A Unified Approach to Portfolio Optimization with Linear Transaction Costs
In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the p…
A Comprehensive Look at the Real-Life Performance of Moving Average Trading Strategies
Despite the enormous current interest in market timing and a series of publications in academic journals, there is still lack of comprehensive research on the evaluation of the profitability of trading rules using methods that are free from the data-snooping bias. In this paper we utilize the longest historical dataset that spans 155 years and extend previous studies on the performance of moving average trading rules in a number of important ways. Among other things, we investigate whether overweighting the recent prices improves the performance of timing rules; whether there is a single optimal lookback period in each trading rule; and how accurately the trading rules identify the bullish …
Optimal Hedging of Option Portfolios with Transaction Costs
One of the most successful approaches to option hedging with transaction costs is the utility based approach pioneered by Hodges and Neuberger (1989). However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. The direct numerical computations of the utility based hedging strategy are cumbersome in a practical implementation. Despite some recent advances in finding an explicit description of the utility based hedging strategy by using either asymptotic, approximation, or other methods, so far they were concerned primarily with hedging a single plain-vanilla option. However, in practice one often faces t…
Not all bull and bear markets are alike: insights from a five-state hidden semi-Markov model
This paper employs the hidden semi-Markov model and a novel model selection procedure to detect different states in the US stock market. The empirical results suggest that the market is switching between five states that can be classified into three bull states and two bear states. The three bull states are categorized as a low volatility bull market, a high volatility bull market, and a stock market bubble. One of the bear states represents a regular bear market, while the other one corresponds to either a stock market crash or a market correction. The paper demonstrates that the five-state model is consistent with a number of stylized facts and provides many valuable insights into the dyn…
Revisiting the Profitability of Market Timing with Moving Averages
In a recent empirical study by Glabadanidis ("Market Timing With Moving Averages" (2015), International Review of Finance, Volume 15, Number 13, Pages 387-425; the paper is also available on the SSRN and has been downloaded more than 7,500 times) the author reports striking evidence of extraordinary good performance of the moving average trading strategy. In this paper we demonstrate that "too good to be true" reported performance of the moving average strategy is due to simulating the trading with look-ahead bias. We perform the simulations without look-ahead bias and report the true performance of the moving average strategy. We find that at best the performance of the moving average stra…
Why Moving Averages?
This chapter presents a brief motivation for using moving averages for trend detection, how moving averages are computed, and their two key properties: the average lag (delay) time and smoothness. The most important thing to understand right from the start is that there is a direct relationship between the average lag time and smoothness of a moving average.
SECULAR MEAN REVERSION AND LONG-RUN PREDICTABILITY OF THE STOCK MARKET
Empirical financial literature documents the evidence of mean reversion in stock prices and the absence of out-of-sample return predictability over periods shorter than 10 years. The goal of this paper is to test the random walk hypothesis in stock prices and return predictability over periods longer than 10 years. Specifically, using 141 years of data, this paper begins by performing formal tests of the random walk hypothesis in the prices of the real S&P Composite Index over increasing time horizons up to 40 years. Even though our results cannot support the conventional wisdom which says that the stock market is safer for long-term investors, our findings speak in favor of the mean revers…
Trading the Standard and Poor’s Composite Index
This chapter utilizes the longest historical sample of data on the SP whether the choice of moving average influences the performance of trading rules; how accurately the trading rules identify the bullish and bearish stock market trends; whether there is any advantage in trading daily rather than monthly; and how persistent is the outperformance delivered by the moving average trading rules. The results of this study allow us to revisit the myths regarding the superior performance of the moving average trading rules in this well-known stock market and fully understand their advantages and disadvantages.
Dynamic Asset Allocation Strategies Basedon Unexpected Volatility
The author documents that at the aggregate stock market level, unexpected volatility is negatively related to expected future returns, and positively related to future volatility. The author demonstrates how the predictive ability of unexpected volatility can be utilized in dynamic asset allocation strategies that deliver a substantial improvement in terms of risk-adjusted performance as compared to traditional buy-and-hold strategies. In addition, the author shows that active strategies based on unexpected volatility outperform the popular active strategy with a volatility target mechanism, and have some edge over the popular market timing strategy with a 10-month simple moving average rul…
American Option Pricing and Exercising with Transaction Costs
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal tra…
Forecasting the Size Premium Over Different Horizons
In this paper, we provide evidence that the small stock premium is predictable both in-sample and out-of-sample through the use of a set of lagged macroeconomic variables. We find that it is possible to forecast the size premium over time horizons that range from one month to one year. We demonstrate that the predictability of the size premium allows a portfolio manager to generate an economically and statistically significant active alpha.
