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

MODELING FINANCIAL SCENARIOS 201negatively correlated with the short-term real interest rate. Fama[18] examines how one-year spot interest rates can be used toforecast its components: the one-year inflation rate and the realreturn on one-year bonds. It is found that the expected values ofthose two components move opposite to one another. As a result,the financial scenario model includes a negative correlationbetween real interest rates and inflation.Equity ReturnsEquity returns are equal to the risk-free nominal interest rate(q + r) and a risk premium or excess equity return attributable tocapital appreciation (x):s t = q t + r t + x t : (3.16)In her model, Hardy [22] assumes that stock prices are lognormallydistributed under each regime. But while Hardy looks attotal equity returns, including dividends and the underlying compensationfrom the risk-free rate, we use the excess equity returnsfrom capital appreciation x. To estimate the parameters ofthe regime-switching equity return model, we follow the procedureoutlined in Hardy [22], maximizing the likelihood functionimplied from the regime-switching process.We estimate the process for the returns of small stocks andlarge stocks separately. Numerous web sites are available tocapture the time series of capital appreciation of these indices(see, for example, http://finance.yahoo.com). The large stocksare based on the Standard and Poor’s (S&P) 500 (or a samplechosen to behave similarly for the years prior to the constructionof the S&P 500). The data are available online at a WebSite generated by Robert Shiller, author of Irrational Exuberance(http://www.econ.yale.edu/»shiller/data/ie data.htm). The smallstock values are based on Ibbotson’s Stocks, Bonds and Bills [30].As expected, the risk and return of small stocks appear higherthan large stocks under both regimes. The following parameterestimates were developed: