Price dynamics in a market with heterogeneous investment horizons and boundedly rational traders

Abstract

This paper studies the effects of multiple investment horizons and investors' bounded rationality on the price dynamics. We consider a pure exchange economy with one risky asset, populated with agents maximizing CRRA-type expected utility of wealth over discrete investment periods. An investor's demand for the risky asset may depend on the historical returns, so that our model encompasses a wide range of behaviorist patterns. The necessary conditions, under which the risky return can be a stationary iid process, are established. The compatibility of these conditions with different types of demand functions in the heterogeneous agents' framework are explored. We find that conditional volatility of returns cannot be constant in many generic situations, especially if agents with different investment horizons operate on the market. In the latter case the return process can display conditional heteroscedasticity, even if all investors are so-called "fundamentalists" and their demand for the risky asset is subject to exogenous iid shocks. We show that the heterogeneity of investment horizons can be a possible explanation of different stylized patterns in stock returns, in particular, mean-reversion and volatility clustering.Keywords: Asset Pricing, Heterogeneous Agents, Multiple Investment Scales, Volatility Clustering J.E.L. Classification: G.10, G.14. RésuméNousétudions l'effet de multiples horizons d'investissement et de la rationalité limitée des investisseurs sur la dynamique des prix. Dans le cadre d'un modèleà agents hétérogènes, nous introduisons de multipleséchelles d'investissement. Nous trouvons que la volatilité conditionnelle des rendements ne peut pasêtre constante dans de nombreuses situations génériques, en particulier si les agents avec des horizons d'investissement différents opèrent sur le marché. Dans ce dernier cas, le processus de rendements peutêtre hétéroscédastique, même si tous les investisseurs sont "fondamentalistes" mais leur demande de l'actif risqué est soumiseà des chocs iid exogènes. Nous montrons que l'hétérogénéité des horizons d'investissement peutêtre une explication possible de différents faits stylisés, observés pour les rendements des actions et, en particulier, du retourà la moyenne et du clustering de la volatilité.

Heterogeneous investment horizons, risk regimes, and realized jumps

“…Second, we contribute to the literature on heterogeneous expectations and agents. Our empirical motivation is based on a trading mechanism in which two types of traders exchange financial securities (e.g., Chauveau & Subbotin, 2013): a fundamentalist (with a long‐term investment horizon) and a day trader (with a short‐term investment horizon). Both types of investors have exposure to jump risk, but the degree of exposure and its transition (from one horizon to another) is unobservable in practice: Does the jump risk that fundamentalists face impact the risk associated with high‐frequency trading?…”