Revisiting the Profitability of Market Timing with Moving Averages
In a recent empirical study by Glabadanidis (“Market Timing with Moving Averages” (2015), International Review of Finance 15(13):387–425), the author reports striking evidence of extraordinarily good performance of the moving average trading strategy. In this paper, we demonstrate that this “too good to be true” reported performance of the moving average strategy is due to simulating trading with look-ahead bias. We perform simulations without look-ahead bias and report the true performance of the moving average strategy. We find that, at best, the performance of the moving average strategy is only marginally better than that of the corresponding buy-and-hold strategy. In statistical terms,…
Portfolio performance evaluation with loss aversion
In this paper we consider a loss-averse investor equipped with a specific, but still quite general, utility function motivated by behavioral finance. We show that, under certain concrete assumptions concerning the form of this utility, one can derive closed-form solutions for the investor's portfolio performance measure. We investigate the effects of loss aversion and demonstrate its important role in performance measurement. The framework presented in this paper also provides a sound theoretical foundation for all known performance measures based on partial moments of the distribution.
Trading in Other Financial Markets
This chapter tests the profitability of various moving average trading rules in different financial markets: stocks, bonds, currencies, and commodities. The results of these tests allow us to better understand the properties of the moving average trading strategies and find out which trading rules are profitable in which markets. The chapter concludes with a few practical recommendations for traders testing the profitability of moving average trading rules. The analysis presented in this chapter also suggests a hypothesis about simultaneous existence, in the same financial market, of several trends with different durations.
Trend Following with Momentum Versus Moving Average: A Tale of Differences
Despite the ever-growing interest in trend following and a series of publications in academic journals, there is still a great shortage of theoretical results on the properties of trend following rules. Our paper fills this gap by comparing and contrasting the two most popular trend following rules, the Momentum (MOM) and Moving Average (MA) rules, from a theoretical perspective. Our approach is based on the return-based formulation of trading rules and modelling the price trends by an autoregressive return process. We provide theoretical results on the similarity between various trend following rules and the forecast accuracy of trading rules. Our results show that the similarity between t…
Optimal Dynamic Portfolio Risk Management
Numerous econometric studies report that financial asset volatilities and correlations are time-varying and predictable. Over the past decade, this knowledge has stimulated increasing interest in various dynamic portfolio risk control techniques. The two basic types of risk control techniques are: risk control across assets and risk control over time. At present, the two types of risk control techniques are not implemented simultaneously. There has been surprisingly little theoretical study of optimal dynamic portfolio risk management. In this paper, the author fills this gap in the literature by formulating and solving the multi-period portfolio choice problem. In terms of dynamic portfoli…
A Generalization of the Mean-Variance Analysis
In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This "mean-partial moments" utility generalizes not only the mean-variance utility of Tobin and Markowitz, but also the mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision…
Volatility Weighting over Time in the Presence of Transaction Costs
Numerous empirical studies demonstrate the superiority of dynamic strategies with a volatility-weighting-over-time mechanism. These strategies control the portfolio risk over time by adjusting the risk exposure according to updated volatility forecasts. Yet, to reap all the benefits promised by volatility weighting over time, the composition of the active portfolio must be revised rather frequently. Transaction costs represent a serious obstacle to benefiting from this dynamic risk control technique. In this article, we propose a modified volatility-weighting strategy that allows one to reduce dramatically the amount of trading costs. The empirical evidence shows that the advantages of the …
The Choice of Performance Measure Does Influence the Evaluation of Hedge Funds
It is widely accepted that, when return distributions are non-normal, the use of the Sharpe ratio can lead to misleading conclusions. It is well documented that deviations of hedge fund return distributions from normality are statistically significant. The literature on performance evaluation that takes into account the non-normality of return distributions is a vast one. However, there is another stream of research that advocates that the choice of performance measure does not influence the evaluation of hedge funds. For example, Eling and Schuhmacher (2007) and Eling (2008) performed empirical studies and, judging by the values of rank correlations, concluded that the choice of performanc…
European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs
Abstract In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: we extend the framework developed by Davis et al. (SIAM J. Control Optim., 31 (1993) 470) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whalley and Wilmott (RISK 7 (1994) 82). We provide a simulation analysis in order …
Abnormal Stock Market Returns Around Peaks in VIX: The Evidence of Investor Overreaction?
