An optimal execution problem with market impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales; otherwise the value function is continuous. Moreover, we show the semigroup property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton–Jacobi–Bellman equation. We present some examples where the form of the optimal strategy changes completely, depending on the amount of the trader’s security holdings, and where optimal strategies in the Black–Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.     

Robust multivariate portfolio choice with stochastic covariance in the presence of ambiguity

This paper provides the optimal multivariate intertemporal portfolio for an ambiguity averse investor, who has access to stocks and derivative markets, in closed form. The stock prices follow stochastic covariance processes and the investor can have different levels of uncertainty about the diffusion parts of the stocks and the covariance structure. We find strong evidence that the optimal exposures to stock and covariance risks are significantly affected by ambiguity aversion. Welfare analyses show that investors who ignore model uncertainty incur large losses, larger than those suffered under the embedded one-dimensional cases. We further confirm large welfare losses from not trading in derivatives as well as ignoring intertemporal hedging, we study the impact of ambiguity in that regard and justify the importance of including these factors in the scope of portfolio optimization. Conditions are provided for a well-behaved solution in general, together with verification theorems for the incomplete market case.     

股权结构代理成本与外部审计需求

本文基于一个两时点大股东掠夺模型,考察了股权结构、代理成本与外部审计需求之间的关系。我们的模型分析结果表明,第一大股东持股比例与企业价值成U型曲线关系,而与外部审计需求成倒U型曲线关系。即:代理成本较高的上市公司更有可能聘请高质量的外部审计师,以降低代理成本,提高公司市场价值。我们以中国A股上市公司2001和2002年的数据,对上述结论进行了实证检验并得到支持,本文分析还表明,债务融资与外部审计在降低代理成本方面具有相互替代性。     

The Post‐Cost Profitability of Momentum Trading Strategies: Further Evidence from the UK

This paper examines the post‐cost profitability of momentum trading strategies in the UK over the period 1988–2003 and provides direct evidence on stock concentration, turnover and trading cost associated with the strategy. We find that after factoring out transaction costs the profitability of the momentum strategy disappears for shorter horizons but remains for longer horizons. Indeed, for ranking and holding periods up to 6‐months, profitable momentum returns would not be available to most average investors as the cost of implementation outweighs the possible returns. However, we find post‐cost profitability for ranking and/or holding periods beyond 6 months as portfolio turnover and its associated cost reduces. We find similar results for a sub‐sample of relatively large and liquid stocks.     

Market or limit orders?

In this paper we investigate the problem of optimal order placement of an asset listed on an exchange using both market and limit orders in a simple model of market dynamics. We seek to understand under which settings it is optimal to place limit or market orders. Limit orders typically lower transaction costs but increase the risk of incomplete order execution, whereas market orders typically have higher transaction costs but are guaranteed to be executed. Rather than considering order book dynamics to determine if a limit order is executed we rely on price dynamics for this. We look at implementation shortfall in this setup with market impact of trading and propose a dynamic program to find the optimal placement of both market and limit orders for risk-neutral and risk-averse traders. With this we find a bound on the expected cost of trading and show that a trader who behaves optimally should always expect to pay less to trade less. We then solve the dynamic program numerically and examine optimal order placement strategies. We find that the decision between market and limit orders is sensitive to price volatility, risk aversion, and trading costs.     

How do bond investors perceive dividend payouts?

We explore how bond investors view corporate cash distributions through dividends and how that view influences corporate cost of debt. Explaining between 45 and 67 percent of variance in credit spreads at the time of issuance, our model reveals a non-linear association between dividend payouts and investment return expected by bondholders. In particular, while bondholders view cash disbursements in small amounts as a positive signal, large dividend payouts are viewed negatively. Our results thus provide support for both the signaling hypothesis and for the agency-cost-of-debt hypothesis. The results are robust even after controlling for firm size, growth opportunities, profitability, leverage, business risk, asset tangibility, and term structure. Exploiting the 2003 dividend tax cut as an exogenous shock, we demonstrate that our results are not vulnerable to endogeneity problems. Finally, we find no evidence of corporations timing the payouts strategically to influence the cost of debt.     

