Accounting-Based Probabilistic Prediction of ROE, the Residual Income Valuation Model and the Assessment of Mispricing in the Swedish Stock Market

Authors


  • We thank Graeme Dean (the editor), Peter Jennergren, James Ohlson, Per Olsson, Stephen Penman, Martin Walker and two anonymous referees for valuable advice and comments. Helpful suggestions have also been received from seminar participants at the Center for Financial Analysis and Managerial Economics in Accounting (BfaC) at Stockholm School of Economics. Special thanks to Erik Eklund at SIX AB for helpful assistance in providing Swedish financial statement and stock market data. Also, we gratefully acknowledge financial support from the Torsten and Ragnar Söderberg Foundation. Work on this project was conducted at Sydney University in 2006. Many thanks to Sid Gray for making this visit possible.

Stina Skogsvik (stina.skogsvik@hhs.se) is Assistant Professor and Kenth Skogsvik (kenth.skogsvik@hhs.se) is the KPMG Professor of Business Administration at the Center for Financial Analysis and Managerial Economics in Accounting, Stockholm School of Economics.

Abstract

Using Swedish stock market data, this study investigates whether an investment strategy based on publicly available accounting information can generate abnormal investment returns. The strategy involves two steps. First, an accounting-based probabilistic prediction model of changes in the medium-term book return on owners' equity (ROE) is estimated. Second, market expectations of changes in medium-term ROE are assessed through observed stock prices and the residual income valuation model. Stock market positions over 36-month holding periods are taken when the accounting-based predictions of ROE and the market expectations differ. Over the period 1983–2003, the investment strategy generated values of Jensen's alpha corresponding to an average monthly excess return for a hedge position of up to 0.8% for a sample of manufacturing companies. In the main this hedge return was caused by strong positive returns to the long positions, and additional analyses show that the returns appear to have been affected by a positive market sentiment bias (i.e., positive ROE surprises being associated with stronger price reactions than negative ROE surprises) making out-of-sample inferences somewhat dubious. Furthermore, most of the investment returns accrued over holding periods up to around 1995, with no indications of market mispricing over the last third (1995–2003) of the investment period. The empirical results are consistent with market investors having become more sophisticated in their use of publicly available accounting information over time.

Present and potential stock market investors are important users of accounting information. To a majority of such investors, the role of financial accounting information is to provide relevant input data for investment decision models. Previous research has shown that stock prices appear to impound publicly available accounting information in a non-timely fashion, indicating that fairly commonplace financial modelling could be rewarding for individual investors (cf. Ou and Penman, 1989; Setiono and Strong, 1998; Frankel and Lee, 1998, in particular). On the other hand, one cannot rule out that investors in general have become better informed and more skilled over time, in turn implying that a more careful analysis of investment returns—and any alleged mispricing—is warranted. To what extent stock prices reflect publicly available accounting information is hence still a viable research question.

This study focuses on whether accounting information in combination with the residual income valuation (RIV) model can be useful in formulating investment strategies. More precisely, the study investigates whether an accounting-based indicator variable strategy can generate abnormal investment returns in a stock market context. There are two main ingredients of this investment strategy—a probabilistic prediction model of medium-term changes in company profitability (ROE) based on published financial statements, and an indicator variable that captures market expectations about changes in company profitability. Investment positions are taken when the accounting-based predictions and the market expectations differ. Previous studies using U.S. and U.K. data have found that publicly available accounting information is not fully reflected in stock market prices (Ou and Penman, 1989; Holthausen and Larcker, 1992; Frankel and Lee, 1998; Setiono and Strong, 1998; Lee et al., 1999; Ali et al., 2003). Testing a new investment strategy on a sample of Swedish companies, this study expands on previous research on market mispricing.

If investors can use publicly available information to profit from deviations between model-based values and stock prices, there is mispricing in the stock market. Mispricing of this kind can be divided into two parts:

  • • Forecasting mispricing; that is, that stock prices do not fully reflect the forecasting ability of published accounting information with respect to some value driver(s).
  • • Modelling mispricing; that is, that stock prices do not reflect the valuation implications of forecasted value driver(s) appropriately.

