Liquidity: Considerations of a Portfolio Manager

This paper examines liquidity and how it affects the behavior of portfolio managers, who account for a significant portion of trading in many assets. We define an asset to be perfectly liquid if a portfolio manager can trade the quantity she desires when she desires at a price not worse than the uninformed expected value. A portfolio manager is limited by both what she needs to attain and the ease with which she can attain it, making her sensitive to three dimensions of liquidity: price, timing, and quantity. Deviations from perfect liquidity in any of these dimensions impose shadow costs on the portfolio manager. By focusing on the trade-off between sacrificing on price and quantity instead of the canonical price-time trade-off, the model yields several novel empirical implications. Understanding a portfolio manager's liquidity considerations provides important insights into the liquidity of many assets and asset classes.     

Equilibrium prices in the presence of delegated portfolio management

This paper analyzes the asset pricing implications of commonly used portfolio management contracts linking the compensation of fund managers to the excess return of the managed portfolio over a benchmark portfolio. The contract parameters, the extent of delegation, and equilibrium prices are all determined endogenously within the model we consider. Symmetric (fulcrum) performance fees distort the allocation of managed portfolios in a way that induces a significant and unambiguous positive effect on the prices of the assets included in the benchmark and a negative effect on the Sharpe ratios. Asymmetric performance fees have more complex effects on equilibrium prices and Sharpe ratios, with the signs of these effects fluctuating stochastically over time in response to variations in the funds' excess performance.     

Dynamic performance measurement with intangible assets

The increasing importance of intangible assets in modern economies is driving companies to include measures of intangible assets in managerial performance evaluations. For the multiperiod principal-agent model analyzed in this paper, a manager must be motivated to invest in intangible assets like customer satisfaction or product quality. The intangible asset is not verifiable for contracting purposes, but the parties can rely on a noisy indicator of the current asset value. I derive a class of value added performance measures, which effectively aggregate the current cash flow and consecutive realizations of the noisy indicator of the intangible asset. This class of performance measures is shown to be optimal for different scenarios regarding contract commitment and observability of the actual investment decisions. Long-term contracts are examined as a baseline. However, in practice firms usually adopt shorter medium-term contracts that are periodically renegotiated. I show that this more realistic contracting scenario yields the same investment patterns and efficiency levels as those obtained under long-term commitment.     

High‐Water Marks: High Risk Appetites? Convex Compensation,Long Horizons,and Portfolio Choice

We study the portfolio choice of hedge fund managers who are compensated by high-water mark contracts. We find that even risk-neutral managers do not place unbounded weights on risky assets, despite option-like contracts. Instead, they place a constant fraction of funds in a mean-variance efficient portfolio and the rest in the riskless asset, acting as would constant relative risk aversion (CRRA) investors. This result is a direct consequence of the in(de)finite horizon of the contract. We show that the risk-seeking incentives of option-like contracts rely on combining finite horizons and convex compensation schemes rather than on convexity alone.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.     

Investment Decision Making with Derivative Securities

This paper examines strategies employing stock options, index options, index futures options, and index futures contracts in an effort to establish under what conditions a portfolio manager should diversify into these derivative assets. The results show that futures option call writing and put buying were dominated by third-order stochastic dominance when compared to similar index options. Thus, when covered call writing or protective put buying are being considered, index options appear to be the better choice.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced byan expected-utility maximizing investor who, over a given timehorizon, is constrained to hold an asset which cannot be replicatedby dynamic trading and which therefore does not have a uniqueno-arbitrage price. We first derive the private valuation whichthe investor assigns to the nontraded asset in order to determinehis optimal investment in the traded assets. We thereby showthat, as part of this portfolio, the investor hedges the privatevaluation process of the nontraded asset, rather than its marketprice process. We also study the price at which the investorwould be willing to sell the nontraded asset if he were subsequentlyprohibited from trading in it, as well as the amount the investorwould be willing to pay to remove the trading restriction. Allthree values are shown to depend in an intuitive manner on theinvestor’s risk aversion, the residual risk of the nontradedasset unhedged by the traded assets, the difference betweenthe constrained holding and optimal unconstrained holding ofthe asset and the length of the time horizon over which theasset cannot be traded. JEL Classification: G11     

Semiparametric estimation of multi-asset portfolio tail risk

When correlations between assets turn positive, multi-asset portfolios can become riskier than single assets. This article presents the estimation of tail risk at very high quantiles using a semiparametric estimator which is particularly suitable for portfolios with a large number of assets. The estimator captures simultaneously the information contained in each individual asset return that composes the portfolio, and the interrelation between assets. Noticeably, the accuracy of the estimates does not deteriorate when the number of assets in the portfolio increases. The implementation is as easy for a large number of assets as it is for a small number. We estimate the probability distribution of large losses for the American stock market considering portfolios with ten, fifty and one hundred assets of stocks with different market capitalization. In either case, the approximation for the portfolio tail risk is very accurate. We compare our results with well known benchmark models.     

