Tail Risk Exposures Research Articles

Sovereign Bond-Backed Securities: A VAR-for-VaR and Marginal Expected Shortfall Assessment

The risk reducing benefits of the sovereign bond-backed security (SBBS) proposal of Brunnermeier et al. (2016) have been assessed in terms of the likely losses that different kinds of holders would suffer under simulated default scenarios. However, the effects of mark-to-market losses that may occur when there is rising uncertainty about defaults, or when self-fulfilling destablising dynamics are prevalent, have not yet been examined. We apply the “VAR-for-VaR” method of Manganelli et al. (2015) and the Marginal Expected Shortfall (MES) approach of Brownlees and Engle (2012, 2017) to estimated yields of SBBS to assess how ex ante exposures and marginal contributions to systemic risk are likely to play-out for different SBBS tranches under various securitisation structures. We compare these with exposures/MES of single sovereigns and a diversified portfolio of sovereigns. We find that the senior SBBS has extremely low ex ante tail risk and that, like the low-risk sovereigns, it acts as a hedge against extreme market-wide yield movements. The mezzanine SBBS has tail risk exposure similar to that of Italian and Spanish bonds. Yields on SBBS appear to be adequate compensation for their risks when compared with single sovereigns or a diversified portfolio.

Sovereign Bond-Backed Securities: A VAR-for-VaR and Marginal Expected Shortfall Assessment

The risk reducing benefits of the sovereign bond-backed security (SBBS) proposal of Brunnermeier et al. (2016) have been assessed in terms of the likely losses that different kinds of holders would suffer under simulated default scenarios. However, the effects of mark-to-market losses that may occur when there is rising uncertainty about defaults, or when self-fulfilling destablising dynamics are prevalent, have not yet been examined. We apply the “VAR-for-VaR” method of Manganelli et al. (2015) and the Marginal Expected Shortfall (MES) approach of Brownlees and Engle (2012, 2017) to estimated yields of SBBS to assess how ex ante exposures and marginal contributions to systemic risk are likely to play-out for different SBBS tranches under various securitisation structures. We compare these with exposures/MES of single sovereigns and a diversified portfolio of sovereigns. We find that the senior SBBS has extremely low ex ante tail risk and that, like the low-risk sovereigns, it acts as a hedge against extreme market-wide yield movements. The mezzanine SBBS has tail risk exposure similar to that of Italian and Spanish bonds. Yields on SBBS appear to be adequate compensation for their risks when compared with single sovereigns or a diversified portfolio. JEL Classification: E43, E44, E52, E53, G12, G14

Digital Average Price Option (DAPO)

In this paper, we present an analytical solution for Digital Average Price Options (DAPO). This is an extension of digital options to incorporate average price or Asian price characteristics. We build on work by Zhang (1998), Turnbull and Wakeman (1991), and Haug (2004). We utilize numerical difference methods to calculate the Greeks based on the derived closed-form solution. These options can be used to manage risk or generate income. These products can effectively manager tail risk exposures with one transaction for an energy company who is exposed to multiple types of tail risk, which otherwise would require insuring each event with separate transactions at additional costs. We present an example of an Electricity Utility managing swing risk of serving demand (load) during peak winter months.

Tail risk in hedge funds: A unique view from portfolio holdings

We develop a new systematic tail risk measure for equity-oriented hedge funds to examine the impact of tail risk on fund performance and to identify the sources of tail risk. We find that tail risk affects the cross-sectional variation in fund returns and that investments in both tail-sensitive stocks and options drive tail risk. Moreover, leverage and exposure to funding liquidity shocks are important determinants of tail risk. We find evidence of some funds being able to time tail risk exposure prior to the 2008–2009 financial crisis.

Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market, and Idiosyncratic Volatility Anomalies?

We examine the impact of aggregate tail risk on return dynamics of size, book-to-market ratio, and idiosyncratic volatility sorted portfolios. Using changes in VIX Tail Hedge Index (ΔVXTH) as a proxy for aggregate tail risk, and controlling for market, size, book-to-market, and aggregate volatility risk, we document significant portfolio return exposures to tail risk. In particular, portfolios that contain small, value and volatile stocks exhibit consistently positive and statistically significant tail risk betas, whereas portfolios of big, growth and non-volatile stocks exhibit negative tail risk betas. We posit that due to their positive tail risk exposures, tail risk-averse investors demand extra compensation to hold small, value, and high idiosyncratic volatility stocks. Our results offer a tail risk-based explanation to size, value, and idiosyncratic volatility anomalies.

The Role of Risk Management in Corporate Governance

Failures of banks' governance and risk management functions have been identified as key causes of the 2007–2008 financial crisis. This article reviews the empirical literature that investigates the relationship between governance structures and risk management functions as well as their impact on banks' risk taking and performance. I first discuss risk management's responsibilities and relevance for a value-maximizing bank. The business nature of financial institutions and their funding structure, together with explicit and implicit government guarantees, set them apart from nonfinancial firms. I argue that conventional governance structures alone may be unable to restrain risk taking in banks and thus the presence of a strong and independent risk management function becomes necessary to monitor and control enterprise-wide risk exposures. Recent evidence shows that a strong risk management function, compatible with the appropriate business model and culture, can restrain tail risk exposures at financial institutions and promote long-term value maximization.