A unique characteristic of the present study is that both forecasting and modelling mispricing will be investigated. Forecasting mispricing with regard to accounting-based probabilistic predictions of the medium-term book return on owners' equity (ROE) is first evaluated, using an investment strategy similar to Ou and Penman (1989) and Skogsvik (2008). Next, modelling mispricing is investigated by comparing these ROE-predictions with the indicator variable. The indicator variable provides information about the probability of an increase in medium-term ROE as implied by observed stock market prices. Investment positions are taken when the accounting-based probabilities of an increase in medium-term ROE differ from the implied stock price expectations. Tests of mispricing in previous research have often ignored expectations incorporated in stock prices (cf., among others, Ou and Penman, 1989; Setiono and Strong, 1998; Skogsvik, 2008) and have hence been restricted to assessments of forecasting mispricing. Other studies have addressed the issue of modelling mispricing only (e.g. Frankel and Lee, 1998; Lee et al., 1999; Abarbanell and Bernard, 2000; Ali et al., 2003), but have then used analysts' forecasts to predict future earnings. As analysts' forecasts presumably incorporate a more extensive information set than historical financial statement information only, these studies have not investigated modelling mispricing with regard to accounting-based predictions of ROE. It is thus still an open question whether stock market prices incorporate such predictions in a timely manner.

The empirical analyses are based on a sample of manufacturing companies quoted on the Swedish stock exchange over the period 1983–2003, hence mitigating problems related to data mining of (in particular) U.S. stock market data. The sample is representative of a Scandinavian institutional setting.1 Medium-term changes of ROE assessed over 3 + 3 consecutive years have been predicted in the evaluation of forecasting mispricing, since forecasts of next year's earnings changes might be more distorted by transitory items. Another unique feature of this study relates to the assessment of terminal values in the residual income valuation model. In previous research such assessments have mostly relied on rather ad hoc long-term forecasts of abnormal earnings and/or abnormal ROE. An opportunity in using the sample of Swedish manufacturing companies is that the conservative bias of reported book values has been carefully estimated for this type of companies in Runsten (1998).

The empirical results can be summarized as follows. The indicator variable strategy generated abnormal CAPM returns corresponding to an average monthly excess return of up to 0.8% for a hedge position over 36-month holding periods. Using the same capital return metric as in Ou and Penman (1989) and Holthausen and Larcker (1992), the market-adjusted returns were found to be remarkably high, and more or less unaffected by conventional risk proxies (i.e., book-to-market, company size, earnings-to-price, and dividend yield). With a return metric corresponding to a more implementable investment strategy (the realistic return metric), the market-adjusted returns were reduced but still non-trivial (average monthly market-adjusted returns for a hedge position of between 0.6% and 1.0%). Both forecasting and modelling mispricing appeared to be important in explaining the performance of the investment strategy, and both types of mispricing were mainly explained by strong returns to the long positions. However, further analyses show that stock price reactions to unexpected positive ROE changes were considerably stronger than price reactions to unexpected negative ROE changes. As this type of market sentiment bias is likely to be time-period specific, the finding casts doubt on the validity of out-of sample inferences. Also, most of the excess returns for the investment strategies could be attributed to positions taken over the first third (1983–91) of the investment period. Both forecasting and modelling mispricing seem to have decreased over time, and there is actually no empirical evidence of any market mispricing for the last third (1995–2003) of the period.

1: RESIDUAL INCOME VALUATION (RIV) AND THE INDICATOR VARIABLE STRATEGY

1.1 RIV Model Application

Setting the valuation date to t= 0 and allowing the discount rate to change over time, a finite-horizon specification of the RIV model2 can be written as:

image(1)

where

  • V0= value of owners' equity at time t= 0,

  • Bt= book value of owners' equity at time t,

  • ρτ= required rate of return on owners' equity in period τ,

  • ROEtIt/Bt−1= book return on owners' equity in period t, with It= net income for period t,

  • mb(BT) = (VTBT)/BT= valuation bias of owners' equity at time t = T, with VT= value of owners' equity at time t = T,

  • E(0)(. . .) = expectation operator, conditioned on available information at time t= 0, and

  • ∼= (denotes) a random variable.

