Risk and Reward

陳展輝 | YANG, Bowen

In general, people lived longer than expected in the last century, largely as a result of economic development and improvements in healthcare. Nevertheless, changes in life expectancy can be rather volatile, with negative shocks occurring from economic recessions, epidemics, natural disasters, wars, and social and political disturbances. In the United States alone, life expectancy increased from just over 74 in 1963 to just over 81 in 2014. In relation to this, longevity risk represents unexpected shocks to life expectancy. Indeed, from the insurance, health, and economic growth perspectives, the economic consequences of longevity risk are well known. For example, the IMF estimates that each additional year of life expectancy adds 3%–4% to the present value of the liabilities of a typical defined benefit pension, and a three-year increase in life expectancy would cost 50% of 2010 GDP in developed countries.

Longevity risk can be interpreted as shocks to time preferences, and it affects pricing through two channels: direct and indirect. First, longevity increases with the time-preference discount rate (direct). Second, time-preference shocks affect cross-sectional income inequality, while longevity risk may capture income inequality and thereby reveal time-preference shocks (indirect). Time-preference shocks affect agents’ preferences for assets with different durations, which represent a systematic risk on agents’ intertemporal consumption and investment choices.

Keen to understand the possible aggregate risks behind momentum profits, a recent paper by Zhanhui Chen and Bowen Yang analyses the cross-sectional asset pricing implications of time-preference shocks arising from longevity risk in the stock market. Following existing literature, Chen and Yang model longevity risk via a stochastic time-preference shock process in the recursive setting using a consumption-based three-factor model, comprising longevity risk, consumption growth rate, and the market portfolio, where longevity is negatively priced.

To test the pricing power of the longevity factor, the authors first apply the two-step generalized method of moments. The test assets include six size and book-to-market sorted portfolios, six size and investment sorted portfolios, six size and operating profitability sorted portfolios, and six size and momentum sorted portfolios. They then employ standard time-series and cross-sectional asset pricing tests by constructing a mimicking consumption portfolio and a mimicking longevity portfolio to test the consumption-based model.

Empirically, the authors find that “The model explains many cross-sectional return variations generated by many well-known portfolios”. First, Chen and Yang show that “Prior winners (losers) provide hedging against mortality (longevity) risk, because winners experience higher dividend growth and thus have much shorter equity durations than losers. Second, as longevity risk varies over time, the study highlights that agents’ preferences for longer or shorter duration stocks change over time, leading to time-varying momentum profits. Third, the frequency domain analysis directly shows that longevity risk and the momentum factor share a common business cycle component, consistent with previous findings. The authors also illustrate that longevity risk is negatively associated with short-run consumption risk, but positively related to long-run consumption risk. Fourth, Chen and Yang discover that longevity risk may reveal income inequality. Specifically, they find that longevity decreases with income inequality, and income inequality partially contributes to the longevity factor. Finally, the study reveals that annual pricing constructed from the consumption-based model is positively serially correlated, further validating their risk-based explanations of momentum strategy.


Associate Professor