A.I.R.A.P. - Alternative RAPMs for Alternative Investments By Milind Sharma
This paper highlights the inadequacies of traditional RAPMs (Risk-Adjusted Performance Measures) and proposes AIRAP (Alternative Investments Risk Adjusted Performance), based on Expected Utility theory, as a RAPM better suited to Alternative Investments. AIRAP is the implied certain return that a risk-averse investor would trade off for holding risky assets. AIRAP captures the full distribution, penalizes for volatility and leverage, is customizable by risk aversion, works with negative mean returns, eschews moment estimation or convergence requirements and can dovetail with stressed scenarios or regime-switching models. A modified Sharpe Ratio is proposed. The results are contrasted with Sharpe, Treynor and Jensen rankings to show significant divergence. Evidence of non-normality and the tradeoff between mean-variance merits vis-a-vis higher moment risks is noted. The dependence of optimal leverage on risk aversion and track record is noted. The results have implications for manager selection and fund of hedge funds portfolio construction.
A.I.R.A.P. - Alternative Views on Alternative Investments By Milind Sharma
This paper investigates issues of risk-adjusted performance, value added and leverage for hedge funds. It applies AIRAP (Alternative Investments Risk Adjusted Performance), which is the power utility implied certain return that a risk-averse investor would trade off for holding risky assets, to hedge fund indices and individual hedge fund data. Inferences are made about the value added by hedge funds and the difference between directional and non-directional strategies. Evidence of non-normality, higher moment risks and the trade-off between mean-variance profile vis-a-vis skewness and kurtosis is noted across style categories. Further, survivorship bias is estimated across style categories in the first four moments.
Valuation of Cancelable Cross Currency Bermudan Swaps By Milind Sharma and Jonathan Stein
This paper presents a framework for the valuation of cancelable cross currency Bermudan swaps. We use a lognormal process for the exchange rate while the domestic & foreign forward rates are assumed to be Gaussian as in Heath et al. (1992). Monte-Carlo simulation is utilized for valuation via an extension to several dimensions of the methodology for simulating American options proposed by Grant et al. (1994). As special cases the model can be used to value cross currency swaps and single exercise Bermudans which can be used for benchmarking purposes.
Hedge Fund Investing (Chapter 7 of Risk Management: A Modern Perspective) By Milind Sharma
This chapter provides a brief overview of hedge fund investing. It contrasts investing for absolute returns vis-á-vis the traditional index-relative case and highlights data caveats as well as benchmarking issues germane to the proper assessment of hedge fund performance. It surveys risk management challenges arising from higher moment exposures and those that occur because of short volatility and non-directional strategies. In the light of these challenges, new risk and risk-adjusted metrics that transcend the mean-variance paradigm are outlined by the chapter. it also considers the implications for asset allocation involving hedge funds. Any pooled investment vehicle that is privately organized, administered by professional investment managers, and not widely available to the public is called hedge fund investing. Hedge funds not only endeavor to deliver alpha for all seasons but typify a new obsession with risk management that attempts to minimize the likelihood of large draw downs, thereby maximizing the benefits to geometric compounding. This stems from the understanding that in the long run, the power of geometric compounding is better harnessed by avoiding catastrophic losses than by only attempting to hit home runs.
Estimating Nonlinear Effects of Management Styles in the US Equity Market By Sandy Warrick, CFA
The vast majority of asset pricing models assume linear relationships between security returns and underlying factors. Among investment practitioners, models of both risk and return derived from such asset pricing models continue the assumption of linear relationships. In this paper, we report on an investment style scoring model of the US equity market that has been in practitioner use for over ten years. Returns associated with the style scores, their squares and interaction terms are investigated using both deciles analysis and via a monthly cross-sectional regression. The style scores are shown to have a high degree of statistical significance in the cross-section of US stock returns from April of 1991 to March of 2001. Identifiable time series properties are found for the coefficients describing the linear relationships to the style scores. Contrary to traditional models, return relationships are also shown for some of the second order and interaction effects for a large fraction of the cross-sections. These relationships appear to be both statistically and economically significant. We conclude from this information that practitioners ought pay substantial attention to second order and interaction effects arising from active management bets. There is also evidence that second order and interaction effects have a meaningful role in asset pricing.
Estimating Returns for Asset Allocation By Sandy Warrick, CFA
When estimating the return and risk of a portfolio, and particularly when estimating the efficient frontier using quadratic optimization, the crucial inputs are the expected returns. What expected returns should we use? We discuss the weakness of using historic estimation, and then examine alternatives including Bayesian adjustment, the capital asset pricing model and the Black-Litterman method of Implied Returns.
Using Lifecycle Funds in a Suitable and Optimal Portfolio By Sandy Warrick, CFA
In recent years, so-called "life cycle" funds have become an important financial vehicle for retail investors. Such funds are designed so as to specifically target the needs of individuals who are planning on retiring at some particular future date. These funds are designed to save the individual investor from the burden of having to periodically reformulate their own asset allocation policies as they move through their lives toward retirement. The investment policies of the fund gradually vary from accumulation of capital during the early years to a more conservative investment stance for the retirement years that emphasizes preservation of capital, income and liquidity. The presentation will demonstrate use of Northfield''s Analytic Hierarchy as an asset allocation process to construct model portfolios that include lifecycle funds for a variety of investor ages and retirement dates. The empirical results of the study show that a combination of a lifecycle fund and complementary global equity and bond funds provides a high degree of optimality with a minimal rebalancing turnover.
