The World of Risk Management

The following sections are included:

• CONTENTS

• INTRODUCTION

• PRACTITIONER'S DIGEST

This paper proposes a functional approach to designing and managing the financial systems of countries, regions, firms, households, and other entities. It is a synthesis of the neoclassical, neo-institutional, and behavioral perspectives. Neoclassical theory is an ideal driver to link science and global practice in finance because its prescriptions are robust across time and geopolitical borders. By itself, however, neoclassical theory provides little prescription or prediction of the institutional structure of financial systems—that is, the specific kinds of financial intermediaries, markets, and regulatory bodies that will or should evolve in response to underlying changes in technology, politics, demographics, and cultural norms. The neoclassical model therefore offers important, but incomplete, guidance to decision makers seeking to understand and manage the process of institutional change. In accomplishing this task, the neo-institutional and behavioral perspectives can be very useful. In this proposed synthesis of the three approaches, functional and structural finance (FSF), institutional structure is endogenous. When particular transaction costs or behavioral patterns produce large departures from the predictions of the ideal frictionless neoclassical equilibrium for a given institutional structure, new institutions tend to develop that partially offset the resulting inefficiencies. In the longer run, after institutional structures have had time to fully develop, the predictions of the neoclassical model will be approximately valid for asset prices and resource allocations. Through a series of examples, the paper sets out the reasoning behind the FSF synthesis and illustrates its application.

Risk management techniques used in banks and trading floors are generally not applicable to insurance companies. Risk measures and risk monitoring approaches must be developed to respond to the challenges to the insurance industry. This paper describes the current risk management practices for both life and general insurance businesses, and proposes the corporate model approach that extends the present approaches to provide corporate management solutions, enterprise risk management in particular, for insurers.

We introduce liquidity into the standard mean–variance portfolio optimization framework by defining several measures of liquidity and then constructing three-dimensional mean–variance–liquidity frontiers in three ways: liquidity filtering, liquidity constraints, and a mean–variance–liquidity objective function. We show that portfolios close to each other on the traditional mean–variance efficient frontier can differ substantially in their liquidity characteristics. In a simple empirical example, the liquidity exposure of mean–variance efficient portfolios changes dramatically from month to month, and even simple forms of liquidity optimization can yield significant benefits in reducing a portfolio's liquidity-risk exposure without sacrificing a great deal of expected return per unit risk.

To maintain constant dollar risk, an investor concerned with his terminal wealth must sell when the stock market rises and buy when it falls. Although an asset with constant dollar risk doesn't exist in nature, it can be approximated with actual investment positions.

Traditional portfolio optimality criteria often have serious theoretical or practical limitations. A financial planning portfolio choice framework consisting of a resampled efficient portfolio set and multiperiod geometric mean analysis is a practical alternative for many situations of investment interest. While Monte Carlo financial planning is a more flexible framework, geometric mean analysis may be less error prone, theoretically justifiable, and convenient. Controversies that have limited applications of geometric mean analysis are resolvable by improved understanding of distributional properties and rational decision-making issues. The geometric mean is also useful in rationalizing a number of investment paradoxes.

Derivative security pricing and risk measurement relies increasingly on lattice representations of stochastic processes, which are a discrete approximation of the movement of the underlying securities. Pricing is undertaken by summation of node values on the lattice. When the lattice is large (which is the case when high accuracy is required), exhaustive enumeration of the nodes becomes prohibitively costly. Instead,Monte Carlo simulation is used to estimate the lattice value by sampling appropriately from the nodes. Most sampling methods become extremely error-prone in situations where the node values vary widely. This paper presents a Markov chain Monte Carlo scheme, adapted from Sinclair and Jerrum (Information and Computation 82 (1989)), that is able to overcome this problem, provided some partial (possibly very inaccurate) information about the lattice sum is available. This partial information is used to direct the sampling, in similar fashion to traditional importance sampling methods. The key difference is that the algorithm allows backtracking on the lattice, which acts in a “self-correcting” manner to minimize the bias in the importance sampling.

One of the underlying assumptions of the Fundamental Law of Active Management is that the active risk of an active investment strategy equates estimated tracking error by a risk model. We show there is an additional source of active risk that is unique to each strategy. This strategy risk is caused by variability of the strategy's information coefficient over time. This implies that true active risk is often different from, and in many cases, significantly higher than the estimated tracking error given by a risk model. We show that a more consistent estimation of information ratio is the ratio of average information coefficient to the standard deviation of information coefficient. We further demonstrate how the interaction between information coefficient and investment opportunity, in terms of cross-sectional dispersion of actual returns, influences the IR. We then provide supporting empirical evidence and offer possible explanations to illustrate the practicality of our findings when applied to active portfolio management.

Musto (1997, Journal of Finance 52(4), 1861–1882) identifies a year-end effect in commercial paper (CP) and suggests that the price of risk may increase at the year-end. Griffiths and Winters (2003, Journal of Business, forthcoming) show that the timing of the year-end effect in CP is consistent with a preferred habitat for liquidity. However, Griffiths and Winters use data from only one risk class, so we extend their analysis by using spreads between different risk classes to determine if the price of risk does increase at the year-end. Using daily spreads between two risk classes of 7 day, 15 day, and 30 day non-financial CP, we find that the spread does increase at this time. However, the timing of the spread increases and decreases aligns with expectations consistent with a preferred habitat for liquidity at the year-end. This suggests that when liquidity is tight at the year-end, money market investors increase the price of risk.

The following sections are included:

• Introduction

• The Referee and The Game

• The Michaud Player

• The Diffuse Bayes Player
  • Basics
  • Diffuse Priors
  • Importance Sampling

• Results

• Questions

• Conclusions

• Acknowledgment

• Notes

• References

The presence of a positive intercept (“alpha”) in a regression of an investment fund's excess returns on a broad market portfolio's excess return (as in the CAPM), and other “factor” portfolios' excess returns (e.g., the Fama and French factors) is frequently interpreted as evidence of superior fund performance. This paper theoretically and empirically supports the notion that the additional factors may proxy for benchmark portfolios that fund managers try to beat, rather than proxying for state variables of future risks that investors (in conventional theory) are supposed to care about.