Nikunj Kapadia

Correlated Default Risk

Using a comprehensive and unique data set of default probabilities from Moody’s, we examine correlations between default risk for over 7,000 US public firms. This is the first paper to empirically document the correlation structure both in the time-series and in the cross-section across almost all US non-financial firms. We find that default probabilities of issuers vary substantially over time, and are positively correlated. Moreover, the correlations across firms also varies over time systematically, in a manner that is related to an economy-wide level of default risk. Joint default risk increases as the default risk in the economy increases. Our results also suggest that the magnitude of joint default depends on the quality of issuers; highest quality issuers have higher default correlations than medium grade firms. The results in this paper are informative for managers of credit portfolios, and for structured products such as collateralized debt obligations. CORRELATED DEFAULT RISK 3

Volatility Risk Premiums Embedded in Individual Equity Options: Some New Insights

The accumulation of trading experience and empirical evidence since the original Black-Scholes (BS) model was developed, have made it increasingly evident that volatility is not a constant parameter, as BS assumed, but stochastic. With a second random factor associated with volatility affecting security returns, it would not be surprising if investors cared about bearing risk related to that factor. And there is considerable evidence from analysis of real world options that volatility risk is indeed a priced factor, with a negative price. That is, investors will pay extra for (accept lower returns on) securities like options whose values increase when volatility goes up. In that case, Black-Scholes implied volatilities will tend to be higher than actual volatilities, which provides one measure of the market price of volatility risk. Research on stochastic volatility has focused largely on stock index options, but modern portfolio theory makes a strong distinction between stochastic factors that are correlated with the market portfolio and those that are not, whose risk can be diversified. In this article, Bakshi and Kapadia look at the pricing of individual stock options to explore the effects of market volatility risk versus firm-specific volatility risk. They find that volatility risk is priced, negatively as expected, and that market volatility risk is more important than firm-specific risk.

The Risk and Return Characteristics of the Buy-Write Strategy on the Russell 2000 Index

This article is motivated by significant recent interest in the use of buy-write strategies for investment purposes. In light of this, the CBOE has introduced a number of buy-write indices based on a variety of equity indices such as the S&P 500, the Dow Jones Industrial Average, the Nasdaq 100 and, most recently in May 2006, the Russell 2000. This article constructs and evaluates returns on a buy-write strategy on the Russell 2000 index. The results demonstrate that the strategy has consistently outperformed the Russell 2000 index on a risk adjusted basis, when implemented with one month to expiration calls and when performance is evaluated using standard performance measures. The outperformance is robust to measures which specifically consider the non-normal distribution of the strategys returns. However, the consistent performance advantage disappears when two month to expiration calls are utilized. On average, written calls end up in-the-money and transaction costs of writing the call at the bid further increases the losses.

An options-based approach to coordinating distributed decision systems

Engineering and operations management decisions have become increasingly complex as a result of recent advances in information technology. The increased ability to access and communicate information has resulted in expanded system domains consisting of multiple agents, each exhibiting autonomous decision-making capabilities, with potentially complex logistics. Challenges regarding the management of these systems include heterogenous utility drivers and risk preferences among the agents, and various sources of system uncertainty. This paper presents a distributed options-based model that manages the impact of multiple forms of uncertainty from a multi-agent perspective, while adapting as both the stream of information and the capabilities of the agents are better known. Because the actions of decision makers may have an impact on the evolution of underlying sources of uncertainty, this endogenous relationship is modeled and a solution approach developed that converges to an equilibrium system state and improves the performance of agents and the system. The final result is a distributed options-based decision-making policy that both responds to and controls the evolution of uncertainty in large-scale engineering and operations management domains.

Fifteen Years of the Russell 2000 Buy-Write

Using data from January 18, 1996 to March 31, 2011, we construct and evaluate returns on a buy-write strategy on the Russell 2000 index. The results demonstrate that the strategy has consistently outperformed the Russell 2000 index on a risk-adjusted basis, when implemented with one month to expiration calls and when performance is evaluated using standard performance measures. Over the 182-month period of analysis, the RUT buy-write strategy using 2% out-of-themoney, one-month calls generated higher returns than the underlying index (8.87% versus 8.11%) at about three-quarters of the standard deviation (16.57% versus 21.06%). The outperformance is robust to measures which specifically consider the non-normal distribution of the strategy’s returns. However, the consistent performance advantage does not remain if we utilize two-month to expiration calls. To evaluate the performance in varying market conditions, we break our sample into sub-periods. Specifically, one of the worst market conditions for the buy-write strategy is March 2003 to October 2007, when the Russell 2000 experiences a high sustained growth at a relatively low volatility. Even in this market environment, we find that the 2% out-of-the-money one-month buy-write strategy outperforms the Russell 2000 on a risk-adjusted basis, returning almost the same returns as the index return at three-quarters its volatility. We provide insight into the sources of the performance. On average, the expiration value of written calls exceeds the premium collected and the transaction costs of writing the call at the bid further increases the losses. However, the buy-write strategy benefits by writing calls at an implied volatility that is generally higher than the realized volatility. In fact, we find that the contribution of the volatility risk premium—the difference between implied and realized volatility—is typically larger than the net losses incurred by the call position or the transaction costs. It appears that the existence of the risk premium is critical to the performance of the strategy. In fact, the (Leland’s) alpha of the strategy is typically significantly smaller than the risk premium implying that the buy-write strategy would not provide excess returns in the absence of the risk premium.