Assuming that the clean surplus relation holds, future expected book values of owners' equity can be calculated as inline image, where inline image= dividends at time t divided by the book value of owners' equity at t− 1. In all specifications of the RIV model it will henceforth be assumed that the horizon point in time is T= 3, and that inline imageand inline imageare constants (equal to inline imageand inline image, respectively, for periods t= 1, 2 and 3. In order to further simplify the modelling, it will be assumed that inline image, inline image, and inline image, where Cov(.,.) is the covariance operator. The assumptions allow (1) to be rewritten as:

image(2)

In the following, the specification in (2) will be representative both for the assessment of model-based values of owners' equity, as well as for the analysis of stock market prices. Values of B0, inline image, inline imageand the discount rate of return ρτ are assumed to be the same in both modelling contexts. Differences between model-based values of owners' equity and stock prices will hence only be due to differences between values of inline imagein the two contexts.

1.2 The Indicator Variable

The indicator variable is defined as the difference between the market price of owners' equity (P0) and a ‘historically motivated’ value of owners' equity (inline image). The latter is specified in accordance with (2) and based on historical average values of ROEt (inline image), the dividend payout share (inline image), and an exogenously determined valuation bias of owners' equity (inline image). The valuation bias presumably consists of company business goodwill and an accounting ‘cost matching bias’ (cf. Feltham and Ohlson, 1995; Skogsvik, 1998). inline imageis hence operationalized as:

image(3)

where inline image= (denotes) value based on publicly available accounting information at the valuation date (t= 0).

Presuming that (2) is a valid representation of P0, it is additionally assumed that the market-based expectation of inline imageis equal to inline imageand that the market-based expectation of the valuation bias of owners' equity coincides with inline image. Letting inline imagedenote the market-based expectation of the medium-term ROE, the price of owners' equity is:

image(4)

where inline image(. . .) = expectation operator representative for the stock market, conditioned on available information at time t= 0.

The indicator variable (IND0) is the difference between the market price of owners' equity in (4) and the historically motivated value in (3), that is, inline image. Given that (4) constitutes a valid representation of the market price, inline imageis explained by the difference between inline imageand the historical book return inline image. In principle, we then have:

image(5a)
image(5b)
image(5c)

The indicator variable thus has the following properties:

  • • A negative value of IND0 means that the stock price is lower than what would be motivated by the historical medium-term ROE. The probability of an increase in medium-term ROE as implied by the market price is hence less than 0.5.
  • • A value of IND0 equal to zero means that the stock price is in line with the historical medium-term ROE. The probability of an increase in the medium-term ROE as implied by the market price is equal to 0.5.
  • • A positive value of IND0 means that the stock price is higher than what would be motivated by the historical medium-term ROE. The probability of an increase in medium-term ROE as implied by the market price is then above 0.5.

Investment positions for the indicator variable strategy are only taken when the market-based probabilities of an increase in the medium-term ROE and the corresponding accounting-based probabilistic predictions differ. As clarified in Figure 1, if the indicator variable is negative and the probability from the accounting-based prediction model is above 0.5, a long position is taken. On the other hand, if the indicator variable is positive and the probability from the accounting-based prediction model is below 0.5, a short position is taken. If the indicator variable is 0 and the accounting-based probability is above (below) 0.5, a long (short) position is taken.

Figure 1.


THE INDICATOR VARIABLE STRATEGY

1.3 Operationalization of the Indicator Variable

In order to empirically measure the indicator variable, inline imageaccording to (3) has to be assessed. For this purpose, the average book return on owners' equity (inline image) and the average dividend payout share (inline image) have been calculated as arithmetic averages over the three years preceding the valuation point in time. The capital asset pricing model (CAPM) has been used in assessing the required rate of return (ρt), with β-values estimated in standard regressions over 48 months of historic market data.3 The risk free rate for t= 1 is the observed one-year rate, and risk free rates for years t= 2 and t= 3 have been estimated from two- and three-year observed risk free rates. The market risk premium was set to 5.0%, in line with Swedish ex post data over the period 1919–89 (cf. Frennberg and Hansson, 1991).

