Two Essays On Stock Price Momentum

Wen, Hua. 2007. Two Essays On Stock Price Momentum. Doctoral Dissertation, NUS.

Essay 1: the study argue that the parallels between the evidence of momentum and synchronicity could be due to the effect of cross-sectional variation in expected returns, which may arise from both the risk and the investor’s psychology. The empirical test results show that the cross-sectional variation in risks contributes to the negative relation between synchronicity and momentum. Further, it is the industry-risk, as well as other omitted common-risks from the two-factor model, but not the market-risk, that contributes to momentum profits. Essay 2: This paper investigates the role of information efficiency in momentum in the emerging markets. It is interesting to note that the momentum strategy works particularly well among stocks with low analyst coverage, decreasing analyst coverage, and high forecast dispersion. The observed relation between analyst behaviors and momentum is unrelated to the analyst herding tendency, and it does not fully support the information uncertainty story.

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Market Frictions, Momentum and Asset Pricing

by

Lorenzo F. Naranjo

A dissertation submitted in partial fulfillment

of the requirements for the degree of

Doctor of Philosophy

Department of Finance

New York University

May 2009

Abstract

The first essay examines theoretically and empirically how borrowing and short-selling costs affect the pricing of derivatives contracts. In the presence of such costs, an agent trading a derivatives contract is unable to perfectly hedge the derivative if she is exposed to exogenous demand shocks. I derive an equilibrium model of the futures market where demand imbalances from traders affect the price of derivatives contracts. In the model, the price of a derivative depends on the risk- free rate and a latent demand factor. I estimate the model using S&P 500 index futures and the Kalman filter, and find that the latent demand factor is priced. I also find that the latent demand factor is closely related to proxies for demand pressure in the futures market, such as large speculator positions as well as investor sentiment. The demand factor is positive (negative) when buying (selling) pressure is high and is difficult to borrow (to short-sell the underlying). I also find that demand imbalances are correlated across different indexes, for both futures and options.

The second essay studies the stochastic behavior of implied interest rates from derivatives contracts. I start from the observation that there are many proxies for the short-term interest rate that are used in asset pricing. Yet, they behave differently, especially in periods of economic stress. Derivatives markets offer a unique laboratory to extract a short-term borrowing and lending rate available to all investors that is relatively free from liquidity and credit effects. Interestingly, implied interest rates do not resemble benchmark interest rates such as the three- month T-bill rate or LIBOR, but instead are much more volatile. I argue that the volatility in the implied short-term rate in futures and option markets is due to frictions arising from borrowing and short-selling costs. By using the techniques developed in the first essay of this dissertation, I propose a methodology to filter the “true” risk free rate from noisy implied interest rates. The risk-free rate that results from this estimation has time-series properties similar to Treasury and LIBOR rates, and anticipates interest rate changes. The spread between the risk-free and the T-bill rate correlates with liquidity proxies of the Treasury market, while the spread between LIBOR and the risk-free rate is related to economic distress.

The third essay examines the effect of improvements in relative rankings among stocks. The fact that the momentum effect survived the widely cited paper by Jegadeesh and Titman (1993) is itself evidence in favor of a behavioral explanation of this hypothesis. The experimental design of Jegadeesh and Titman (2001) excludes the possibility that the results are some artifact of thin trading or small stocks. However, to validate the behavioral hypothesis we must consider other possible implications. If the momentum effect is indeed under-reaction and delayed overreaction to news events as suggested in Jegadeesh and Titman (2001), then we should anticipate an even greater effect when there are improvements in relative rankings. We refer to this as the acceleration hypothesis and find that it is a significant and distinct factor that has interesting implications for the cross section of security returns.

1.1 Introduction

In this paper I study theoretically and empirically the effect of borrowing and short-selling costs in the pricing of derivatives contracts. In the presence of such costs, an arbitrageur that provides liquidity in a particular derivatives market will be unable to perfectly hedge the derivative if she is exposed to exogenous demand shocks. Thus, demand imbalances for the derivative affect prices, in a similar manner as in the model originally studied by Garleanu, Pedersen, and Poteshman (2007) for options, and Vayanos and Vila (2007) for fixed-income markets.

In perfect markets, it is well-known that the cost of carrying forward a hedged derivatives position should be equal to the risk-free rate minus the dividend yield of the underlying asset. Thus, in frictionless markets it is possible to use derivatives contracts to borrow or lend funds at the risk-free rate. Borrowing funds is accomplished by selling the derivative and buying the risky asset, whereas lending funds is accomplished by buying the derivative and short-selling the risky asset.

In general, though, there are costs faced by agents when they want to borrow funds or short-sell the risky asset. As a result, if a group of agents borrow funds using the derivatives market, the equilibrium derivative’s price should reflect the costs associated with borrowing to preclude arbitrage opportunities. Agents borrowing through the derivatives market generate demand pressure for the derivative, affecting its price because of the borrowing costs. A similar effect follows if a group of agents generate demand pressure in the derivatives market to short-sell the risky asset. Thus, in the presence of borrowing and short-selling costs the equilibrium price of a derivatives contract depends on its demand imbalance.

Even though the intuition can be applied to price any derivative contract, in this paper I specialize the analysis to the pricing of futures contracts. There are several reasons for doing this. First, the pricing formulas can be derived in closed-form, which is convenient for empirical tests of the model. Second, futures contracts are very simple instruments with linear payoffs, which makes their valuation more robust to model assumptions. Third, futures contracts have been trading for a long time, which provides with a long time series of observations to use in empirical tests. Fourth, futures contracts are very liquid instruments, which makes their prices less susceptible to deviate from fair value for liquidity reasons.

The model setup is described in Section 1.2. There are two types of agents: arbitrageurs and traders. Arbitrageurs are rational agents that maximize their expected utility and operate in a competitive market in which there are no-arbitrage opportunities. Traders can be speculators or hedgers, although I do not distinguish between them and assume that all traders have an exogenous demand for the derivative. Arbitrageurs take the opposite position in the derivatives market and hedge their position using the risky asset and risk-free bonds.

