Investment Under Uncertainty: A Theory

There must be a restricted time horizon within which investors trust their anticipations in an uncertain condition. In this circumstance investors are concerned about what happens if the worst condition (i.e. decreasing prices) occurs. A best-worst strategy in a discounted payback period framework is applied to examine the effect of uncertainty on the time horizon and investment. The model shows that increasing uncertainty will reduce the time horizon as well as investment. Moreover, the calculated time horizon can be considered as a benchmark for the adjusted payback period approach in finance.Uncertainty, Investment, Discounted payback period, best-worst strategy

Epstein-Zin Utility Maximization on a Random Horizon

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed-horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies

Optimal Investment Horizons

In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established that the distribution of returns exhibits ``fat tails'' indicating that large returns occur more frequently than what is expected from standard Gaussian stochastic processes (Mandelbrot-1967,Stanley1,Doyne). Instead of estimating this ``fat tail'' distribution of returns, we propose here an alternative approach, which is outlined by addressing the following question: What is the smallest time interval needed for an asset to cross a fixed return level of say 10%? For a particular asset, we refer to this time as the {\it investment horizon} and the corresponding distribution as the {\it investment horizon distribution}. This latter distribution complements that of returns and provides new and possibly crucial information for portfolio design and risk-management, as well as for pricing of more exotic options. By considering historical financial data, exemplified by the Dow Jones Industrial Average, we obtain a novel set of probability distributions for the investment horizons which can be used to estimate the optimal investment horizon for a stock or a future contract.Comment: Latex, 5 pages including 4 figur

The investment horizon problem: A resolution

In the canonical model of investments, the optimal fractions in the risky assets do not depend on the time horizon. This is against empirical evidence, and against the typical recommendations of portfolio managers. We demonstrate that if the intertemporal coefficient of relative risk aversion is allowed to depend on time, or the age of the investor, the investment horizon problem can be resolved. Accordingly, the only standard assumption in applied economics/finance that we relax in order to obtain our conclusion, is the state and time separability of the intertemporal felicity index in the investor’s utility function. We include life and pension insurance, and we also demonstrate that preferences aggregate.The investment horizon problem; complete markets; life and pension insurance; dynamic programming; Kuhn-Tucker; directional derivatives; time consistency; aggregation

OPTIMAL DEMAND FOR LONG-TERM BONDS WHEN RETURNS ARE PREDICTABLE

This paper further explores the horizon effect in the optimal static and dynamic demand for risky assets under return predictability as documented by Barberis (2000). Contrary to the case of stocks, the optimal demand for long-term Government bonds of a buy-and-hold investor is not necessarily increasing in the investment horizon, and may in fact be decreasing for some initial levels of the predicting variable. The paper provides an analytical explanation based on the dependence of the mean variance ratio on the investor´s time horizon. Under stationarity of the predicting variable, unusually high or unusually low levels of the predictor tend to dissapear over time inducing the mean of cumulative returns to grow less or more than linearly as the investment horizon increases. If this effect dominates that on the variance, optimal demands can either be increasing or decresing in the investment horizon. On the other hand, the solution to the investor´s dynamic allocation problem in the presence of bonds indicates that long-term Government bonds do not provide a good hedge for adverse changes in the investor´s opportunity set: optimal dynamic demands for bonds do not differ from static portfolio choices at any horizon.

Time and risk diversification in real estate investments: assessing the ex post economic value

Welfare gains to long-horizon investors may derive from time diversification that exploits non-zero intertemporal return correlations associated with predictable returns. Real estate may thus become more desirable if its returns are negatively serially correlated. While it could be important for long horizon investors, time diversification has been mostly investigated in asset menus without real estate and focusing on in-sample experiments. This paper evaluates ex post, out-of-sample gains from diversification when E-REITs belong to the investment opportunity set. We find that diversification into REITs increases both the Sharpe ratio and the certainty equivalent of wealth for all investment horizons and for both Classical and Bayesian (who account for parameter uncertainty) investors. The increases in Sharpe ratios are often statistically significant. However, the out-of sample average Sharpe ratio and realized expected utility of long-horizon portfolios are frequently lower than that of a one-period portfolio, which casts doubts on the value of time diversification.Real estate investment

Saving Decisions of the Working Poor: Short-and Long-Term Horizons

We explore the predictive capacity of short-horizon time preference decisions for long-horizon investment decisions. We use experimental evidence from a sample of Canadian working poor. Each subject made a set of decisions trading off present and future amounts of money. Decisions involved both short and long time horizons, with stakes ranging up to six hundred dollars. Short horizon preference decisions do well in predicting the long-horizon investment decisions. These short horizon questions are much less expensive to administer but yield much higher estimated discount rates. We find no evidence that the present-biased preference measures generated from the short-horizon time preference decisions indicate any bias in long-term investment decisions. We also show that individuals are heterogeneous with respect to discount rates generated by short-horizon time preference decisions and long-horizon time preference decisions. Dans cet article, nous évaluons si les préférences exprimées pour le présent peuvent prédire les décisions d’investissement dans le long terme. L’article mobilise l’approche de l’économie expérimentale avec comme participants des travailleurs canadiens à faibles revenus. Chaque participant est invité à choisir entre une somme qu’il peut toucher à très court terme et un montant plus élevé, mais qui ne lui sera versé que plus tard dans le temps. Pour certains choix, les montants ne seront disponibles que dans 7 ans et peuvent atteindre jusqu’à 600 $. Nous trouvons que les décisions entre le présent et un horizon de court terme permettent de prédire les arbitrages réalisés par les participants entre le présent et des décisions à plus long terme. Ce résultat est important dans la mesure où il est plus difficile et coûteux d’étudier les décisions de long terme que celles de court terme. Nous observons également une forte hétérogénéité entre les participants relativement à leurs taux d’escompte de court et de long terme.intertemporal choice, field experiments, risk attitudes, choix intertemporels, économie expérimentale, attitudes vis-à-vis le risque

Optimal Value and Growth Tilts in Long-Horizon Portfolios

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon who faces an investment opportunity set with time-varying risk premia, real interest rates and inflation. The variation in investment opportunities is captured by a flexible vector autoregressive parameterization, which readily accommodates a large number of assets and state variables. We find that the optimal dynamic portfolio strategy is an affine function of the vector of state variables describing investment opportunities, with coefficients that are a function of the investment horizon. We apply our method to the optimal portfolio choice problem of an investor who can choose between value and growth stock portfolios, and among these equity portfolios plus bills and bonds. For equity-only investors, the optimal mean allocation of short-horizon investors is heavily tilted away from growth stocks regardless of their risk aversion. However, the mean allocation to growth stocks increases dramatically with the investment horizon, implying that growth is less risky than value at long horizons for equity-only investors. By contrast, long-horizon conservative investors who have access to bills and bonds do not hold equities in their portfolio. These investors are concerned with interest rate risk, and empirically growth stocks are not particularly good hedges for bond returns. We also explore the welfare implications of adopting the optimal dynamic rebalancing strategy vis a vis other intuitive, but suboptimal, portfolio choice schemes and find significant welfare gains for all long-horizon investors.