ROBUST PORTFOLIOS AND WEAK INCENTIVES IN LONG‐RUN INVESTMENTS

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage‐free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex.     

THE NUMÉRAIRE PROPERTY AND LONG‐TERM GROWTH OPTIMALITY FOR DRAWDOWN‐CONSTRAINED INVESTMENTS

We consider the portfolio choice problem for a long‐run investor in a general continuous semimartingale model. We combine the decision criterion of pathwise growth optimality with a flexible specification of attitude toward risk, encoded by a linear drawdown constraint imposed on admissible wealth processes. We define the constrained numéraire property through the notion of expected relative return and prove that drawdown‐constrained numéraire portfolio exists and is unique, but may depend on the investment horizon. However, when sampled at the times of its maximum and asymptotically as the time‐horizon becomes distant, the drawdown‐constrained numéraire portfolio is given explicitly through a model‐independent transformation of the unconstrained numéraire portfolio. The asymptotically growth‐optimal strategy is obtained as limit of numéraire strategies on finite horizons.     

MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS

We consider a class of asset pricing models, where the risk‐neutral joint process of log‐price and its stochastic variance is an affine process in the sense of Duffie, Filipovic, and Schachermayer. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results on the long‐term behavior of the model, including an expression for the invariant distribution of the stochastic variance process. We study moment explosions of the price process, and provide explicit expressions for the time at which a moment of given order becomes infinite. We discuss applications of these results, in particular to the asymptotics of the implied volatility smile, and conclude with some calculations for the Heston model, a model of Bates and the Barndorff‐Nielsen–Shephard model.     

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.     

REAL CONVERGENCE AND PRICE LEVELS: LONG‐TERM TENDENCIES VERSUS SHORT‐TERM PERFORMANCE IN THE ENLARGED EUROPEAN UNION

A cross‐country regression relating the relative price level to the relative GDP level is statistically significant and stable over time. Price and GDP levels for EU member countries tend to gravitate to that line. The conclusion that there is a shorter‐term trade‐off between fast real convergence and low inflation is unwarranted. Higher inflation is not a necessary companion of fast convergence. Giving up national currency, or pegging it to the euro, may prevent real convergence or precipitate divergence. A weak initial price level may be insufficient. While retaining national currency is not risk‐free, it allows a corrective devaluation.     

基于VaR和两基金分离的投资组合模型

本文使用VaR来度量投资组合的市场风险,构造了一个在可接受期末财富约束条件下,使VaR达到最小的投资组合模型,同时,发现该模型发生了两基金分离现象,因此存在多风险资产情形下的投资组合模型可以退化成为单风险资产情形下的投资组合模型。最后,本文使用简化的单风险模型对我国上海股票市场进行了实证分析,探讨投资者如何在股票和银行借贷中进行最优资产分配。     

CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH

The existence of the growth optimal portfolio (GOP), also known as the Kelly portfolio, is vital for a financial market to be meaningful. The GOP, if it exists, is uniquely determined by the market parameters of the primary security accounts. However, markets may develop and new security accounts become tradable. What happens to the GOP if the original market is extended? In this paper we provide a complete characterization of market extensions which are consistent with the existence of a GOP. We show that a three fund separation theorem applies for the extended GOP. This includes, in particular, the introduction of a locally risk free security, the savings account. We give necessary and sufficient conditions for a consistent exogenous specification of the prevailing short rates.     

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.     

MUTUAL FUND PORTFOLIO CHOICE IN THE PRESENCE OF DYNAMIC FLOWS

We analyze the implications of dynamic flows on a mutual fund's portfolio decisions. In our model, myopic investors dynamically allocate capital between a riskless asset and an actively managed fund which charges fraction‐of‐fund fees. The presence of dynamic flows induces “flow hedging” portfolio distortions on the part of the fund, even though investors are myopic. Our model predicts a positive relationship between a fund's proportional fee rate and its volatility. This is a consequence of higher‐fee funds holding more extreme equity positions. Although both the fund portfolio and investors' trading strategies depend on the proportional fee rate, the equilibrium value functions do not. Finally, we show that our results hold even if investors are allowed to directly trade some of the risky securities.     

LONG HORIZONS,HIGH RISK AVERSION,AND ENDOGENOUS SPREADS

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as the limits of their isoelastic counterparts for high levels of risk aversion. The results are robust with respect to finite horizons, and extend to multiple uncorrelated risky assets. In this setting, we study a Stackelberg equilibrium, led by a risk‐neutral, monopolistic market maker who sets the spread as to maximize profits. The resulting endogenous spread depends on investment opportunities only, and is of the order of a few percentage points for realistic parameter values.     

Discrete-time risk sensitive portfolio optimization with proportional transaction costs

In this paper we consider a discrete-time risk sensitive portfolio optimization over a long time horizon with proportional transaction costs. We show that within the log-return i.i.d. framework the solution to a suitable Bellman equation exists under minimal assumptions and can be used to characterize the optimal strategies for both risk-averse and risk-seeking cases. Moreover, using numerical examples, we show how a Bellman equation analysis can be used to construct or refine optimal trading strategies in the presence of transaction costs.     