As noted in section 1.2, the valuation bias of owners' equity consists of company business goodwill and the accounting cost matching bias. Presuming that business goodwill is negligible at the future point in time t=Tx and estimating the measurement bias of owners' equity at t= 3 as a weighted average of (P0/B0− 1) and the expected cost matching bias inline image, one gets:

image(6)

At time t = Tx, inline imagehas presumably stabilized at some firm-specific (‘steady-state') level (cf. Skogsvik, 1998; Zhang, 2000). Empirical evidence for U.S. companies in Penman (1991) indicates that an adjustment process of this kind on average takes about five to six years. Assuming that business goodwill diminishes linearly over six years,4w in (6) has been set to 0.5. Empirical estimates of the cost matching bias for companies quoted at the Swedish stock exchange are reported in Runsten (1998). Five of the industries in that report consist of manufacturing companies and an arithmetic average of the cost matching bias for these industries—equal to 0.49—has been used for all sample companies in this study.5 Consequently, the valuation bias of owners' equity (inline image) in (3) and (4) has been calculated as 0.5·(P0/B0− 1) + 0.5·0.49.

1.4 The Accounting-Based ROE Prediction Model

Logit analysis has been used for the accounting-based probabilistic prediction model of medium-term ROE. The change in medium-term ROE (henceforth denoted inline image) has been operationalized as6:

image(7)

Changes in medium-term ROE have been predicted in univariate logit models, with the historical medium-term ROE as the single independent variable. The choice of a naive prediction model of this kind is supported by empirical results in Skogsvik (2008), showing that univariate logit models have superior performance—as compared to more elaborate multivariate logit models—for the probabilistic prediction of medium-term ROE.

2: EMPIRICAL DATA

The sample companies have been listed on the Stockholm Stock Exchange and the study covers data from 1970 through the beginning of 2003. Only manufacturing companies are included, using the industry classification of a well-reputed Swedish business magazine (Affärsvärlden) to identify companies.7 In order to enlarge the sample, a number of non-classified but similar companies have also been included.8 All data were collected from the Swedish database Finlis (SIX AB, http://www.six.se).

The accounting-based probabilistic prediction models of changes in medium-term ROE were estimated separately using pooled samples over the subperiods 1972–79, 1975–82, 1978–85, 1981–88, 1984–91 and 1987–94. The calculation of inline imagerequired data for six consecutive years,9 and the estimation samples only included companies that were listed during the required years. As can be seen from Table 1, the number of firm-year observations varied between 330 and 412 over the estimation periods.

Table 1. 
DATA SAMPLE
 Estimation of ROE prediction modelsEvaluation of investment strategies
  • For each calendar year, the dependent variable inline imagerequires ROEt data for years t− 2, t− 1, t, t+ 1, t+ 2, and t+ 3.

  • No. of unique companies.

Subperiod I1972–79a1983–85
Subperiod II1975–82a1986–88
Subperiod III1978–85a1989–91
Subperiod IV1981–88a1992–94
Subperiod V1984–91a1995–97
Subperiod VI1987–94a1998–2000
No. of observations
Subperiod I396 (59b)170
Subperiod II412 (63b)190
Subperiod III392 (69b)165
Subperiod IV330 (74b)152
Subperiod V359 (76b)141
Subperiod VI338 (67b)150

Investment positions have been formed at the end of the third month after financial year-ends 1983 to 2000, see Table 1. Financial statement data required for the probabilistic ROE prediction models were assumedly publicly available at each investment point in time.10 All positions have been held for 36 consecutive months and the investment returns were evaluated over the years 1983 to 2003. For example, based on the ROE prediction model estimated over the subperiod 1972–79 and values of the indicator variable in the beginning of 1983, 1984 and 1985, three investment positions were formed; the first in 1983, the second in 1984 and the third in 1985. A second ROE prediction model was used when forming positions in 1986, 1987, 1988 and so on. The investment strategies have been evaluated with a total of 968 firm-year observations, only including companies listed over the three financial years that were required to calculate inline image.

