Do Investors Understand Really Dirty Surplus?

Do Investors Understand Really Dirty Surplus? Ken Peasnell CFA UK Society Masterclass, 19 October 2010

Do Investors Understand Really Dirty Surplus? Wayne Landsman (UNC Chapel Hill), Bruce Miller (UCLA), Ken Peasnell (Lancaster), Shu Yeh (National Taiwan University) The Accounting Review, January 2011 What we found in a nutshell: Using a measure we call really dirty surplus (RDS), for a sample of 28,346 firm-year observations drawn from the US compustat database for firms with assets > $10m, we were able to generate riskadjusted one-year hedge returns of 4% during the period 1976-2006. Assuming this is not simply due to an unmodeled risk factor, we attribute it to difficulties investors face in properly taking account of dilution effects of firms equity transactions.

Genesis of the study Our prior work on how stock prices reflect accounting information. In particular, Landsman, Peasnell, Pope, Yeh, Which approach to accounting for employee stock options best reflects market pricing? Review of Accounting Studies, 2006 Landsman, Miller, Yeh, Implications of components of income excluded from pro forma earnings for future profitability and equity valuation Journal of Business Finance & Accounting, 2007

So what is Really Dirty Surplus (RDS)? Clean Surplus is earnings that includes all changes in equity, other than share transactions & dividends, both reported net income and other comprehensive income (= total comprehensive income) Dirty surplus is the gains/losses in OCI Really dirty surplus are gains and losses arising from accountants recording own share transactions at amounts other than fair value

Dirty surplus (DS) is readily observable from the financial statements Statement of Owners Equity Examples include gains/losses on investments, deferred pension costs, translation gains/losses. Really dirty surplus (RDS) is not readily observable Examples include employee stock option exercises, preferred stock and debt conversions to equity, and business combinations accounted for under pooling of interests Investors might not know the transaction dates and hence prices of equity and therefore properly allow for dilution.

Research Question Do share prices correctly reflect the earnings implications of DS and RDS? DS items are components of earnings that are excluded from reported earnings RDS items are violations of super clean surplus accounting arising from equity transactions not recorded at fair market value Prior research has largely settled the dirty surplus question. We use it to benchmark the really dirty surplus results

Our Approach We assess whether investors get it right using two related approaches Estimate a residual income forecasting equation and attendant valuation model that includes estimates of both DS and RDS components Test predictions linking the valuations coefficients of DS and RDS to their forecasting properties Construct hedge portfolios based on magnitude of DS and RDS as a fraction of equity book value. Conjecture if mispricing is present, then it s likely to be most pronounced for small firms that are less well followed and for whom detailed accounting analysis can be more costly. Therefore conduct analyses separately for small/medium/large firms.

Results Summarized Primary Findings Forecasting/Value Relevance tests DS and RDS are forecasting irrelevant for all size firms. Consistent with this, DS is also valuation irrelevant for all size firms. In contrast, investors undervalue RDS (which tends to be negative): suggests that investors cannot readily assess dilution effects of RDS transactions. Hedge return tests Support the findings linking the forecasting/valuation equations. Hedge returns are zero for DS. Hedge returns are positive for RDS.

Research Design The clean surplus equation is: BVE t = BVE t 1 + X t + DS t Div t + P t A (N t N t 1 ) (1) N is number of shares outstanding, P A is accounting price per share used to record issuance/reacquisition. If DS is 0, then (1) satisfies clean surplus accounting. In this case, current equity book value and future residual income sum to equity market value Let P M be market price per share at issuance/reacquisition. RDS t (N t N t 1 )(P t A P t M ) (2)

Because typically P M >P A and N t > N t-1, RDS is typically negative. Combining (1) and (2) yields Research Design DS t + RDS t = BVE t BVE t 1 X t + Div t P t M (N t N t 1 ). (3) If DS and RDS are zero, then (3) satisfies super clean surplus accounting (Christensen and Feltham, 2003). PV of net dividends sum to market value of equity of existing shares. Note that because DS and the RHS of (3) can be computed (with error) from observable accounting numbers, RDS can be determined without having to estimate P A.

