The Opportunity Cost of a Mean-Variance Efficient Choice

The mean-variance criterion is one of the most frequently used methods for selecting investment portfolios. Yet, because it is an approximation of an investor's maximum expected utility choice, some theoreticians and practitioners have criticized the approach. This paper examines the investment loss that different investors experience by accepting a mean-variance efficient portfolio. Simulated security returns with extreme distributional characteristics are used to determine the extent of an investor's loss. The results indicate that even under very unreasonable investment distributional assumptions, an investor's loss by accepting a mean-variance efficient choice rarely exceeds a small fraction of one percent per invested dollar.     

A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q.JEL Classification: D52, G13     

Optimal mean-reversion strategy in the presence of bid-ask spread and delays in capital allocations

A portfolio optimization problem for an investor who trades T-bills and a mean-reverting stock in the presence of proportional and convex transaction costs is considered. The proportional transaction cost represents a bid-ask spread, while the convex transaction cost is used to model delays in capital allocations. I utilize the historical bid-ask spread in US stock market and assume that the stock reverts on yearly basis, while an investor follows monthly changes in the stock price. It is found that proportional transaction cost has a relatively weak effect on the expected return and the Sharpe ratio of the investor's portfolio. Meantime, the presence of delays in capital allocations has a dramatic impact on the expected return and the Sharpe ratio of the investor's portfolio. I also find the robust optimal strategy in the presence of model uncertainty and show that the latter increases the effective risk aversion of the investor and makes her view the stock as more risky.     

DIVERSIFICATION AND SKEWNESS IN OPTION PORTFOLIOS

Skewness in returns is relevant to option investors. Because options possess positively skewed distributions, the traditional maxim of diversification, which can destroy positive skewness, is not necessarily consistent with investment objectives. The results indicate that the majority of skewness in option portfolios is diversified with a relatively small portfolio size, suggesting a strategy of antidiversification for option investors. Even though the investment performance of options is inferior to stocks on a risk-return basis, the data indicate the suitability of option portfolios in an environment where an investor's utility is measured by the return, risk, and skewness of the return distribution.     

Money Doctors

We present a new model of investors delegating portfolio management to professionals based on trust. Trust in the manager reduces an investor's perception of the riskiness of a given investment, and allows managers to charge fees. Money managers compete for investor funds by setting fees, but because of trust, fees do not fall to costs. In equilibrium, fees are higher for assets with higher expected return, managers on average underperform the market net of fees, but investors nevertheless prefer to hire managers to investing on their own. When investors hold biased expectations, trust causes managers to pander to investor beliefs.     

Dynamic Volatility Trading Strategies in the Currency Option Market

The conditional volatility of foreign exchange rates can be predicted using GARCH models or implied volatility extracted from currency options. This paper investigates whether these predictions are economically meaningful in trading strategies that are designed only to trade volatility risk. First, this article provides new evidence on the issue of information content of implied volatility and GARCH volatility in forecasting future variance. In an artificial world without transaction costs both delta-neutral and straddle trading stratgies lead to significant positive profits, regardless of which volatility prediction method is used. Specifically, the agent using the Implied Stochastic Volatility Regression method (ISVR) earns larger profits than the agent using the GARCH method. Second, it suggests that the currency options market is informationally efficient. After accounting for transaction costs, which are assumed to equal one percent of option prices, observed profits are not significantly differentfrom zero in most trading strategies. Finally, these strategies offered returns have higher Sharpe ratio and lower correlation with several major asset classes. Consequently, hedge funds and institutional investors who are seeking alternative “marketneutral” investment methods can use volatility trading to improvethe risk-return profile of their portfolio through diversification. This revised version was published online in November 2006 with corrections to the Cover Date.     

Investment,consumption, and hedging under incomplete markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. We extend the standard real options approach to an incomplete markets environment and analyze the joint decisions of business investments, consumption/savings, and portfolio selection. For a lump-sum investment payoff and an agent with a sufficiently strong precautionary savings motive, an increase in volatility can accelerate investment, contrary to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. Finally, when the investment payoff is a series of flows, the agent's idiosyncratic risk exposure alters both the implied option value and the implied project value, causing a reversal of the results in the lump-sum payoff case.     

Sufficient conditions for expected utility to imply drawdown-based performance rankings

The least restrictive sufficient condition for expected utility to imply Sharpe ratio rankings is the location and scale (LS) property (see [Sinn, 1983] and [Meyer, 1987]). The normal, the extreme value, and many other distributions commonly used in finance satisfy this property. We argue that the LS property is also sufficient for expected utility to imply drawdown-based performance measure rankings, because for investment funds satisfying the LS condition, the Sharpe ratio and drawdown-based performance measures result in identical rankings. Hence, the same conditions that provide an expected utility foundation for the Sharpe ratio also provide a foundation for drawdown-based performance measures. We conclude that from a decision-theoretic perspective, drawdown-based performance measures are as good as the Sharpe ratio.     

