Mixing fair-value and historical-cost accounting: predictable other-comprehensive-income and mispricing of bank stocks

Abstract

Other comprehensive income (OCI) items are often considered to be transitory (Chambers et al. 2007; IASB 2013; CFA2014). In this paper, we show that a significant portion of OCI, namely unrealized gains and losses (UGL) from available-for-sale (AFS) debt securities, is non-transitory: a negative correlation between accumulated unrealized gains and losses in the current period and next period UGL is predicted, and we show that this correlation is economically and statistically significant. This correlation is due to a mix of accounting methods of measurement of income from fixed-income securities: UGL are recognized based on fair values, whereas interest income is measured based on historical cost. We document that (1) this negative correlation helps explain a previously unexplained negative correlation in other comprehensive income (OCI), and (2) investors seem to price total UGL disregarding (or not understanding) the predictable, accounting-driven component of UGL.

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Notes

  1. 1.

    We use the term “comprehensive income” to mean regular income (which is the bottom line of the income statement) plus “other comprehensive income” as defined in Statement of Financial Accounting Standards No. 130 Reporting Comprehensive Income (SFAS 130).

  2. 2.

    The Financial Accounting Standards Board (FASB) Accounting Standards Codification incorporates SFAS 115 as ASC 320 Investments, Debt and Equity Securities. The issues we raise regarding SFAS 115 also apply to International Accounting Standard (IAS) 39: Financial Instruments: Recognition and Measurement.

  3. 3.

    We elaborate on and explain this predictability in section 2.1.

  4. 4.

    Chambers et al. (2007), for instance, document that investors price other comprehensive income items almost dollar-for-dollar, consistent with the transitory nature of fair value changes.

  5. 5.

    See SFAS 115, IAS 39 and IAS 36: Impairment of Assets.

  6. 6.

    Very few banks in our sample (3%) recorded OTTIs before the global financial crises, but 24% recorded OTTIs during the crisis and 28% have recorded OTTIs in the years post the crisis. This significant number of OTTIs suggests that managers take the recognition of OTTIs seriously, and, if an unrealized loss is not recorded as an OTTI (and hence remains in AUL), it signals that the bank will not sell the security before maturity; no such signal exists for AUG.

  7. 7.

    The literature debates the usefulness/relevance of the Fama and French and Carhart risk factors in controlling for differences in risk of bank stocks (for example, Barber and Lyon 1997; Petakova 2006; Viale et al. 2009). This inconclusive debate leads us to include the Fama and French and Carhart factors as well as the Viale et al. risk factors as controls for risk explanations for stock and portfolio returns.

  8. 8.

    Our paper is closely related to the work of Dong et al. (2014), who examine the pricing of explicit/disclosed reclassifications of accumulated other comprehensive income (AOCI) associated with UGL on AFS securities to net income upon sale or other than temporary impairment of the securities; as of 1998, FAS 130 requires financial report disclosure of these reclassifications. Our paper, instead, examines the pricing of implicit/undisclosed reclassifications of AOCI and UGL associated with the FAS 115-required accrual of interest revenue on AFS debt securities each period in the amount of the effective interest rate times the beginning-of-period amortized cost of the securities, rather than as the current relevant market interest rate times the beginning-of-period fair value of the securities.

  9. 9.

    Similar examples are presented by Wahlen et al. (1999), Ryan (2007), and Ryan (2012), showing how the interest revenue and net income under SFAS 115 can be overstated or understated compared to the amount of interest revenue and net income under true mark-to-market accounting.

  10. 10.

    The numerical example also provides guidance for our research design. Notice that even though UGLt and UGLt-1 are negatively correlated in year 2, they are positively correlated in year 3. In contrast, AUGLt-1 and UGLt are negatively correlated in both years. In our empirical tests, we focus on the negative correlation between AUGLt-1 (AUGt-1, AULt-1) and UGLt.

  11. 11.

    Jones and Smith (2011) explain the recycling scenario as follows. Consider a simple scenario where an available-for-sale security is purchased for $100, increases in value by $25 during the first year, holds that value for two more years, and then is sold for $125. In the first year, the $25 gain would be recorded as an OCI gain. However, OCI for years two and three would be zero, and so the $25 gain could be viewed as transitory. But, since the $25 is recycled out of accumulated OCI upon sale and recognized as a gain in net income, the OCI amount for year three is a $25 loss. Thus, in this scenario, OCI would have zero persistence in the short run, but 100% negative persistence in the long run, i.e., the $25 gain in year one would reverse in year three.

  12. 12.

    Conceptually it is not clear why investors rely on OCI information, such as UGL, when the fair value of the underlying assets is shown on the balance sheet. We conjecture that it might be, at least partially, due to the fact interest income from AFS securities is aggregated with the interest income from other bank assets, which prevents investors from taking an asset-by-asset approach when valuing banks.

  13. 13.

    Although UGL are measured on an after-tax basis, it is conceivable that factors such as tax can cause market valuation of UGL to deviate from the benchmark case of dollar-for-dollar.

  14. 14.

    In nonreported analyses, we have separately studied observations from the pre-crisis and the post-crisis periods. Results are similar across these two periods, although effects that are statistically significant when these two sets of observations are combined are sometimes not significant when the samples are separated.

  15. 15.

    Similar differences are not observed between the crisis- and the noncrisis years for UGL due to the significant increase in other-than-temporary impairments during the crisis years. Impairment became permanent due to a decrease in credit quality during the financial crisis and a significant portion of AUGL was realized via OTTI. Evidence on the increase in OTTI is provided by Badertscher et al. (2012).

  16. 16.

    The Spearman correlation is, however, significantly positive; this correlation appears to be driven by observations in the crisis years.

  17. 17.

    The correlation between AULt-1 and AUGt-1 is very high (for example in the noncrisis years, the Pearson correlation is 0.71), and therefore we do not put much weight on these simple correlations but rather focus on the results from our multiple regression, which includes both of these variables. These results are reported in Table 3.

  18. 18.

    Following Petersen (2009), we include year dummies in these regressions, with t-statistics adjusted for clustering by firm. In all regressions, we remove the top and bottom 1 % of observations to avoid the effects of outliers.

  19. 19.

    Note that our sample is different from that of Jones and Smith (2011), which includes 236 companies, mostly industrial, with nonzero OCI gains or losses in years 1986–2005. We also repeat the tests in Table 4 for subsamples with high, medium, low FI as well as for the financial crisis and noncrisis years. Untabulated results show that, in all subsample tests, the estimated coefficients on OCIt-1 and AOCIt-1 are not significantly different from zero when lagged AUG and lagged AUL are included in the regression.

  20. 20.

    We limit the variables in the prediction model to lagged AUL, lagged AUG, and partitions on FI because we found that other variables designed to capture bank characteristics, such as size, book-to market, and proxies for CAMELS characteristics provide little incremental predictive power with respect UGL beyond these three variables. Nonetheless, as a sensitivity check, we repeat our analysis with these additional variables included and calculate the predicted component based on AUG, AUL, and FI. Our results are robust to this variation in research design.

  21. 21.

    For example, the predictions of UGL for 2006 are based on regression of UGL on lagged AUG and lagged AUL for each of the years 1999 to 2005. For the entire sample, this continues to be the case for all years; the predictions for 2011 are based on regression parameters from 1999 to 2010. In the subsample where we remove the crisis years (2007 to 2009), the forecasts for 2011 are based on parameters estimated for years 1999–2006 and 2010. Note that the prediction is formed after the announcement of AUG and AUL; i.e., the prediction is formed 12 months before the actual UGL is known.

  22. 22.

    In addition, we have also included the Sloan (1996) accrual variable (ACCU). The results show that, unlike the results for industrial firms, ACCU does not load for our sample of banks.

  23. 23.

    On the other hand, larger banks may attract more sophisticated investors and more analysts, which can reduce the magnitude of mispricing.

  24. 24.

    http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

  25. 25.

    The three bank-risk factors in regression (4) are time-specific factors and therefore appropriate for time-series regression (4), whereas the two variables, GAP and PCL used in regression (3) are firm-specific variables and therefore appropriate for that cross-sectional regression.

