Liquidity risk and arbitrage pricing theory

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.Received: 1 November 2003, Mathematics Subject Classification: 60G44, 60H05, 90A09JEL Classification: G11, G12, G13Umut Çetin: This work was performed while Dr. Çetin was at the Center for Applied Mathematics, Cornell UniversityPhilip Protter: Supported in part by NSF grant DMS-0202958 and NSA grant MDA-904-03-1-0092 The authors wish to thank M. Warachka and Kiseop Lee for helpful comments, as well as the anonymous referee and Associate Editor for numerous helpful suggestions, which have made this a much improved paper.     

How efficiency shapes market impact

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two-thirds of peak impact.     

The pricing of volatility risk in the US equity market

We analyze whether the pricing of volatility risk depends on the asset pricing framework applied in the tests, the specified volatility proxies, and the portfolio sorts used for spanning the asset universe. For this purpose, we compare the results using a macroeconomic and fundamental based asset pricing model using three proxies of volatility and uncertainty, using size/value sorted and industry sector portfolios. Our results reveal that the marginal pricing effect of the VIX volatility factor is strong and statistically significant throughout the models and specifications, while the effect of an EGARCH-based volatility factor is mixed, mostly smaller but with the correct sign. In most cases, the EGARCH factor does not impair the pricing effect of the VIX. The portfolio sorts have a substantial impact on the volatility premiums in both model frameworks. The size of the volatility risk premium is more uniform across the models if the industry sector portfolio sort is used. Finally, the size/value portfolio sort generates larger volatility risk premiums for both models.     

Option augmented density forecasts of market returns with monotone pricing kernel

Basic financial theory indicates that the ratio of the conditional density of the future value of a market index and the corresponding risk neutral density should be monotone, but a sizeable empirical literature finds otherwise. We therefore consider an option augmented density forecast of the market return obtained by transforming a baseline density forecast estimated from past excess returns so as to monotonize its ratio with a risk neutral density estimated from current option prices. To evaluate our procedure, we compare baseline and option augmented monthly density forecasts for the S&P 500 index over the period 1997–2013. We find that monotonizing the pricing kernel leads to a modest improvement in the calibration of density forecasts. Supplementary results supportive of this finding are given for market indices in France, Germany, Hong Kong, Japan and the UK.     

The short-term impact of director trading in UK closed-end funds

Most closed-end funds are transparent entities that hold securities that are actively traded in liquid markets. In such a setting, the argument that director transactions mitigate information asymmetry has very limited applicability. Our results provide support for the theory of Barber and Odean [2008. “All that Glitters: The Effect of Attention and News on the Buying Behavior of Individual and Institutional Investors.” Review of Financial Studies 21: 785–818]: retail investor decision-making is influenced by attention-grabbing events. Director purchases are one such attention-grabbing event and are associated with significant positive price returns – the magnitudes of which are linked to the size of the purchase, the size of the fund, and the investment mandate. Trading volumes increase at the time of the purchase but most of the initial price responses and trading volumes dissipate over the following 15 days.     

Evaluation of the adaptive market hypothesis as an evolutionary perspective on market efficiency: Evidence from the Tehran stock exchange

This study evaluates the existence of the adaptive market hypothesis (AMH) as an evolutionary alternative to the efficient market hypothesis (EMH) by applying daily returns on the TEPIX index in the Tehran stock exchange (TSE) in Iran. The data span of daily returns is from 1999 to 2013. In this paper four different tests in the form of two distinguished classes (linear and nonlinear) have been used to study adaptive behavior of returns. The results that were obtained from linear (automatic variance ratio and automatic portmanteau) and nonlinear (generalized spectral and McLeod–Li) tests represent the oscillatory manner of returns about dependency and independency which corresponds with the adaptive market hypothesis.     

Relationship between franking credits and the market risk premium: a comment

This paper examines two arguments presented in Gray and Hall (2006). First, that the generally used estimate of 0.06 for the market risk premium within the Officer version of the capital asset pricing model (CAPM) and the generally used estimate of 0.50 for the parameter ‘gamma’ within the Officer framework are jointly inconsistent with evidence concerning the market risk premium in the standard version of the CAPM. Second, that the first two of these parameter estimates are also jointly inconsistent with the observed cash dividend yield on the Australian market. To resolve these problems, Gray and Hall recommend setting gamma to zero. The present paper shows that the first argument does not account for the fact that imputation induces a reduction in the market risk premium as defined in the standard version of the CAPM. The present paper also shows that both arguments identify a problem that characterizes only parts of the Officer framework, and these parts are not generally used in Australia. Therefore, rather than suggesting that gamma should be zero, Gray and Hall's analysis identifies parts of the Officer framework that should be avoided.     