The Systemic Effects of Benchmarking

We show that the competitive pressure to beat a benchmark may induce institutional trading behavior that exposes retail investors to tail risk. In our model, institutional investors are different from a retail investor because they derive higher utility when their benchmark outperforms. This forces institutional investors to take on leverage to overinvest in the benchmark. Institutional investors execute fire sales when the benchmark experiences shock. This behavior increases market volatility, raising the tail risk exposure of the retail investor. Ex post, tail risk is only short lived. All investors survive in the long run under standard conditions, and the most patient investor dominates. Ex ante, however, benchmarking is welfare reducing for the retail investor, and beneficial only to the impatient institutional investor.

Tail Risk: Challenges, Mitigation, and Research Opportunities

This article discusses the multifaceted topic of tail risk. Topics include tail-risk perception, portfolio and enterprise management, and mitigation. We start by summarizing the key insights of the authors who have contributed to this special issue on tail risk and the applications of this work. We then propose a simple rule of thumb to evaluate tail-risk exposure and the viability of hedging strategies in the portfolio context. We add to the menu of these strategies by introducing the idea of whether protection on idiosyncratic risk is a cost-effective hedge against systemic risk. Empirical evidence and the dynamics that unfold during a systemic crisis appear to collectively indicate that the market may misprice the systemization of idiosyncratic risk. The evidence is compelling enough to warrant further research into the basis between idiosyncratic and systemic risk amid stress.

A Microfounded Design of Interconnectedness-Based Macroprudential Regulation

The failure of large, complex and interconnected banks has severe consequences to the real economy. To address the challenges posed by globally systemically important banks (G-SIBs), the Basel Committee on Banking Supervision recommended an “additional loss absorbency requirement” for these institutions. Motivated by this instrument of macroprudential regulation, which reflects concern over contagion, I develop a microfounded design of interconnectedness-based capital charges. These charges increase the costs of establishing interbank connections, which leads to a non-monotonic welfare effect. While reduced interconnectedness decreases welfare by restricting banks’ ability to insure against liquidity shocks, it also increases it by reducing contagion in default states. Thus, the regulator faces a trade-off between efficiency and financial stability. I show that the trade-off implied by incentive compatible interconnectedness-based charges is steeper the stronger G-SIBs implicit support is when banks’ tail risk exposure is private information. This finding underscores the importance of complementary measures, such as resolution regimes, which mitigate these frictions and consequently reinforce the efficiency and effectiveness of these capital requirements.

The Role of Risk Management in Corporate Governance

Failures of banks’ governance and risk management functions have been identified as key causes of the 2007-2008 financial crisis. This article reviews the empirical literature that investigates the relationship between governance structures and risk management functions as well as their impact on banks’ risk-taking and performance. I first discuss risk management’s responsibilities and relevance for a value-maximizing bank. The business nature of financial institutions and their funding structure, together with explicit and implicit government guarantees, set them apart from non-financial firms. I argue that conventional governance structures alone may be unable to restrain risk-taking in banks and thus the presence of a strong and independent risk management function becomes necessary to monitor and control enterprise-wide risk exposures. Recent evidence shows that a strong risk management function, compatible with the appropriate business model and culture, can restrain tail risk exposures at financial institutions and promote long-term value maximization.

Delegation and the Dynamics of Capital Flows

In this paper, I build a model where financial intermediation slows the flow of capital. Investors optimally learn from intermediary performance to allocate capital toward profitable intermediaries. Intermediaries reach for yield, i.e invest in high tail risk assets, in an attempt to drive flows and reduce liquidation risk. Reaching for yield is stronger among intermediaries with weak opportunities, resulting in a reduction in the informativeness of performance; investors take longer to learn and capital flows become less responsive to performance. Capital becomes slow moving because the reach for yield dampens learning. The model predicts capital immobility to be stronger when tail risk is high; when tail risk is underpriced; and in asset classes with large cross-sectional variation in tail risk exposures.

Robust and Practical Estimation for Measures of Tail Risk

We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting and comparing methodologies to compute and backtest estimates for these risk measures, from a practical perspective. We also consider the regulators' requirements regarding tail risk measures, especially in the framework provided by the most recent accords of the Basel Committee on Banking Regulation, known as Basel II, 2.5, and III.

Do Bond Investors Price Tail Risk Exposures of Financial Institutions?

We analyze whether bond investors price tail risk exposures of financial institutions using a comprehensive sample of bond issuances by U.S. financial institutions. Although primary bond yield spreads increase with an institutions' own tail risk (expected shortfall), systematic tail risk (marginal expected shortfall) of the institution doesn't affect its yields. The relationship between yield spreads and tail risk is significantly weaker for depository institutions, large institutions, government-sponsored entities, politically-connected institutions, and in periods following large-scale bailouts of financial institutions. Overall, our results suggest that implicit bailout guarantees of financial institutions can exacerbate moral hazard in bond markets and weaken market discipline.