Do ADRs enhance portfolio performance for a domestic portfolio? Evidence from the 1990s

American depository receipts (ADRs) represent an increasingly popular and convenient mechanism for international investing. We analyze ADRs traded throughout the 1990s and find that these securities offer a diversification and portfolio performance benefit when combined with a domestic portfolio (proxied by the S&P 500). While we find that emerging market ADRs are effective instruments for reducing portfolio risk, they do not improve portfolio performance as measured by the Sharpe ratio. Developed market ADRs do improve portfolio performance as measured by the Sharpe ratio. The asset allocation which maximizes the Sharpe ratio is 84 percent domestic stocks, 16 percent developed ADRs, and 0 percent emerging ADRs. Further, due to problems in defining an appropriate market index for ADRs, the Sharpe ratio is viewed to be the preferred performance measure. Other measures such as Jensen’s alpha and the Treynor measure are susceptible to being “gamed” to distort portfolio performance.     

Equilibrium Exchange Rate Hedging

We assume a world like the one that gives the capital asset pricing model, but with many goods and many countries. We assume that investors in a given country have homothetic utility functions with the same weights, and a currency that has a sure end-of-period value using a price index with those weights. Siegel's paradox (derived from Jensen's inequality) makes investors want a positive amount of exchange risk. When average risk tolerance is the same across countries, every investor will hold the same mix of market risk (through the world market portfolio of all assets) and exchange risk (in a diversified basket of foreign currencies). In fact, the ratio of exchange risk to market risk is equal to the average investor's risk tolerance. We can write the ratio of exchange risk to market risk (and the fraction of the market's exchange risk that investors hedge) as depending on an average of world market risk premia, an average of world market volatilities, and an average of exchange rate volatilities. The weights in these averages are the same as the weights of the different countries in the currency basket. Given these averages, the ratio (and the fraction hedged) will not depend directly on exchange rate means or covariances. In equilibrium, we can use the ratio of exchange risk to market risk to measure average risk tolerance: in this model, risk tolerance is observable.     

Buy-and-hold mean-variance portfolios with a random exit strategy

We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.     

A knowledge‐based framework for incorporating investor's preference into portfolio decision‐making

This paper describes a framework for the integration of a rule‐based system capable of identifying an investor's risk preference into a quantitative portfolio model based on risk and expected return. By inferring rules consisting of an investor's objective and subjective risk preferences, the integrated methodology provides the assets suitable for the preferences. Through investment in the portfolio composed of the assets, the investor is able to obtain the following bene?ts: reduction of costs and time spent to determine target assets, and alleviation of anxiety from ‘out‐of‐favor’ assets. The framework is applied to the development of a knowledge‐based portfolio system for constructing an investor's preference‐oriented portfolio. In the procedure of the system for ?nding an optimal portfolio, the system uses an arti?cial intelligence method of a case‐based reasoning to obtain preference thresholds for an investor when the investor's past investment records are available. Experimental results show that the framework contributes signi?cantly to the construction of a better portfolio from the perspective of an investor's bene?t/cost ratio than that produced by the existing portfolio models. Copyright © 2004 John Wiley & Sons, Ltd.     

The Diversification Effects of Initial Public Offerings

Abstract:  A firm's stock becomes publicly tradable through an initial public offering (IPO). This study suggests a portfolio diversification perspective to explore IPOs. We examine whether investors can gain diversification benefits by adding an IPO portfolio to a set of benchmark portfolios sorted by firm size and book-to-market ratio. Using US IPOs from 1980-2002, we find that adding a value-weighted IPO portfolio does lead to a statistically and economically significant enlargement of the investment opportunity set for investors relative to investing solely in a set of benchmark portfolios. Specifically, the Sharpe ratio of the tangency portfolio increases by 5.50% on average after including IPO stocks. Furthermore, IPOs associated with prestigious lead underwriters are the main source of this augmentation of the mean-variance investment opportunity set. Finally, our study implies that issuing IPO exchange traded funds or similar products can provide diversification gains to investors.     

Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets

The paper presents an incomplete market pricingmethodology generating asset pricebounds conditional on the absence of attractiveinvestment opportunities in equilibrium.The paper extends and generalises the seminal article ofCochrane and Saá-Requejowho pioneered option pricing based on the absenceof arbitrage and high Sharpe Ratios. Ourcontribution is threefold:We base the equilibrium restrictions on an arbitrary utility function, obtaining theCochrane and Saá-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms ofGeneralised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide aconsistent ranking of investment opportunities even when asset returns are highlynon-normal. Last but not least, we demonstrate that for Itô processes theCochrane and Saá-Requejo price bounds are invariant to the choice of the utilityfunction, and that in the limit they tend to a unique price determined by theminimal martingale measure.     

International asset allocation using the market implied cost of capital

The Black and Litterman (Financ Anal J 48(5):28–43, 1992) (BL) approach to portfolio optimization requires investor views on expected asset returns as an input. I demonstrate that the market implied cost of capital (ICC) is ideal for quantifying those views on a country level. I benchmark this approach against a BL optimization using time-series models as investor views, the equally weighted portfolio, and allocation methods based on stock market capitalization and GDP. I find that the ICC portfolio offers an increase in average return of 2.1 percentage points (yearly) as compared to the value-weighted portfolio, while having a similar standard deviation. The resulting difference in Sharpe ratios is statistically significant and robust to the inclusion of transaction costs, varying BL parameters, and a less strictly defined investment universe.     

The Role of the Investment Horizon in Optimal Portfolio Sequencing (An Intuitive Demonstration in Discrete Time)

This paper examines the role played by the investor's investment horizon in the choice of optimal portfolios. A complete discrete-time, multiperiod, portfolio model is presented with a choice criterion that is consistent with the traditional utility approach but which is more amenable to a multiperiod environment. It is shown that investors should choose progressively less risky single-period portfolios as their investment horizons grow shorter, even if they do not become more risk averse. This result holds both in the presence and in the absence of a riskless asset. The results are consistent with empirical evidence and the financial planning practice of moving investors into progressively less risky portfolios as they grow older.     

Dynamic Investment Strategy with Factor Models Under Regime Switches

A model for dynamic investment strategy is developed where assets’ returns are represented by multiple factors. In a mean–variance framework with factor models under regime switches, we derive a semi-analytic solution for the optimal portfolio with transaction costs. Due to the existence of transaction costs, the optimal portfolio is characterized as a linear combination of current and target portfolios, the latter of which maximizes the value function in the current regime. For some special cases of interest, we also derive simplified analytical solutions. To see the effect of regime switches, the proposed model is applied to US equity market in which small minus big and high minus low are employed as factors. Investment strategy based on our model demonstrates empirically that the regime switching models exhibit superior performance over the single regime model for such performance measures as realized utility and Sharpe ratio which are of particular interest in practice. Taking a close look at the time series of portfolio returns, the result shows the usefulness of the regime switching model as investors flexibly optimize asset allocations depending on the state of the market.     

Volatility‐Managed Portfolios

Managed portfolios that take less risk when volatility is high produce large alphas, increase Sharpe ratios, and produce large utility gains for mean‐variance investors. We document this for the market, value, momentum, profitability, return on equity, investment, and betting‐against‐beta factors, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in volatility are not offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions. This rules out typical risk‐based explanations and is a challenge to structural models of time‐varying expected returns.     

Variable Selection for Portfolio Choice

We study asset allocation when the conditional moments of returns are partly predictable. Rather than first model the return distribution and subsequently characterize the portfolio choice, we determine directly the dependence of the optimal portfolio weights on the predictive variables. We combine the predictors into a single index that best captures time variations in investment opportunities. This index helps investors determine which economic variables they should track and, more importantly, in what combination. We consider investors with both expected utility (mean variance and CRRA) and nonexpected utility (ambiguity aversion and prospect theory) objectives and characterize their market timing, horizon effects, and hedging demands.     

Convex risk measures based on generalized lower deviation and their applications

Considering the implementability and the properties that a reasonable and realistic risk measure should satisfy, we propose a new class of risk measures based on generalized lower deviation with respect to a chosen benchmark. Besides convexity and monotonicity, our new risk measure can reflect the investor's degree of risk aversion as well as the fat-tail phenomenon of the loss distribution with the help of different benchmarks and weighted functions. Based on the new risk measure, we establish a realistic portfolio selection model taking market frictions into account. To examine the influence of the benchmarks and weighted functions on the optimal portfolio and its performance, we carry out a series of empirical studies in Chinese stock markets. Our in-sample and out-of-sample results show that the new risk measure and the corresponding portfolio selection model can reflect the investor's risk averse attitude and the impact of different trading constraints. Most importantly, with the new risk measure we can obtain an optimal portfolio which is more robust and superior to the optimal portfolios obtained with the traditional expected shortfall risk measures.