Bank Value at Risk Disclosures and Risk Predictability: the Effect of Derivative Use

Bank Value at Risk Disclosures and Risk Predictability: The Effect of Derivative Use

Abstract

Banks disclose value at risk (VaR) data that is, in principle, instrumental in predicting the subsequent variability of trading income. Using a sample of 18 United States commercial bank holding companies from 1997 to 2006, we find that VaR is a predictive risk measure. Nevertheless, we find that derivative use reduces the predictability of VaR-based measures of volatility. Thus, investors and analysts are cautioned when using VaR disclosures of banks with large derivative positions.

Keywords: value at risk disclosures, predictability, derivatives, trading income, moderating effect

INTRODUCTION

The increase in the number, range, and scope of mandatory disclosures by bank holding companies has been notable; in particular, the publication of value at risk (VaR) estimates by banks has received considerable attention. This was mandated by Financial Reporting Release No. 48 published in 1997 that requires public traded firms to disclose their market risk exposure using a tabular presentation, a sensitivity analysis, or value-at-risk (VaR) (Linsmeier and Pearson 1997). Since then, VaR disclosures have been used by analysts to gauge the market risk of banks. However, several papers have questioned the suitability of VaR as a risk measure. Berkowitz and O’Brien (2002) indicate that banks’ VaR models are not superior to a simple volatility measure. Dowd and Blake (2006) further argue that VaR is seriously flawed as a measure of risk. On the other hand, Jorion (2002) and Liu, Ryan, and Tan (2004) find evidence that banks’ trading value-at-risk disclosures are informative in predicting the variability of future trading revenues. They also find that derivative use by banks increases the variability of unexpected trading revenues.

Banks, acting both as derivative dealer and end-user, participate in the derivative markets. Over the past decade, banks have been increasing their use of derivatives. Banks’ trading revenues have also gradually become more and more important for their profitability.[1] Banks’ use of derivatives leads to greater variability of future trading revenues. The use of derivatives by banks is sophisticated. As a derivative dealer, banks provide quotes to other market participants, while, as end-user, they use derivative contracts to manage portfolios, or to hedge risk. Empirical evidence on the relation between banks’ derivative use and risk is inconclusive. Some studies argue that there is no correlation between derivative usage and firm risk (Koski and Pontiff, 1999; Hentschel and Kothari, 2001; Guay and Kothari, 2003; Bali, Hume and Martell, 2007). However, Venkatachalam (1996) and Yang, Song, Yi, and Yoon (2006) find that bank holding companies use derivative contracts to reduce risk. Sinkey and Carter (2000) also note that banks with a higher likelihood of financial distress are more likely to use derivatives to hedge. Furthermore, it is even argued that interest rate derivatives actually increase the exposure of banks to interest rate risk (Hirtle, 1997; Yong, Faff and Chalmers, 2009). Nijskens and Wagner (2011) find that the market considers the banks that use credit derivatives to be riskier. Thus, the relation between derivative use and risk is an empirical question.

VaR disclosures seem not to properly account for derivative use. In part, this is due to the fact that VaR models have their strengths and weaknesses and work best with particular types of portfolios (Jorion 2000; Linsmeier and Pearson 2000). When optionality in portfolios is significant, the predictability of VaR measures will be adversely affected if the appropriate VaR models are not used. Beder (1995) points out that the increasing complexity and optionality of derivatives makes the scenario selection for VaR calculations even harder. VaR is difficult to apply when portfolios include significant non-linear derivatives such as options and option-like instruments (El-Jahel, Perraudin, and Sellin 1999). For instance, the delta-normal approach entails mapping instruments to delta-equivalent positions and mapping derivatives, especially options, can be more complicated than other assets (Linsmeier and Pearson 2000). The delta-equivalent method inadequately measures the risk of non-linear instruments with asymmetric payoffs because it does not take account of their gamma (convexity) (Jorion 2000; Hull 2007). However, it works well for portfolios with little option content, especially when the holding period is short (Linsmeier and Pearson 2000).

