005; in particular, Property, Motor, Pecuniary, Health and Accident, and Liability. In each sector, the growth rates of aggregate insurance premiums are viewed as portfolio returns which we attribute to a number of factors such as realized and expected losses and expenses, their uncertainty and market power, using the Sharpe (Determining the Fund’s Effective Asset Mix. Investment Management Review, November–December, pp. 59–69, 1988; J. Portfolio Manag. 18:7–19, 1992) Style Analysis. Our estimation method differs from the standard least squares practice which does not provide confidence intervals for style betas and adopts a Bayesian approach, resulting in a robust estimate of the entire empirical distribution of each beta coefficients for the full sample. We also perform a rolling analysis of robust estimation for a window of seven overlapping samples. Our empirical findings show that there are some main differences across industries as far as the weights attributed to the underlying factors. Rolling regressions assist us to identify the variability of these weights over time, but also across industries.