15 Years of the Russell 2000 Buy-Write

Using data from January 18, 1996 to March 31, 2011, we construct and evaluate returns on a buy-write strategy on the Russell 2000 index. The results demonstrate that the strategy has consistently outperformed the Russell 2000 index on a risk adjusted basis, when implemented with one month to expiration calls and when performance is evaluated using standard performance measures. Over the 182 month period of analysis, the RUT buy-write strategy using 2% out-of-the-money, one-month calls generated higher returns than the underlying index (8.87% versus 8.11%) at about three-quarters of the standard deviation (16.57% versus 21.06%). The outperformance is robust to measures which specifically consider the non-normal distribution of the strategys returns. However, the consistent performance advantage does not remain if we utilize two month to expiration calls. To evaluate the performance in varying market conditions, we break our sample into sub-periods. Specifically, one of the worst market conditions for the buy-write strategy is March 2003 to October 2007, when the Russell 2000 experiences a high sustained growth at a relatively low volatility. Even in this market environment, we find that the 2% out-of-the-money one-month buy-write strategy outperforms the Russell 2000 on a risk adjusted basis, returning almost the same returns as the index return at three-quarters its volatility. We provide insight into the sources of the performance. On average, the expiration value of written calls exceeds the premium collected and the transaction costs of writing the call at the bid further increases the losses. However, the buy-write strategy benefits by writing calls at an implied volatility that is generally higher than the realized volatility. In fact, we find that the contribution of the volatility risk premium - the difference between implied and realized volatility – is typically larger than the net losses incurred by the call position or the transaction costs. It appears that the existence of the risk premium is critical to the performance of the strategy. In fact, the (Lelands) alpha of the strategy is typically significantly smaller than the risk premium implying that the buy-write strategy would not provide excess returns in the absence of the risk premium.

Negative Vega? Understanding Options on Spreads

During recent months, interest in the impact of various spread trades on hedge fund returns has increased. For instance, the option on a spread can decrease in value when the volatility of one of the assets of the spread goes up. This article explains theoretically why this may happen, and clarifies the market conditions under which an increase in the volatility of one of the assets may increase or decrease the value of the spread option.

Market-based Security for Distributed Applications

Ethereum contracts can be designed to function as fully decentralized applications called DAPPs that hold financial assets, and many have already been fielded. Unfortunately, DAPPs can be hacked, and the assets they control can be stolen. A recent attack on an Ethereum decentralized application called The DAO demonstrated that smart contract bugs are more than an academic concern. Ether worth hundreds of millions of US dollars was extracted by an attacker from The DAO, sending the value of its tokens and the overall exchange price of ether itself tumbling. We present two market-based techniques for insuring the ether holdings of a DAPP. These mechanisms exist and are managed as part of the core programming of the DAPP, rather than as separate mechanisms managed by users. Our first technique is based on futures contracts indexed by the trade price of ether for DAPP tokens. Under fairly general circumstances, our technique is capable of recovering the majority of ether lost from theft with high probability even when all of the ether holdings are stolen; and the only cost to DAPP token holders is an adjustable ether withdrawal fee. As a second, complementary, technique we propose the use of Gated Public Offerings (GPO) as a mechanism that mitigates the effects of attackers that exploit DAPP withdrawal vulnerabilities. We show that using more than one public offering round encourages attackers to exploit the vulnerability early, or depending on certain factors, to delay exploitation (possibly indefinitely) and short tokens in the market instead. In both cases, less ether is ultimately stolen from the DAPP, and in the later case, some of the losses are transferred to the market.

Write on the Money

An unusual combination of assumptions - markets have frictions, but nonetheless are price efficient - is required to justify the generic buy-write strategy. In theory, a buy-write strategy allows investors to earn the variance risk premium (VRP) when they cannot access the variance swap market because of market frictions. But whether the strategy earns the expected VRP is contingent on markets being efficient. We show that the performance of the generic buy-write strategy that writes at-the-money options deteriorates rapidly in the presence of short-lived anomalies. Empirically, an alternative strategy that is designed to protect against market reversals outperforms the generic strategy. Our analysis provides a potential explanation of why, in practice, these popular option-write strategies earn but a fraction of the expected variance risk premium.

The Conservative Issuer Bias of Corporate Ratings

In contrast to existing literature that relates positive issuer bias in ratings to a conflict of interest, we document a bias in corporate ratings resulting from a conservative rating policy that accounts for the asymmetric impact of a rating downgrade on firms’ access to capital. Specifically, using Moody’s issuer ratings over 1982-2009, firms with greater external financing constraints are less likely to be downgraded. Economically, external financing constraints are more important than the default risk of the firm in determining the outcome of a rating review. Severely constrained firms whose ratings are affirmed or upgraded have long-term positive excess equity returns.