THE INCENTIVES OF HEDGE FUND FEES AND HIGH‐WATER MARKS

Hedge fund managers receive a large fraction of their funds' profits, paid when funds exceed their high‐water marks. We study the incentives of such performance fees. A manager with long‐horizon, constant investment opportunities and relative risk aversion, chooses a constant Merton portfolio. However, the effective risk aversion shrinks toward one in proportion to performance fees. Risk shifting implications are ambiguous and depend on the manager's own risk aversion. Managers with equal investment opportunities but different performance fees and risk aversions may coexist in a competitive equilibrium. The resulting leverage increases with performance fees—a prediction that we confirm empirically.     

DYNAMIC TRADING VOLUME

We derive the process followed by trading volume, in a market with finite depth and constant investment opportunities, where a large investor, with a long horizon and constant relative risk aversion, trades a safe and a risky asset. Trading volume approximately follows a Gaussian, mean‐reverting diffusion, and increases with depth, volatility, and risk aversion. Unlike the frictionless theory, finite depth excludes leverage and short sales because such positions may not be solvent even with continuous trading.     

Who should sell stocks?

Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their portfolio weight is too low and otherwise hold them, letting dividends rebalance to cash over time rather than selling. With capital gains taxes, this policy outperforms both static buy‐and‐hold and dynamic rebalancing strategies that account for transaction costs. Selling stocks becomes optimal if either their target weight is low or intermediate consumption is substantial.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

CLOSED-FORM SOLUTIONS FOR OPTIMAL PORTFOLIO SELECTION WITH STOCHASTIC INTEREST RATE AND INVESTMENT CONSTRAINTS

We examine the portfolio choice problem of an investor with constant relative risk aversion in a financial market with partially hedgeable interest rate risk. The individual shadow price of the portfolio constraint is characterized as the solution of a new backward equation involving Malliavin derivatives. A generalization of this equation is studied and solved in explicit form. This result, applied to our financial model, yields closed-form solutions for the shadow price and the optimal portfolio. The effects of parameters such as risk aversion, interest rate volatility, investment horizon, and tightness of the constraint are examined. Applications of our method to a monetary economy with inflation risk and to an international setting with currency risk are also provided.     

STATIC FUND SEPARATION OF LONG‐TERM INVESTMENTS

This paper proves a class of static fund separation theorems, valid for investors with a long horizon and constant relative risk aversion, and with stochastic investment opportunities. An optimal portfolio decomposes as a constant mix of a few preference‐free funds, which are common to all investors. The weight in each fund is a constant that may depend on an investor's risk aversion, but not on the state variable, which changes over time. Vice versa, the composition of each fund may depend on the state, but not on the risk aversion, since a fund appears in the portfolios of different investors. We prove these results for two classes of models with a single state variable, and several assets with constant correlations with the state. In the linear class, the state is an Ornstein–Uhlenbeck process, risk premia are affine in the state, while volatilities and the interest rate are constant. In the square root class, the state follows a square root diffusion, expected returns and the interest rate are affine in the state, while volatilities are linear in the square root of the state.     

The Intraday Pattern of Information Asymmetry,Spread, and Depth: Evidence from the NYSE

Studies suggest that investment flows, liquidity imbalances, and institutional trading may create intraday trading patterns and opportunities for investors to time their trades to reduce transaction costs. Motivated by these studies, we divide each trading day into 13 half‐hour trading intervals and measure information asymmetry from price changes, trade sizes, and trade directions. We find that information asymmetry starts high in the morning, drops continuously until it reaches a midday low during Interval 7, rises to a midday high during Interval 10, and drops continuously after. In contrast, neither the spread nor the depth exhibit similar midday extreme values. Essentially, we identify a 90‐min window in the afternoon when net valuable information arrives to the market in high frequency while liquidity is stable, and that may be an opportunity for some investors to time their trades. In addition, we show that market makers employ dynamic strategies that change the spread, the depth, or both to manage information asymmetry. This is particularly evident during the last three trading intervals, where the significant drop in information asymmetry is countered primarily by a significant increase in the depth while the spread is almost constant.     