In the model arbitrageurs pay borrowing and short-selling costs. One way to motivate this is to assume that arbitrageurs trade with a bank that provides brokering services. In order to derive a closed-form solution for the model, I make the simplifying assumption that borrowing costs increase linearly with demand. The assumption is consistent with the fact that borrowing rates may differ from lending rates, and that it is more expensive to borrow larger amounts of the riskless or risky asset. If traders take a long position in futures contracts, arbitrageurs will take a short position in the futures market. In order to hedge the additional risk carried by the futures, arbitrageurs will simultaneously take a long position in the risky asset. If this position is sufficiently large, they will have to borrow and pay borrowing costs. Equivalently, if traders short the futures, arbitrageurs will have to take the opposite position in the futures market and hedge it by selling the risky asset. If the shorting demand by traders is sufficiently large, arbitrageurs will have to sell short the risky asset, incurring in short-selling costs.

In Section 1.3 I derive an equilibrium model of the futures market where demand imbalances from traders affect the price of futures contracts. The mechanism is as follows. If traders’ demand is positive, then arbitrageurs short the derivative, buy the risky asset and borrow. In equilibrium, arbitrageurs borrow when traders’ demand is positive, which is precisely when borrowing costs are high. In a competitive market, arbitrageurs set the price of the derivative such that they are indifferent between taking the opposite side of the trade or doing nothing. This equilibrium price will be higher than the price obtained in an otherwise equivalent frictionless economy. A similar logic applies if traders want to short the derivative. In that case, arbitrageurs buy the derivative, short the underlying asset and pay short-selling costs. In equilibrium, the price of the derivative should be set lower than in an otherwise equivalent frictionless economy in order to motivate arbitrageurs to take the long position.

In this economy the futures price in the presence of borrowing and short-selling costs depends on the risk-free rate and a latent demand factor. Essentially, the model predicts that the difference between the usual cost-of-carry formula and observed prices is given by the latent demand factor. Thus, derivatives “mispricings” could just be proxying for demand pressure and borrowing and short-selling costs. Moreover, the futures price is equal to the expected spot price under a “local” equivalent risk-neutral measure, implying that arbitrageurs receive a time-varying risk premium for providing liquidity to traders.

The theory has several testable implications. First, the model predicts the existence of a risk premium for the demand factor. Intuitively, if borrowing and short-selling costs are high when demand is high, and vice-versa, then the arbitrageur is exposed to an additional source of risk when hedging her portfolio and commands a premium. Second, the latent demand factor should be related to proxies for demand pressure in the futures market. In other words, proxies for demand pressure in the futures market should be priced factors in the term-structure of futures prices. Third, the demand factor in equilibrium should be related to the borrowing and short-selling costs of the marginal trader. Thus, the model predicts that the latent demand factor is positive when buying pressure is high and it is difficult to borrow irrespective of short-selling costs. Similarly, the latent demand factor is negative when selling pressure is high and it is difficult to short-sell the underlying asset regardless of borrowing costs. Fourth, if demand pressure for derivatives is driven by a common factor, deviations from fair-value should be correlated across markets and derivative instruments.

I estimate the model parameters and state variables using S&P 500 index futures and the Kalman filter in Section 1.4. This is possible because the model delivers a closed-form solution for the valuation of futures contracts and the state- variables follow a system of Gaussian processes. I estimate sixteen parameters by maximizing the likelihood function of price innovations.

The estimation reveals that the demand factor that enters the pricing formula is significantly priced. Thus, engaging in index futures arbitrage is risky and should be compensated. This provides a rationale for the existence of a large industry dedicated to arbitrage deviations from fair-value in derivatives markets. Any agent who has a competitive advantage in borrowing cheaper than others enjoys an economic surplus.

I also verify that the latent demand factor is related to proxies for demand pressure in the futures market, such as large speculators positions in S&P 500 futures and market sentiment for large institutional investors (Han, 2008). If on average the pressure is generated by large speculators, it follows that hedgers are actually paid a premium for the services they provide.

Moreover, I find that the latent demand factor is positive when buying pressure is high and it is difficult to borrow independently of short-selling costs. The opposite effect is also true. The latent demand factor is negative when selling pressure is high and it is difficult to short-sell the risky asset, independently of borrowing costs. This implies that borrowing costs affect the pricing of derivatives only when there is demand pressure to buy the derivative but not to sell it. Similarly, short-selling costs are relevant only when when there is demand pressure to short the derivative but not to buy it.

Finally, I look at whether latent demand imbalances co-move across instruments and markets. Since the demand factor is essentially capturing deviations from fair value in a market without frictions, it is possible to obtain estimates of this factor for other indexes and also put-call parity relations on stock index options. I find that mispricings in futures and put-call parity relations in three indexes (S&P 500, DJIA and Nasdaq 100) are significantly correlated with each other and also with the sentiment proxy, suggesting co-movement in demand imbalances across instruments and markets.

This paper is closely related to two papers that show how demand imbalances for a derivative affect its price. Garleanu et al. (2007) show how demand for options affect options prices, while Vayanos and Vila (2007) analyze a similar effect for fixed-income markets. The main difference with these two papers is that I analyze both theoretically and empirically the effect of borrowing and short-selling costs in the pricing of derivatives.

Also, this study contributes to the literature that studies index futures arbitrage. The main focus of this literature has been to understand absolute mispricings, whereas this paper contributes understanding the sign and magnitude of mispricings.

Finally, this paper fits into a broader literature that looks at how market frictions prevent arbitrageurs in some circumstances from profiting of arbitrage opportunities. Effectively, I show that borrowing costs open a channel through which demand imbalances in the derivatives market can affect no-arbitrage prices, even when the payoff is linear in the underlying asset.

