Credit variance risk premiums

• Published date: 01 September 2023
• Author: Manuel Ammann,Mathis Moerke
• Date: 01 September 2023
• DOI: http://doi.org/10.1111/eufm.12394

DOI: 10.1111/eufm.12394

ORIGINAL ARTICLE

Credit variance risk premiums

Manuel Ammann |Mathis Moerke

Swiss Institute of Banking and Finance,

University of St. Gallen, St. Gallen,

Switzerland

Correspondence

Mathis Moerke, Swiss Institute of

Banking and Finance, University of St.

Gallen, St. Gallen, Switzerland.

Email: mathis.moerke@unisg.ch

Abstract

This paper studies variance risk premiums in the credit

market using a novel data set of swaptions quotes on

the CDX North America Investment Grade and High‐

Yield indices. The returns of credit variance swaps are

negative and economically large, irrespective of the

credit rating class. They are robust to transaction costs

and cannot be explained by established risk factors and

structural model variables. We also dissect the overall

variance risk premium into receiver and payer variance

risk premiums. We show that credit variance risk

premiums are mainly driven by the payer corridor,

which is associated with worsening macroeconomic

conditions.

KEYWORDS

CDS implied volatility, CDS variance swap, variance risk

premium

JEL CLASSIFICATION

G12, G13

Eur Financ Manag. 2023;29:1304–1335.1304

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This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits

use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or

adaptations are made.

© 2022 The Authors. European Financial Management published by John Wiley & Sons Ltd.

We have benefited from comments by the editor (John A. Doukas), an anonymous referee, Torben Andersen, Marc

Arnold, Nils Friewald, Joachim Grammig, Jens Jackwerth, Axel Kind, Angelo Ranaldo, Stefan Ruenzi, Christian

Schlag, Stace Sirmans, Erik Theissen, Viktor Todorov, Michael Weber and Florian Weigert, as well as the participants

of the 7th annual meeting of the Paris Financial Management Conference 2019, the SoFiE Financial Econometrics

Summer School 2019, of the doctoral workshop at the 26th annual meeting of the German Finance Association 2019,

the Brown Bag Seminar of the University of St. Gallen, the 2019 joint seminar session of the University of St. Gallen and

the University of Konstanz and the 2018 Topics in Finance Seminar in Davos.

1|INTRODUCTION

The analysis of variance risk and its associated market price has gained a lot of interest over the

last one and a half decades. Carr and Wu (2009) document in their seminal work strongly

negative variance risk premiums in equity markets. Similar findings have been documented in

most asset classes. However, variance risk is much less understood in credit markets than in

other asset classes. This is surprising given that credit derivatives constitute a nonnegligible

part of the global over‐the‐counter derivatives market. Moreover, credit volatility products have

sparked interest by investment banks and the asset management industry during the last years.

In case of equity markets, negative variance risk premiums have been reconciled with

exposure to rare disasters (see Dew‐Becker et al., 2017). Previous literature has shown that

credit default swaps (CDS) feature similar characteristics (Kelly et al., 2019; Wang et al., 2013)

and can be explained by similar underlying principles (Bai et al., 2020; Gabaix, 2012;

Gourio, 2013). From this perspective, the existence and magnitude of a risk premium related to

variability in CDS spreads are ambiguous. Moreover, it remains a priori unclear if variance risk

premia differ for various credit rating classes. Prior literature has found that a large market

price of risk for jumps is needed to explain investment grade CDS spreads, whereas high‐yield

CDS spreads are more sensitive to diffusive risks (Bai et al., 2020; Huang & Huang, 2012;

Huang et al., 2019), hence pointing towards notable differences between the two rating classes.

To the best of our knowledge, we are the first to study variance risk premiums in credit

markets, drawing upon a new data set of options written on two of the most prominent

corporate credit indices in the world, the CDX North America Investment Grade and High‐

Yield 5‐Year indices. We use the notion of synthetic variance swaps to assess the sign,

significance and magnitude of credit variance risk premiums (CVP, hereafter) over the period

from 2012 to 2021. In a variance swap, the ex‐post realized variance is exchanged for a fixed

variance swap rate, set at swap inception. The difference between the swap rate and the ex‐post

realized variance constitutes the variance risk premium. We use a model‐free estimation

approach to explicitly avoid any stand on microfoundations. Moreover, we follow the latest

developments for calculating realized variance to avoid biases due to discretization errors and

jumps (see Bondarenko, 2014; Neuberger, 2012).