The historical simulation method is onerous for complex portfolio structures (Jorion 2000). The Monte Carlo simulation involves model risk because it requires the stochasticity of underlying market risk factors and pricing models for options. Given these modeling issues, the predictability of VaR is reduced when banks use more derivatives.

Banks’ disclosures are intended to reveal their market risk profile. Jorion (2002) was the first to examine the predictability of banks’ VaR disclosures. Using a sample of eight banks for the period 1994 to 2000, he finds that VaR disclosures are informative in forecasting the subsequent variability of their trading revues. Using a larger sample of 17 banks from 1997 through 2002, Liu, Ryan, and Tan (2004) also find that VaR disclosures have predictive power for trading revenues variability.

In this paper, we reexamine the question using a larger and extended sample of 18 commercial banking holding companies from 1997 to 2006. As with earlier studies, we find that banks’ trading VaRs have predictive power in accounting for the variability of trading revenues, but find that derivative use significantly reduces predictability. To investigate the moderating role of derivative use, we include a variable that interacts the volatility measure inferred from VaR disclosures with the derivative use variable. To our knowledge, the current study is the first to examine the moderating effects of derivative use on the relation between forecasted trading revenues volatility—inferred from VaR disclosures—and unexpected trading revenues.

The remainder of the paper proceeds as follows. Section 2 introduces the sample, data, and research design. In Section 3, we present the empirical results from which we offer some conclusions and their implications in Section 4.

DATA AND METHODOLOGY

To examine the moderating effects of derivative use on the predictability of the VaR numbers, we collect data on U.S. commercial bank holding companies from their 10-Q and 10-K filings from the EDGAR database for the period of 1997-2006.[2] Larger banks generally have more technical sophistication with which to develop VaR systems and thus better capability of using VaRs to predict unexpected trading revenues (Liu, Ryan, and Tan 2004).[3] Moreover, these banks generally engage in derivative markets. We therefore collect the data for the largest 100 banks in terms of total assets. Banks without trading revenues, VaR and derivative use disclosures in their 10-Q and 10-K reports are excluded. The final sample includes 18 commercial bank holding companies and 396 firm-quarter observations. Table 1 provides the sample banks’ names, total assets, SIC and CIK codes, and the time they first disclosed VaRs in their quarterly and annual filings. Table 2 shows the descriptive statistics for the sample banks.

(Insert Tables 1 and 2 about here)

We first scale up daily VaRs collected from banks’ 10-Q and 10-K filings to quarterly VaRs using the square root of time rule (Smithson 1999; Jorion 2002; Liu, Ryan, and Tan 2004). According to this rule, we multiply daily VaRs by the square root of 63 to obtain quarterly VaRs based on the assumption that a quarter has 63 working days. We then infer the volatility in quarterly trading revenues from the quarterly VaR divided by a, the standard normal variable. For one-tailed 99%, 97.5%, and 95% confidence levels, the values of are 2.33, 1.96, and 1.645, respectively. In our sample, most banks present their VaR under the confidence level of 99%. If banks report the VaR under different confidence levels, however, we follow Linsmeier and Pearson (2000) to normalize the VaR.[4]

We measure the unexpected quarterly trading revenues as the difference between the actual quarterly trading revenues and the expected quarterly trading revenues. Like Jorion (2002) and Liu, Ryan, and Tan (2004), the expected quarterly trading revenues are proxied by their moving average over the previous four quarters.

Following Jorion (2002) and Liu, Ryan, and Tan (2004), we examine the predictability of VaR disclosures by estimating the following equation:

Unexpected trading revenues t = f (VaR-based volatility, Derivative use, VaR-based volatility×Derivative use) + (1)

where the unexpected trading revenues are proxied by the difference between the actual quarterly trading revenues and the expected quarterly trading revenues; VaR-based volatility is the standard deviation inferred from the VaR disclosures; derivative use is the notional amount of derivatives used by banks, deflated by firm size; VaR-based volatility×Derivative use is the interaction between VaR-based volatility and derivative use.