Chapter 2

Implied Interest Rates in a Market with Frictions

2.1 Introduction

Measuring and understanding the risk-free rate is a fundamental question in financial economics. The risk-free rate is a required input in many theories that are extensively used by academics and practitioners in finance, like the CAPM, the APT and the no-arbitrage valuation of derivatives products. The valuation of real and financial assets depends crucially on using the correct risk-free rate. In complete markets, the risk-free rate is uniquely determined as the conditional expectation of the inverse of the stochastic discount factor. In incomplete markets, however, the risk-free rate might not trade at all. If that is the case, there might be several ways of defining what we understand for the risk-free rate (see e.g. Cochrane, 2005, Section 6.5). In this paper, I define the risk-free rate for a particular maturity to be the yield of a zero-coupon bond that is free of liquidity and credit risk effects.

In Section 2.2 I start analyzing the two main proxies for the short-term interest rate that are commonly used in asset pricing. On the one hand, it is common for empirical researchers in finance to use the yield on three-month T-bills as a proxy for the risk-free rate. The intuition for this practice is simple: T-bills are backed by the full faith and credit of the U.S. government. As such, they are the safest investment available for an investor whose consumption is denominated in U.S. dollars. One problem with using T-bill yields as a proxy of the risk-free rate is that only the U.S. government can borrow at this rate. Also, Treasury rates can exhibit periods of flight-to-liquidity during which investors are willing to pay more for the benefit of holding a liquid security (Longstaff, 2004). On the other hand, it is common for practitioners to use LIBOR rates as a proxy for the risk-free rate when valuing derivatives contracts. The intuition for this practice is also simple: practitioners regard LIBOR as their opportunity cost of capital. However, LIBOR represents the interest rate charged on an uncollateralized loan between banks and hence is subject to credit risk.

As a result, these interest rates behave differently, especially in periods of economic stress. As an example, Figure 2.1 shows how Treasury and LIBOR rates have being drifting apart during the 2007-08 credit and liquidity crisis. The so- called TED spread, defined as the difference between LIBOR and Treasury rates, was at an all time high (461 bp) during October 2008.

Fortunately, there are other markets that investors can use to lend or borrow from which it is possible to infer short-term interest rates. For example, an investor can borrow by entering into a long position in a forward contract and selling the underlying asset. Similarly, an investor can lend by shorting a forward and buying the underlying asset. If this transaction is performed through an organized exchange, standard features such as margin requirements and the existence of a clearing corporation significantly reduce the credit risk of the transaction. Also, since derivatives contracts are in zero net-supply, flight-to-liquidity problems are mitigated. Thus, derivatives markets offer a unique laboratory to extract a short- term borrowing and lending rate available to all investors that is free from liquidity and credit risk effects.

In perfect markets, it is well-known that the cost of carrying a forward position should be equal to the risk-free rate minus the underlying asset’s dividend yield. Thus, in frictionless markets2 it is possible to use forward and futures contracts as substitutes for risk-free bonds to derive risk-free rate estimates.

In Section 2.4 I study the implied risk-free rate obtained from futures contracts and put-call parity relations written on major indexes: S&P 500, Nasdaq 100 and Dow Jones Industrial Average (DJIA). The data used in this section is described  in Section 2.3. I find that on average implied interest rates from both futures and options lie between Treasury and LIBOR rates. From January 1998 to December 2007, three-month rates implied from futures prices are on average 48 bp above Treasury and 5 bp below LIBOR, whereas implied interest rates from options are on average 50 bp above Treasury and 3 bp below LIBOR. Thus, implied interest rates are very similar regardless of whether they are extracted from futures or options, and are on average much closer to borrowing (LIBOR) rather than lending (Treasury) rates. This result is consistent with the common industry practice of using LIBOR rates as a proxy for the risk-free rate when valuing derivatives contracts, and also with previous findings in the literature (Brenner and Galai, 1986).

Interestingly, the time-series of implied interest rates do not resemble that of benchmark interest rates such as the three-month T-bill rate or LIBOR, but instead is much more volatile. As discussed in Chapter 1, the phenomenon is expected if we account for market frictions. In the presence of borrowing and short-selling costs, an arbitrageur that provides liquidity in a particular derivatives market will  be unable to hedge the derivative perfectly if she is exposed to exogenous demand shocks. In this case demand imbalances for the derivative will affect prices, making implied interest rates to be correlated with demand, increasing their volatility and affecting their level.

However, it is possible to use the methodology outlined in Chapter 1 to estimate the risk-free rate implied in derivatives prices. Using the Kalman filter, it is possible to infer the time-series of the risk-free rate from the price of a derivative contract. The main identifying assumption used in the estimation is that the risk-free rate is much more persistent than the demand factor driving the “mispricing” of the derivative.

I restrict the estimation of the risk-free rate to S&P 500 futures contracts because they provide with the longest time-series of observations, and they are one of the most liquid derivatives contracts available. In Section 2.5 I show that the risk-free rate that results from this estimation has similar time-series properties as Treasury and LIBOR rates.

The estimated spot rate is on average 15 bp above the fed funds rate, and short-term rates are on average lower than implied rates computed in Section 2.4. Most interestingly, the spot rate seems to be forecasting the Federal funds rate, suggesting that futures markets anticipate changes in short-term interest rates. Also, the spread between LIBOR and the risk-free rate is high in periods of market stress, as proxied by the VIX and the credit spread between AAA and BAA bonds. The spread between the risk-free rate and three-month T-bill rates is high in periods of market illiquidity. These results suggest that the estimated risk-free rate is less affected by liquidity and credit risk than Treasury rates and LIBOR, respectively.

While there is a huge literature on dynamic term structure modeling3 using Treasury bonds and LIBOR rates, the use of derivatives for extracting information about the risk-free rate has been mostly ignored by financial economists. A notable exception is Brenner and Galai (1986), who are probably the first to estimate implied risk-free rates from put-call parity relations on stock option prices. In related work, Brenner et al. (1990) also look at implied risk-free rates using Nikkei index futures data. Liu, Longstaff, and Mandell (2006) obtain implied risk-free rates from plain-vanilla swap contracts, but they use the three-month General Collateral (GC) repo rate as a proxy for the three-month risk-free rate. I make no initial assumptions about what the risk-free rate should be. Feldhütter and Lando (2008) also use swap data to estimate the risk-free rate. However, I use a much larger time-series and I cross-validate my implied rate with different assets. I also account for the fact that demand pressure can affect derivatives prices, distorting implied risk-free rate estimates in significant ways.