Even though the VIX index was intended to be a measure of future volatility of the stock market, researchers argue that in reality VIX measures the investor sentiment. Anecdotal evidence suggests that peaks in VIX coincide with stock market bottoms followed by rallies, yet so far there have been no scientific evidence confirming this casual observation. In this paper we perform an event study of abnormal stock market returns around peaks in VIX and discuss our findings within the framework of behavioral finance theory. First of all, we detect peaks in VIX using formal turning-point identification procedures and provide detailed descriptive statistics of periods of rising and falling VIX. Th…
Revisiting the Duration Dependence in the US Stock Market Cycles
There is a big controversy among both investment professionals and academics regarding how the termination probability of a market state depends on its age. Using more than two centuries of data on the broad US stock market index, we revisit the duration dependence in bull and bear markets. Our results suggest that the duration dependence for both bull and bear markets is a nonlinear function of the state age. It appears that the duration dependence in bear markets is strictly positive. For 93% of the bull markets, the duration dependence is also positive. Only about 7% of the bull markets, those with the longest durations, do not exhibit positive duration dependence. We also compare a few …
A Test of Covariance-Matrix Forecasting Methods
Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this article the author evaluates alternative covariance matrix-forecasting methods by looking at: (1) their forecast accuracy, (2) their ability to track the volatility of a minimum-variance portfolio, and (3) their ability to keep the volatility of a minimum-variance portfolio at a target level. The author finds large differences between the methods. The results suggest that shrinking the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample …
Block bootstrap methods and the choice of stocks for the long run
Financial advisors commonly recommend that the investment horizon should be rather long in order to benefit from the ‘time diversification’. In this case, in order to choose the optimal portfolio, it is necessary to estimate the risk and reward of several alternative portfolios over a long-run given a sample of observations over a short-run. Two interrelated obstacles in these estimations are lack of sufficient data and the uncertainty in the nature of the return generating process. To overcome these obstacles researchers rely heavily on block bootstrap methods. In this paper we demonstrate that the estimates provided by a block bootstrap method are generally biased and we propose two metho…
Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs
In a market with transaction costs the option hedging is costly. The idea presented by Leland (1985) was to include the expected transaction costs in the cost of a replicating portfolio. The resulting Leland's pricing and hedging method is an adjusted Black-Scholes method where one uses a modified volatility in the Black-Scholes formulas for the option price and delta. The Leland's method has been criticized on different grounds. Despite the critique, the risk-return tradeoff of the Leland's strategy is often better than that of the Black-Scholes strategy even in the case when a hedger starts with the same initial value of a replicating portfolio. This implies that the Leland's modification…
Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations
In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of…
Anatomy of Trading Rules
This key chapter presents a methodology for examining how the trading signal in a moving average rule is computed. Then using this methodology the chapter examines the computation of trading signals in all moving average rules and investigates the commonalities and differences between the rules. The main conclusion that can be drawn from this study is that the computation of the trading indicator in every rule, based on either one or multiple moving averages, can equivalently be interpreted as the computation of a single weighted moving average of price changes. The analysis presented in this chapter uncovers the anatomy of moving average trading rules, provides very useful insights about p…
Dynamic Asset Allocation Strategies Based on Unexpected Volatility
In this paper we document that at the aggregate stock market level the unexpected volatility is negatively related to expected future returns and positively related to future volatility. We demonstrate how the predictive ability of unexpected volatility can be utilized in dynamic asset allocation strategies that deliver a substantial improvement in risk-adjusted performance as compared to traditional buy-and-hold strategies. In addition, we demonstrate that active strategies based on unexpected volatility outperform the popular active strategy with volatility target mechanism and have the edge over the widely reputed market timing strategy with 10-month simple moving average rule.
