Asset allocation and liquidity breakdowns: what if your broker does not answer the phone?

Abstract

This paper analyzes the portfolio decision of an investor facing the threat of illiquidity. In a continuous-time setting, the efficiency loss due to illiquidity is addressed and quantified. We show that the efficiency loss for a logarithmic investor with 30 years until the investment horizon is a significant 22.7% of current wealth if the illiquidity part of the model is calibrated to the Japanese data of the aftermath of WW II. Furthermore, it is demonstrated that the threat of illiquidity can change the demand for risky securities tremendously and that a logarithmic investor will not behave myopically anymore.

Investment/Consumption Problem in Illiquid Markets with Regime-Switching

“…(λ 1 , λ 2 ) P 1 (1) P 2 (1) (1,1) 0.257 0.224 (5,5) 0.112 0.103 (10,10) Define W as the space of continuous functions on R + , I the space of cadlag I d -valued functions, N the space of nondecreasing cadlag N-valued functions. On W × I × N , define the filtration (B 0 t ) t≥0 , where B 0 t is the smallest σ-algebra making the coordinate mappings for s ≤ t measurable, and define B 0 t+ = s>t B 0 s .…”

“…First, we extend the papers [19] and [15] by considering stochastic intensity trading times and regime switching in the asset prices. For a two-state Markov chain modulating the market liquidity, and in the limiting case where the intensity in one regime goes to infinity, while the other one goes to zero, we recover the setup of [5] and [14] where an investor can trade continuously in the perfectly liquid regime but faces a threat of trading interruptions during a period of market freeze. On the other hand, regime switching models in optimal investment problems was already used in [23], [20] or [21] for continuous-time trading.…”

European Option Pricing With Liquidity Shocks

“…Remark 2.1. More generally (see [5,17]) the market need not be static during the illiquid periods. Thus, one may postulate modified dynamics for the stock during the liquidity shock and also include instantaneous price drops when the liquidity regime changes.…”

“…In recent years a number of approaches for dealing with market illiquidity within optimal investment frameworks have been developed. Schwartz and Tebaldi [21] considered the optimal portfolio problem with permanent trading interruptions; Diesinger et al [5] addressed terminal wealth maximization for CRRA utilities. Ludkovski and Min [17] and Gassiat et al [9] analyzed the impact of illiquidity on optimal consumption strategies.…”

Optimal Consumption and Investment for a Large Investor: An Intensity‐based Control Framework

“…Related Literature There are large strands of literature concerning both regime‐shift models on the one hand and large investor models on the other. Models with possible regime shifts related to optimal investment problems include the articles of BR, Sass and Haussmann (2004), Diesinger, Kraft, and Seifried (2010), or Kashiwabara and Nakamura (2011), among others; see also the monograph of Elliott, Aggoun, and Moore (1994).…”