风险态度、金融教育与家庭金融资产选择

文章基于中国城市居民消费金融调查数据,研究了风险态度、金融教育对家庭金融资产选择和家庭金融市场参与的影响。结果发现,风险态度显著影响家庭金融资产组合分散化程度,风险厌恶程度越高,金融资产组合分散化程度越低。风险态度对家庭正规金融市场参与有显著影响,风险厌恶程度的提高会显著降低家庭在股票、基金、债券、储蓄性保险市场的参与概率,风险厌恶程度增加一单位,家庭参与股票市场的可能性会降低10.5%。风险厌恶程度对股票、基金、债券、储蓄性保险资产在家庭金融资产中的比例具有显著的负向影响。家庭的金融教育投入对风险资产持有比重条件分布的影响上,呈先上升后下降趋势,中间分位的要大于两端。文章相应的政策含义是,政府及金融管理部门需要普及金融教育知识,提高居民的金融风险认知水平,从而优化家庭金融资产选择,改善居民金融福利。     

Risk aversion,disappointment aversion,and futures hedging

This article examines the effect of disappointment aversion on futures hedging. We incorporated a constant‐absolute‐risk‐aversion (CARA) utility function into the disappointment‐aversion framework of Gul (1991). It is shown that a more disappointment‐averse hedger will choose an optimal futures position closer to the minimum‐variance hedge than will a less‐disappointment‐averse hedger. The effect of disappointment aversion is stronger when the hedger is less risk averse. A small disappointment aversion will cause a near‐risk neutral hedger to take a drastically different position. In addition, a more‐risk‐averse or disappointment‐averse hedger will have a lower reference point. Numerical results indicate that the reference point of a disappointment‐averse hedger tends to be lower than that of a conventional loss‐averse hedger. Consequently, the disappointment‐averse hedger will act more conservatively, not exploiting profitable opportunities as much as the conventional loss averse hedger will. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:123–141, 2002     

Nonlinear price impact and portfolio choice

In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square‐root impact law and, as extreme cases, linear impact and proportional transaction costs.     

INVESTING WITH LIQUID AND ILLIQUID ASSETS

We find optimal trading policies for long‐term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset's weight when the illiquid asset's weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.     

Regulatory procedures,investment opportunities and stock valuation

Electric utilities differ in their accounting procedures. By regulatory commission directive some use normalization and some use flow through to arrive at their earnings figures. Because regulation is on an allowed return on investment standard these reported earnings are relevant for stock valuation. Any variation in price/earnings ratios between flow through and normalizing companies therefore must be explained by differences in risk to equity investors, differences in investment opportunities, or market inefficiency involving erroneous restatement of earnings. Empirical work demonstrates that there is a difference in price/earnings ratios. Firms that normalize enjoy a premium. The evidence also indicates that the premium is not explained by risk difference. Because the perverse form of market inefficiency required as an explanation seems unlikely, the most reasonable conclusion is that the premium relates to investment opportunities associated with regulatory climate. If so it promises no excess return to stock buyers because it is already impounded in stock price.     

Strict local martingales and optimal investment in a Black–Scholes model with a bubble

There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen–Ledoit–Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between these previously disconnected approaches. While the original JLS model is never a strict local martingale, there are relaxations that can be strict local martingales and that preserve the key assumption of a log‐periodic power law for the hazard rate of the time of the crash. We then study the optimal investment problem for an investor with constant relative risk aversion in this model. We show that for positive instantaneous expected returns, investors with relative risk aversion above one always ride the bubble.     

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION

The objective of this paper is to study the mean–variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in Basak and Chabakauri where the authors assumed a constant risk aversion parameter. This assumption leads to an equilibrium control where the dollar amount invested in the risky asset is independent of current wealth, and we argue that this result is unrealistic from an economic point of view. In order to have a more realistic model we instead study the case when the risk aversion depends dynamically on current wealth. This is a substantially more complicated problem than the one with constant risk aversion but, using the general theory of time‐inconsistent control developed in Björk and Murgoci, we provide a fairly detailed analysis on the general case. In particular, when the risk aversion is inversely proportional to wealth, we provide an analytical solution where the equilibrium dollar amount invested in the risky asset is proportional to current wealth. The equilibrium for this model thus appears more reasonable than the one for the model with constant risk aversion.     

