Asset Allocation Via The Conditional First Exit Time or How To Avoid Outliving Your Money

The risk of outliving your money (or shortfall) with low risk, low return investments is very often more serious than the risk of losing money on high risk investments, until quite late in life. A stochastic process model incorporating mortality tables for men and women of retirement age, random rates of return and fixed initial wealth and desired level of consumption provides the analytical tool. A simulation using Canadian mortality tables and rates of return shows that almost all retirees should invest some of their wealth in equity, and for many the optimal allocation is 70–100% equity. The risk of shortfall is surprisingly high for a reasonable range of values of the variables, especially for an allocation of 100% in treasury bills. Women face much greater risk of shortfall than men. The analytical model also permits calculation of the distribution of the bequest and hence allows an individual to trade off changes in shortfall risk against changes in the expected bequest to the heirs.     

What Drives the Owner‐Occupied and Rental Housing Markets? Evidence from an Estimated DSGE Model

Most dynamic stochastic general equilibrium (DSGE) models with a housing market do not explicitly include a rental market and assume a tight mapping between house prices and rents over the business cycle. However, rents are much smoother than house prices in the data. We match this feature of the data by adding both an owner‐occupied housing market and a rental market in a standard DSGE model. The intertemporal preference shock accounts for more than half of the variation in house prices and contributes to residential investment fluctuations through the liquidity constraint, and nominal rigidity in rental contracts captures the variation in the price‐rent ratio.     

An Unobserved Components Model of the Yield Curve

We develop an unobserved component model in which the short‐term interest rate is composed of a stochastic trend and a stationary cycle. Using the Nelson–Siegel model of the yield curve as inspiration, we estimate an extremely parsimonious state‐space model of interest rates across time and maturity. The time‐series process suggests a specific functional form for the yield curve. We use the Kalman filter to estimate the time‐series process jointly with observed yield curves, greatly improving empirical identification. Our stochastic process generates a three‐factor model for the term structure. At the estimated parameters, trend and slope factors matter while the third factor is empirically unimportant. Our baseline model fits the yield curve well. Model generated estimates of uncertainty are positively correlated with estimated term premia. An extension of the model with regime switching identifies a high‐variance regime and a low‐variance regime, where the high‐variance regime occurs rarely after the mid‐1980s. The term premium is higher, and more so for yields of short maturities, in the high‐variance regime than in the low‐variance regime. The estimation results support our model as a simple and yet reliable framework for modeling the term structure.