Chapter 3

Momentum and the Acceleration Hypothesis (joint with Stephen Brown )

Introduction

A seminal paper by Jegadeesh and Titman (1993) showing that there is strong evidence of serial dependence in the return rankings of stocks has been highly influential in subsequent research for both by academics and practitioners. To date there have been 305 citations of this research in refereed journal publications, and altogether 1188 citations including citations in unpublished working papers that have been electronically circulated1. The results of this research are widely accepted among practitioners and have been used to develop trading strategies both in the United States and abroad. The analysis has been extended in a number of ways to examine whether it applies in other countries (for example Rouwenhorst, 1998) and to other financial statistics (for example, earnings reports). Despite the influence of this research and the importance of its application, the momentum phenomenon remains mysterious. What is the source of this momentum and is it likely to persist in the context of numerous trading strategies designed to exploit it?

One curious finding difficult to reconcile with rational market behavior is the result that the strength of the momentum effect is if anything greater after the effect was described and published in 1993 (Jegadeesh and Titman, 2001). While the results of the 1993 paper appear to diminish and even disappear when the 1993 study is extended to 2004 and to NASDAQ listed stocks (Table 3.1), Jegadeesh and Titman (2001) exclude microcap stocks from the analysis. The results are if anything much stronger once we exclude from the analysis stocks trading under $5.00 (Table 3.2). This result is important, not only as a post sample test of the momentum hypothesis, but also because it excludes the possibility that the momentum effect is an artifact of thin trading and/or small stocks in the sample.

These results leave standing the behavioral hypothesis of Jegadeesh and Titman (2001). These results alone however cannot exclude other possible explanations for the observed momentum effect. One approach is to examine other possible implications of the behavioral hypothesis. The purpose of this paper is to examine one such implication. If the momentum effect arises from delayed overreactions that are eventually reversed, then we should anticipate that improvements in the relative ranking of stocks have an even more extreme effect. We identify this additional implication as the acceleration hypothesis and find that it is a significant and distinct factor that has implications that differ for small and large traded equities. This would appear to be confirmation of the behavioral hypothesis.

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The Profitability of Momentum Investing Testing a Practical Momentum Strategy

by

Ekkehard Arne Friedrich

Dissertation presented in fulfilment of the requirements for the degree

MSc (Engineering Management) at the

University of Stellenbosch

Supervisor: Mr. Konrad von Leipzig

Department of Industrial Engineering

March 2010

Abstract

Several studies have shown that abnormal returns can be generated simply by buying past winning stocks and selling past losing stocks. Being able to predict future price behavior by past price movements represents a direct challenge to the Efficient Market Hypothesis, a centre piece of contemporary finance.

Fund managers have attempted to exploit this effect, but reliable footage of the performance of such funds is very limited. Several academic studies have documented the presence of the momentum effect across different markets and between different periods. These studies employ trading rules that might be helpful to establish whether the momentum effect is present in a market or not, but have limited practical value as they ignore several practical constraints.

The number of shares in the portfolios formed by academic studies is often impractical. Some studies (e.g. Conrad & Kaul, 1998) require holding a certain percentage of every share in the selection universe, resulting in an extremely large number of shares in the portfolios. Others create portfolios with as little as three shares (e.g. Rey & Schmid, 2005) resulting in portfolios that are insufficiently diversified. All academic studies implicitly require extremely high portfolio turnover rates that could cause transaction costs to dissipate momentum profits and lead the returns of such strategies to be taxed at an investor’s income tax rate rather than her capital gains tax rate. Depending on the tax jurisdiction within which the investor resides these tax ramifications could represent a tax difference of more than 10 percent, an amount that is unlikely to be recovered by any investment strategy.

Critics of studies documenting positive alpha argue that momentum returns may be due to statistical biases such as data mining or due to risk factors not effectively captured by the standard CAPM. The empirical tests conducted in this study were therefore carefully designed to avoid every factor that could compromise the results and hinder a meaningful interpretation of the results. For example, small-caps were excluded to avoid the small firm effect from influencing the results and the tests were conducted on two different samples to avoid data mining from being a possible driver. Previous momentum studies generally used long/short strategies. It was found, however, that momentum strategies generally picked short positions in volatile and illiquid stocks, making it difficult to effectively estimate the transaction costs involved with holding such positions. For this reason it was chosen to test a long-only strategy.

Three different strategies were tested on a sample of JSE mid-and large-caps on a replicated S&P500 index between January 2000 and September 2009. All strategies yielded positive abnormal returns and the null hypothesis that feasible momentum strategies cannot generate statistically significant abnormal returns could be rejected at the 5 percent level of significance for all three strategies on the JSE sample.  However, further analysis showed that the momentum profits were far more pronounced in “up” markets than in “down” markets, leaving macroeconomic risk as a possible explanation for the vast returns generated by the strategy. There was ample evidence for the January anomaly being a possible driver behind the momentum returns derived from the S&P500 sample.

Introduction

The main critic of momentum investing is the Efficient Market Hypothesis (EMH), a fundamental theorem in contemporary finance. The EMH claims that past price information cannot be used to predict future price patterns, one of the core principles upon which momentum investing relies. Jegadeesh and Titman (2001) remark that “the momentum effect represents perhaps the strongest evidence against the Efficient Market Hypothesis”. It is safe to say that momentum investing is one of the most disputed topics in investment finance academia today.