Optimal investment and pricing in the presence of defaults

We consider the optimal investment problem with random endowment in the presence of defaults. For an investor with constant absolute risk aversion, we identify the certainty equivalent, and compute prices for defaultable bonds and dynamic protection against default. This latter price is interpreted as the premium for a contingent credit default swap, and connects our work with earlier articles, where the investor is protected upon default. We consider a multiple risky asset model with a single default time, at which point each of the assets may jump in price. Investment opportunities are driven by a diffusion X taking values in an arbitrary region . We allow for stochastic volatility, correlation, and recovery; unbounded random endowments; and postdefault trading. We identify the certainty equivalent with a semilinear parabolic partial differential equation with quadratic growth in both function and gradient. Under minimal integrability assumptions, we show that the certainty equivalent is a classical solution. Numerical examples highlight the relationship between the factor process, market dynamics, utility‐based prices, and default insurance premium. In particular, we show that the holder of a defaultable bond has a strong incentive to short the underlying stock, even for very low default intensities.     

A Note on Loss Aversion and Futures Hedging

This note examines the effect of loss aversion on the futures trading behavior of a short hedger. Using a modified constant‐absolute‐risk‐aversion utility function, I show that loss aversion has no effect in an unbiased futures market. It has different, predictable impacts when the futures market is in backwardation or contango. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 681–692, 2001     

DYNAMIC PORTFOLIO OPTIMIZATION WITH A DEFAULTABLE SECURITY AND REGIME‐SWITCHING

We consider a portfolio optimization problem in a defaultable market with finitely‐many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time Markov process. By separating the utility maximization problem into a predefault and postdefault component, we deduce two coupled Hamilton–Jacobi–Bellman equations for the post‐ and predefault optimal value functions, and show a novel verification theorem for their solutions. We obtain explicit constructions of value functions and investment strategies for investors with logarithmic and Constant Relative Risk Aversion utilities, and provide a precise characterization of the directionality of the bond investment strategies in terms of corporate returns, forward rates, and expected recovery at default. We illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economic and numerical analysis.     

Governance mechanisms, investment opportunity set and SMEs cash holdings

This study analyses the effect of firm characteristics and governance mechanisms on cash holdings for a sample of UK SMEs. The results show that UK SMEs with greater cash flow volatility and institutional investors hold more cash; whereas levered and dividend paying SMEs with non-executive ownership hold less cash. We also find that ownership structure is significant only in explaining the cash holdings for firms with high growth investment opportunities, and leverage is only significant in explaining the cash held by firms with low growth investment opportunities. Our findings suggest that internal governance mechanisms are more effective for SMEs with high growth investment opportunities, while external governance mechanisms, such as capital market monitoring, are more effective for firms with low growth investment opportunities.     

High ownership concentration and exporting of emerging market firms: evidence from Peru

Despite the extraordinarily high ownership concentration widely observed in emerging market firms as a result of institutional voids, there is little research on how this high ownership concentration affects the exporting behavior of emerging market firms. From principal–agent and institutional perspectives, we hypothesize that high ownership concentration has a negative relationship with export intensity, because, in emerging markets, highly concentrated ownership bridges the interests of owners (principals) and managers (agents) so that principals must be prudent in exploring risky international markets. Moreover, we hypothesize that export country diversification strengthens the relationship between ownership concentration and export intensity, because broad geographic dispersion increases risk exposure and principal-agent problems. Empirical analysis based on a panel dataset for publicly listed firms in Peru from 2005 to 2014 supports the hypotheses. The study highlights the risk aversion attitude activated by ownership concentration, an attitude that protects emerging market firms from overconfidently exploring international business opportunities. The study extends the conventional literature on the interface between ownership concentration and international business in an emerging market context. We also discuss the generalizability of the findings to other emerging markets, e.g. China.     

RISK-AVERSION BEHAVIOR IN CONSUMPTION/INVESTMENT PROBLEMS1

In this paper, we study the risk-aversion behavior of an agent in the dynamic framework of consumption/investment decision making that allows the possibility of bankruptcy. Agent's consumption utility is assumed to be represented by a strictly increasing, strictly concave, continuously differentiable function in the general case and by a HARA-type function in the special case treated in the paper. Coefficients of absolute and relative risk aversion are defined to be the well-known curvature measures associated with the derived utility of wealth obtained as the value function of the agent's optimization problem. Through an analysis of these coefficients, we show how the change in agent's risk aversion as his wealth changes depends on his consumption utility and the other problem parameters, including the payment at bankruptcy. Moreover, in the HARA case, we can conclude that the agent's relative risk aversion is nondecreasing with wealth, while his absolute risk aversion is decreasing with wealth only if he is sufficiently wealthy. At lower wealth levels, however, the agent's absolute risk aversion may increase with wealth in some cases.