Endogenous Information Acquisition with Cournot Competition

This paper studies information production in a model where both entry of analysts and their optimal information quality is endogenous. We show existence of the Bayesian–Nash equilibrium and solve for it in closed form. The model displays rich behavior. In particular, we find that the precision of an individual signal will always be bounded from above by the precision of the prior belief on payoff uncertainty. Furthermore, we give examples that contradict the naive intuition about information acquisition. For instance, we show how a change in the cost structure that makes information cheaper decreases price informativeness, while at the same time market liquidity and the amount of resources society spends on information acquisition can change either way. The model gives a simple, fully rational explanation on why the number of analysts following a stock can be quite large. Endogenizing the cost of information by allowing the manager to choose an optimal informational policy, we find a variety of optima that depend discontinuously on the model parameters. As a consequence, among two similar firms, one may find it optimal to attract many analysts, the other will cooperate with only a few.I am greatly indebted to Antonio Bernardo and Avanidhar Subrahmanyam, whose support, encouragement, insight, and many valuable comments made this paper possible. In addition, I also thank Justin Chan, Sudipto Dasgupta, Jason Hsu, Martin Nielsen, and Elena Sernova, the editor and an anonymous referee.     

Current account sustainability in the US: What did we really know about it?

We analyze the sustainability of the US current account (CA) deficit by means of unit-root tests. First, we argue that there are several reasons to believe that the CA may follow a non-linear mean-reversion behavior under the null of stationarity. Using a non-linear ESTAR model we can reject the null of non-stationarity favoring the sustainability hypothesis. Second, we ask whether unit-root tests are a useful indicator of sustainability by comparing in-sample results for the 1960–2004 period to the developments observed up to the end of 2008. We find that the non-linear model outperforms the linear and random walk models in terms of forecast performance. The large shocks to the CA observed in the last five years induced a faster speed of mean reversion, ensuring the necessary adjustment to meet the inter-temporal budget constraint.     

On derivatives with illiquid underlying and market manipulation

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren [Appl. Math. Finance, 2003, 10(1), 1–18]. Specifically, we consider a financial market model with several strategically interacting players who hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish the existence and uniqueness of equilibrium results for risk-neutral and CARA investors and show that the equilibrium dynamics can be characterized in terms of a coupled system of possibly nonlinear PDEs. For the linear cost function used by Almgren, we obtain a (semi) closed-form solution. Analysing this solution, we show how market manipulation can be reduced.     

Contracting costs and the window of opportunity for straight debt issues

We analyze whether fluctuation in economy-wide factors cause time-series variation in the contracting costs of moral hazard, adverse selection, and financial distress for a sample of straight debt issues. We find that the announcement period abnormal returns to debt issues are more negative in periods of higher interest rates and in industry downturns. When we partition the impact of each issue- and firm-specific measure of contracting costs across high and low levels of each economy-wide variable, we find that only the measures of agency cost are significant in general, and measures of financial distress become relevant for those debt issues that constitute a leverage increase for the firms.     

Underpricing, Overhang, and the Cost of Going Public to Preexisting Shareholders

Abstract:  IPO underpricing has been extensively studied; however, its impact on the wealth of preexisting shareholders has not been closely examined. We address the question of whether or not periods of high underpricing adversely affect preexisting shareholders. We find that high levels of underpricing are associated with increased share retention, which effectively offsets much of the potential cost. Overall, we find that the percentage of shareholder wealth lost is surprisingly stable over time, unlike underpricing itself. We also find that many factors known to be related to underpricing are not significant determinants of the cost of going public to preexisting owners.     

The impact of cost allocation errors on price and product-mix decisions

We use simulations to examine the impact of cost allocation errors on pricing and product-mix decisions. We compare the imperfect cost allocation of cost systems based on heuristics to the ideal cost allocation of a benchmark model. First, we find that more complex cost systems are associated with substantially lower profit errors. Second, we decompose the profit error and find that production quantity errors are larger than product portfolio errors indicating that reducing product portfolio errors is less critical in designing cost systems. We also document that overproduction errors are larger than underproduction errors and errors from keeping unprofitable products are larger than errors from dropping profitable products suggesting that cost systems tend to underestimate full costs. Third, we find that profit errors increase for more complex cost systems as resource sharing levels rise, which is an interesting counter intuitive result.     

Robust portfolio choice with ambiguity and learning about return predictability

We analyze the optimal stock-bond portfolio under both learning and ambiguity aversion. Stock returns are predictable by an observable and an unobservable predictor, and the investor has to learn about the latter. Furthermore, the investor is ambiguity-averse and has a preference for investment strategies that are robust to model misspecifications. We derive a closed-form solution for the optimal robust investment strategy. We find that both learning and ambiguity aversion impact the level and structure of the optimal stock investment. Suboptimal strategies resulting either from not learning or from not considering ambiguity can lead to economically significant losses.     

