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

226 MODELING FINANCIAL SCENARIOSbut no one bin produces as large a proportion of the outcomes asthe one occurrence out of 78 years of the historical experienceto be as obvious on the graph.The mean dividend yield for equities is 1.5% for the firstyear and 2.3% for the 50th-year values. The 1st—99th percentilerange after 10 years is 0.6% to 3.9%. The funnel of doubt graphof the dividend yield (Figure 18) increases over time as interestrates and inflation do. Figure 19 displays the histogram ofthe modeled dividend yields and the actual dividend yields overthe period 1871 through 2003, based on data available fromRobert Shiller [39]. Historically, dividend yields have variedmore widely than the model predicts and have been centered ata higher level. This may be a result, in part, of a structural shiftin the dividend payment history in the United States. Bernstein[6] notes that prior to the late 1950s, stock dividends tendedto be higher than interest rates on corporate bonds. This wasbased on the understanding that stocks were riskier than bondsand therefore should pay a higher return. Since 1959 though,dividend yields have tended to be lower than interest rates, rangingfrom 1.1% to 5.4%, which is in line with the simulationresults.Unemployment and Real Estate ReturnsThe mean value of the unemployment rate, as shown in Table1, begins at 6.0% and increases to 6.1% (which is the longrunmean value) for the end of 50 years. The 1st—99th percentilerange after 10 years is 3.5% to 8.7%. Figure 20 shows that thefunnel of doubt graph neither increases over time (as interestrates and inflation do) nor decreases (as stock returns do). Thehistogram of modeled unemployment rates along with the distributionof historical values over the period from 1948 through2003 are shown in Figure 21. By selecting only a single unemploymentrate from each year (January), the frequency of the historicalvalues corresponds with that of the model values, whichare the unemployment rates indicated after the first year of the