  26. 26.

    Alternatively, the predictive component of UGL may be viewed as a proxy for a bank risk factor that is not captured by the known control factors.

  27. 27.

    SFAS 12 (1975) requires the recognition of valuation allowance when the aggregate market value of a portfolio of securities is below the cost of the portfolio. In scenario 2, we assume that the company holds only one security.

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Acknowledgements

We thank David Aboody, Ashiq Ali, Brad Badertscher, Michael Chin, Valentin Dimitrov, Lakshmana Krishnamoorthy, Ram Natarajan, Russell Lundholm (editor), Jeffrey Ng, James Ohlson, Peter Pope, Suresh Radhakrishna, Gil Sadka, Kate Suslava, Nir Yehuda, Jieying Zhang, three anonymous referees, and workshop participants at University of Auckland, Hong Kong PolyTech University, University of Melbourne, the University of New South Wales, Rutgers University, University of Texas at Dallas, and the Tel Aviv Accounting Conference for helpful comments.

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Correspondence to Xiao-Jun Zhang.

Appendices

Appendix 1: Variable defintions

AOCI::

Accumulated other comprehensive income items. This is the sum of derivative gains and losses (Compustat item AOCIDERGL), pension gains and losses (Compustat item AOCIPEN), foreign currency gains and losses (Compustat item RECTA), other (Compustat item AOCIOTHER), plus accumulated unrealized gains and losses from AFS securities.

AUGL::

Accumulated unrealized holding gains and losses from available-for-sale securities. Data are hand-collected from sample bank annual reports.

AUG (AUL)::

Accumulated unrealized holding gains (losses) from available-for-sale securities. Data are hand-collected from sample bank annual reports.

BETA::

CAPM beta estimated using 60 monthly return data up to the third month after fiscal year-end.

BM::

Book-to-market ratio, calculated as the book value of the bank (Compustat item CEQ) divided by the CRSP market capitalization of the bank at the end of the third month after fiscal year-end.

BOND::

Amortized cost of AFS securities invested in corporate bonds.

CB10Y: :

Residual from a vector-autoregression of the 10-year Moody’s AAA corporate bonds yield over the yield on 10-year Treasury securities, together with three-month Treasury bill and 10-year Treasury securities. Data are obtained from the Federal Reserve’s online FRED database.

CMA::

Return on a portfolio of stocks that is long in banks with high growth in total assets and short in stocks with low growth in total assets.

COSTAFS: :

Amortized cost of all AFS securities.

FI::

Estimate of the percentage of AFS securities invested in fixed-income securities.

GAP::

Difference between short-term investment (Compustat item IST) and short-term liabilities (Compustat item DLC), deflated by total assets (Compustat item AT).

GTA::

Annual growth in total assets.

GS10Y: :

Residual from a vector-autoregression of 10-year Treasury securities, together with three-month Treasury bill and 10-year Moody’s AAA corporate bonds. Data obtained from the Federal Reserve’s online FRED database.

HML::

Monthly return on a portfolio of stock, which is long in stock with a high book-to market ratio and short in stocks with a low book-to-market ratio.

MBS::

Amortized cost of AFS securities invested in mortgage-backed securities.

MOMENTUM: :

Return on the equity of the bank for the 12 months ending in the third month of the trailing fiscal year.

MUNI::

Amortized cost of AFS securities invested in Municipal obligations.

NI::

Net income (Compustat item IBCOM).

OCI::

Other comprehensive income items, which is the sum of foreign currency gains and losses (Compustat item CICURR), derivative gains and losses (Compustat item CIDERGL), pension gains and losses (Compustat item CIPEN), other (Compustat item CIOTHER), plus accumulated unrealized gains and losses from AFS securities.

OTTI::

Other than temporary impairments.

PCL::

Provision for credit and loan loss (Compustat item PCL), as a percentage of total interest income (Compustat item IDIT).

PUGL::

Predicted unexpected gains and losses.

RECL: :

Reclassified AFS security gains and losses.

RGL::

Realized gains and losses on AFS securities.

