PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

202 MODELING FINANCIAL SCENARIOSExcess Monthly ReturnsLarge Stocks (1871—2002) Small Stocks (1926—1999)Low HighLow HighVolatility Volatility Volatility VolatilityRegime Regime Regime RegimeMean 0.8% ¡1.1% 1.0% 0.3%Standard Deviation 3.9% 11.3% 5.2% 16.6%Probability of Switching 1.1% 5.9% 2.4% 10.0%Note that while the expected return in the high volatilityregime is lower, it is more likely that if the high volatility regimeis ever reached, the equity market will revert back to the lowvolatility regime since the probability of switching is higher. Theregime switches are correlated, so if large stocks are in the lowvolatility regime, then small stocks are more likely to be in thelow volatility regime as well.Equity Dividend YieldsSimilar to the process used by HMT and Wilkie [44], we assumethat the log of the dividend yield follows an autoregressiveprocess:d(lny t )=·y(¹ y ¡ lny t )dt + ¾ y dB yt : (3.17)One source of difficulty associated with estimating the dividendyield process involves obtaining data. There is no longtime series of dividend yields that is publicly available for equityindices. To obtain this information, we used a proprietarysource of financial data (Telerate). However, one may be ableto estimate the dividend yield of indices that contained a limitednumber of stocks (such as the Dow Jones industrial average).It should be noted that the process for dividend yields isclearly time-dependent. Average dividend yields have fallen dramaticallyover the last 50 years given the recognition of doubletaxation effects. Recent tax changes that levy lower taxes on div-