社会保障基金入市的经济效应与运行监管

市场化运营是西方成熟市场经济国家社保基金运营改革的方向。我国社保基金总量不足且运营不规范 ,保值增值压力很大 ,社保基金的入市将带来正负两方面的经济效应 ,其负面效应的存在 ,对社保基金的监管提出了更高的要求。从社保基金入市的经济效应入手 ,在借鉴成熟市场经济国家社保基金的监管经验的基础上 ,对我国社保基金的监管提出了相应的政策建议。     

PRICE‐ADMISSIBILITY CONDITIONS FOR ARBITRAGE‐FREE LINEAR PRICE FUNCTION MODELS FOR THE TERM STRUCTURE OF INTEREST RATES

To assure price admissibility—that all bond prices, yields, and forward rates remain positive—we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices.     

COMMENT ON “SKEWNESS‐AWARE ASSET ALLOCATION”

This paper discusses risk measures proposed by Low et al. One of their new risk measures is skewness‐aware deviation, which is closely related to constant absolute risk aversion utility functions. This measure captures downside risk more effectively than traditional variance does. The authors also propose a second measure, skewness‐aware variance, which is derived from skewness‐aware deviation. This measure simplifies asset allocation problems and empirical results indicate that it captures risk better than traditional variance. However, this measure is also found to be inconsistent due to factor selection. Additionally, in the aspect of skewness‐aware deviation, optimal portfolios based upon skewness‐aware variance are sometimes less efficient than optimal portfolios that base themselves on traditional variance.     

ON THE DYBVIG‐INGERSOLL‐ROSS THEOREM

The Dybvig‐Ingersoll‐Ross (DIR) theorem states that, in arbitrage‐free term structure models, long‐term yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that long‐term rates at earlier dates can dominate long‐term rates at later dates. The viability assumption imposed on the market model is weaker than those appearing previously in the literature.     

Cover's universal portfolio,stochastic portfolio theory,and the numéraire portfolio

Cover's celebrated theorem states that the long‐run yield of a properly chosen “universal” portfolio is almost as good as that of the best retrospectively chosen constant rebalanced portfolio. The “universality” refers to the fact that this result is model‐free, that is, not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory: the market portfolio is taken as the numéraire, and the rebalancing rule need not be constant anymore but may depend on the current state of the stock market. By fixing a stochastic model of the stock market this model‐free result is complemented by a comparison with the numéraire portfolio. Roughly speaking, under appropriate assumptions the asymptotic growth rate coincides for the three approaches mentioned in the title of this paper. We present results in both discrete and continuous time.     

Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation

The mean‐variance formulation by Markowitz in the 1950s paved a foundation for modern portfolio selection analysis in a single period. This paper considers an analytical optimal solution to the mean‐variance formulation in multiperiod portfolio selection. Specifically, analytical optimal portfolio policy and analytical expression of the mean‐variance efficient frontier are derived in this paper for the multiperiod mean‐variance formulation. An efficient algorithm is also proposed for finding an optimal portfolio policy to maximize a utility function of the expected value and the variance of the terminal wealth.     

On utility maximization under model uncertainty in discrete‐time markets

We study the problem of maximizing terminal utility for an agent facing model uncertainty, in a frictionless discrete‐time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either on the positive real line or on the whole real line, is bounded from above. We further find that the boundedness assumption can be dropped, provided that we impose suitable integrability conditions, related to some strengthened form of no‐arbitrage. These results are obtained in an alternative framework for model uncertainty, where all possible dynamics of the stock prices are represented by a collection of stochastic processes on the same filtered probability space, rather than by a family of probability measures.     

Reduced‐fat foods: the shopper’s viewpoint

The inclusion of reduced‐fat foods in the daily diet affords consumers the potential to reduce overall dietary fat. Nevertheless, despite an increased range of these food products throughout the market, there has remained a lack of widespread consumer acceptance. The aim of the study was therefore to understand why consumers choose or reject reduced‐fat foods. Ninety consumers were interviewed by means of a qualitative approach within food retail outlets in the United Kingdom. Thematic content analysis indicated that uptake or rejection of these products is influenced by health concerns, ‘goodness of fit’ with individual dietary health strategies, the preferences of different household members, perceived sensory properties and scepticism towards these products. The results imply a need to explore and innovate ‘natural’ fat substitutes and to improve the sensory quality of reduced‐fat products. Further research is required to determine how these foods are used within the household and incorporated within the overall diet. Policy must seek to restore consumer trust in reduced‐fat food products and the food supply generally.     

ARBITRAGE‐FREE MULTIFACTOR TERM STRUCTURE MODELS: A THEORY BASED ON STOCHASTIC CONTROL

We present an alternative approach to the pricing of bonds and bond derivatives in a multivariate factor model for the term structure of interest rates that is based on the solution of an optimal stochastic control problem. It can also be seen as an alternative to the classical approach of computing forward prices by forward measures and as such can be extended to other situations where traditionally a change of measure is involved based on a change of numeraire. We finally provide explicit formulas for the computation of bond options in a bivariate linear‐quadratic factor model.