The performance of model based option trading strategies

This paper analyzes returns to trading strategies in options markets that exploit information given by a theoretical asset pricing model. We examine trading strategies in which a positive portfolio weight is assigned to assets which market prices exceed the price of a theoretical asset pricing model. We investigate portfolio rules which mimic standard mean-variance analysis is used to construct optimal model based portfolio weights. In essence, these portfolio rules allow estimation risk, as well as price risk to be approximately hedged. An empirical exercise shows that the portfolio rules give out-of-sample Sharpe ratios exceeding unity for S&P 500 options. Portfolio returns have no discernible correlation with systematic risk factors, which is troubling for traditional risk based asset pricing explanations.     

Finally, a way to put your Internet portfolio in order

Eager to capitalize on the Internet's potential, many companies have allowed scores of on-line projects to bubble up throughout their organizations. The result? More harm than good, as companies find themselves confusing customers, aggravating employees, and wasting bushels of money. In this article, consultant Anthony Tjan explains how companies can do better. By adapting classical portfolio strategy to the digital age, executives can coordinate their Internet initiatives to avoid the needless headaches and spending, he says. Much of the market and industry data that underpin traditional portfolio analysis is unavailable for the Internet space, so Tjan replaces the two criteria used in traditional portfolio analysis--market position and industry attractiveness--with business viability and business fit. Viability captures the available quantitative data about an investment's likely payoff. Fit is qualitative; it measures the degree to which an investment dovetails with a company's existing processes, capabilities, and culture. Using viability and fit to assess their online initiatives, companies can then plot these efforts onto a simple matrix, called an Internet portfolio map. Their location on the matrix will suggest whether each initiative should be invested in, redesigned, sold or spun out, or killed. As Tjan notes, the process of organizing and evaluating new investment options against coherent, meaningful criteria isn't new. In the digital era, what is new are the tools you use. Internet portfolio planning is one such tool.     

Strategy as a portfolio of real options

In financial terms, a business strategy is much more like a series of options than like a single projected cash flow. Executing a strategy almost always involves making a sequence of major decisions. Some actions are taken immediately while others are deliberately deferred so that managers can optimize their choices as circumstances evolve. While executives readily grasp the analogy between strategy and real options, until recently the mechanics of option pricing was so complex that few companies found it practical to use when formulating strategy. But advances in both computing power and our understanding of option pricing over the last 20 years now make it feasible to apply real-options thinking to strategic decision making. To analyze a strategy as a portfolio of related real options, this article exploits a framework presented by the author in "Investment Opportunities as Real Options: Getting Started on the Numbers" (HBR July-August 1998). That article explained how to get from discounted-cash-flow value to option value for a typical project; in other words, it was about reaching a number. This article extends that framework, exploring how, once you've worked out the numbers, you can use option pricing to improve decision making about the sequence and timing of a portfolio of strategic investments. Timothy Luehrman shows executives how to plot their strategies in two-dimensional "option space," giving them a way to "draw" a strategy in terms that are neither wholly strategic nor wholly financial, but some of both. Such pictures inject financial discipline and new insight into how a company's future opportunities can be actively cultivated and harvested.     

The duration of option portfolios

Duration is a value-weighted measure of average maturity which is commonly associated with portfolios of fixed-income securities. However, the concept finds application in option pricing theory also. This article shows that if options are valued by the Black (1976) formula and a comparative-statics methodology is employed, then the interest rate sensitivity of a portfolio of European options is equal to its duration. If the options are instead valued through the Black-Scholes (1973) formula, then the interest rate sensitivity is equal to only the ‘bond-equivalent duration’ inherent in a dynamic replication strategy for the option portfolio.     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