EMPRICAL RESULTS

Table 3 shows the pooled ordinary least squares regression results for the unexpected trading revenues. The adjusted R-squared across models ranges from 0.31 to 0.37, and their F-tests are all significant at the 0.01 level. As expected, VaR-based volatility has statistically significantly positive effects on unexpected trading revenues, suggesting that banks’ VaR disclosures have predictive power in forecasting the next quarter’s variability of unexpected trading revenues with/without controlling for derivative use. This finding is consistent with Jorion (2002) and Liu, Ryan, and Tan (2004). We also find that the coefficients of derivative use are positive and highly significant. This suggests that banks’ derivative use increases the risk of next quarter’s trading revenues.

(Insert Table 3 about here)

Finally, we find that the coefficients for the interaction term, VaR-based volatility×Derivative use, is significantly negatively related to unexpected trading revenues, indicating that derivative use adversely affects the predictive power of VaR disclosures.[5] This is possibly because banks’ portfolios may include large quantities of options or option-like instruments with asymmetric payoffs. The asymmetric payoff of these instruments reduces the ability of VaR to correctly capture the risk.

CONCLUSION

Prior research has suggested that VaR disclosures reveal the market risk profile of firms. Jorion (2002) and Liu, Ryan, and Tan (2004) finds that banks’ VaR numbers significantly predict the next quarter’s risk. Due to the complexity of derivative instruments, it is to be expected that the predictability of VaR disclosures should be reduced for banks with large derivative positions in their portfolios.

In this paper, we provide evidence that this has been the case. Using a sample of 18 U.S. commercial bank holding companies reporting trading VaR during the period 1997 to 2006, we find that VaR predicts the subsequent variability of trading revenues. Furthermore, we find that the predictability will be reduced for banks with significant derivative positions.

Our study has a significance for those interested in using risk disclosures made by financial institutions, such as regulatory authorities, analysts, and stakeholders. They are cautioned about the predictability of VaR numbers disclosed by banks heavily engaged in the derivative markets.

REFERENCES

Bali, T.G., S.R. Hume and T.F. Martell (2007), ‘A New Look at Hedging with Derivatives: Will Firms Reduce Market Risk Exposure?’, Journal of Futures Markets, 27: 1053-83.

Beder, T.S. 1995. "VAR: Seductive but Dangerous." Financial Analysts Journal, vol. 51, no. 5 (September/October):12-24.

Berkowitz, J., and J. O’Brien. 2002. "How Accurate are Value-at-Risk Models at Commercial Banks?" Journal of Finance, vol. 57, no. 3 (June):1093-1111.

Dowd, K., and D. Blake. 2006. "After VaR: the Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures." Journal of Risk and Insurance, vol. 73, no. 2 (June):193-229.

El-Jahel, L., W. Perraudin, and P. Sellin. 1999. "Value at Risk for Derivatives." Journal of Derivatives, vol. 6, no. 3 (Spring):7-26.

Guay, W.R.(1999), ‘The Impact of Derivatives on Firm Risk: An Empirical Examination of New Derivatives Users’, Journal of Accounting and Economics, 26: 319-51.

Hentschel, L. and S.P. Kothari (2001), ‘Are Corporations Reducing or Taking Risks with Derivatives?’, Journal of Financial and Quantitative Analysis, 36: 93-118.

Hull, J. 2007. Risk Management and Financial Institutions, first edition, Pearson Prentice Hall. USA.

Jorion, P. 2000. Value at Risk, second edition, McGraw-Hill. USA.

Jorion, P. 2002. "How Informative are Value-at-Risk Disclosures?" Accounting Review, vol. 77, no. 4 (October):911-931.

Koski, J.L. and J. Pontiff (1999), ‘How Are Derivatives Used? Evidence from the Mutual Fund Industry’, Journal of Finance, 54: 791-816.

