Survey_MS_2002

Abstract

We analyze the five strategies described above in terms of wealth levels (or total returns) and required regulatory capital. Since there are no closed-form expressions for the statistics of interest, we use Monte Carlo simulation to generate a large number of paths for the evolution of the savings plans. The relevant statistics for total returns (relative to a benchmark) and regulatory capital are then evaluated on the basis of these scenarios. The key ingredient in such a simulation is a suitable model to describe the dynamics of the relevant funds and the short rate of interest. For the funds we use the standard capital market model, representing asset price movements by means of correlated Wiener processes. The dynamics of the short rate are given by the one-factor model suggested by Cox/Ingersoll/Ross (CIR, 1985). While we assume constant correlations between the risk factors, the covariances will vary due to the fact that the conditional standard deviation for the short rate will in general not be equal to the unconditional value. The time series used to estimate the process parameters (mean returns, volatilities, correlations) are the monthly log returns of the German stock index DAX representing the stock index fund, the log returns of the bond performance index REXP as the bond index fund as well as the 1-year interest rate as a proxy for the short rate. Parameters were estimated via a maximum-likelihood approach, the estimates are presented in table 2 and 3. As discussed above we subtracted the equivalent of 0.5% p.a. from the monthly average return on the investments to take potential administration costs into account. To ensure stability of the simulation results, we base our analysis on 3,000,000 simulations for each of the respective strategies.