Asymptotic arbitrage with small transaction costs

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ _n on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λ _n -consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λ _n >0 on market n; there does not exist any form of asymptotic arbitrage. In one case, (λ _n ) can even converge to 0, but not too fast.     

Risk arbitrage and hedging to acceptability under transaction costs

The classical discrete-time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing convex transaction costs and assuming that increments of the portfolio process belong to the sum of a solvency set and a family of multivariate acceptable positions, e.g. with respect to a dynamic risk measure. We describe the sets of superhedging prices, formulate several no (risk) arbitrage conditions and explore connections between them. In the special case when multivariate positions are converted into a single fixed asset, our framework turns into the no-good-deals setting. However, in general, the possibilities of assessing the risk with respect to any asset or a basket of assets lead to a decrease of superhedging prices and the no-arbitrage conditions become stronger. The mathematical techniques rely on results for unbounded and possibly non-closed random sets in Euclidean space.

     

Price reversal,transaction costs,and arbitrage profits in the real estate securities market

This paper studies the return reversals of exchange traded real estate securities using an arbitrage portfolio approach. Using the approach, we find that there exist significant return reversals in such securities. These return reversals could be exploited by arbitrage traders if trading costs can be ignored. However, the arbitrage profits disappear after deducting trading costs and taking into account the implicit cost of bid-ask spread. Thus, the real estate securities market is efficient at weekly intervals in the sense that one could not exploit the price reversals via some simple trading rules.     

Inference,arbitrage, and asset price volatility

Does the presence of arbitrageurs decrease equilibrium asset price volatility? I study an economy with arbitrageurs, informed investors, and noise traders. Arbitrageurs face a trade-off between “inference” and “arbitrage”: they would like to buy assets in response to temporary price declines—the arbitrage effect—but sell when prices decline permanently—the inference effect. In equilibrium, the presence of arbitrageurs increases volatility when the inference effect dominates the arbitrage effect. From a technical point of view, the paper offers closed form solutions to a dynamic equilibrium model with asymmetric information and non-Gaussian priors.     

Nonnegative wealth, absence of arbitrage, and feasible consumption plans

A restriction to nonnegative wealth is sufficient to precludeall arbitrage opportunities in financial models that have noarbitrage in limits of simple strategies. Imposing nonnegativewealth does not constrain agents from making the choice theywould make under the standard integrability condition. Theseconclusions do not depend on whether markets are complete.     

Speculative trading,prospect theory and transaction costs

A speculative agent with prospect theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset to maximise the expected utility of the round-trip profit net of transaction costs. The optimisation problem is formulated as a sequential optimal stopping problem, and we provide a complete characterisation of the solution. Depending on the preference and market parameters, the optimal strategy can be “buy and hold”, “buy low, sell high”, “buy high, sell higher” or “no trading”. Behavioural preference and market friction interact in a subtle way which yields surprising implications on the agent’s trading patterns. For example, increasing the market entry fee does not necessarily curb speculative trading, but instead may induce a higher reference point under which the agent becomes more risk-seeking and in turn is more likely to trade.

     

Option arbitrage and strategy with large price changes

Arbitrage pricing theorems are derived for options on stocks with jumps as a well as local movements. The resulting valuation formulas depend on observable variables only. Closed-form valuation expressions are obtained in the case of large positive and negative jumps. These results translate into a simple algebra for characterizing the risk of arbitrage and investment portfolios. A continuous-time formulation of the infinite variance hypothesis leads to isomorphic pricing expressions.     

On the game interpretation of a shadow price process in utility maximization problems under transaction costs

To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S ^?, lying in the bid/ask price interval $[\underline{S}, \overline{S}]$ . Such a process S ^? is called a shadow price if it provides the same optimal utility value as in the original model with bid-ask spread. We call S ^? a generalized shadow price if the above property is true for the relaxed utility function in the frictionless model. This relaxation is defined as the lower semicontinuous envelope of the original utility, considered as a function on the set $[\underline{S}, \overline{S}]$ , equipped with some natural weak topology. We prove the existence of a generalized shadow price under rather weak assumptions and mark its relation to a saddle point of the trader/market zero-sum game, determined by the relaxed utility function. The relation of the notion of a shadow price to its generalization is illustrated by several examples. Also, we briefly discuss the interpretation of shadow prices via Lagrange duality.     

Hysteresis bands on returns,holding period and transaction costs

In the presence of transactions costs, no matter how small, arbitrage activity does not necessarily render equal all riskless rates of return. When two such rates follow stochastic processes, it is not optimal immediately to arbitrage out any discrepancy that arises between them. The reason is that immediate arbitrage would induce a definite expenditure of transactions costs whereas, without arbitrage intervention, there exists some, perhaps sufficient, probability that these two interest rates will come back together without any costs having been incurred. Hence, one can surmise that at equilibrium the financial market will permit the coexistence of two riskless rates that are not equal to each other. For analogous reasons, randomly fluctuating expected rates of return on risky assets will be allowed to differ even after correction for risk, leading to important violations of the Capital Asset Pricing Model. The combination of randomness in expected rates of return and proportional transactions costs is a serious blow to existing frictionless pricing models.     