Focusing on the worst state for robust investing

Despite its shortcomings, the Markowitz model remains the norm for asset allocation and portfolio construction. A major issue involves sensitivity of the model's solution to its input parameters. The prevailing approach employed by practitioners to overcome this problem is to use worst-case optimization. Generally, these methods have been adopted without incorporating equity market behavior and we believe that an analysis is necessary. Therefore, in this paper, we present the importance of market information during the worst state for achieving robust performance. We focus on the equity market and find that the optimal portfolio in a market with multiple states is the portfolio with robust returns and observe that focusing on the worst market state provides robust returns. Furthermore, we propose alternative robust approaches that emphasize returns during market downside periods without solving worst-case optimization problems. Through our analyses, we demonstrate the value of focusing on the worst market state and as a result find support for the value of worst-case optimization for achieving portfolio robustness.     

Do Convertible Bond Issuers Cater to Investor Demand?

We examine the impact of fluctuations in investor demand for convertible securities on convertible bond issue volumes, pricing, and design. We find evidence of a positive impact of investor demand proxies on convertible bond issue volumes. We also document significantly lower convertible bond underpricing in periods with higher investor demand. The results hold in a variety of specifications, and are robust to controlling for firm‐specific and macroeconomic financing cost proxies. However, we obtain only limited evidence that issuers adjust the design of their convertible bond offerings in response to investor demand.     

Technological advances and the decision to invest

Technological advances impact a firm’s investment decision, as they affect the investment cost. They can also affect the profitability due to demand shocks. We study a firm’s optimal investment decision when technological advances occur as surprises and induce uncertain reductions in the investment cost and in earnings. Despite this complex setting we derive closed-form solutions for the investment option value and the investment threshold. When technological advances only impact the investment cost, we demonstrate significant contributions compared to existing research, which restricts the analysis by keeping the expected investment cost path constant. For example, we show that, albeit the investment threshold is constant, the option value is very sensitive in the expected impact of technological advances. Leaving the restrictive setting, we obtain more intuitive results, e.g. that more frequent technological advances increase the option value. When technological advances impact future earnings we find important long-term effects: the investment threshold increases, whereas the option value decreases. Finally, earnings volatility postpones investment, while uncertainty due to technological advances expedites investment.     

The Behavior of Stock Prices Around Institutional Trades

All trades executed by 37 large investment management firms from July 1986 to December 1988 are used to study the price impact and execution cost of the entire sequence (“package”) of trades that we interpret as an order. We find that market impact and trading cost are related to firm capitalization, relative package size, and, most importantly, to the identity of the management firm behind the trade. Money managers with high demands for immediacy tend to be associated with larger market impact.     

Liquidity and conditional portfolio choice: A nonparametric investigation

This paper studies the relation between liquidity and optimal portfolio allocations. Given that the portfolio problem of a constant relative risk aversion investor does not have a closed-form solution, we use a nonparametric approach to estimate the optimal allocations. Using a sample of NYSE stocks from 1963–2000, we find that the optimal portfolio weight in small stocks is strongly increasing in liquidity at short daily and weekly horizons. This result is consistent for three different measures of liquidity: price impact, dollar volume, and turnover. However, liquidity does not influence the optimal portfolio choice for large stocks, nor for longer monthly investment horizons.     

Optimal and equilibrium execution strategies with generalized price impact

This paper examines the execution problems of large traders with a generalized price impact. Constructing two related models in a discrete-time setting, we solve these problems by applying the backward induction method of dynamic programming. In the first problem, we formulate the expected utility maximization problem of a single large trader as a Markov decision process and derive an optimal execution strategy. Then, in the second model, we formulate the expected utility maximization problem of two large traders as a Markov game and derive an equilibrium execution strategy at a Markov perfect equilibrium. Both of these two models enable us to investigate how the execution strategies and trade performances of a large trader are affected by the existence of other traders. Moreover, we find that these optimal and equilibrium execution strategies become deterministic when the total execution volumes of non-large traders are deterministic. We also show, by some numerical examples, the comparative statics results with respect to several problem parameters.     

Stress testing German banks against a global credit crunch

This paper investigates the impact of a global credit crunch on the corporate credit portfolios of large German banks using a two-stage approach. First, a macroeconometric simulation model (NiGEM) is used to forecast the impact of a substantial increase in the cost of business capital for firms worldwide in three particularly export-oriented industry sectors in Germany. Second, the impact of this economic multi-sector stress on bank credit portfolios is captured by a state-of-the-art Credit Metrics-type portfolio model with sector-dependent unobservable risk factors as drivers of the systematic risk. In our assessment of capital ratios, we confirm that both the increase of the capital charge for the unexpected loss and the increase in banks’ expected losses need to be considered. We also find that the availability of granular information at the level of borrower-specific probabilities of default has a significant impact on the stress test results.