Portfolio optimization in the case of an asset with a given liquidation time distribution

Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses in this case we need to develop new methods. One of the steps moving the theory towards practical needs is to take into account the time lag of the liquidation of an illiquid asset. This task became especially significant for the practitioners in the time of the global financial crises. Working in the Merton's optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. While a standard Black-Scholes market describes the liquid part of the investment the illiquid asset is sold at a random moment with prescribed liquidation time distribution. In the moment of liquidation it generates additional liquid wealth dependent on illiquid assets paper value. The investor has the logarithmic utility function as a limit case of a HARA-type utility. Different distributions of the liquidation time of the illiquid asset are under consideration - a classical exponential distribution and Weibull distribution that is more practically relevant. Under certain conditions we show the existence of the viscosity solution in both cases. Applying numerical methods we compare classical Merton's strategies and the optimal consumption-allocation strategies for portfolios with different liquidation-time distributions of an illiquid asset.Comment: 30 pages, 1 figur

Illiquid Assets and Optimal Portfolio Choice

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.

Pricing Illiquid Assets

The present paper investigates the portfolio allocation decisions of an investor with infinite horizon when available financial assets differ in their degrees of liquidity. A model with risk neutral agents allows us to endogenously determine the liquidity premium. With risk averse agents, we develop a nontrivial portfolio allocation problem, which enables us to calculate the demand for an illiquid asset for any given yield premium. We calibrate and numerically simulate both models. Reasonable parameter values imply a liquidity premium of 1.7% for the risk neutral case. In the portfolio allocation problem we find that a reasonable amount of illiquidity can cause a substantial drop of demand for the asset. We are also able to calculate the price discount at which an agent would be indifferent between immediate sale and waiting for a buyer with a fundamentally justified price.

Asset Allocation and Location over the Life Cycle with Survival-Contingent Payouts

This paper shows how lifelong survival-contingent payouts can enhance investor wellbeing in the context of a portfolio choice model which integrates uninsurable labor income and asymmetric mortality expectations. Our model generates optimal asset location patterns indicating how much to hold in liquid versus illiquid survival-contingent payouts over the lifetime, and also asset allocation paths, showing how to invest in stocks versus bonds. We conrm that the investor will gradually move money out of her liquid saving into survivalcontingent assets to retirement and beyond, thereby enhancing her welfare by as much as 50 percent. The results are also robust to the introduction of uninsurable consumption shocks in housing expenses, income flows during the worklife and retirement, sudden changes in health status, and medical expenses.

Open-end real estate funds : danger or diamond?

Both banks and open end real estate funds effectuate liquidity transformation in large amounts and high scales. Because of this similarity the latter should be analyzed using the same methodologies as usually applied for banks. We show that the work in the tradition of Diamond and Dybvig (1983), especially Allen and Gale (1998) and Diamond and Rajan (2001), provides an applicable theoretical framework. We used this as the basis for our model for open end real estate funds. We then examined the usefulness of the modeling structure in analyzing open end real estate funds. First, we could show that withdrawing of capital resulting in a run is not always inefficient. Instead, withdrawing can as well be referred to the situation where the low return of an open end fund unit in comparison to other opportunities makes, (partial) withdrawal viewed from the risk-sharing perspective optimal. Even with costly liquidation, this result will hold, though we will have deadweight losses in such a situation. Second, introducing a secondary market in our model does, not in general, resolve the problem of deadweight losses associated with foreclosure. If assets are sold during a run, we do not only have a transfer of value but it can also create an economic cost. Because funds are forced to liquidate the illiquid asset in order to fulfill their obligations, the price of the real estate asset is forced down making the crisis worse. Rather than providing insurance, such that investors receive a transfer in negative outcomes, the secondary market does the opposite. It provides a negative insurance instead. Third, our model proves that the open end structure provides a monitoring function which serves as an efficient instrument to discipline the funds management. Therefore, we argue that an open end structure can represent a more adequate solution to securitize real estate or other illiquid assets. Instead of transforming open end in closed end structures, fund runs should be accepted as a normal phenomenon to clear the market from funds with mismanagement

Central Bank Haircut Policy

We present a model of central bank collateralized lending to study the optimal choice of the haircut policy. We show that a lending facility provides a bundle of two types of insurance: insurance against liquidity risk as well as insurance against downside risk of the collateral. Setting a haircut therefore involves balancing the trade-off between relaxing the liquidity constraints of agents on one hand, and increasing potential inflation risk and distorting the portfolio choices of agents on the other. We argue that the optimal haircut is higher when the central bank is unable to lend exclusively to agents who actually need liquidity. Finally, for an unexpected drop in the haircut, the central bank can be more aggressive than when setting a permanent level of the haircut.Payment, clearing, and settlement systems; Central bank research; Monetary policy implementation; Financial system regulation and policies; Financial services

A Fully-Rational Liquidity-Based Theory of IPO Underpricing and Underperformance

I present a fully-rational symmetric-information model of an IPO, as well as a dynamic imperfectly competitive model of the aftermarket trading that follows. The model helps explain why IPO share allocations favor large institutional investors. It also helps to explain IPO underpricing, and underperformance, and the large fees charged by underwriters. The critical assumption in the model is that underwriters need to sell a fixed number of shares at the IPO or soon thereafter in the aftermarket, but they want to avoid selling in the aftermarket because there are some aftermarket investors who have market power and can affect the prices received by the underwriter. To maximize revenue and avoid unnecessary aftermarket sales, the underwriter distorts share allocations toward those those investors who have market power, and he sets the offer price at the IPO below the aftermarket price that will prevail shortly after the IPO. In the aftermarket model, I show that there are share allocations that can generate arbitrarily high levels of return underperformance for very long periods of time. In some simulations, the distorted share allocations at the IPO generate return underperformance that persists for more than one year. The underwriter can dilute investor's market power by participating for longer periods of time in the aftermarket. By doing so, he sometimes substantially increase the revenue that is raised by the IPO issuerIPO, Asset Pricing, Market Microstructure, Liquidity