Time Series Momentum in the US Stock Market: Empirical Evidence and Theoretical Implications
There is much controversy in the academic literature on the presence of short-term trends in financial markets and the trend-following strategy's profitability. This paper restricts its attention to the study of time-series momentum (TSMOM) in the US stock market. The paper aims to suggest answers to several important questions regarding TSMOM and to explain the existing controversy. Our answer to the question, whether short-term trends exist, is strongly affirmative. For the first time, we suppose that the returns follow a p-order autoregressive process with p>1 and evaluate this process's parameters. Fairly accurate knowledge of the momentum generating process allows us to provide analyti…
Stock earnings and bond yields in the US 1871–2017 : The story of a changing relationship
Abstract Using historical data spanning almost 150 years, we examine whether there is a long-run equilibrium relationship between the stock's earnings and bond yields. The novelty of our econometric methodology consists in using a vector error correction model where we allow multiple structural breaks in the equilibrium relationship. The results of our analysis suggest the existence of an equilibrium relationship over 1871–1932 and 1958–2017. On the two historical segments, our analysis finds that the stock's earnings yield followed the bond yield in both the short run and long run, but not the other way around. Perhaps the most important and surprising finding of our empirical study is tha…
On the Consistent Use of VaR in Portfolio Performance Evaluation: A Cautionary Note
The portfolio performance measures based on the Value at Risk (VaR) concept have gained widespread popularity and are often used in empirical studies. In the majority of empirical studies, however, a VaR-based performance measure is inconsistently used. In this article, Zakamouline emphasizes how to consistently use VaR in portfolio performance evaluation. He also elaborates on a simple framework that allows the derivation of a general formula for a portfolio performance measure that is not limited to the use of VaR-based reward and risk measures, but is valid for all reward and risk measures that satisfy a few plausible properties.
The term structure of volatility predictability
Volatility forecasting is crucial for portfolio management, risk management, and pricing of derivative securities. Still, little is known about the accuracy of volatility forecasts and the horizon of volatility predictability. This paper aims to fill these gaps in the literature. We begin this paper by introducing the notions of the spot and forward predicted volatilities and propose to describe the term structure of volatility predictability by the spot and forward forecast accuracy curves. Then we perform a comprehensive study on the term structure of volatility predictability in the stock and foreign exchange markets. Our results quantify the volatility forecast accuracy across horizons …
Basics of Moving Averages
This chapter introduces the notion of a general weighted moving average and shows that each specific moving average can be uniquely characterized by either a price weighting function or a price-change weighting function. It also demonstrates how to quantitatively assess the average lag time and smoothness of a moving average. Finally, the analysis provided in this chapter reveals two important properties of moving averages when prices trend steadily.
Fooled by Data-Mining: The Real-Life Performance of Market Timing with Moving Averages
In this paper, we revisit the myths regarding the superior performance of market timing strategies based on moving average and time-series momentum rules. These active timing strategies are very appealing to investors because of their extraordinary simplicity and because they promise substantial advantages over their passive counterparts (see, for example, the paper by M. Faber (2007) "A Quantitative Approach to Tactical Asset Allocation" published in the Journal of Wealth Management). However, the ``too good to be true" reported performance of these market timing rules raises a legitimate concern as to whether this performance is realistic and whether investors can expect that future perfo…
Trend following with momentum versus moving averages: a tale of differences
Despite the ever-growing interest in trend following and a series of publications in academic journals, there is a dearth of theoretical results on the properties of trend-following rules. Our pape...
Stock Earnings and Bond Yields in the US 1871 - 2016: The Story of a Changing Relationship
Using historical data that spans almost 150 years, we examine whether there is a long-run equilibrium relationship between the stock's earnings and bond yields. The novelty of our econometric methodology consists in using a vector error correction model where we allow multiple structural breaks in the equilibrium relationship. The results of our analysis suggest the existence of equilibrium relationship over 1871-1929 and 1958-2017. On the two historical segments, our analysis finds that the stock's earnings yield followed the bond yield in both the short- and long-run, but not the other way around. Perhaps the most important and surprising finding of our empirical study is that, after the …
Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs
One of the most successful approaches to option hedging with transaction costs is the utility-based approach, pioneered by Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239]. Judging against the best possible trade-off between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. We overcome this drawback by presenting a simple yet efficient analytic approximation of the solution. We provide an empirical testing of our approximation strategy against the asymptotic and some other …
Secular Mean Reversion and Long-Run Predictability of the Stock Market
Empirical financial literature documents the evidence of mean reversion in stock prices and the absence of out-of-sample return predictability over periods shorter than 10 years. The goal of this paper is to test the random walk hypothesis in stock prices and return predictability over periods longer than 10 years. Specifically, using 141 years of data, this paper begins by performing formal tests of the random walk hypothesis in the prices of the real S&P Composite Index over increasing time horizons up to 40 years. Even though our results cannot support the conventional wisdom which says that the stock market is safer for long-term investors, our findings speak in favor of the mean revers…
Market Timing with a Robust Moving Average
In this paper we entertain a method of finding the most robust moving average weighting scheme to use for the purpose of timing the market. Robustness of a weighting scheme is defined its ability to generate sustainable performance under all possible market scenarios regardless of the size of the averaging window. The method is illustrated using the long-run historical data on the Standard and Poor's Composite stock price index. We find the most robust moving average weighting scheme, demonstrates its advantages, and discuss its practical implementation.