ROE::

Return on equity, used as a measure of profitability.

RF::

Rate of return on three-month treasury bills, measured over 12 months in regression (3) and over one month in regression (4).

R j ::

One-year-ahead buy-and-hold returns on the stock of bank j.

R M : :

Rate of return on the CRSP Value weighted index, measured over 12 months in regression (3) and over one month in regression (4).

R p ::

Monthly return on a portfolio of stocks formed by going long stocks with high PUGL and short stocks with low PUGL.

RMW::

Monthly return on a portfolio of stocks that is long in stocks with high profitability and short in stocks with low profitability.

SIZE::

The logarithm of the equity market value on the last trading date in the third month after the fiscal year-end. Price and number of shares outstanding are obtained from the CRSP.

SMB::

Monthly return on a portfolio of stock, which is long in small stocks and short in stocks with a high market capitalization.

TA::

Total assets (Compustat item AT).

TB::

Amortized cost of AFS securities invested in Treasury bills.

TB3 M::

Residual from a vector-autoregression of three-month Treasury bill, together with 10-year treasury securities and 10-year Moody’s AAA corporate bonds. Data obtained from the Federal Reserve’s on-line FRED database.

UGL::

Un realized gains and losses on AFS debt securities.

UMD::

Return on a portfolio of stocks that is long in stocks with high returns over the past 12 months and short in stocks short in stocks with low past returns.

Appendix 2: Numerical example of the accounting mechanism leading to negative correlation between UGLt and AUGLt-1

$100 invested in AFS, three-year, 10% annual coupon debt security issued at par.

Scenario 1a: Discount rate decreases to 8% at end of year 1; bank holds the AFS debt security.

   Post SFAS 115 Pre SFAS 115
Date Fair Value AUGL UGL RGL Interest AUGL RGL Interest
12/31/×0 $100.00        
12/31/×1 $103.57 $3.57 $3.57 $0.00 $10.00 $0.00 $0.00 $10.00
12/31/×2 $101.85 $1.85 ($1.72) $0.00 $10.00 $0.00 $0.00 $10.00
12/31/×3 $0.00 $0.00 ($1.85) $0.00 $10.00 $0.00 $0.00 $10.00

Scenario 1b: Discount rate decreases to 8% at end of year 1; bank sells the AFS debt security at the beginning of year 2.

    Post SFAS 115 Pre SFAS 115
Date Fair Value AUGL UGL RECL RGL Interest AUGL RGL Interest
12/31/×0 $100.00         
12/31/×1 $103.57 $3.57 $3.57 $0.00 $0.00 $10.00 $0.00 $0.00 $10.00
12/31/×2 $0.00 $0.00 0.00 -$3.57 $3.57 $0.00 $0.00 $3.57 $0.00
12/31/×3 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

Scenario 2: Discount rate increases to 12% at end of year 1; bank holds the AFS debt security.

   Post SFAS 115 Pre SFAS 115Footnote

SFAS 12 (1975) requires the recognition of valuation allowance when the aggregate market value of a portfolio of securities is below the cost of the portfolio. In scenario 2, we assume that the company holds only one security.

Date Fair Value AUGL UGL RGL Interest AUGL RGL Interest
12/31/×0 $100.00        
12/31/×1 $96.62 ($3.38) ($3.38) $0.00 $10.00 ($3.38) $0.00 $10.00
12/31/×2 $98.21 ($1.79) $1.59 $0.00 $10.00 ($1.79) $0.00 $10.00
12/31/×3 $0.00 $0.00 $1.79 $0.00 $10.00 $0.00 $0.00 $10.00

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Easton, P., Zhang, X. Mixing fair-value and historical-cost accounting: predictable other-comprehensive-income and mispricing of bank stocks. Rev Account Stud 22, 1732–1760 (2017). https://doi.org/10.1007/s11142-017-9423-1

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Keywords

  • Market mispricing
  • Bank risk factors
  • Holding gains and losses
  • Available-for-sale securities
  • Commercial banks
  • Fair value accounting
  • Other comprehensive income

JEL classifications

  • M41
  • G14
  • G21