 Momentum investing was used by investors and fund managers long before the academic debate even started. One of the most prominent examples is Gerald Tsai, who used a momentum approach to manage Fidelity’s Capital Fund with great success throughout the bullish “Go-Go” years on Wall Street from 1958 to 1965 (Ellis & Vertin, 2001). Today momentum investing is utilized by many mutual fund managers and private investors. Momentum investing is a widespread investment style in the US and other equity markets (Taffler, 1999). Jeff Saunders, fund manager of the UK Growth Fund and the winner of the 1997 and 1999 Standard and Poor's Micropal award for the best UK mutual fund, publicly attributes his investment success to the principle of running the winners and cutting the losers (Saunders, 2004).

Tom de Lange1 outperformed the FTSE/JSE All Share index over most of the past decade using a unique momentum investing strategy. He also conducted several back tests for different periods on JSE stock price data and found that he could earn abnormal returns in almost every randomly selected period in the history of the JSE, even when taking trading costs into account.

Momentum research to date investigates hypothetical trading strategies that are far from being implementable in practice. There exists sufficient evidence of successful practical implementations of size and value strategies2; but a similar practical implementation of a momentum strategy has never been formally documented (Keim, 2003).

1.2 PURPOSE OF THE STUDY

While the methodologies used by momentum researchers (e.g. Jegadeesh and Titman, 1993; Conrad and Kaul, 1998) to date were found to be able to earn abnormal returns it is questionable whether such strategies can be readily implemented in practice. On the other hand, it is likewise questionable whether practical strategies similar to the one used by De Lange (2009) yield abnormal returns when tested in an academic setting.

This paper will seek to test the practical approach followed by De Lange (2009) which relies on technical indicators and reflects the restrictions imposed by practical portfolio management and taxation considerations within a formal academic framework to establish whether momentum strategies are viable in practice.

While De Lange’s results could be explained by factors such as data mining bias, this paper will seek to design and conduct a robust statistical test of De Lange’s method. This will entail simulating De Lange’s approach on two different sets of historical data and recording returns and risk measures.

This study is very relevant as little or no academic research has taken on such a perspective. Most published momentum studies focus on proving the existence of the momentum anomaly or investigating the sources of momentum profits, rather than testing the performance of realistic and implementable investment strategies based on the momentum effect (Rey & Schmid, 2005).

1.3 RESEARCH QUESTIONS AND HYPHOTHESES

The research questions and hypotheses of the study deal with the profitability of feasible momentum strategies.

Hypotheses:

H0: Feasible momentum strategies do not yield statistically significant abnormal returns.

Ha: Feasible momentum strategies yield statistically significant abnormal returns.

Rejection of the null hypothesis would lead to accepting the alternative hypothesis.

More general research questions pertaining to the subject area include:

-     Are feasible momentum strategies profitable across different markets?

-     Do the optimized technical momentum indicators used in practice deliver superior portfolio performance as opposed to simply ranking stocks in terms of past performance as done in most academic studies?

-     Do the momentum returns persist through time and through different macroeconomic states?

-     Are momentum profits robust with regard to trading costs?

The hypotheses and research questions will be refined in Section 6.1 and form the core focus of this dissertation.

1.4 SCOPE OF THE STUDY

This study is conducted in fulfillment of an MSc (Engineering Management) degree, which requires a relatively narrow focus on a subject area. It does not necessitate the creation of new theory. However, a formal framework for testing feasible momentum strategies such as the one used by De Lange (2009) has never been devised before, in essence requiring the creation of new knowledge and a new testing framework.

As this report is compiled from the perspective of engineering management, basic financial concepts terminology will be discussed in more detail than in the case of conventional papers stemming from this context.

Engineering can be defined as: “The application of scientific and mathematical principles to practical ends such as the design, manufacture, and operation of efficient and economical structures, machines, processes, and systems.” Engineering management involves managing engineered solutions. In other words, engineering is concerned with applying theoretical knowledge to a practical problem. Managing portfolios is similar to managing any other complex system. Establishing whether feasible momentum strategies can earn abnormal returns is a practical problem that requires to be substantiated by academic theory in order to arrive at a result that can be used by practitioners.

This dissertation fuses the academic theory around momentum investing with a practical investment strategy and its results have practical and academic implications.

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Essays on Idiosyncratic Volatility and Asset Pricing

by

Fatma Sonmez Saryal

A thesis submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Graduate Department of the Joseph L. Rotman School of Management

University of Toronto

Abstract

In this thesis, I study three aspects of idiosyncratic volatility. First, I examine the relation between idiosyncratic volatility and future stock returns. Next, I examine the share price effect and its interaction with the idiosyncratic volatility on stock returns. Finally, I examine the time series pattern of monthly aggregate monthly idiosyncratic volatility. In the first chapter, I examine the relation between idiosyncratic volatility and future stock returns. In their paper, Ang, Hodrick, Xing, and Zhang [AHXZ (2006)] show that idiosyncratic volatility is inversely related to future stock returns: low idiosyncratic volatility stocks earn higher returns than do high idiosyncratic volatility stocks. The main contribution of this paper is to provide evidence that it is the month to month changes in idiosyncratic volatility that produce AHXZ’s results. More specifically, a portfolio of stocks that move from Quintile 1 (low idiosyncratic volatility) to Quintile 5 (high idiosyncratic volatility) earns an average risk-adjusted return of 5.64% per month in the month of the change. Whereas, a portfolio of stocks that move from the highest to the lowest idiosyncratic volatility quintiles earns -0.94% per month in the month of the change. Eliminating all firm- month observations with idiosyncratic volatility quintile changes, I find the opposite results to AHXZ: it is persistently low idiosyncratic volatility stocks that earn lower returns than do persistently high idiosyncratic volatility stocks. I find that many of the extreme changes in idiosyncratic volatility are related to business events. In general, the pattern usually observed is that an announcement or an event increases uncertainty about a stock and hence, its idiosyncratic volatility increases. After the event, uncertainty is resolved and the stock returns to a lower idiosyncratic volatility quintile.