Research Design Generally, DS and RDS will be non-zero. We therefore will allow for this and super clean surplus accounting by redefining income as very comprehensive net income, VCNI, which is earnings, DS, and RDS, i.e., VCNI t = X t + DS t + RDS t When super-clean surplus holds, then application of residual income valuation model yields an estimate of equity value that equals market value of existing shares.

Research Design Returning to our research question: Do share prices correctly reflect DS and RDS? If so, then forecasting properties of DS and RDS for VCNI should be reflected appropriately in contemporaneous share prices. If they are under- or over-valued, then it will be possible to develop a trading rule based on magnitude of each. We expect RDS to be a particularly good candidate for a hedge strategy. Unlike DS, RDS is not readily observable in financial statements. RDS is complex e.g., no necessary reversal in future periods.

Computation of DS and RDS Research Design Dirty Surplus DS = sum of (a) change in MS unrealized gains/losses, (b) cumulative FX adjustment, and (c) 0.65 times change in additional pension liability in excess of UPSC). Really Dirty Surplus Follow equation (3), i.e., RDS = change in BVE DS NI + DIV P(year-end) x change in common shares outstanding. Note that we measure RDS with error because we don t use prices as of dates of equity transactions during the year.

VCNI = NI + DS + RDS Research Design Forecasting equation: a VCNI it +1 VCNI t a = VCNI t rbve t 1 = ω 0 + ω 1 VCNI it a + ω 2 DS it + ω 3 RDS it + ω 4 BVE it + ε it +1 ω 1 reflects persistence of abnormal VCNI Based on prior research we expect ω 1 > 0. ω 2 and ω 3 reflect incremental effects on the forecast of abnormal VCNI of knowing DS and RDS.

Research Design Valuation equation: MVE = α + αvcni + α DS + α RDS + α BVE + u a it 0 1 it 2 it 3 it 4 it it α 1 reflects valuation coefficient on abnormal VCNI Based on prior research (and assuming a correspondence in sign between ω 1 and α 1 ), we expect α 1 > 0. α 2 and α 3 reflect incremental effects on valuation of knowing DS and RDS.

DS is forecasting irrelevant if, for purposes of forecasting abnormal VCNI, {NI t, RDS t, BVE t, BVE t 1 } contains the same information as Research Design {NI t, DS t, RDS t, BVE t, BVE t 1 } We test forecasting relevancy of DS by testing whether ω 1 +ω 2 0

Research Design Similarly RDS is forecasting irrelevant if, for purposes of forecasting abnormal VCNI, {NI t, DS t,bve t, BVE t 1 } contains the same information as {NI t, DS t, RDS t, BVE t, BVE t 1 } We test forecasting relevancy of DS by testing whether ω 1 + ω 3 0

Research Design DS is valuation irrelevant if, for purposes of valuation, {NI t, RDS t, BVE t, BVE t 1 } contains the same information as {NI t, DS t, RDS t, BVE t, BVE t 1 } We test valuation relevancy of DS by testing whether α 1 +α 2 0

Research Design Similarly RDS is valuation irrelevant if, for purposes of valuation {NI t, DS t, BVE t, BVE t 1 } contains the same information as {NI t, DS t, RDS t, BVE t, BVE t 1 } We test valuation relevancy of RDS by testing whether α 1 + α 3 0

Hedge Strategy If apparent evidence of mispricing, then strategy of going long in relatively underpriced stocks and short in relatively overpriced stocks should yield excess returns. If small firms are more difficult to properly price because they are less closely followed and detailed accounting analysis is more costly, then we would expect the hedge portfolio returns to be greater than in the case of larger firms. Therefore, we look for consistency between our forecasting and valuation results and conduct hedge return tests using small/medium/large firms.

