Illiquid Assets and Optimal Portfolio Choice

The presence of illiquid assets, such as human wealth or a family owned business, complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset allocation and consumption in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless asset. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and to the liquid holdings held by the agent. We provide what we believe to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets.

Growth options and firm valuation

This paper studies the relation between firm value and a firm's growth options. We find strong empirical evidence that (average) Tobin's Q increases with firm-level volatility. However, the significance mainly comes from R&D firms, which have more growth options than non-R&D firms. By decomposing firm-level volatility into its systematic and unsystematic part, we also document that only idiosyncratic volatility (ivol) has a significant effect on valuation. Second, we analyze the relation of stock returns to realized contemporaneous idiosyncratic volatility and R&D expenses. Single sorting according to the size of idiosyncratic volatility, we only find a significant ivol anomaly for non-R&D portfolios, whereas in a four-factor model the portfolio alphas of R&D portfolios are all positive. Double sorting on idiosyncratic volatility and R&D expenses also reveals these differences between R&D and non-R&D firms. To simultaneously control for several explanatory variables, we also run panel regressions of portfolio alphas which confirm the relative importance of idiosyncratic volatility that is amplified by R&D expenses

A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives

We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.

Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives

We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in the crude-oil market. We then develop a tractable model for pricing commodity derivatives in the presence of unspanned stochastic volatility. The model features correlations between innovations to futures prices and volatility, quasi-analytical prices of options on futures and futures curve dynamics in terms of a low-dimensional affine state vector. The model performs well when estimated on an extensive panel data set of crude-oil futures and options.

A Model of R&D Valuation and the Design of Research Incentives

We develop a real options model of R&D valuation, which takes into account the uncertainty in the quality of the research output, the time and cost to completion, and the market demand for the R&D output. The model is then applied to study the problem of pharmaceutical under-investment in R&D for vaccines to treat diseases affecting the developing regions of the world. To address this issue, world organizations and private foundations are willing to sponsor vaccine R&D, but there is no consensus on how to administer the sponsorship effectively. Different research incentive contracts are examined using our valuation model. Their effectiveness is measured in the following four dimensions: cost to the sponsor, the probability of development success, the consumer surplus generated and the expected cost per person successfully vaccinated. We find that, in general, purchase commitment plans (pull subsidies) are more effective than cost subsidy plans (push subsidies), while extending patent protection is completely ineffective. Specifically, we find that a hybrid subsidy constructed from a purchase commitment combined with a sponsor co-payment feature produces the best results in all four dimensions of the effectiveness measure.

R&D Investments with Competitive Interactions

In this article we develop a model to analyze patent-protected R&D investment projects when there is (imperfect) competition in the development and marketing of the resulting product. The competitive interactions that occur substantially complicate the solution of the problem since the decision maker has to take into account not only the factors that affect her/his own decisions, but also the factors that affect the decisions of the other investors. The real options framework utilized to deal with investments under uncertainty is extended to incorporate the game theoretic concepts required to deal with these interactions. Implementation of the model shows that competition in R&D, in general, not only increases production and reduces prices, but also shortens the time of developing the product and increases the probability of a successful development. These benefits to society are countered by increased total investment costs in R&D and lower aggregate value of the R&D investment projects.

Patents and R&D as Real Options

This article develops and implements a simulation approach to value patents and patent-protected R&D projects based on the Real Options approach. It takes into account uncertainty in the cost-to-completion of the project, uncertainty in the cash flows to be generated from the project, and the possibility of catastrophic events that could put an end to the effort before it is completed. It also allows for the possibility of abandoning the project when costs turn out to be larger than expected or when estimated cash flows turn out to be smaller than anticipated. This abandonment option represents a very substantial part of the project's value when the project is marginal or/and when uncertainty is large. The model presented can be used to evaluate the effects of regulation on the cost of innovation and the amount on innovative output. The main focus of the article is the pharmaceutical industry. The framework, however, applies just as well to other research-intensive industries such as software or hardware development.

Are all Credit Default Swap databases equal?

The presence of different prices in different databases for the same securities can impair the comparability of research efforts and seriously damage the management decisions based upon such research. In this study we compare the six major sources of corporate Credit Default Swap prices: GFI, Fenics, Reuters EOD, CMA, Markit and JP Morgan, using the most liquid single name 5-year CDS of the components of the leading market indexes, iTraxx (European firms) and CDX (US firms) for the period from 2004 to 2010. We find systematic differences between the data sets implying that deviations from the common trend among prices in the different databases are not purely random but are explained by idiosyncratic factors as well as liquidity, global risk and other trading factors. The lower is the amount of transaction prices available the higher is the deviation among databases. Our results suggest that the CMA database quotes lead the price discovery process in comparison with the quotes provided by other databases. Several robustness tests confirm these results.Credit Default Swap prices, Databases, Liquidity

Cash Flow Multipliers and Optimal Investment Decisions

By postulating a simple stochastic process for the firm's cash flows in which the drift and the variance of the process depend on the investment policy of the firm, we develop a theoretical model, determine the optimal investment policy and, given this policy, calculate the ratio of the current value of the firm and the current cash flow which we call the "cash flow multiplier''. The main contribution of the paper, however, is empirical. Using a very extensive data set comprised of more than 13,000 fims over 44 years we examine the determinants of the cash flow multiplier using as explanatory variables macro and firm specific variables suggested by the theoretical model. We find strong support for the variables suggested by the model. Perhaps the most interesting aspect of the paper is the formulation of a parsimonious empirical asset pricing model, based on the fundamental discounted cash flow approach but using current macroeconomic variables and firm specific variables easily observable for its implementation. We obtain valuation equations that could potentially form part of a new valuation framework which does not require estimating future cash flows nor risk adjusted discount rates.