Optimal investment and hedging under partial and inside information

This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time $0$ of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy

Optimal investment and hedging under partial and inside information

This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time $0$ of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy

Incentive Contracts and Hedge Fund Management: A Numerical Evaluation Procedure

The behavior of a hedge-fund manager naturally depends on her compensation scheme, her preferences, and constraints on her risk-taking. We propose a numerical method which can be used to analyze the impact of these influences. The model leads to several interesting and novel results concerning her risk-taking and other managerial decisions. We are able to relate our results to partial results in the literature and show how they fit in a more general context. We also allow the manager to voluntarily shutdown the fund as well as enhancing the fund’s Sharpe Ratio through additional effort. Both these extensions generate additional insights. Throughout the paper, we find that even slight changes in the compensation structure or the extent of managerial discretion can lead to drastic changes in her risk-taking.

Incentive Contracts and Hedge Fund Management

This paper investigates dynamically optimal risk-taking by an expected-utility maximizing manager of a hedge fund. We examine the effects of variations on a compensation structure that includes a percentage management fee, a performance incentive for exceeding a specified highwater mark, and managerial ownership of fund shares. In our basic model, there is an exogenous liquidation barrier where the fund is shut down due to poor performance. We also consider extensions where the manager can voluntarily choose to shut down the fund as well as to enhance the fund’s Sharpe Ratio through additional effort. We find managerial risk-taking which differs considerably from the optimal risk-taking for a fund investor with the same utility function. In some portions of the state space, the manager takes extreme risks. In another area, she pursues a lock-in style strategy. Indeed, the manager’s optimal behavior even results in a trimodal return distribution. We find that seemingly minor changes in the compensation structure can have major implications for risk-taking. Additionally, we are able to compare results from our more general model with those from several recent papers that turn out to be focused on differing parts of the larger picture.

Arbitrage and Control Problems in Finance. Presentation.

The theory of asset pricing takes its roots in the Arrow-Debreu model (see,for instance, Debreu 1959, Chap. 7), the Black and Scholes (1973) formula,and the Cox and Ross (1976) linear pricing model. This theory and its link to arbitrage has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1981, 1983), and Du¢e and Huang (1986). In these models, security markets are assumed to be frictionless: securities can be sold short in unlimited amounts, the borrowing and lending rates are equal, and there is no transaction cost. The main result is that the price process of traded securities is arbitrage free if and only if there exists some equivalent probability measure that transforms it into a martingale, when normalized by the numeraire. Contingent claims can then be priced by taking the expected value of their (normalized) payo§ with respect to any equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage and it can be perfectly hedged (i.e. duplicated) by dynamic trading. When the markets are dynamically complete, there is only one such a and any contingent claim is priced by arbitrage. The of each state of the world for this probability measure can be interpreted as the state price of the economy (the prices of $1 tomorrow in that state of the world) as well as the marginal utilities (for consumption in that state of the world) of rational agents maximizing their expected utility.arbitrage, control problem

Portfolio Performance Gauging in Discrete Time Using a Luenberger Productivity Indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (Fama and French 1996; 1997) using US monthly data from January 1931 to August 2007.shortage function, mean-variance, mean-variance-skewness, efficient portfolios, Luenberger portfolio productivity indicator