Hedge Strategy For each sample year, rank firms according to DS or RDS as a fraction of BVE, forming 10 portfolios; 1 (10) has smallest (largest) fraction. Within each of ten DS or RDS portfolios, assign each firm to one of three equal sized groups of small/medium/large firms. Results in 10 portfolios within each of three firm size groups, and ensures magnitude of DS or RDS does not vary systematically across firm size groups, thereby mitigating the confounding effect of firm size when conducting our hedge portfolio tests.

Research Design Combine data from sample years, retaining firm size and DS/RDS portfolio rankings Compute mean risk-adjusted return, RAR, for each of the 10 portfolios within firm size groups Hedge return = mean RAR of most over-valued firms less mean RAR of under-valued (or least over-valued) firms.

Research Design Note that RDS is generally zero or negative because the accounting procedures that give rise to RDS result in equity transactions that are recorded at less than market value. Based on our findings (to follow) that investors appear to undervalue RDS, our hedge strategy is go long in firms with least negative RDS and short in firms with most negative RDS.

Research Design We employ similar strategy for DS but don t expect it to yield positive returns. Hedge return for each of the three firm size groups is computed by going long (short) in the firms in the top three (bottom three) DS or RDS portfolios. Mitigates potential effects of measurement error in the extreme DS or RDS portfolios, which is likely to be problematic for RDS because we use end-of-year market prices rather than unobservable transaction date prices

Research Design Hedge Portfolio Implementation Details Calculate firm s expected equity return for month t+1 as of month t, ER i,t+1, conditional on expected FF and momentum factor returns in month t+1: ER i,t +1 =R f,t +1 +β RMRF,i,t +1 (R M,t +1 R f,t +1 )+β SMB,i,t +1 SMB t +1 +β HML,i,t +1 HML t +1 +β MOM,i,t +1 MOM t +1 Risk-adjusted return for month t+1, is realized return, R i,t+1, less expected return, ER i,t+1. Firm betas are calculated using firm-specific timeseries regression.

Research Design Hedge Portfolio Implementation Details We compute hedge returns over one-, two-, and three-year horizons. If hedge returns continue to increase over longer horizons, then such evidence would be indicative of unmodeled risk differences. Therefore, we expect hedge returns to flatten over the three year horizon.

Findings Table 2: Forecasting equations Dirty Surplus ω 1 + ω 2 is insignificantly different from zero for all three firm size groups. Conclusion: DS is forecasting irrelevant. Therefore DS should be valuation irrelevant if investors understand it has zero persistence.

Findings Table 2: Forecasting equations Really Dirty Surplus ω 1 + ω 3 is insignificantly different from zero for all three firm size groups (almost positive for medium firms). Conclusion: RDS is forecasting irrelevant. Therefore RDS should be valuation irrelevant if investors understand it has zero persistence (possibly positively priced for medium firms).

Findings Table 2: Valuation equations Dirty Surplus α 1 + α 2 is insignificantly different from zero for all three firm size groups. Conclusion: DS is valuation irrelevant. This is consistent with DS forecasting irrelevance.

Findings Table 2: Valuation equations Really Dirty Surplus α 1 + α 3 is also significantly negative for all three firm size groups. Conclusion: RDS is forecasting irrelevant Investors appear to value RDS as if it has negative persistence. Based on RDS forecasting properties, we expect it to be valuation irrelevant (possibly positively priced for medium firms). This inconsistency raises the possibility that investors fail to comprehend correctly the persistence for RDS, i.e., they appear to under-value the RDS component of income.

Table 3: DS Hedge Returns Findings For medium and large firms, mean risk-adjusted returns for all three horizons are essentially zero for the top and bottom three deciles, and therefore, not surprisingly, the associated hedge returns are also zero, Although for small firms the mean risk-adjusted returns are positive and monotonically increasing over the three-year horizon, hedge returns are also zero, with all t-statistics <= 0.54 in absolute value. Although FF risk adjustments may not perfectly eliminate the pricing effects of risk associated with small firms, there is no evidence that investors fail to price DS correctly.