HEDGING FIXED-RATE PREFERRED STOCK INVESTMENTS

Corporations seeking to maximize the return on their cash reserve resources have an incentive to invest in traditional preferred stock because of their right to exclude 70% of the dividends from taxation. Nevertheless, fixed-rate preferred stock investments may contribute significantly to the return volatility of a cash portfolio and cause unacceptable losses to the corporate investors. As a result, many corporations might consider such higher-return investments only if they can hedge away a sufficient amount of risk. The research presented in this article seeks to evaluate how much of the return variation of fixed-rate preferred equity portfolios can be reduced with various hedging strategies.
This research shows that it is possible to reduce the risk of preferred stock investments significantly through the use of hedges employing some combination of fixed income futures and/or options. Although some risk remains even with the hedged preferred stock portfolio, the author demonstrates that money market assets can be combined with a hedged preferred stock portfolio to create a position that has no material chance of loss but expected after-tax returns higher than those on money market investments. In addition, the article also shows the high level of profitability associated with a strategy of increasing the size of liquid reserves in order to allow for losses related to an unhedged preferred stock component of those reserves.     

Strategic technology adoption and hedging under incomplete markets

We investigate the implications of technological innovation and non-diversifiable risk on entrepreneurial entry and optimal portfolio choice. In a real options model where two risk-averse individuals strategically decide on technology adoption, we show that the impact of non-diversifiable risk on the option timing decision is ambiguous and depends on the frequency of technological change. Compared to the complete market case, non-diversifiable risk may accelerate or delay the optimal investment decision. Moreover, strategic considerations regarding technology adoption play a central role for the entrepreneur’s optimal portfolio choice in the presence of non-diversifiable risk.     

The Effect of “Private” and “Public” Risks on Oilfield Asset Pricing: Empirical Insights into the Georgetown Real Option Debate

The Spring 2005 issue of this journal featured a “debate” over the best way of applying real options. In “Real Options Analysis: Where Are the Emperor's Clothes?,” Adam B orison criticized most practices that go under the name real options and recommended an “integrated” approach that combines real options techniques with a traditional approach known as “decision tree analysis.” This approach breaks valuation problems into two components—“market” risks (say, oil price changes) and “private” risks (the possibility that actual reserves fall well short of estimated) — and then uses option pricing models to evaluate the market risks and decision trees for the private risks. In response to Borison's article, Tom Copeland and Vladimir Antikarov argued that these two components can be evaluated in a single analysis that uses both DCF (to calculate the value of the “underlying asset”) and Monte Carlo simulation (to estimate the volatility of the underlying), thereby expanding the range of real options applications. In this article, the authors attempt to shed light on this debate with the findings of their extensive empirical analysis of U.K. oilfield expansion options. The bottom line of their study is that size matters in the context of oilfields, presumably because it offers a reliable guide to the kind and size of risks associated with the project. In the case of the larger oilfields, where market risks are likely to outweigh the private risks, the author's findings suggest that both approaches are reasonably effective and provide roughly the same degree of accuracy. In the case of smaller fields, however, where private risks are proportionally larger, the authors conclude that Borison's approach is likely to be more reliable.     

Real Options: Meeting the Georgetown Challange

In response to the demand for a single, generally accepted real options methodology, this article proposes a four‐step process leading to a practical solution to most applications of real option analysis. The first step is familiar: calculate the standard net present value of the project assuming no managerial flexibility, which results in a value estimate (and a “branch” of a decision tree) for each year of the project's life. The second step estimates the volatility of the value of the project and produces a value tree designed to capture the main sources of uncertainty. Note that the authors focus on the uncertainty about overall project value, which is driven by uncertainty in revenue growth, operating margins, operating leverage, input costs, and technology. The key point here is that, in contrast to many real options approaches, none of these variables taken alone is assumed to be a reliable surrogate for the uncertainty of the project itself. For example, in assessing the option value of a proven oil reserve, the relevant measure of volatility is the volatility not of oil prices, but of the value of the operating entity—that is, the project value without leverage. The third step attempts to capture managerial flexibility using a decision “tree” that illustrates the decisions to be made, their possible outcomes, and their corresponding probabilities. The article illustrate various kinds of applications, including a phased investment in a chemical plant (which is treated as a compound option) and an investment in a peak‐load power plant (a switching option with changing variance, which precludes the use of constant risk‐neutral probabilities as in standard decision tree analysis). The fourth and final step uses a “no‐arbitrage” approach to form a replicating portfolio with the same payouts as the real option. For most corporate investment projects, it is impossible to locate a “twin security” that trades in the market. In the absence of such a security, the conventional NPV of a project (again, without flexibility) is the best candidate for a perfectly correlated underlying asset because it represents management's best estimate of value based on the expected cash flows of the project.     