A new estimate of transaction costs

Transaction costs are important for a host of empirical analysesfrom market efficiency to international market research. Buttransaction costs estimates are not always available, or whereavailable, are cumbersome to use and expensive to purchase.We present a model that requires only the time series of dailysecurity returns to endogenously estimate the effective transactioncosts for any firm, exchange, or time period. The feature ofthe data that allows for the estimation of transaction costsis the incidence of zero returns. Incorporating zero returnsin the return-generating process, the model provides continuousestimates of average round-trip transaction costs from 1963to 1990 that are 1.2% and 10.3% for large and small decile firms,respectively. These estimates are highly correlated (85%), withthe most commonly used transaction cost estimators.     

Legal constraints,transaction costs and the evaluation of mutual funds

The paper considers the legal restrictions on investment and the transaction costs related to optimal turnover that affect mutual funds. A method is developed for mutual fund performance evaluation when both these factors are included in the reference portfolios, and it is applied to a sample of available Spanish mutual funds. The poor performance results reflected in previous studies are not significantly modified. However, when net returns on the reference portfolios are used in the evaluation the performance is clearly improved.     

International equity portfolio allocations and transaction costs

In spite of the critical role of transaction cost, there are not many papers that explicitly examine its influence on international equity portfolio allocation decisions. Using bilateral cross-country equity portfolio investment data and three direct measures of transaction costs for 36 countries, we provide evidence that markets where transaction costs are lower attract greater equity portfolio investments. The results imply that future research on international equity portfolio diversification cannot afford to ignore the role of transaction costs, and policy makers, especially in emerging markets, will have to reduce transaction costs to attract higher levels of foreign equity portfolio investments.     

Shadow prices,fractional Brownian motion,and portfolio optimisation under transaction costs

The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes), and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, we are able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market.     

Trading costs and price discovery

The price discovery roles of a set of related markets or securities have been investigated in many different settings where trading costs effect is often commingled with other trading arrangement factors. In Hong Kong, regular futures and mini futures contracts as well as their underlying spot asset are all traded on a same electronic trading platform. The trading arrangements thus provide us with a unique setting where we can isolate the impacts of transaction costs on price discovery. Using Hasbrouck’s (J Finance 50:1175–1199, 1995) information share approach, it is found that in Hong Kong, the regular futures contracts market plays a dominant role in price discovery while the mini futures and cash index markets play minor roles. The results in this paper provide an unequivocal support to the trading costs hypothesis.     

Conditions on option prices for absence of arbitrage and exact calibration

Under the assumption of absence of arbitrage, European option quotes on a given asset must satisfy well-known inequalities, which have been described in the landmark paper of Merton [Merton, R., 1973. Theory of rational option pricing. Bell Journal of Economics and Management Science 4 (1), 141–183]. If we further assume that there is no interest rate volatility and that the underlying asset continuously pays deterministic dividends, cross-maturity inequalities must also be satisfied by the bid and ask option prices.     

Technical trading revisited: False discoveries,persistence tests,and transaction costs

We revisit the apparent historical success of technical trading rules on daily prices of the Dow Jones Industrial Average index from 1897 to 2011, and we use the false discovery rate (FDR) as a new approach to data snooping. The advantage of the FDR over existing methods is that it selects more outperforming rules, which allows diversifying against model uncertainty. Persistence tests show that, even with the more powerful FDR technique, an investor would never have been able to select ex ante the future best-performing rules. Moreover, even in-sample, the performance is completely offset by the introduction of low transaction costs. Overall, our results seriously call into question the economic value of technical trading rules that has been reported for early periods.     

Trends and determinants of Australian managed fund transaction costs

The present paper examines the often-overlooked managed fund fee that is incurred when investors enter and exit managed fund products. The present paper documents that transaction costs for investors, measured by the application-redemption spread, are above stock market brokerage rates although they have declined since 1995. The study analyses the relationship between this transaction fee and several variables. In summary, retail fund transaction costs are positively related to retail funds’ assets under management, whilst this relationship is negative for larger wholesale funds, consistent with economies of scale. Direct entry and exit fees and initial commissions are positively related to transaction costs which raises the possibility that the commissions are used to levy soft-dollar payments. The paper also documents a relationship between transaction costs and fund flows which differs between retail and wholesale funds. Overall, the findings are consistent with the proposition that the various fees are used by managers as interchangeable and the different fee regimes reflect different products and markets.     

Market viability via absence of arbitrage of the first kind

It is shown that, in a semimartingale financial market model, there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.     

Portfolio revision under mean-variance and mean-CVaR with transaction costs

The portfolio revision process usually begins with a portfolio of assets rather than cash. As a result, some assets must be liquidated to permit investment in other assets, incurring transaction costs that should be directly integrated into the portfolio optimization problem. This paper discusses and analyzes the impact of transaction costs on the optimal portfolio under mean-variance and mean-conditional value-at-risk strategies. In addition, we present some analytical solutions and empirical evidence for some special situations to understand the impact of transaction costs on the portfolio revision process.