Mathematical programming methods of pattern classification

Mathematical programming methods of pattern classificatio

Anomalous price impact and the critical nature of liquidity in financial markets

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.Comment: 16 pages, 7 figure

How many independent bets are there?

The benefits of portfolio diversification is a central tenet implicit to modern financial theory and practice. Linked to diversification is the notion of breadth. Breadth is correctly thought of as the number of in- dependent bets available to an investor. Conventionally applications us- ing breadth frequently assume only the number of separate bets. There may be a large discrepancy between these two interpretations. We uti- lize a simple singular-value decomposition (SVD) and the Keiser-Gutman stopping criterion to select the integer-valued effective dimensionality of the correlation matrix of returns. In an emerging market such as South African we document an estimated breadth that is considerably lower than anticipated. This lack of diversification may be because of market concentration, exposure to the global commodity cycle and local currency volatility. We discuss some practical extensions to a more statistically correct interpretation of market breadth, and its theoretical implications for both global and domestic investors.Comment: Less technical rewrite. 12 Pages, 6 Figures (.eps

A simple scheme for allocating capital in a foreign exchange proprietary trading firm

We present a model of capital allocation in a foreign exchange proprietary trading firm. The owner allocates capital to individual traders, who operate within strict risk limits. Traders specialize in individual currencies, but are given discretion over their choice of trading rule. The owner provides the simple formula that determines position sizes – a formula that does not require estimation of the firm-level covariance matrix. We provide supporting empirical evidence of excess risk-adjusted returns to the firm-level portfolio, and we discuss a modification of the model in which the owner dictates the choice of trading rule

Client-contractor bargaining on net present value in project scheduling with limited resources

The client-contractor bargaining problem addressed here is in the context of a multi-mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity-on-Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two-party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights

The Sharpe ratio of estimated efficient portfolios

Investors often adopt mean-variance efficient portfolios for achieving superior risk-adjusted returns. However, such portfolios are sensitive to estimation errors, which affect portfolio performance. To understand the impact of estimation errors, I develop simple and intuitive formulas of the squared Sharpe ratio that investors should expect from estimated efficient portfolios. The new formulas show that the expected squared Sharpe ratio is a function of the length of the available data, the number of assets and the maximum attainable Sharpe ratio. My results enable the portfolio manager to assess the value of efficient portfolios as investment vehicles, given the investment environment

Intraday Patterns in the Cross-section of Stock Returns

Motivated by the literature on investment flows and optimal trading, we examine intraday predictability in the cross-section of stock returns. We find a striking pattern of return continuation at half-hour intervals that are exact multiples of a trading day, and this effect lasts for at least 40 trading days. Volume, order imbalance, volatility, and bid-ask spreads exhibit similar patterns, but do not explain the return patterns. We also show that short-term return reversal is driven by temporary liquidity imbalances lasting less than an hour and bid-ask bounce. Timing trades can reduce execution costs by the equivalent of the effective spread

Algorithms for flows over time with scheduling costs

Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering the arc; flows are time-varying. We consider a setting which is very standard within the transportation economic literature, but has received little attention from an algorithmic perspective. The flow consists of users who are able to choose their route but also their departure time, and who desire to arrive at their destination at a particular time, incurring a scheduling cost if they arrive earlier or later. The total cost of a user is then a combination of the time they spend commuting, and the scheduling cost they incur. We present a combinatorial algorithm for the natural optimization problem, that of minimizing the average total cost of all users (i.e., maximizing the social welfare). Based on this, we also show how to set tolls so that this optimal flow is induced as an equilibrium of the underlying game

Market ecologies: The effect of information on the interaction and profitability of technical trading strategies

Technical trading strategies make profits by identifying and exploiting patterns in market prices—patterns generated by the interaction of market participants. Using a model market populated by individuals using a range of trading rules we show that the presence of technical traders may be beneficial, in some cases reducing volatility and increasing price efficiency. In particular, contrarian traders who base their decisions on high frequency data have the largest positive effect. It is also found that if technical traders condition their actions using ‘real time’ information, they partially emulate arbitrageurs and make positive profits