Life Cycle Portfolio Choice With Liquid And Illiquid Assets

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.

The presence of illiquid assets, such as human wealth or a family owned business, complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset allocation and consumption in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless asset. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and to the liquid holdings held by the agent. We provide what we believe to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets.

We present a model of optimal allocation over liquid and illiquid assets, where illiquidity is the restriction that an asset cannot be traded for intervals of uncertain duration. Illiquidity leads to increased and state-dependent risk aversion, and reduces the allocation to both liquid and illiquid risky assets. Uncertainty about the length of the illiquidity interval, as opposed to a deterministic non-trading interval, is a primary determinant of the cost of illiquidity. We allow market liquidity to vary from `normal' periods, when all assets are fully liquid, to 'illiquidity crises,' when some assets can only be traded infrequently. The possibility of a liquidity crisis leads to limited arbitrage in normal times. Investors are willing to forego 2% of their wealth to hedge against illiquidity crises occurring once every ten years.

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.

Motivated by the success of internal habit formation preferences in explaining asset pricing puzzles, we introduce these preferences in a life-cycle model of consumption and portfolio choice with liquidity constraints, undiversifiable labor income risk and stock-market participation costs. In contrast to the initial motivation, we find that the model is not able to simultaneously match two very important stylized facts: A low stock market participation rate, and moderate equity holdings for those households that do invest in stocks. Habit formation increases wealth accumulation because the intertemporal consumption smoothing motive is stronger. As a result, households start participating in the stock market very early in life, and invest their portfolios almost fully in stocks. Therefore, we conclude that, with respect to its ability to match the empirical evidence on asset allocation behavior, the internal habit formation model is dominated by its time-separable utility counterpart.

Jaroslaw Morawski offers a practicable and theoretically well-founded solution to the problems encountered when investing in illiquid assets and develops a model of the liquidation process for this category of investments. The result is a coherent investment decision framework designed specifically for private real estate but applicable also to other illiquid assets.

This paper explores the implications of the additive and endogenous habit formation preferences in the context of a life-cycle model of an investor who has stochastic uninsurable labor income. To solve the model, I analytically derive the habit - wealth feasibility constraints and show that they depend on the worst possible path of future labor income and on the habit strength, but not on the probability of the worst income. When there is only a slim chance of a severe income shock, the model implies much more conservative portfolios. The model also predicts that for some low to moderately wealthy households, the portfolio share allocated to stocks increases with wealth. Because of this feature, the model can generate more conservative portfolios for younger than for middle-aged households. One controversial finding is that for high values of the habit strength parameter, usually required for the resolution of asset pricing puzzles in general equilibrium, the life-cycle model predicts counterfactually high wealth accumulation.

Using error-free data on life-cycle portfolio allocations of a large sample of Norwegian households, we document a double adjustment as households age: a rebalancing of the portfolio composition away from stocks as they approach retirement and stock market exit after retirement. When structurally estimating an extended life-cycle model, the parameter combination that best fits the data is one with a relatively large risk aversion, a small per-period participation cost, and a yearly probability of a large stock market loss in line with the frequency of stock market crashes in Norway.