The Role of Covariance Matrix Forecasting Method in the Performance of Minimum-Variance Portfolios
Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this paper, we evaluate alternative covariance matrix forecasting methods by looking at (1) their forecast accuracy, (2) their ability to track the volatility of the minimum-variance portfolio, and (3) their ability to keep the volatility of the minimum-variance portfolio at a target level. We find large differences between the methods. Our results suggest that shrinkage of the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample covariance ma…
Forecasting Stock Market Volatility: The Gains from Using Intraday Data
There is evidence that volatility forecasting models that use intraday data produce superior forecast accuracy as compared with that delivered by the models that use daily data. However, this evidence is still sparse and incomplete in the stock markets. This paper extends previous studies on forecasting stock market volatility in several important directions and comprehensively assesses the gains in forecast accuracy provided by intraday data. First, we use an extensive set of intraday data on 28 single stocks and 23 stock market indices. Second, in our study we use forecast horizons ranging from 1 day to 6 months. Third, we compare forecasting abilities of several competing models. We find…
On the Pricing and Hedging of Options on Commodity Forward and Futures Contracts - A Note
In recent years there appeared some organized markets for forward contracts and options on these contracts. In this paper we review shortly the organization of trade on a centralized forward market. Assuming a friction-free market with constant interest rate we build a consistent continuous time framework for the valuation and hedging of options on a forward or a futures contract. This framework takes into account the peculiarities of a forward/futures contract. In our framework we consider the pricing and hedging of options on a forward contract and reconsider the Black-76 model for the pricing and hedging of options on a futures contract.
A Generalisation of the Mean-Variance Analysis
In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This ‘mean-partial moments’ utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker i…
The real-life performance of market timing with moving average and time-series momentum rules
In this article, we revisit the myths regarding the superior performance of market timing strategies based on moving average and time-series momentum rules. These active timing strategies are very appealing to investors because of their extraordinary simplicity and because they promise substantial advantages over their passive counterparts. However, the ‘too good to be true’ reported performance of these market timing rules raises a legitimate concern as to whether this performance is realistic and whether investors can expect that future performance will be the same as the documented historical performance. We argue that the reported performance of market timing strategies usually contains…
Moving Averages for Market Timing
This paper begins by presenting the moving average methodology of detecting the direction of a trend and identifying turning points in the trend in real time. The paper then proceeds to introduce the general weighted moving average, derives some of its key properties, and discusses how to quantitatively assess the two important characteristics of a moving average: the average lag time and the smoothness. Finally the paper aims to give an overview of some specific types of moving averages used in market timing. These types include regular moving averages, moving averages of moving averages, and mixed moving averages with less lag time. Different types of moving averages are compared to each …
THE CARMA INTEREST RATE MODEL
In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.
Market Timing with Moving Averages: Anatomy and Performance of Trading Rules
The underlying concept behind the technical trading indicators based on moving averages of prices has remained unaltered for more than half of a century. The development in this field has consisted in proposing new ad-hoc rules and using more elaborate types of moving averages in the existing rules, without any deeper analysis of commonalities and differences between miscellaneous choices for trading rules and moving averages. The first contribution of this paper is to uncover the anatomy of market timing rules with moving averages. Our analysis offers a new and very insightful reinterpretation of the existing rules and demonstrates that the computation of every trading indicator can equiva…
Time series momentum in the US stock market: Empirical evidence and theoretical analysis
There is much controversy in the academic literature on the presence of short-term trends in financial markets and the trend-following strategy’s profitability. We restrict our attention to studying the time series momentum in the S&P Composite stock price index. Our contributions are both empirical and theoretical. On the empirical side, we present compelling evidence of the presence of short-term momentum. For the first time, we suppose that the returns follow a -order autoregressive process and evaluate this process’s parameters. On the theoretical side, we develop a tractable theoretical model that contributes to our fundamental understanding of the trend-following strategy’s risk, retu…
Block Bootstrap Methods and the Choice of Stocks for the Long Run
Financial advisors commonly recommend that the investment horizon should be rather long in order to benefit from the "time diversification". In this case, in order to choose the optimal portfolio, it is necessary to estimate the risk and reward of several alternative portfolios over a long-run given a sample of observations over a short-run. Two interrelated obstacles in these estimations are lack of sufficient data and the uncertainty in the nature of the return generating process. To overcome these obstacles researchers rely heavily on block bootstrap methods. In this paper we demonstrate that the estimates provided by a block bootstrap method are generally biased and we propose two metho…
Transaction Costs and Returns to a Trading Strategy
This chapter starts with a review of transaction costs in capital markets. Then it demonstrates how to simulate the returns to a moving average trading strategy in the presence of transaction costs. The following two cases are considered when a trading indicator generates a sell signal: case one where the trader switches to cash, and case two where the trader alternatively sells short a financial asset.