Price discovery in the U.S. stock and stock options markets: A portfolio approach

Option prices vary with not only the underlying asset price, but also volatilities and higher moments. In this paper, we use a portfolio of options to seclude the value change of the portfolio from the impact of volatility and higher moments. We apply this portfolio approach to the price discovery analysis in the U.S. stock and stock options markets. We find that the price discovery on the directional movement of the stock price mainly occurs in the stock market, more so now than before as an increasing proportion of options market makers adopt automated quoting algorithms. Nevertheless, the options market becomes more informative during periods of significant options trading activities. The informativeness of the options quotes increases further when the options trading activity generates net sell or buy pressure on the underlying stock price, even more so when the pressure is consistent with deviations between the stock and the options market quotes. JEL Classification C52, G10, G13, G14     

Should there exist secondary markets for executive stock options?

This paper investigates the potential disadvantages of the secondary markets for executive stock options (ESOs). The benefits of such markets are evident, but they might also have negative effects for shareholders. Executives might, for example, use inside information to time their ESO selling. We investigate two personal motives of managers that can be assumed to affect their optimal selling decision, that is, managers' personal portfolio management issues and the use of inside information. We explore these motives by analyzing unique data from Finland, where there are secondary markets for ESOs. The results of the study support the traditional portfolio diversification hypothesis according to which managers tend to sell their ESOs when holding an ESO is equivalent to holding the underlying stock; that is, in such a case a manager's wealth is closely tied to the stock price of the firm. With respect to the use of inside information the results indicate that ESO selling activity is not related to future stock price behaviour, suggesting that managers do not use inside information to determine the selling time of their ESOs. These results imply that the existence of secondary markets for ESOs does not weaken the usefulness of ESOs as the management compensation, although the benefits of such markets are evident.     

Taking Real Options Beyond the Black Box

Finance theorists have long argued that DCF undervalues investment opportunities with significant flexibility to respond to future events and that real options valuation methods provide a solution to that problem. But for most corporate managers, real options analysis continues to be a "black box" when applied to real investment decisions.
This paper begins by considering why these approaches have not yet made it to the mainstream of practical application. It then shows how a traditional DCF approach can undervalue a project that provides management with operating flexibility and illustrates a case study that demonstrates to senior management how a real options valuation method with a few clear value drivers can build upon and be made consistent with the traditional DCF framework.
Critical to this process is ensuring consistency with the company's planning assumptions such as future price forecasts and discount rates. The article shows how to separate the static ("optionless") DCF value from the additional real options value that is shown to be a direct consequence of the assumptions about price dynamics.     

Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications

This article presents a general framework for identifying andmodeling the joint-tail distribution based on multivariate extremevalue theories. We argue that the multivariate approach is themost efficient and effective way to study extreme events suchas systemic risk and crisis. We show, using returns on fivemajor stock indices, that the use of traditional dependencemeasures could lead to inaccurate portfolio risk assessment.We explain how the framework proposed here could be exploitedin a number of finance applications such as portfolio selection,risk management, Sharpe ratio targeting, hedging, option valuation,and credit risk analysis.     

Characteristic-based mean-variance portfolio choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.     