Financial Network Systemic Risk Contributions

We propose the realized systemic risk beta as a measure of financial companies' contribution to systemic risk, given network interdependence between firms' tail risk exposures. Conditional on statistically pre-identified network spillover effects and market and balance sheet information, we define the realized systemic risk beta as the total time-varying marginal effect of a firm's Value-at-risk (VaR) on the system's VaR. Statistical inference reveals a multitude of relevant risk spillover channels and determines companies' systemic importance in the US financial system. Our approach can be used to monitor companies' systemic importance, enabling transparent macroprudential supervision.

Stronger Risk Controls, Lower Risk: Evidence from U.S. Bank Holding Companies

ABSTRACTWe construct a risk management index (RMI) to measure the strength and independence of the risk management function at bank holding companies (BHCs). The U.S. BHCs with higher RMI before the onset of the financial crisis have lower tail risk, lower nonperforming loans, and better operating and stock return performance during the financial crisis years. Over the period 1995 to 2010, BHCs with a higher lagged RMI have lower tail risk and higher return on assets, all else equal. Overall, these results suggest that a strong and independent risk management function can curtail tail risk exposures at banks.

Why Optimal Diversification Cannot Outperform Naive Diversification: Evidence from Tail Risk Exposure

This paper examines the outperformance of naive diversification relative to optimal diversification. From out-of-sample analysis using portfolios consisting of individual stocks as well as diversified equity portfolios, we find that optimal diversification fails to consistently outperform naive diversification. Our results show that naive diversification increases tail risk measured by skewness and kurtosis and makes portfolio returns more concave relative to equity benchmarks. In addition, tail risk exposure and concavity increases with the number of stocks in the portfolio. These results imply that the outperformance of naive diversification relative to optimal diversification represents a compensation for the increase in tail risk and the reduced upside potential associated with the concave payoff. JEL classification: G11; G12

Financial Network Systemic Risk Contributions

We propose the realized systemic risk beta as a measure for financial companies’ contribution to systemic risk given network interdependence between firms’ tail risk exposures. Conditional on statistically pre-identified network spillover effects and market and balance sheet information, we define the realized systemic risk beta as the total time-varying marginal effect of a firm’s Value-at-Risk (VaR) on the system’s VaR. Suitable statistical inference reveals a multitude of relevant risk spillover channels and determines companies’ systemic importance in the U.S. financial system. Our approach can be used to monitor companies’ systemic importance allowing for a transparent macroprudential regulation.

Tailing Tail Risk in the Hedge Fund Industry

This paper aims to assess dynamic tail risk exposure in the hedge fund sector using daily data. We use a copula function to model both lower and upper tail dependence between hedge-fund and broad-market returns as a function of market uncertainty. We proxy the latter by means of a single index that combines the options-implied market volatility, the volatility risk premium, and the swap and term spreads. We find substantial time-variation in both lower- and upper-tail dependence, even for hedge fund styles that exhibit little unconditional tail dependence. In particular, dependence between hedge fund and equity market returns decreases in both tails significantly with market uncertainty. There are only a few styles that feature neither unconditional nor conditional tail dependence, e.g., convertible arbitrage and equity market neutral. We also fail to observe any tail dependence with bond and currency markets, though we find strong evidence that the lower-tail risk exposure of macro hedge funds to commodity markets increases with liquidity risk. Finally, further analysis shows mixed evidence on how much hedge funds contribute to systemic risk.

Demand for Crash Insurance and Stock Returns

We propose a new measure of financial intermediary constraints based on how the intermediaries manage their tail risk exposures. Using a unique dataset for the trading activities in the market of deep out-of-the-money S&P 500 put options, we identify periods when the variations in the net amount of trading between financial intermediaries and public investors are likely to be mainly driven by shocks to intermediary constraints. We then infer tightness of intermediary constraints from the quantities of option trading during such periods. We show that a tightening of intermediary constraint according to our measure is associated with increasing option expensiveness, higher risk premia for a wide range of financial assets, deterioration in funding liquidity, and deleveraging of broker-dealers.

Forward-Looking Tail Risk Exposures at U.S. Bank Holding Companies

This paper develops a simple method for quantifying banks’ exposures to large (negative) shocks in a forward-looking manner. The method is based on estimating banks’ share prices sensitivities to (market) put options and does not require the actual observation of tail risk events. We find that estimated (excess) tail risk exposures for U.S. Bank Holding Companies are negatively correlated with their share price beta, suggesting that banks which appear safer in normal periods are actually more crisis prone than their beta would suggest. We also study the determinants of banks’ tail risk exposures and find that their key drivers are uninsured deposits and non-traditional activities that leave assets on banks’ balance sheets.