A dynamic programming approach to constrained portfolios

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption

CEO Personal Attributes and Corporate Decisions

This thesis examines the effect of CEOs’ personal attributes on CEOs’ optimistic behaviour and further investigates their effect on corporate leasing and hedging decisions. We integrate behavioural finance with management, leadership and psychological approaches to provide a better understanding of the influence of personal attributes on CEO optimistic behaviour and decision making. By investigating 248 CEOs who worked with the UK FTSE 100 firms from 2000 to 2013, we find that CEO personal attributes (traits, skills & experiences, and networking) do cultivate CEOs’ optimistic behaviour (acquisitiveness in the Mergers and Acquisitions (M&A) market). CEO personal traits that were examined in this study are age, gender, nationality and marital status. We find (chapter 2) that for CEO personal traits; younger, male, married and UK nationality CEOs are likely to be optimistic. CEO skills and experiences (e.g. their educational background (MBA, or PhD holder), founder status, financial literacy, duality, tenure as CEO, and emoluments) have also been found to have significant positive relationships with CEO optimism. In the case of CEO networking attributes, we examine CEOs’ internal networking (tenure with the firm, and internal promotion), and CEO external networking ties (external directorships, and social networking prestige) and find that CEO networking ties have a significant positive influence on triggering CEO optimistic behaviour. In addition, we propose three personal attributes indexes, namely Traits Index (TI), Skills and Experiences Index (SEI), and Networking Index (NI). Once again all the indexes have a significant influence on cultivating CEO optimistic behaviour. This thesis adds to the growing literature on behavioural finance by proposing an alternative proxy to managerial optimism (chapter 2) – the CEO Optimism Index (CEOOI) - and by investigating the influence of CEOOI on corporate decisions such as corporate leasing (chapter 3) and hedging decisions (chapter 4). This study uses manually collected information relating to Mergers and Acquisitions, Stock Option exercise behaviour, Insider Transaction and CEO personal attributes. In addition, we also manually collected data on operating lease, finance lease and total lease for corporate leasing analysis (chapter 3) and the derivative instruments data for a study of corporate hedging (chapter 4). The results (chapter 3) suggest that optimistic CEOs tend to use more lease financing. This finding is in line with the notion that optimistic CEOs are reluctant to raise external funding by issuing new equity as they believe that the capital market tends to undervalue their firms (Heaton, 2002). Additionally, since optimistic CEOs are highly confident of their own ability to bring in future earnings, they are unwilling to share the potential earnings with new equity holders and avoid this by choosing lease financing (lease is a type of debt). Hedging decisions results (chapter 4) indicate that optimistic CEOs employ more financial derivatives to hedge potential firm risks. Optimistic CEOs have high self-confidence, are committed to the firm’s good outcome and believe they themselves can control the firm’s future earnings; hence they use derivative instruments to control and reduce the firm’s cash flow volatility to deliver more predictable outcomes. Our findings provide evidence that CEOs’ personal attributes and optimistic behaviour affected corporate leasing and hedging decisions. Our study suggests that recognizing the presence and importance of CEO personal behaviour will help bridge the gap between the theory and practice of corporate decisions

Why Do Firms Engage in Selective Hedging?

Surveys of corporate risk management document that selective hedging, where managers incorporate their market views into firms’ hedging programs, is widespread in the U.S. and other countries. Stulz (1996) argues that selective hedging could enhance the value of firms that possess an information advantage relative to the market and have the financial strength to withstand the additional risk from market timing. We study the practice of selective hedging in a 10-year sample of North American gold mining firms and find that selective hedging is most prevalent among firms that are least likely to meet these valuemaximizing criteria -- (a) smaller firms, i.e., firms that are least likely to have private information about future gold prices; and (b) firms that are closest to financial distress. The latter finding provides support for the alternative possibility suggested by Stulz that selective hedging may also be driven by asset substitution motives. We detect weak relationships between selective hedging and some corporate governance measures, especially board size, but find no evidence of a link between selective hedging and managerial compensation.Corporate risk management, selective hedging, speculation, financial distress, corporate governance, managerial compensation

Real World Pricing of Long Term Contracts

Long dated contingent claims are relevant in insurance, pension fund management and derivative pricing. This paper proposes a paradigm shift in the valuation of long term contracts, away from classical no-arbitrage pricing towards pricing under the real world probability measure. In contrast to risk neutral pricing, the long term excess return of the equity market, known as the equity premium, is taken into account. Further, instead of the savings account, the numeraire portfolio isused, as the fundamental unit of value in the analysis. The numeraire portfolio is the strictly positive, tradable portfolio that when used as benchmark makes all benchmarked non negative portfolios supermartingales, which means intuitively that these are downward trending or at least trendless. Furthermore, the benchmarked real world price of a benchmarked claimis defined to be its real world conditional expectation. This yields the minimal possible price for its hedgable part and minimizes the variance of the benchmarked hedge error. The pooled total benchmarked replication error of a large insurance company or bank essentially vanishes due to diversification. Interestingly, in long terml iability and asset valuation, real world pricing can lead to significantly lower prices than suggested by classical no-arbitragea rguments. Moreover, since the existence of some equivalent risk neutral probability measure is no longer required, a wider and more realistic modeling framework is available for exploration. Classical actuarial and risk neutral pricing emerge as special cases of real world pricing.long term pricing; real world pricing; risk neutral pricing; numeraire portfolio; law of the minimal price; strong arbitrage; hedges imulation; diversification; liquidity premium