In the second chapter, I examine how the level of the share price interacts with idiosyncratic volatility to affect future stock returns. Ignoring transaction costs, a trading strategy that is long high-priced and short low-priced stocks earns positive abnormal returns with respect to the Fama-French (1992) three factor model. However, the observed positive abnormal returns are less significant if momentum is taken into account via the Carhart (1997) four factor model. Also the relation between idiosyncratic volatility and future stock returns differs for price sorted portfolios: it is negative for low and mid-priced stocks but positive for high-priced ones. These results are robust for low and-mid-priced stocks evenafter momentum is included. However, the positive relation for high-priced stocks disappears due to relatively large loadings on momentum for high idiosyncratic volatility stocks. I also show that skewness and momentum are significant determinants of idiosyncratic volatility for low-priced stocks and high-priced stocks respectively. One implication is that the importance of idiosyncratic volatility for future stock returns may in part be due its role as a disguised risk factor: either for momentum for high-priced stocks and skewness for low and mid-priced stocks.

In the third chapter, I investigate the time series pattern of aggregate monthly idiosyncratic volatility. It has been shown that new riskier listings in the US stock markets are a reason for the increase in idiosyncratic volatility during the period 1963-2004. First, I show that this is more pronounced for Nasdaq new listings. Second, I show that for Nasdaq, prior to 1994 low-priced new listings became riskier, whereas during the internet bubble period it is the higher-priced listings that became riskier. Third, I show that institutional holdings have increased over time and have had a different impact on each new listing group: a negative for pre-1994 listings and a positive impact for post-1994 listings. Hence, I conclude that the observed time-series pattern of idiosyncratic volatility is a result of the changing nature of Nasdaq’s investor clientele.

Introduction

There is a fast-growing and controversial literature dealing with the impact of idiosyncratic volatility (Ivol) on stock returns. Standard asset pricing models, such as the Capital Asset Pricing and Fama-French (1992) models conclude that only systematic risk factors should be related to future returns. This is because firm specific (idiosyncratic) risk can be eliminated by diversification, and therefore investors do not require a risk premium for bearing that risk. However many investors hold undiversified portfolios for a variety of reasons. In these situations, firm specific risk may play a role in affecting future returns.

The pricing of idiosyncratic risk in the cross-section of security returns has been the subject of research for almost 40 years. In early work, Douglas (1969) and Lintner (1965) found that the variance of the residuals from the market model was highly significant in explaining the cross-section of stock returns. More recently the debate on the relevance of Ivol has been revived with conflicting results. Lehmann (1990), Goyal and Santa-Clara (2003), Malkiel and Xu (2003), Spiegel and Wang (2005), and Fu (2008) present evidence of a positive relationship between Ivol and future returns. Bali, Cakici, Yan and Zhang (2005) and Bali and Cakici (2008) find that there is no significant relation between firm specific risk and future returns. Finally, Ang, Hodrick, Xing, and Zhang [AHXZ (2006)] find a strongly significant negative relationship between Ivol and security returns. In a follow-up paper [AHXZ (2008)], they show that this pattern is also visible internationally. After controlling for almost all related firm characteristics, AHXZ call their result a “puzzle”: why do low Ivol firms earn higher future returns than ones with higher Ivol? This “puzzle” has attracted recent attention and there has been increasing interest in explaining AHXZ’s controversial result.

In this paper, I replicate AHXZ’s results for the period from July 1963 to December 2000 and confirm the “puzzle”1. On average the value-weighted low Ivol portfolio earns approximately 1% per month more than that of the value-weighted high Ivol portfolio. These results are even more pronounced when equally-weighted portfolio returns are used. I then investigate the effect of changes in a firm’s Ivol on its future return. The AHXZ results are generated by relating returns earned in month t with the stock’s Ivol in month t–1. I relate the returns earned in month t with the stock’s Ivol in month t–1 and month t. I consider three cases: the Ivol is similar in both months, the Ivol in month t–1 is significantly less than that in month t, and the Ivol in month t–1 is significantly greater than that in month t. The behavior of these three groups is markedly different. For those stocks that experience a significant change in Ivol, the return earned in month t is consistent with the contemporaneous Ivol and is inconsistent with the Ivol in month t−1.

I find that it is the change in Ivol from month to month that produces AHXZ’s results. Stocks that move from the lower to the higher Ivol quintiles earn significantly high contemporaneous positive returns. For example, if a firm moves from Quintile 1 (low Ivol) to Quintile 5 (high Ivol) it earns an average risk adjusted return of 5.64%per month in the month of the change. Similarly stocks that move from the highest to the lowest Ivol quintiles earn lower returns in the month of the change. The set of stocks that experiences moves from the lowest to the highest or highest to the lowest quintile is about one quarter of the total sample. If I eliminate all firm months in which Ivol changes, I find that low Ivol stocks earn consistently lower returns than these of high Ivol stocks, which is opposite to the results of AHXZ and in line with the theory.

The change in idiosyncratic risk ranking from one month to the next has an asymmetric impact on future returns. If the change is from low to high Ivol, then it has a higher impact (5.64% per month) than when the change is from high to low (−0.94% per month). This is similar to the differential stock market reaction to good versus bad news.

The changes in Ivol that drive AHXZ’s apparent anomaly appear to be related to identifiable business events. Many of the extreme changes in Ivol from the lowest to the highest quintile are related to merger and acquisition activity (M&A), earnings announcements, CEO changes, law suits and so on. While not all events lead to extreme changes in Ivol, many extreme changes in Ivol are related to some identifiable event. The pattern usually observed is that an announcement or an event increases uncertainty about a stock and hence its Ivol increases. After the event, uncertainty is resolved and the security returns to a lower Ivol. For example, about 10% of all migrations from the lowest to the highest Ivol quintile are firms that have an acquisition announcement around the time of the change in Ivol. More than 50% of all stocks that migrate from the lowest to the highest Ivol quintile and then return to the lowest quintile within two months have M&A related news during that period. Another source of increased uncertainty that leads to an increase in Ivol is earnings announcements. About 6% of all migrations from the lowest Ivol quintile to the highest quintile are firms that have an earnings announcement month around the time of the change in Ivol.