CUSUM Analysis for Manager Evaluation and Monitoring By Dan diBartolomeo and Sandy Warrick, CFA
CUSUM is a technique originally developed for the study of digital signals. It has been successfully adapted for use in monitoring the returns achieved by active managers. The method involves calculating the rolling sum of standardized active returns, and then identifying key inflection points in this time series. We can then analyze returns subsequent to the key inflection point as being the most relevant for making judgments about manager performance.
Finding Proxy Holdings for a Hedge Fund with Undisclosed Holdings + An Empirical Study of Style distributions among Hedge Funds By Daniel Mostovoy and Sandy Warrick, CFA
A common problem for "fund of hedge funds" managers is the need to include and analyze a hedge fund with undisclosed holdings. This session updates a procedure we created in 2001 for estimating proxy holdings for a fund where the underlying holdings are unknown using a combination of returns based style analysis and portfolio optimization. The resulting proxy portfolio serves as a reasonable estimate of the typical style bets of the fund, the degree of portfolio position concentration and the balance between asset specific and factor risks. We have incorporated a number of recent refinements to this technique, and we are currently in the process of implementing these updates into full production in order to add risk analysis of thousands of hedge funds to the coverage universe of our Everything, Everywhere risk model. This presentation will include extensive samples of empirical results.
Making covariance-based portfolio risk models sensitive to the rate at which markets reflect new information By Dan diBartolomeo and Sandy Warrick, CFA
Multiple factor models of security covariance have been widely adopted by investment practitioners as a means to forecast the volatility of portfolios. In that such models arise from the tradition of Markowitz’s Modern Portfolio Theory, they have generally been based on a single period assumption, where future risk levels are presumed to not vary over time. In reality, risk levels do vary substantially and modifications of the underlying assumptions of multiple factor covariance models must change to reflect this fact. Our paper reviews the way new information is absorbed by financial markets and contributes a model of how such information can be reflected more efficiently in estimates of future covariance, through the inclusion of implied volatility information. We conclude with an empirical example regarding market conditions before and after the events of September 11, 2001. Not only does this example illustrate the value of including implied volatility as a component to covariance forecasts, but also suggests that some market participants may have acted in anticipation of the tragedies.
Matching Investors with Suitable, Optimal and Investable Portfolios By Paul Bolster and Sandy Warrick, CFA
Suitability is a legal concept that refers to the propriety of the match between the individual and his or her portfolio. The authors develop a model of suitability using the Analytic Hierarchy Process (AHP) to create unique asset allocations for individual investors based on their personal attributes. They then compare the mean-variance performance of these suitable model portfolios with portfolios generated using mean-variance optimization. They find that minor alterations to the AHP model and optimization inputs minimize the distinction from a mean-variance efficient portfolio. Finally, they show that a wide range of model portfolios can be closely matched with a small selection of mutual funds.
Suitability and Optimality in the Asset Allocation Process: Conflict and Resolution Using the Analytic Hierarchy Process and Mean Variance Optimization By Paul Bolster and Sandy Warrick, CFA
Suitability is a legal concept that refers to the propriety of the match between the individual and his or her portfolio. Financial advisors and investment companies employ numerous models to profile investors and then recommend a suitable asset allocation. However, there is no guarantee that the recommended asset allocation is also optimal in a mean-variance sense. We develop a model of suitability using the Analytic Hierarchy Process (AHP) to create unique asset allocations for individual investors based on their personal attributes. We then compare the mean-variance performance of these suitable portfolios with independent portfolios generated using traditional mean-variance optimization (MVO) methodology. Our results indicate that the AHP and MVO approaches yield portfolios with risk-return attributes that are not significantly different.The AHP portfolios are more likely to underperform the MVO portfolios for individuals with very high risk tolerance. Finally, we find that minor alterations to the AHP model can further minimize any distinction from a pure MVO portfolio.
Managing Legacy Portfolios with Concentrated Positions By Paul Bolster and Sandy Warrick, CFA
In many cases, asset managers are faced with the task of taking over the management of a taxable portfolio with concentrated and low cost basis positions. Although there are a number of things the manager can do to reduce the risk of this position, the difficulty in measuring the effectiveness in managing the portfolio often results in the manager liquidating a large portion of the portfolio. One way to handle this situation is to use a multi-manager portfolio using a tax overlay, which controls the tracking error of each portfolio sleeve while minimizing the tax drag. This paper investigates the effectiveness of modeling capital gains taxes as a transaction cost, reducing the attractiveness of sales of concentrated positions to reduce risk or increase return expectations. As an empirical example, we compare the gross (before taxes) and after tax returns and risk of four different approaches to managing a familys stock portfolio. To compare several different approaches to managing taxable assets, 244we use a Wilcoxs utility equation that estimates an appropriate risk level given a familys financial circumstances, requirements and goals.
Implementation of Finite Difference Technique for Exotic Double Barrier Options By Pratik Sharda, CFA and Ravishekar Subramanian
This paper attempts to price a complex barrier option using Finite Difference (FD) techniques. The focus is to demonstrate the strength of the FD to deal with various seemingly complicated issues like jump diffusion, Early exercise in a relatively easy way and at a lower computational cost compared to the normal Monte Carlo (MC) techniques. The prices were reliable and efficiency gains are benchmarked against the results from a pure Monte Carlo simulation and other analytical values. The paper also deals with issues on implication of dividend incorporation, treatment of boundary conditions, and hedging.