Linsmeier, T.J., and N.D. Person. 1997. "Quantitative Disclosures of Market Risk in the SEC Release." Accounting Horizons, vol. 11, no. 1 (March):107-135.

Linsmeier, T.J., and N.D. Person. 2000. "Value at Risk." Financial Analysts Journal, vol. 56, no. 2 (March/April):47-65.

Liu, C., S.G. Ryan., and H. Tan. 2004. "How Banks' Value-at-Risk Disclosures Predict Their Total and Priced Risk: Effects of Bank Technical Sophistication and Learning over Time." Review of Accounting Studies, vol. 9, no. 2:265-294.

Nijskens, R. and W. Wagner. 2011. “Credit Risk Transfer Credit risk transfer activities and systemic risk: How banks became less risky individually but posed greater risks to the financial system at the same time.” Journal of Banking and fiancé, vol. 35, no. 6: 1391-1398.

Sinkey, J.F., and D.A. Carter. 2000. "Evidence on the Financial Characteristics of Banks that Do and Do Not Use Derivatives." The Quarterly Review of Economics and Finance, vol. 40, no. 4 (Winter):431-449.

Smithson, C.W. 1999. Managing Financial Risk, third edition, McGraw-Hill, USA.

Venkatachalam, M. 1996. "Value-Relevance of Banks’ Derivatives Disclosures." Journal of Accounting and Economics, vol. 22, 327-355.

Yang, D., I. Song, J. Yi, and Y. Yoon. 2006. "Effects of Derivatives on Bank Risk." Review of Pacific Basin Financial Markets and Policies, vol. 9, no. 2 (June):275-295.

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Table 1. Description for the 18 U.S. Commercial Bank Holding Companies

Bank / Total assets as of end of 2006
(in millions of $) / SIC / CIK / First VaR disclosure
10-K / 10-Q
CITIGROUP INC. / 1,884,318 / 6021 / 0000831001 / 1997 / 1998, Q2
BANK OF AMERICA CORPORATION / 1,463,685 / 6021 / 0000070858 / 1998 / 1998, Q3
JPMORGAN CHASE & CO. / 1,351,520 / 6021 / 0000019617 / 1994 / 1995, Q1
WACHOVIA CORPORATION / 707,121 / 6021 / 0000036995 / 1997 / 1998, Q1
WELLS FARGO & COMPANY / 527,715 / 6021 / 0000072971 / 2002 / 2004, Q1
SUNTRUST BANKS, INC. / 478,159 / 6021 / 0000750556 / 2002 / 2003, Q1
REGIONS FINANCIAL CORPORATION / 430,398 / 6021 / 0001281761 / 2004 / 2004, Q3
NATIONAL CITY CORPORATION / 261,217 / 6021 / 0000069970 / 1997 / NA
STATE STREET CORPORATION / 219,232 / 6022 / 0000093751 / 1997 / 1998, Q1
BANK OF NEW YORK COMPANY / 103,455 / 6022 / 0000009626 / 1998 / 1998, Q1
PNC FINANCIAL SERVICES GROUP / 101,854 / 6021 / 0000713676 / 1997 / 1998, Q1
KEYCORP / 92,337 / 6021 / 0000091576 / 1997 / 1998, Q1
NORTHERN TRUST CORPORATION / 60,712 / 6022 / 0000073124 / 1997 / NA
UNIONBANCAL CORPORATION / 52,620 / 6021 / 0001011659 / 1997 / 2003, Q1
POPULAR / 47,404 / 6022 / 0000763901 / 1999 / NA
MELLON FINANCIAL CORPORATION / 41,478 / 6021 / 0000064782 / 1996 / 1996, Q1
BOK FINANCIAL CORPORATION / 18,060 / 6021 / 0000875357 / 1998 / 1998, Q1
UMB FINANCIAL CORPORATION / 8,918 / 6021 / 0000101382 / 2003 / 2004, Q1

Table 2. Descriptive Statistics of Sample Banks (unit: in millions of $)