Valuing Partial Interests in Trusts
The financial interests of a trust's beneficiaries are often diametrically opposed and conflict among trust beneficiaries is common. Although applicable law requires that trustees adhere to lofty standards of 'good faith' and 'fair dealing' they must make tangible, specific decisions, and sometimes under circumstances in which the settlor's expectations regarding investments and distributions as set forth in the trust document are unclear. Traditional methods for valuing partial interests in trusts offer insufficient guidance to courts in assessing the prudent investor standard, as they often disregard many of the important factors which go into investment decisions--notably, the allocations to different asset classes.
In this paper, we develop a valuation methodology based on Monte Carlo Simulation techniques which allows for economically feasible ex ante valuation of partial interests in trusts. The MCS technique is widely used in modern finance and economics, and is especially useful for valuing partial interests because it can incorporate mortality risk, portfolio asset allocation, varying distributions and the discretionary sale of the trust's assets to fund distributions. We explain how the MCS method can incorporate a variety of assumptions about the income beneficiary's mortality and the trustee's decisions, and show how these factors affect the valuation of partial interests.
Rethinking the Comparable Companies Valuation Method
This paper studies a commonly used method of valuing companies, the comparable companies method, also known as the method of multiples. We use an intuitive graphical presentation to show why the comparable companies method is arbitrary and imprecise. We then show how valuations can be significantly improved using regression analysis. Regression analysis is superior to the comparable companies method because, by using more of the available data and imposing fewer unreasonable assumptions, it is more accurate and can value more firms.
The Properties of Short Term Investing in Leveraged ETFs
Published in the Journal of Financial Transformation, Fall 2012, Journal 35.
The daily returns on leveraged and inverse-leveraged exchange-traded funds (LETFs) are a multiple of the daily returns of a reference index. Because LETFs rebalance their leverage daily, their holding period returns can deviate substantially from the returns of a leveraged investment. While about half of LETF investors hold their investments for less than a month, the standard analysis of these investments uses a continuous time framework that is not appropriate for analyzing short holding periods, so the true effect of this daily rebalancing has not been properly ascertained.
In this paper, we model tracking errors of LETFs compared to a leveraged investment in discrete time. For a period lasting a month or less, the continuous time model predicts tracking errors to be small. However, we find that in a discrete time model, daily portfolio rebalancing introduces tracking errors that are not captured in the continuous time framework. On average, portfolio rebalancing accounts for approximately 25% of the total tracking error, and in certain scenarios the rebalancing tracking error could rise to as high as 5% in 3 weeks and can dominate the total tracking error. Since investors in LETFs have short average holding periods and high average turnover ratios, the effects of portfolio rebalancing must be accurately accounted for in the analysis of LETF returns.
The VXX ETN and Volatility Exposure
Published in the PIABA Bar Journal, Vol. 18, No. 24, pp. 235-252.
Exposure to the CBOE Volatility Index (VIX) has been available since 2004 in the form of futures and since 2006 in the form of options, but recently new exchange-traded products have offered retail investors an easier way to gain exposure to this popular measure of market sentiment. The most successful of these products so far has been Barclays's VXX ETN, which has grown to a market cap of just under $1.5 billion. However, the VXX ETN has lost more than 90% of its value since its introduction in 2009, compared to a decline of only 60% for the VIX index. This poor relative performance is because the VXX ETN tracks an index of VIX futures contracts that can incur negative roll yield. In this paper we review the VIX index and assess the opportunities and risks associated with investing in the VXX ETN.
Modeling Autocallable Structured Products
Published in the Journal of Derivatives & Hedge Funds 17, 326-340 (November 2011).
Since first introduced in 2003, the number of autocallable structured products in the U.S. has increased exponentially. The autocall feature immediately converts the product if the reference asset's value rises above a pre-specified call price. Because an autocallable structured product matures immediately if it is called, the autocall feature reduces the product's duration and expected maturity.
In this paper, we present a flexible Partial Differential Equation (PDE) framework to model autocallable structured products. Our framework allows for products with either discrete or continuous autocall dates. We value the autocallable structured products with discrete autocall dates using the finite difference method, and the products with continuous autocall dates using a closed-form solution. In addition, we estimate the probabilities of an autocallable structured-product being called on each call date. We demonstrate our models by valuing a popular autocallable product and quantify the cost to the investor of adding this feature to a structured product.
Futures-Based Commodities ETFs
Published in The Journal of Index Investing, Summer 2011, Vol. 2, No. 1: pp. 14-24.
Commodities Exchange Traded Funds (ETFs) have become popular investments since first introduced in 2004. These funds offer investors a simple way to gain exposure to commodities, which are thought of as an asset class suitable for diversification in investment portfolios and as a hedge against economic downturns. However, returns of futures-based commodities ETFs have deviated significantly from the changes in the prices of their underlying commodities. The pervasive underperformance of futures-based commodities ETFs compared to changes in commodity prices calls into question the usefulness of these ETFs for diversification or hedging.
This paper examines the sources of the deviation between futures-based commodities ETF returns and the changes in commodity prices using crude oil ETFs. We show that the deviation in returns is serially correlated and that a significant portion of this deviation can be predicted by the term structure of the oil futures market. We conclude that only investors sophisticated enough to understand and actively monitor commodities futures market conditions should use these ETFs.