3: THE ESTIMATION AND PERFORMANCE OF THE ROE PREDICTION MODEL

Consistent with the idea of probabilistic prediction modelling, there is an unobservable variable Zj (j denoting a specific firm) postulated to be larger than a company-specific threshold value inline imagewhen there is a positive change in medium-term ROE, and vice versa. Values of inline imagefollow a logistic distribution in logit analysis, and Zj has been modelled as a univariate linear function of the past average book return on owners' equity, that is:

image(8)

As indicated in Table 1, one prediction model has been estimated for each of the six subperiods, and chi-square tests showed that all models were strongly significant. The estimated coefficient inline imagewas significantly (α≤ 0.05) negative in all models, implying that inline imagehas been mean reverting.11

As the proportion of increases/decreases in inline imagein the estimation samples typically has differed from the a priori probability π= 0.5, the model-based probabilities have been adjusted (cf. Palepu, 1986; Skogsvik, 2005). The adjusted probabilities—denoted inline image—have been calculated in accordance with the calibration formula in Skogsvik (2005): 12

image(9)

where π=a priori probability of increase in medium-term ROE (= 0.5),

prop= proportion of increases in medium-term ROE in estimation sample, and

inline image= model-based (unadjusted) probability of an increase in inline image.

With a probability cut-off value of 0.5 for inline image, holdout sample prediction results for the logit models are reported in Table 2. For all years, 73.7% of the observations were correctly predicted,13 with a contingency table test chi-squareof 160.64 (p-value = 0.00). Prediction results are also reported for the holdout periods separately in the table, in the main revealing a stable prediction performance for the estimated models.14

Table 2. 
HOLD-OUT SAMPLE PREDICTION PERFORMANCE FOR THE PROBABILISTIC ROE PREDICTION MODELS
 Holdout period I: 1982–84Holdout period II: 1985–87Holdout period III: 1988–90Holdout period IV: 1991–93Holdout period V: 1994–96Holdout period VI: 1997–99All years
  1. Probabilistic changes in medium-term ROE have been predicted with six separately estimated logit models, using the probability calibration formula (9) with π= 0.5 and a probability cut-off value of 0.5 (χ2-values are from 2·2 contingency table tests).

No. of firm-year observations14213211211711198712
% overall correct predictions66.2%70.5%75.9%81.2%74.8%76.5%73.7%
χ2-value24.4423.610.3237.7831.8719.19160.64
(p-value)(0.00)(0.00)(0.57)(0.00)(0.00)(0.00)(0.00)
% increases correctly predicted52.8%33.9%25.0%94.8%64.6%62.1%61.1%
% decreases correctly predicted88.7%97.4%84.4%55.0%89.1%82.6%84.7%

4: EVALUATION OF INVESTMENT RETURNS

4.1 The Investment Strategies

The base case strategy has been operationalized in order to capture forecasting mispricing. In the spirit of Ou and Penman (1989) this strategy is based on the probabilistic ROE predictions alone, and positions have been formed as follows:

  • • If inline image: Long investment position.
  • • If inline image: Short investment position.

As clarified in section 1.2 previously, market positions have been formed as follows according to the indicator variable strategy:

  • • If IND0 < 0:Long investment position if inline image, in the ROE prediction model.
  • • If IND0= 0:Long investment position if inline image, andshort investment position if inline image in the ROE prediction model.
  • • If IND0 > 0:Short investment position if inline image in the ROE prediction model.

Considering the inherent measurement problem associated with the indicator variable, three alternative operationalizations of IND0= 0 have been evaluated; that is, IND0 has been set to 0 when IND0/B0∈[−0.4, 0.4], IND0/B0∈[−0.2, 0.2], or IND0/B0∈[−0.1, 0.1].

Investment positions have been formed at the end of the third month after financial year-ends both for the indicator variable and the base case strategy. Based on publicly available financial statements, inline imagewas calculated using the most current ROE prediction model and the indicator variable was assessed as of the investment date.15 Investment positions have then been held over 36 months, corresponding to the period over which the future medium-term ROE would be revealed.

Some background statistics for the indicator variable are presented in Table 3. The average price-to-book ratio (P0/B0) was 2.2751 over the whole investment period 1983–2000, somewhat lower than the average model-based value-to-book ratio (inline image) of 2.3783. The indicator variable divided by the book value of owners' equity has an average value of −0.1031, meaning that on average market expectations have implied that medium-term ROE will decrease. However, the average value is not significantly different from 0 (non-reported t-value of −0.37). This corroborates the validity of the RIV model operationalization, in the sense that inline imageon average appears to be an unbiased estimate of P0. However, note that the median value of IND0/B0 is positive (0.1336), implying a somewhat skewed distribution of the indicator variable. It can also be noted both the average and the median value of the accounting-based probability inline imageare less than 0.5, indicating a somewhat negative outlook for the medium-term ROE.