A perfect storm in the financial market

This study provides a model explaining how small changes in asset prices may disrupt an entire financial market. Based on the capital asset pricing model (CAPM), our model implies that during a market crash, asset price changes affect the relative distribution of the CAPM betas of individual assets and force all tradable assets to co-move. Using US stock market data, our empirical results are consistent with the model’s predictions. Overall, the study aids understanding of the price patterns of assets during substantial market downturns, such as financial crises.     

Linear beta pricing with inefficient benchmarks in a given factor structure*

ABSTRACT

We show the equivalence between the zero-beta version of a multi-factor arbitrage pricing model and a linear pricing model utilizing undiversified inefficient benchmarks in a given factor structure. The resulting linear model is a two-beta model, with one beta related to the inefficient benchmark and another adjusting for its inefficiency. This linear model shows that there are only two distinctive and computable sources of risk, affecting security expected returns, despite the existence of several risk factors. In a short empirical example we demonstrate that the model can be employed to provide guidance and allow researchers to test for the validity of their selection of the underlying risk factors driving variations in security returns.     

The prospects of BRIC countries: Testing weak-form market efficiency

The main purpose of the study is to determine whether the equity markets of Brazil, Russia, India and China (BRIC) may be considered weak-form efficient in recent years. The major findings using daily data and a bias-free statistical technique with a sample spanning from September 1995 to March 2010 indicate that the results from the last sub-periods, including the subprime crisis, support the belief that these markets may have been approaching a state of being fairly weak-form efficient, which reflects the future prospects of BRIC countries.     

Tests of the efficiency of the U.S. rights offering market: An option pricing approach

The efficiency of the U.S. market for stock purchase rights is empirically analyzed in an options framework, in which prices of rights, given the prices of underlying stock, are examined with regard to the possibilities of actually earning above-normal profits, considering the risk taken. Two neutral hedging tests for market efficiency, along with a simple buy-and-exercise trading strategy, are applied to daily traded rights data. Results from ex-post hedging tests suggest that the trading strategy based on the rights valuation model is able to differentiate between overpriced and underpriced rights so as to generate substantial book profits. The positive ex-ante hedge return, found to exist empirically, is completely eliminated once transaction costs are introduced, lending support for the efficient U.S. rights offering market on an after-transaction cost basis.     

A brief history of market efficiency

Every finance professional employs the concept of market efficiency. The theory, evidence and counter-evidence focus on a couple of dozen highly influential articles published during the twentieth century. We summarise the origins of and interlinkages between these contributions to the history of finance.     

Arbitrage violations and implied valuations: the option market

The ideas presented in this paper are those of the authors and not necessarily reflect the views of the National bank of Canada. Both authors thank the National Bank of Canada and the SSHRC of Canada for their help. Thanks are also due to Professor Y. Tian for his comments, and for participating, together with students of the Financial Engineering program at York University, in the data preparation and the execution of the Matlab programs. In this paper, we propose a necessary and sufficient condition for bid and ask prices of European options to be free of arbitrage, and derive from it an efficient numerical methodology to determine its satisfaction by a given set of prices. If the bid and ask prices satisfy the no-arbitrage (NA) condition, our methodology produces a vector of NA prices that lie between the bid and ask prices. Otherwise, our methodology generates a vector of arbitrage-free prices that is as close as possible, in some sense, to the bid–ask strip. The arbitrage-free prices detected by our methodology render the commonly used practice of using mid-points and then ‘cleaning’ arbitrage from them as unnecessary. Moreover, a vector of ‘cleaned’ prices obtained from mid-point prices may be outside the bid–ask spread even in an arbitrage-free market and, hence, in this case will not be representative of the current market. A new procedure of estimating implied valuation operators is also suggested here. This procedure is rooted in the economic properties of put and call prices and is based on Phillips and Taylor's approximation of a convex function. This approach is superior to common estimation techniques in that it produces an analytical expression for the implied valuation operator and is not data intensive as some other studies. Empirical findings for the new methods are documented and their economic implications are discussed.     

(How) has the market become more efficient?

Using a portfolio of Dow Jones Industrial Average index constituents and the index ETF, we document significant intraday deviations from the law of one price. These are especially pronounced at very short time intervals. The extent of deviations is related to volatility, liquidity, and transaction costs of both the index constituents and the ETF. Further, the influence of news arrival, and liquidity (volatility) shocks on the deviations persists for several hours. Finally, we document significant decline (by at least 80%) in the deviations between 1998 and 2010. We find that this decline is largely due to decimalization, the repeal of the uptick rule, and the introduction of automated updating of the NYSE order book. Overall, our findings indicate an increase in operational market efficiency.     