The market of dynamic hybrid products in Germany: concept, risk-return profiles, and market overview

This article analyzes dynamic hybrid products along with their diverse characteristics and contract variations that are currently available in the German market. Dynamic hybrid products are innovative life insurance contracts combining features of traditional participating life insurance with those of unit-linked policies. This approach is thereby implemented by a mathematical algorithm based on a constant proportion portfolio insurance strategy that periodically reallocates funds (e.g. once per month or day) between the policy reserve stock (with an interest rate guarantee), a guarantee fund and/or equity fund. In this paper, we contribute to the literature by examining the concepts and key features of available dynamic hybrid products with particular focus on the embedded options, which allows the identification of key contract characteristics associated with them. In addition, risk-return profiles are studied and compared, which is of high relevance for regulators and policyholders. Our results show that these strongly vary, depending on the individual rebalancing mechanism and the type and amount of embedded options.     

The individual's tax-exempt bond portfolio decision under income uncertainty

In this article, an individual's tax-exempt bond portfolio decision is investigated. A model capturing the relationship between income uncertainty and optimal portfolio choice is defined when an individual decision-maker has the opportunity to hold higher yielding private-activity bonds. The findings in this article show that in most cases risk-averse individuals will maximize the expected utility of after-tax income by holding a large proportion of private-activity bonds in their portfolio even under income uncertainty and the risk of a minimum tax liability. Those individuals who would benefit from holding private-activity bonds in a tax-exempt portfolio are identified and the magnitude of the benefit is quantified.     

Portfolio selection with higher moments

We propose a method for optimal portfolio selection using a Bayesian decision theoretic framework that addresses two major shortcomings of the traditional Markowitz approach: the ability to handle higher moments and parameter uncertainty. We employ the skew normal distribution which has many attractive features for modeling multivariate returns. Our results suggest that it is important to incorporate higher order moments in portfolio selection. Further, our comparison to other methods where parameter uncertainty is either ignored or accommodated in an ad hoc way, shows that our approach leads to higher expected utility than competing methods, such as the resampling methods that are common in the practice of finance.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.     

A real-world way to manage real options

Each corporate growth project is an option, in the sense that managers face choices--push ahead or pull back--along the way. Yet many companies hesitate to apply options theory to initiatives such as R&D and geographic expansion, partly because these "real" options are highly complex. In this article, the authors make the case that the complexity of real options can be eased through the use of a binomial valuation model. Many of the problems with real-options analysis stem from the use of the Black-Scholes-Merton model, which isn't suited to real options. Binomial models, by contrast, are simpler mathematically, and you can tinker with a binomial model until it closely reflects the project you wish to value. Suppose your company is considering investing in a new plant. To use the binomial model, you must create an "event tree" to figure out the full range of possible values for the plant during the project's lifetime--next year, at the end of the design phase, upon completion. Then you work backward from the value at completion, factoring in the various investments, to determine the value of the project today. These calculations provide you with numbers for all the possible future values of the option at the various points where a decision needs to be made on whether to continue with the project. The authors also address another criticism of real options: that gaps often arise between theoretical and realized values of options of all types. Such gaps may be largely the result of managers exercising options at the wrong time. To improve the way it manages its real options, a company can look out for the decision trigger points that correspond to the nodes on a binomial decision tree. The trigger points should not only tell managers when they need to decide on exercise but also specify rules governing the exercise decisions.     

Estimating the Value of Employee Stock Option Portfolios and Their Sensitivities to Price and Volatility

The costs associated with compiling data on employee stock option portfolios is a substantial obstacle in investigating the impact of stock options on managerial incentives, accounting choice, financing decisions, and the valuation of equity. We present an accurate method of estimating option portfolio value and the sensitivities of option portfolio value to stock price and stock-return volatility that is easily implemented using data from only the current year's proxy statement or annual report. This method can be applied to either executive stock option portfolios or to firm-wide option plans. In broad samples of actual and simulated CEO option portfolios, we show that these proxies capture more than 99% of the variation in option portfolio value and sensitivities. Sensitivity analysis indicates that the degree of bias in these proxies varies with option portfolio characteristics, and is most severe in samples of CEOs with a large proportion of out-of-the-money options. However, the proxies' explanatory power remains above 95% in all subsamples.