Predictable Dynamics in the Small Stock Premium
We start this paper by providing a detailed study of how the mean monthly return on the Small-Minus-Big (SMB) Fama-French factor is affected by the January effect and the stock market return during the preceding month and preceding calendar year. We then proceed to building a predictive model for the monthly SMB factor return that incorporates the January effect and the dependence on both the market return during the preceding month and preceding calendar year. Our findings suggest that a positive small stock premium appears mainly during the years following the years with a negative return on the market as the result of a delayed and stronger reaction of small stocks to good news and a str…
Forecasting the size premium over different time horizons
Abstract In this paper, we provide evidence that the small stock premium is predictable both in-sample and out-of-sample through the use of a set of lagged macroeconomic variables. We find that it is possible to forecast the size premium over time horizons that range from one month to one year. We demonstrate that the predictability of the size premium allows a portfolio manager to generate an economically and statistically significant active alpha.
The Limits to Volatility Predictability: Quantifying Forecast Accuracy Across Horizons
Volatility forecasting is crucial for portfolio management, risk management, and pricing of derivative securities. Still, little is known about how far ahead one can forecast volatility. First, in this paper we introduce the notions of the spot and forward predicted volatilities and propose to describe the term structure of volatility predictability by the spot and forward forecast accuracy curves. Then, by employing a few popular time-series volatility models, we perform a comprehensive empirical study on the horizon of volatility predictability. Our results suggest that, whereas the spot volatility can be predicted over horizons that extend to 35 weeks, the horizon of the forward volatili…
Testing Profitability of Technical Trading Rules
Technical traders typically rely on back-testing which is defined as the process of testing a trading strategy using relevant historical data. Back-testing usually involves “data mining” which denotes the practice of finding a profitable trading strategy by extensive search through a vast number of alternative strategies. This chapter explains that the data-mining procedure tends to find a strategy which performance benefited most from luck. As a result, the performance of the best strategy in a back test is upward biased. This fact motivates that any back-test must be combined with a data-mining correction procedure that adjusts downward the estimated performance. Another straightforward m…
Stock Volatility Predictability in Bull and Bear Markets
Recent literature on stock return predictability suggests that it varies substantially across economic states being strongest during bad economic times. In line with this evidence, we document that stock volatility predictability is also state dependent. In particular, using a large data set of high-frequency data on individual stocks and a few popular time-series volatility models, in this paper we comprehensively examine how volatility forecastability varies across bull and bear states of the stock market. We find that the volatility forecast horizon is substantially longer when the market is in a bear state than when it is in a bull state. In addition, the volatility forecast accuracy is…
Superiority of Optimized Portfolios to Naive Diversification: Fact or Fiction?
Abstract DeMiguel, Garlappi, and Uppal (2009) conducted a highly influential study where they demonstrated that none of the optimized portfolios consistently outperformed the naive diversification. This result triggered a heated debate within the academic community on whether portfolio optimization adds value. Nowadays several studies claim to defend the value of portfolio optimization. The commonality in all these studies is that various portfolio optimization methods are implemented using the datasets generously provided by Kenneth French and the performance is measured by means of the Sharpe ratio. This paper aims to provide a cautionary note regarding the use of Kenneth French datasets …
Types of Moving Averages
This chapter presents a detailed review of all ordinary types of moving averages, as well as some exotic types of moving averages. These exotic moving averages include moving averages of moving averages and mixed moving averages with less average lag time. For the majority of moving averages, this chapter computes the closed-form solutions for the average lag time and smoothness. This chapter also demonstrates that the average lag time of a moving average can easily be manipulated; therefore the notion of the average lag time has very little to do with the delay time in the identification of turning points in a price trend.