We find large and significant variance risk premiums in credit markets. Moreover, CVP is

equally high across credit rating classes. An investment strategy capturing CVP by means of

shorting 1‐month variance swaps yields average monthly excess returns of 0.58% (0.73%) for

investment grade (high‐yield) credit. Our results are also quantitatively the same across rating

classes in terms of risk‐adjusted performance measures. The associated annualized Sharpe

ratios are well above 0.8.

After having established our main results, we aim at uncovering more details on CVP: What

drives the richness in CVP? How does it compare to other trading strategies capturing volatility

risk in credit and other asset classes? Can CVP be explained by standard asset pricing risk

factors or structural model variables?

1

Are there commonalities between equity and fixed‐

income variance risk premiums? To shed light on the sources of CVP, we use corridor variance

risk premiums following Andersen and Bondarenko (2010) and Kaeck (2018). In corridor

variance swaps, price moves of the underlying contribute only to a realized variance if they

1

We refer to variables implied by structural credit risk models as ‘structural model variables’. These include interest

rates and the leverage ratio, among others.

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happen to be within a specific price corridor. We decompose CVP into payer and receiver

variance risk. Payer (receiver) variance risk premiums are associated with price moves of the

CDS spread above (below) the CDS spread observed at swap inception. Therefore, payer

variance risk premiums are associated with bad economic states and receiver variance

risk premiums with good economic states of the world. We find that both corridor variance risk

premiums are significantly different from zero and sizeable. However, payer variance risk

premiums are larger in absolute magnitude compared to receiver variance risk premiums.

To address the second question, we first contrast CVP with another popular trading strategy

exposed to variance risk, namely, investing in at‐the‐money straddles. Additionally, we

compare CVP to shorting equity and fixed‐income variance swaps. None of the strategies

generate similar pure return or risk‐adjusted performances. As our data set spans the onset of

the Covid‐19 pandemic, we are able to compare CVP with risk premiums in other asset classes

across different market regimes. Precisely, we find that, though shorting credit variance swaps

have generated negative returns during the first half of 2020, its performance quickly regained

its relative differential to variance strategies in other asset classes in the second half of 2020, as

evident before 2020.

Subsequently, we show that CVP cannot be explained by structural model variables.

Moreover, we find that CVP and also corridor variance risk premiums remain largely unaltered

when we consider standard asset pricing factors, such as the Fama and French (2018) six‐factor

equity model, augmented by the intermediary capital risk factor of He et al. (2017) or the four‐

factor model of Bai et al. (2019) for corporate bonds.

Next, we analyse the comovement of CVP with equity, fixed‐income and variance‐of‐

variance risk premiums. We show that CVP loads significantly and positively on equity

variance risk premiums. However, the latter are not sufficient to fully explain CVP.

Finally, our analysis yields credit‐implied volatility indices as by‐products. We study the

informational content of credit‐implied variance and its term structure. Credit‐implied variance

possesses strong predictive power for financial stress, measured by the St. Louis Fed Stress

Index (Federal Reserve Bank (2021).

Our paper is related to various strands of the literature. First, our results extend findings by

Kita and Tortorice (2021) to the index level. Credit indices are the most liquid and most traded

credit derivatives in the world. We find that investors pay high‐risk premiums to be insured

against credit volatility risk. In contrast to Kita and Tortorice (2021), our analysis does not need

to rely on a structural model, as it is completely model‐free and employs credit swaptions.

Although we confirm the author's findings that CVP are larger than equity variance risk

premiums, we do not find support that this relation is inversely related to the leverage ratio.

Second, we add to the research on documenting variance risk premiums in other asset

classes. Carr and Wu (2009) have been the first to document negative and economically large

variance risk premiums, focusing on equity markets. Ammann and Buesser (2013) adopt the

approach and study foreign exchange variance risk premiums. Trolle and Schwartz (2010) and

Prokopczuk et al. (2017) analyze commodity markets and Trolle and Schwartz (2014) and Choi

et al. (2017) focus on a fixed income. In line with other asset classes, we document strongly

negative CVP. However, CVP dwarf their analogue in all other asset classes. Rather, our

findings suggest that CVP serve as catastrophic risk premiums. Credit index tranches are

conceptually similar, but not equal to credit index swaptions. Previous research has shown that

these instruments also contain catastrophic or systemic risk premiums. Longstaff and Rajan

(2008) estimate that 8% of the credit index spread is attributable to a systemic event in which

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