The rest of this paper is organized as follows. In Section 2, I confirm AHXZ’s results using their sample period.2 In Section 3, I investigate the effect of changes in Ivol ranking on future realized stock returns. The asymmetric impact of changes in a security’s ranking on future returns is examined. In Section 4, I consider robustness checks. In Section 5, I provide a discussion of the possible explanations for the empirical results in the paper. In Section 6, I discuss the related issues in the Ivol literature while extending the sample period to 2008. Conclusions are in Section 7.

©Copyright by Fatma Sonmez Saryal (2010)

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ANALYSIS OF A MOMENTUM STRATEGY TO CONTROL THE EQUITY EXPOSURE MOMENTUM AS A SIGNAL FOR MARKET TIMING

PHILIPPE HUNGERBUEHLER

MASTER THESIS

IM MAAS 6

8049 ZURICH

PHUNGERBUEHLER@YMAIL.COM

SEPTEMBER 11, 2009

UNIVERSITY OF ZURICH

SWISS BANKING INSTITUTE

Executive Summary

Not only since the publication by Jegadeesh and Titman (1993) Fama’s Efficient Market Hypothesis has been questioned by trend followers but since then the profitability of momentum trading has been documented. Momentum or relative strength is the phenomenon that prices of rising assets will rise in the future or that past winners will out-perform past losers significantly. This is widely studied and accepted. However, whether momentum or trend following can be used to control the equity exposure of a whole portfolio has not been analyzed yet. There are studies that investigate momentum as a signal for tactical asset allocation decisions within the same asset class (see for instance Bhojraj and Swaminathan, 2006). Momentum strategies to control and to time the exposure of a whole asset class, namely the equities, are barely studied. Tactical asset allocation decisions regarding the equity exposure are often made based on macroeconomic factors and on expectations of the development of the economy.

The main contribution of the thesis at hand is the evaluation of three momentum strategies as investment strategies to control the equity exposure in multi-asset class portfolios. Not only are the returns adjusted for systematic risk and analyzed subsequently but the thesis tests also whether macroeconomic factors can explain the success of the momentum strategies.

Problem Description

In a first step, momentum strategies have to be found that are applicable as an investment strategy to control the exposure to the equity market. Existing approaches sell assets with the worst recent return and buy the ones with the best return. This is not possible in the case of a weighting decision across asset classes. In a second step, the rules are applied on a very simple portfolio that can only invest either in the equity market or in a risk  free asset. The momentum strategies will assign the point of time to invest in the equity market and when to invest in the risk free asset. In a further step, the portfolio becomes a balanced portfolio consisting of equities and bonds and the momentum strategies control the equity exposure of the portfolio; that is they will assign an over-, underweight or neutral position for the equity quota.

Methodology

The study is executed individually in five different regional markets on the basis of historic equity index futures prices, namely the S&P 500, the Nikkei 225, the SMI, the DJ Euro Stoxx 50 and the FTSE 100. Futures contracts have been chosen because of their low transaction costs and high transaction volumes. The portfolio that applies the momentum strategy is compared to a benchmark portfolio that uses a buy-and-hold strategy. One out of three momentum strategies excels as the most successful. This strategy is then analyzed in more detail. The strategy applies a very simple method of trend following: It assigns a maximum overweight in the equity exposure as long as the actual index price is higher than the one prior to 232 trading days, otherwise a maximum underweight.

Whether the success of the strategy is statistically significant, is tested using the traditional Capital Asset Pricing Model and a model that tests benchmark timing, which means it tests if the portfolio has a significant lower beta in down markets than in rising markets. Moreover, macroeconomic factors, namely the price earnings ratio and the realized equity risk premium, are tested whether they can explain the excess return.

Results

The most successful investment strategy exceeds the benchmark in all regional markets in the case of assigning only whether or not to invest in the equity market as well as in the case of controlling the equity exposure against the bond market. Moreover, the statistical analysis shows weak evidence for significance. Adjusting for market risk cannot explain the excess return, nor can the tested macroeconomic factors, realized equity risk premium and price earnings ratio.

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ESSAYS ON INVESTOR BEHAVIOR AND TRADING ACTIVITY

PETRI KYRÖLÄINEN

ACTA UNIVERSITATIS OULUENSIS

G Oeconomica 28

Academic dissertation

Copyright © 2007

Acta Univ. Oul. G 28, 2007

ISBN 978-951-42-8435-9 (Paperback)

ISBN 978-951-42-8436-6 (PDF)

http://herkules.oulu.fi/isbn9789514284366/

ISSN 1455-2647 (Printed)

ISSN 1796-2269 (Online)

http://herkules.oulu.fi/issn14552647/

OULU UNIVERSITY PRESS

OULU 2007

Kyröläinen, Petri, Essays on investor behavior and trading activity

Faculty of Economics and Business Administration, Department of Accounting and Finance,

University of Oulu, P.O.Box 4600, FI-90014 University of Oulu, Finland

Acta Univ. Oul. G 28, 2007

Oulu, Finland

Abstract

This thesis investigates a set of equity market phenomena associated with investors' trading activity, using a comprehensive Finnish Central Securities Depository (FCSD) database that records practically all trades by Finnish investors. This database enables us to classify a large number of heterogeneous investors using both economic and institutional characteristics.

The first essay classifies investors by trading activity. It analyzes trading styles of active and passive investors during the boom in technology stocks 1997-2000. We find that the herding tendency of active investors grew monotonically, year by year. Particularly large active investors used momentum and growth strategies. Moreover, buy pressures of active investors were positively related to contemporaneous daily returns. Passive investors, on the other hand, herd very strongly and their trading exhibited a contrarian style throughout the sample period.

The second essay focuses on the relation between day trading of individual investors and intraday stock price volatility. I find a strong positive relation between the individual investors' day trades and volatility for actively day traded stocks. This finding suggests that day trading tends to increase volatility and/or day traders tend to become more active on the days of high volatility.