Findings Table 4: RDS Hedge Returns We get a very different picture for RDS than we get for DS Let s look at some numbers

Findings Table 4 Mean Fama-French Risk-adjusted Stock Returns in Top and Bottom Three Deciles of Really Dirty Surplus Deflated by Book Value of Owner Equity for a Sample of 28,346 Firm-Year Observations, 1976-2003 Small Firms Portfolio Bottom 30% Top 30% Hedge Return t-stat. Empirical p-value no. of obs. MVE RDS/BVE 1 year 2 Year 3 Year 2,870 114.23-0.046 0.03 0.06 0.08 2,860 54.91 0.004 0.08 0.12 0.17 0.06 0.07 0.09 3.61 2.61 2.81 <0.01 0.01 <0.01

Findings Table 4 Mean Fama-French Risk-adjusted Stock Returns in Top and Bottom Three Deciles of Really Dirty Surplus Deflated by Book Value of Owner Equity for a Sample of 28,346 Firm-Year Observations, 1976-2003 Medium Firms Portfolio Bottom 30% Top 30% Hedge Return t-stat. Empirical p-value no. of obs. MVE RDS/BVE 1 year 2 Year 3 Year 2,834 670.28-0.046-0.02-0.05-0.07 2,824 351.69 0.004 0.01 0.01 0.00 0.03 0.06 0.07 2.71 3.92 3.94 <0.01 <0.01 <0.01

Findings Table 4 Mean Fama-French Risk-adjusted Stock Returns in Top and Bottom Three Deciles of Really Dirty Surplus Deflated by Book Value of Owner Equity for a Sample of 28,346 Firm-Year Observations, 1976-2003 Large Firms Portfolio Bottom 30% Top 30% Hedge Return t-stat. Empirical p-value no. of obs. MVE RDS/BVE 1 year 2 Year 3 Year 2,812 10,156.35-0.047-0.02-0.04-0.06 2,805 5,625.89 0.004 0.01 0.02 0.02 0.04 0.06 0.08 4.25 5.39 5.83 <0.01 <0.01 <0.01

Findings Table 4: RDS Hedge Results summarized In contrast to DS, risk-adjusted returns generally differ from zero for all firm size groups across all three horizons. In addition, the returns move increasingly away from zero in absolute terms over the investing horizon. E.g., for the top three RDS decile small firms, the one-, two-, and three risk-adjusted returns are 0.08, 0.12, and 0.17. Note that the risk-adjusted return for small firms probably arrise from measurement error in E(return). Deducting average of the two portfolio returns in table 3 may yield a better estimate of risk-adjusted returns for small firms: top 30% (bottom 30%) portfolios of 0.01, 0.02, and 0.02 (-0.06, -0.04, -0.07).

Measurement of RDS Average instead of year-end stock prices Alternative to buy-hold investment procedure Monthly calendar-time portfolios with hedge returns based on Jensen s alpha (controlling for FF and momentum returns Sources of RDS Excluding merger & acquisition firm-years Compare pre-and post-sfas123 years Sorting by difference between basic and diluted EPS Controlling for other anomalies Robustness Checks Accruals, price reversal, share issuance/repurchase

Conclusions DS and RDS are forecasting irrelevant for abnormal comprehensive income for all firms, regardless of their size Consistent with this, DS is valuation irrelevant. However, RDS is valuation relevant (undervalued). Hedge returns support these findings; DS hedge returns are zero, RDS hedge returns are positive.

The findings are consistent with investors under-estimating dilution. Our findings are potentially relevant to FASB and IASB deliberations Our results suggest that concern over the precise location in the financial statements is of little consequence to investors. However, issues relating to RDS transactions, such as how to account for share-based payments, are of considerable importance to investors. Supplemental disclosure of key transactional information, including market prices at date of equity issuances. Investors: it may pay to dig deeper! Conclusions