Portfolio Choice Over The Business Cycle And The Life Cycle

Do households holding risky financial securities tend to invest in the stock market, buying at the top and selling at the bottom? Do they reduce their risk exposure with age and especially when approaching retirement? We answer these questions using data on retirement savings contracts from a large French insurer over the period 2002 to 2009. Subscribers can invest their savings in two types of investment vehicles: a euro fund composed primarily of money market securities with almost no risk, and unit-linked funds representing UCITS shares invested in risky securities. We show that the share of capital invested in unit-linked funds is sensitive to market conditions, but mainly at the date of subscription. Once the initial share has been selected, inertia of portfolio choice is observed as investors rarely revise their position subsequently. We observe a steep procyclicality of investment choices which can be explained by extrapolation of recent market performance. New subscribers buy risky assets when the stock market rises and stop buying them when it drops. This leads them to hold a minimum share of risky assets in 2004, a beginning of a 4-year rising phase and a maximum share in 2008 at the beginning of a fall market.We also find that the risky share declines with age once time effects are controlled for and cohort effects are excluded. The age profile also declines in the reverse configuration (taking into account cohort effects and excluding time effects) but the decline is less pronounced. After a discussion of the plausibility of the different effects, we estimate a probability of unit-linked detention which decreases by about 12 percentage points with age between ages 40 and 60, and a conditional equity share which decreases by about 6 percentage points with age between 40 and 60 years. This decrease is too small to bring the invested share to zero when approaching retirement.

Empirical evidence shows that changes in aggregate labor income and stock market returns exhibit only weak correlation at short horizons. As we document below, however, this correlation increases substantially at longer horizons, which provides at least suggestive evidence that stock returns and labor income are cointegrated. In this paper, we investigate the implications of such a cointegrated relation for life-cycle optimal portfolio and consumption decisions of an agent whose non-tradable labor income faces permanent and temporary idiosyncratic shocks. We find that, under economically plausible calibrations, the optimal portfolio choice for the young investor is to take a substantial ¿Xem short} position in the risky portfolio, in spite of the large risk premium associated with it. Intuitively, this occurs because the cointegration effect makes the present value of future labor income flows stock-like' for the young agent. However, for older agents who have shorter times-to-retirement, the cointegration effect does not have sufficient time to act, and the remaining human capital becomes more bond-like.' Together, these effects create a hump-shaped optimal portfolio decision for the agent over the life cycle, consistent with empirical observation

We study the life cycle of portfolio allocation following for 15 years a large random sample of Norwegian households using error-free data on all components of households' investments drawn from the Tax Registry. Both, participation in the stock market and the portfolio share in stocks, have important life cycle patterns. Participation is limited at all ages but follows a hump-shaped profile which peaks around retirement; the share invested in stocks among the participants is high and flat for the young but investors start reducing it as retirement comes into sight. Our data suggest a double adjustment as people age: a rebalancing of the portfolio away from stocks as they approach retirement, and stock market exit after retirement. Existing calibrated life cycle models can account for the first behavior but not the second. We show that incorporating in these models a reasonable per period participation cost can generate limited participation among the young but not enough exit from the stock market among the elderly. Adding also a small probability of a large loss when investing in stocks, produces a joint pattern of participation and of the risky asset share that is similar to the one observed in the data. A structural estimation of the relevant parameters of the model reveals that the parameter combination that fits the data best is one with a relatively large risk aversion, small participation cost and a yearly large loss probability of around 1.3 percent.

Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.

We develop a machine-learning solution algorithm to solve for optimal portfolio choice in a detailed and quantitatively-accurate lifecycle model that includes many features of reality modelled only separately in previous work. We use the quantitative model to evaluate the consumption-equivalent welfare losses from using simple rules for portfolio allocation across stocks, bonds, and liquid accounts instead of the optimal portfolio choices. We find that the consumption-equivalent losses from using an age-dependent rule as embedded in current target-date/lifecycle funds (TDFs) are substantial, around 2 to 3 percent of consumption, despite the fact that TDF rules mimic average optimal behavior by age closely until shortly before retirement. Our model recommends higher average equity shares in the second half of life than the portfolio of the typical TDF, so that the typical TDF portfolio does not improve on investing an age-independent 2/3 share in equity. Finally, optimal equity shares have substantial heterogeneity, particularly by wealth level, state of the business cycle, and dividend-price ratio, implying substantial gains to further customization of advice or TDFs in these dimensions.

Traditionally, quantitative models that have studied households' portfolio choices have focused exclusively on the different risk properties of alternative financial assets. We introduce differences in liquidity across assets in the standard life-cycle model of portfolio choice. More precisely, in our model, stocks are subject to transaction costs, as considered in recent macro literature. We show that, when these costs are calibrated to match the observed infrequency of households' trading, the model is able to generate patterns of portfolio stock allocation over age and wealth that are constant or moderately increasing, thus more in line with the existing empirical evidence.