Technical Trading Rules
This chapter reviews the most common trend-following rules that are based on moving averages of prices. It also discusses the principles behind the generation of trading signals in these rules. This chapter also illustrates the limitations of these rules and argues that the moving average trading rules are advantageous only when the trend is strong and long-lasting.
The Best Hedging Strategy in the Presence of Transaction Costs
Considerable theoretical work has been devoted to the problem of option pricing and hedging with transaction costs. A variety of methods have been suggested and are currently being used for dynamic hedging of options in the presence of transaction costs. However, very little was done on the subject of an empirical comparison of different methods for option hedging with transaction costs. In a few existing studies the different methods are compared by studying their empirical performances in hedging only a plain-vanilla short call option. The reader is tempted to assume that the ranking of the different methods for hedging any kind of option remains the same as that for a vanilla call. The …
On the Irrelevance of Expected Stock Returns in the Pricing of Options in the Binomial Model: A Pedagogical Note
The option pricing theory is now either a standard or a main part of many financial courses on both intermediate and advanced levels. All the textbooks that include the option pricing theory present a detailed treatment of the binomial model. However, the binomial model, although quite simple and intuitive in appearance, is rather tricky when it comes to its practical implementations and applications. In fact, it is amazing that the students often get totally confused when it finally comes to the issue of the choice of the parameters of the binomial model. The reason for all this confusion lies in the fact that all the textbooks emphasize the irrelevance of the binomial option price from th…
Performance Measurement and Outperformance Tests
This chapter explains how to evaluate the performance of a trading strategy and how to carry out a statistical test of the hypothesis that a moving average trading strategy outperforms the corresponding buy-and-hold strategy. In particular, it argues that there is no unique performance measure, reviews the most popular performance measures, and points to the limitations of these measures. The chapter then surveys the parametric methods of testing the outperformance hypothesis and the current “state of the art” non-parametric methods.
Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance
The main purpose of this paper is to present a theoretically sound portfolio performance measure that takes into account higher moments of the distribution of returns. First, we perform a study of the investor's preferences to higher moments of distribution within expected utility theory and discuss the performance measurement. To illustrate the investor's preferences to higher moments and the computation of a performance measure, we provide an approximation analysis of the optimal capital allocation problem and derive a formula for the Sharpe ratio adjusted for skewness of distribution. This performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges…
Dynamic Volatility Weighting in the Presence of Transaction Costs
Numerous empirical studies demonstrate the superiority of dynamic strategies with volatility weighting over time mechanism. These strategies control the portfolio risk over time by adjusting the risk exposure according to updated volatility forecasts. Yet, in order to reap all benefits promised by volatility weighting over time, the composition of the active portfolio must be revised rather frequently. Transaction costs represent a serious obstacle to benefiting from this dynamic risk control technique. In this paper we propose a modified volatility weighting strategy that allows one to reduce dramatically the amount of trading costs. The empirical evidence shows that the advantages of the …
Warren Buffett versus Zvi Bodie: Should You Buy Or Sell Put Options?
Academics and investment professionals often disagree when it comes to investment advice. Legendary investor Warren Buffett is a proponent of time diversification and firmly believes that stocks are less risky in the long run. Therefore, he often sells long-term put options instead of buying them for portfolio protection. By contrast, the famous finance professor Zvi Bodie argues that time diversification is a fallacy and, therefore, his advice to fund managers is to buy long-term portfolio insurance. In this article, we consider the optimal portfolio choice problem for a loss-averse investor. First, we demonstrate that our loss-averse investor subscribes to the principle of time diversific…
On the Consistent Use of VaR in Portfolio Performance Evaluation: A Cautionary Note
The portfolio performance measures based on the Value-at-Risk (VaR) concept have gained widespread popularity and are often used in empirical studies. Unfortunately, we have noticed that in majority of empirical studies a VaR-based performance measure is used inconsistently. The goal of this paper is, therefore, to emphasize how to consistently use VaR in portfolio performance evaluation. We also elaborate on a simple framework that allows to derive a general formula for a portfolio performance measure which is not limited to the use of VaR-based reward and risk measures, but is valid for all reward and risk measures that satisfy a few plausible properties.