Using futures contracts for corporate hedging: The problem of expiry and a possible solution

Companies using futures contracts for hedging purposes need to roll over their contracts if the maturity of their exposure exceeds that of the futures contracts. This entails basis risk that can reduce significantly the effectiveness of the hedge. In this paper an alternative form of futures contract is proposed. the contract never expires and can be used for long-term hedging without the need for rolling-over into a new contract. the contract is shown to be equivalent to a portfolio of conventional futures contracts of differing maturities. Its price is determined by arbitrage against the underlying asset.     

Optimal commodity asset allocation with a coherent market risk modeling

This paper fills a fundamental gap in commodity price risk management and optimal portfolio selection literatures by contributing a thorough reflection on trading risk modeling with a dynamic asset allocation process and under the supposition of illiquid and adverse market settings. This paper analyzes, from a portfolio managers' perspective, the performance of liquidity adjusted risk modeling in obtaining efficient and coherent investable commodity portfolios under normal and adverse market conditions. As such, the author argues that liquidity risk associated with the uncertainty of liquidating multiple commodity assets over given holding periods is a key factor in formalizing and measuring overall trading risk and is thus an important component to model, particularly in the wake of the repercussions of the recent 2008 financial crisis. To this end, this article proposes a practical technique for the quantification of liquidity trading risk for large portfolios that consist of multiple commodity assets and whereby the holding periods are adjusted according to the specific needs of each trading portfolio. Specifically, the paper proposes a robust technique to commodity optimal portfolio selection, in a liquidity-adjusted value-at-risk (L-VaR) framework, and particularly from the perspective of large portfolios that have both long and short positions or portfolios that consist of merely pure long trading positions. Moreover, in this paper, the author develops a portfolio selection model and an optimization-algorithm which allocates commodity assets by minimizing the L-VaR subject to applying credible operational and financial constraints based on fundamental asset management considerations. The empirical optimization results indicate that this alternate L-VaR technique can be regarded as a robust portfolio management tool and can have many uses and applications in real-world asset management practices and predominantly for fund managers with large commodity portfolios.     

Agency and brokerage of real assets in competitive equilibrium

Brokerage contracts for many categories of real assets are characterizedby a common, constant commission rate payable upon sale, exclusiveagency, and contractual asking prices. For a large market insteady state, these conventional contracts produce in equilibriumno agency problem between a broker and his clients. Each brokerspends the same time or effort selling each client's asset asthe broker would spend on his own assets. As in standard agencyproblems, extra effort by a broker generates first-order stochasticallydominant distributions of bids by potential buyers. Unlike standardagency problems, each broker can allocate his time or effortbetween selling the assets of his multiple clients and searchingfor new clients in competition with other brokers. Because brokers'time spent searching for new sellers is dissipative, entry bybrokers is excessive in equilibrium.     

An International Portfolio Optimization Model Hedged with Forward Currency Contracts

We will propose a new method for constructing an optimal portfolio in which the fund is allocated to assets and currencies of several countries. Traditionally, two or three stage method is adopted in this field. However, it neglects the risk associated with variations of the rate of return of individual assets and the exchange rate of currencies. Instead, the new method enables one to simultaneously determine the optimal amount of fund to be allocated to each asset and the amount of the forward contracts on currencies. The resulting optimization problem is apparently a nonconvex minimization problem due to the existence of product terms in the objective function. We will show, however, that a globally optimal solution can be calculated by a standard algorithm in an efficient way. Also we will demonstrate that the new method leads to a substantially better result using historical data of U.S., Japan and Germany.     

Time to wealth goals in capital accumulation

This paper considers the problem of investment of capital in risky assets in a dynamic capital market in continuous time. The model controls risk, and in particular the risk associated with errors in the estimation of asset returns. The framework for investment risk is a geometric Brownian motion model for asset prices, with random rates of return. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently over time. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormal distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function, under the multivariate lognormal distribution assumption. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth. The wealth goals approach with random rebalancing times is compared to the expected utility approach with fixed rebalancing times in an asset allocation problem involving stocks, bonds, and cash.     

Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model

We investigate the implications of time-varying expected returnand volatility on asset allocation in a high dimensional setting.We propose a dynamic factor multivariate stochastic volatility(DFMSV) model that allows the first two moments of returns tovary over time for a large number of assets. We then evaluatethe economic significance of the DFMSV model by examining theperformance of various dynamic portfolio strategies chosen bymean-variance investors in a universe of 36 stocks. We findthat the DFMSV dynamic strategies significantly outperform variousbenchmark strategies out of sample. This outperformance is robustto different performance measures, investor’s objectivefunctions, time periods, and assets.     

International capital market equilibrium with investment barriers

This paper outlines models of capital market equilibrium when there are explicit barriers to international investment in the form of a tax on holdings of assets in one country by residents of another country. There is a corresponding subsidy on short positions in foreign assets. Asset prices deviate from the predictions of the world capital asset pricing model. Investors do not hold a mixture of national market portfolios, but the mix of risky assets is the same for every investor in a country. Optimal portfolios tend to be heavy in domestic assets, and light in foreign assets. Tax free investors, however, tend to hold assets anywhere in the world that are taxed heavily. Estimates of the magnitude of the average tax (or the magnitude of effective barriers to international investment) can be made by comparing the average return on the minimum variance zero β portfolio, z, with the average across countries and time of the short-term interest rate. When barriers are ineffective, the expected return on portfolio z will be the average short-term interest rate, and the world capital asset pricing model will hold.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

Portfolio Selection with Quadratic Utility Revisited

Considering a simple portfolio selection problem by agents with quadratic utility, an apparently counterintuitive outcome results. When such a choice is over two assets that can be ordered in terms of riskiness, an agent that is more risk averse may optimally invest a larger portion of wealth in the riskier asset. It is shown that such an outcome is not counterintuitive, since for the portfolios from which agents optimally choose, a larger proportion of investment in the riskier asset leads to a less risky portfolio.     

Portfolio Optimization under Solvency Constraints: A Dynamical Approach

We develop portfolio optimization problems for a nonlife insurance company seeking to find the minimum capital required that simultaneously satisfies solvency and portfolio performance constraints. Motivated by standard insurance regulations, we consider solvency capital requirements based on three criteria: ruin probability, conditional Value-at-Risk, and expected policyholder deficit ratio. We propose a novel semiparametric formulation for each problem and explore the advantages of implementing this methodology over other potential approaches. When liabilities follow a Lognormal distribution, we provide sufficient conditions for convexity for each problem. Using different expected return on capital target levels, we construct efficient frontiers when portfolio assets are modeled with a special class of multivariate GARCH models. We find that the correlation between asset returns plays an important role in the behavior of the optimal capital required and the portfolio structure. The stability and out-of-sample performance of our optimal solutions are empirically tested with respect to both the solvency requirement and portfolio performance, through a double rolling window estimation exercise.     

Hedge funds and optimal asset allocation: Bayesian expectations and spanning tests

This paper analyzes the contribution of hedge funds to optimal asset allocations between 1993 and 2010. The preferences of specific institutional investors are captured by implementing a Bayesian asset allocation framework that incorporates heterogeneous expectations regarding hedge fund alpha. Mean-variance spanning tests are used to infer the ability of hedge funds to significantly enhance the mean-variance efficient frontier. Further, a novel democratic variance decomposition procedure sheds light on the dynamics in the co-movement of hedge fund returns with a set of common benchmark assets. The empirical findings indicate that portfolio benefits of hedge funds are time-varying and strongly depend on investor optimism regarding hedge funds’ ability to generate alpha. In general, allocations to hedge funds improve the global minimum variance portfolio even after controlling for short-selling restrictions and minimum diversification constraints. However, due to dynamics underlying the composition of the aggregate hedge fund universe, the factor structure of hedge fund returns has become more similar to the benchmark assets over time.     

Optimal asset allocation for a large number of investment opportunities

This paper introduces a stock‐picking algorithm that can be used to perform an optimal asset allocation for a large number of investment opportunities. The allocation scheme is based upon the idea of causal risk. Instead of referring to the volatility of the assets time series, the stock‐picking algorithm determines the risk exposure of the portfolio by concerning the non‐forecastability of the assets. The underlying expected return forecasts are based on time‐delay recurrent error correction neural networks, which utilize the last model error as an auxiliary input to evaluate their own misspecification. We demonstrate the profitability of our stock‐picking approach by constructing portfolios from 68 different assets of the German stock market. It turns out that our approach is superior to a preset benchmark portfolio. Copyright © 2005 John Wiley & Sons, Ltd.