The third essay tests the theoretical proposition of Amihud and Mendelson (1986) that investors hold assets with higher bid-ask spreads for longer periods. We measure holding periods of individual investors directly and find that they are positively related to spreads. The models control for a variety of other stock characteristics (e.g. value vs. growth orientation) and investors' attributes (e.g. gender) affecting holding periods.

The fourth essay studies how both individual and institutional investors with different levels of capital gains and losses react to earnings announcements. I find that both sign and magnitude of capital gains affect individual investors' abnormal trading volumes. Individual investors are less prone to sell when they are carrying loses rather than gains. Furthermore, they react less to earnings announcements when capital gains or losses are large (over 20%). Taken together these findings provide support for prospect theory. Institutional investors appear to be less affected by psychological factors underlying prospect theory.

Keywords: bid-ask spread, day trading, momentum trading, Prospect Theory, trading activity, volatility

Introduction

1.1 Background

Traditional neoclassical finance theory assumes a single representative investor who rationally sets asset prices. This rationality in the beliefs of the representative investor implies that markets are efficient in the sense that actual asset values coincide with their fundamental values. Furthermore, the lack of investor heterogeneity in the neoclassical framework implies no trading. The famous examples of the models built on the concept of rational representative investor are portfolio theory by Markowitz (1952) the capital asset pricing model by Sharpe (1964) and Lintner (1965), and capital structure theory by Modigliani and Miller (1958). In the late 1970s, however, asymmetric information models were introduced to the finance literature. These models typically contain two types of investors: informed and uninformed investors (or noise traders). The early examples of these models are Grossman (1976) and Holmström (1979). Although asymmetric information models provided some challenge for traditional finance theory, the neoclassical model with its representative investor remained, in the language of Kuhn (1970), as the dominant paradigm.

The mid-80s witnessed the gradual rise of the new paradigm – behavioral finance – in this young branch of science. The theoretical and experimental premises of behavioral finance were already laid down in the psychology literature in the 70s by Kahneman and Tversky (1972, 1973, 1979). The most prominent early behavioral finance applications included the work of Shefrin and Statman (1985), who applied the prospect theory of Kahneman and Tversky to explain the so-called diposition effect. Behavioral finance is characterized by investors’ limited ability to analyze information and systematic biases in their decision making. By the end of the millennium behavioral finance gathered more momentum: various theoretical models and multiple empirical papers were published in the leading finance journals. Behavioral finance was already competing for the status of leading paradigm in finance on par with neoclassical paradigm. But how about the representative investor? Did the behavioral finance literature recognize differences in behaviour and institutional characters of different types of investors? Mostly it did not.

The leading theoretical models of behavioral finance such as Daniel, Hirshleifer and  Subrahmanyam (1998) and Barberis, Shleifer and Vishny (1998) were built on the traditional premise of a representative investor. Empirical behavioral finance literature did not fare much better. In the absence of more comprehensive data sets, usually only a single investor group was analyzed at a time, such as a sample of mutual funds, or trades by the clients of a single brokerage firm. Although these studies made huge contributions to the knowledge of how investors actually behave, they lacked the overall picture of market dynamics when various investor groups behave in potentially different fashion.

1.2 Purpose of the dissertation

The purpose of this dissertation is to analyse a set of important equity market phenomena that are related to investors’ trading activity. The thesis consists of four empirical essays. These essays seek to answer the following research questions: How are the activity characteristics of investors related to trading strategies? Did active or passive investors  use destabilizing trading strategies during the boom in technology stocks? How is trading activity related to the volatility of stock prices? How is trading activity associated with transaction costs? Do capital gain positions affect selling activity following earnings announcements? Each essay makes its unique contributions which we describe more specifically in the review section of the essays.

We search contribution from extensive data covering practically all trades by Finnish investors. These data allow us to classify a wide range of heterogeneous investors using both institutional and economic characteristics. Two of the essays use an economic characterization as a basis for an investor classification. These classification criteria are: trading activity and level of capital gains. In addition, we also apply more traditional criteria, by sorting market participants as individual investors and institutional investors.

Our aim is to apply these investor classes to analyze various market phenomena, such as trading strategies and price impacts of active and passive investors during the boom in technology stocks at the turn of the millennium, relation between day trading and stock price volatility, impact of bid-ask spreads on the market equilibrium in terms of investment horizon, and information usage and trading strategies by investors with different levels of capital gains around earnings announcements.

We find a number of interesting empirical results. The first essay documents that active investors followed momentum and growth strategies during the boom in technology stocks. Herding of passive investors was very strong but remained constant during the sample period. Herding of active investors, on the other hand, show an increasing trend towards the peak of the technology stock bubble. The second essay finds that the day trading of individual investors is strongly associated with intraday volatility of stock prices. The third essay documents a strong positive relation between bid-ask spreads and individual investors’ holding periods. The fourth essay finds that individual investors holding large capital losses are less inclined to sell following earnings announcements than individuals in other capital gain classes. Furthermore, investors with the price of a holding close to the assumed reference point – the purchase price of a stock – appear to be more sensitive to corporate news than are those investors carrying a stock with a price further from the reference point.

The rest of the thesis is organized as follows. Section 2.1 explains from the methodological perspective why understanding investor behavior is an important endeavor. Section 2.2 characterizes the traditional neoclassical investor as a benchmark to which deviations in investor behavior can be compared. Sections 2.3 and 2.4 present theoretical background and earlier evidence related to momentum trading and herding and explain how they may be related to asset pricing bubbles. These trading patterns are then analyzed in the first empirical essay of this thesis in the context of the technology stock boom. Section 2.5 describes the prospect theory and mental accounting framework, which provide theoretical background for the essay studying the relation between capital gains and reaction to earnings announcements. Section 2.6 explains how investment horizons relate to transaction costs and volatility of stock prices, providing a background for the second and third essays. Section 3 briefly reviews the empirical essays. Finally, the original essays are presented at the end of the thesis.

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