| Abstract: | The present contribution deals with the problem of an adequate determination of the “fair value” of the stock portfolio of a life insurance company taking an economical and statistical point of view. The starting point consists of three standard models from mathematical finance for the development of stock prices, the martingale model, the random walk model and the AR(l)-process, the latter as a basic model capturing mean reversion effects. The best (with respect to mean square error) forecast of the future value of the process given the information about its history then is a natural and model-based concept of a “fair value”. The question remaining now is which of the alternative models gives the best representation of the data. First of all it is explained, that the martingale hypothesis is valid neither from a theoretical from an empirical point of view. However, only in the case of a martingale the market value is the best forecast, i.e. only in this case the market value would correspond with the fair value in an economical-statistical sense. This implies that the common understanding in accounting practice that the market value is a natural candidate for the fair value is not justified in theoretical terms. With respect to the question “random walk or mean reversion?” we perform a statistical-econometrical analysis of a thirty year time series of the monthly price earnings ratios (PER) of the German stock index DAX. As a result, the AR(l)-process reveals to be a better statistical representative of the time series as the random walk. This implies, that the long term equilibrium value of the AR(l)-process is the best forecast of the fair value of the DAX-PER. Given that DAX-PER then — based on different assumptions about the earnings growth rate and the time horizon — corresponding forecasts are calculated for the DAX itself. Finally it is explained that because of the pronounced long term character of life insurance business this model based conception of a long-term fair value is ideally suited for an application to life insurance companies. |