On the real estate market efficiency

This reseach reexamines the efficiency hypothesis of the real estate market using monthly data and the vector autoregressive (VAR) modelling technique. The tests focus on the causal linkage between real estate returns and a number of relevant financial and economic variables. An eight-by-eight VAR model is estimated using the FPE and the specific gravity criteria, in conjunction with an extensive series of specification tests. The empirical results distilled from system estimations suggest that the real estate market is efficient with respect to available information on the industrial production, the risk premia, the term structure of interest rates, and the monetary base. Movements in these variables are quickly and fully utilized by market agents, perhaps owing to the intensity with which their relationship with stock returns has been discussed in the literature and the popular media. However, the results also suggest the presence of a significant lagged relationship between real estate returns and fiscal policy moves, even when the paths through other potential determinants of these returns are taken into account. Of course, our finding that the fiscal policy measure is useful in predicting stock returns does not necessarily imply that the real estate market is inefficient. At a minimum, inefficiency is revealed only if a careful analysis of the budgetary process can help design a profitable (exploitable) trading strategy.     

Market impact: a systematic study of the high frequency options market

This paper deals with a fundamental subject that has seldom been addressed in recent years, that of market impact in the options market. Our analysis is based on a proprietary database of metaorders—large orders that are split into smaller pieces before being sent to the market—on one of the main Asian markets. In line with our previous work on the equity market [Said, E., Bel Hadj Ayed, A., Husson, A. and Abergel, F., Market impact: A systematic study of limit orders. Mark. Microstruct. Liq., 2018, 3(3&4), 1850008.], we propose an algorithmic approach to identify metaorders, based on some implied volatility parameters, the at the money forward volatility and at the money forward skew. In both cases, we obtain results similar to the now well-understood equity market: Square-Root Law, Fair Pricing Condition and Market Impact Dynamics.     

Overreaction in the Hong Kong stock market

Overreaction reported in the equity markets of the United States, Spain, and Brazil is also observed in the Hong Kong stock market. The “loser” portfolios of the 33 stocks in the Hang Seng Index (HSI), on average, outperform the “winner” portfolios by 9.9% 1 year after the formation periods. Besides its emphasis on the importance of the Hong Kong market in international investment, this paper is unique in some special features related to the overreaction study. Hong Kong has markets for index futures and stock futures. Only three stocks are used in the portfolios. All the stocks in the HSI have large market capitalization and liquidity and can be shorted with no up-tick rule. Unlike other studies in international stock markets, the “arbitrage” portfolio of buying the loser portfolio and shorting the winner portfolio can actually be formed with minimum cost and easy execution, which makes the overreaction phenomena in this study very powerful.     

Order book characteristics and the volume–volatility relation: Empirical evidence from a limit order market

Using unique data, we address the issue of price formation in a limit order market. A standard volume–volatility relation is documented with the number of trades acting as the important component of volume. The main contribution of the paper is to identify strong evidence that volume, volatility, and the volume–volatility relation are negatively related to the order book slope. These results are robust to the inclusion of several liquidity measures. A significant empirical relationship between the order book slope and the coefficient of variation in earnings forecasts by financial analysts suggests that the slope is proxying for disagreement among investors. Hence, our results support models where investor heterogeneity intensifies the volume–volatility relation.     

The optimal bid-ask price strategies of high-frequency trading and the effect on market liquidity

We propose a model for determining the optimal bid-ask spread strategy by a high-frequency trader (HFT) who has an informational advantage and receives information about the true value of a security. We employ an information cost function that includes volatility and the volume of the asset. Subsequently, we characterize the optimal bid-ask price strategies and obtain a stable bid-ask spread. We assume that orders submitted by low-frequency traders (LFTs) and news events arrive at the market with Poisson processes. Additionally, our model supports the trading of the two-sided quote in one period. We find that more LFTs and a higher exchange latency both hurt market liquidity. The HFT prefers to choose a two-sided quote to gain more profits while cautiously chooses a one-sided quote during times of high volatility. The model generates some testable implications with supporting empirical evidence from the NASDAQ-OMX Nordic Market.     

强制保险能否提高保险市场效率分析

本文以社会福利为衡量保险市场效率的标准,分析了实施强制保险是否有助于保险市场效率的提高。文章首先证明了在信息不对称的保险市场中存在着市场失灵现象;然后通过比较实施强制保险前后社会福利的差异,得出结论:实施强制保险有助于社会福利的改善,从而可以提高保险市场效率。