Table 3. 
SUMMARY STATISTICS FOR THE INVESTMENT PERIOD
YearNo. of firmsP0/B0inline imageIND0/B0inline image
MeanMedianMeanMedianMeanMedianMeanMedian
  1. Arithmetic average values and medians for the sample firms. P0 is the stock price (ex dividend) at the end of the third month in the financial year; inline imageis the historically motivated value of owners' equity at the end of the third month in the financial year; B0 is the book value of owners' equity (ex dividend) at the end of the previous financial year; IND0/B0 is the difference between P0 and inline imagedivided by B0; and inline imageis the adjusted probability of an increase in medium-term ROE according to the accounting-based prediction model.

1983512.22131,40771.64491.20850.57650.25150.51990.5121
1984562.56841.93881.82601.45330.74240.36730.45440.4160
1985631.73321.37101.57031.31590.16290.04360.34360.3224
1986622.01331.64842.15211.5663−0.13970.04400.33020.2800
1987642.58241.92582.07061.74980.51180.17940.33600.3289
1988642.23751.80601.86311.60850.37440.25450.34620.3322
1989592.71222.25802.20261.89730.50970.35880.39000.4013
1990582.34841.87191.83721.61490.51120.30130.38900.4031
1991481.93401.30861.74031.43320.1937−0.08430.41320.4080
1992501.50861.18721.44111.17930.0675−0.06670.60870.6060
1993521.42231.02361.35481.07240.0675−0.03840.72970.7868
1994502.08281.80521.50451.20580.57830.49440.78680.8950
1995471.97931.58891.61181.24870.36750.34110.59110.5635
1996461.88341.71001.94771.7105−0.0644−0.06160.44160.4237
1997482.64792.03672.20911.98630.43880.09800.38170.3592
1998532.98832.15923.62742.1580−0.63910.01570.34930.2502
1999522.51711.62804.66181.9190−2.1448−0.23600.40350.3708
2000453.64671.64678.62381.9702−4.9771−0.19400.40690.3368
All years 2.27511.70842.37831.5843−0.10310.13360.44950.4154

The number of firm-year observations in the long and short positions for the investment strategies are provided in Table 4. Notably, the numbers of observations in the long positions have been considerably lower than the corresponding numbers in the short positions over the period 1983–2003. In principle this means that the combination of the indicator variable being non-positive (negative market outlook) and the accounting-based probability of an increase in medium-term ROE being above 0.5, has been less frequent than the combination of the indicator variable being non-negative (positive market outlook) and the accounting-based probability being less than 0.5.

Table 4. 
NUMBER OF FIRM-YEAR OBSERVATIONS IN THE INVESTMENT STRATEGIES 1983–2003
Investment strategyPositionAll firmsDecember year-end firms
Base case strategyLong position355335
Short position613588
Total968923
Indicator variable strategy   
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long position113110
Short position377354
Total490464
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
Long position151148
Short position427402
Total:578550
 Zero interval for IND0:
 [–0.4·B0, 0.4·B0]
Long position221211
Short position506482
Total:727693

4.2 Abnormal CAPM Returns

As a first return metric, abnormal CAPM returns—commonly referred to as Jensen's alpha—have been estimated for the investment positions. Monthly portfolio returns less the risk-free rate have hence been regressed on the market risk premium, with the intercept measuring the abnormal return, that is:16

image(10)

where

  • inline image= average portfolio excess return to the hedge position in month z,

  • inline image= average portfolio excess return to the long position in month z,

  • inline image= average portfolio excess return to the short position in month z,

  • Rm,z= market return for month z, and

  • Rf,z= risk-free rate for month z.

Estimated values of α and β are reported in Table 5. For the base case strategy, α= 0.004 for the hedge position (p-value 0.002), with a significant positive return to the long position but a non-significant return to the short position. The indictor variable strategy generated positive and clearly significant α-values for the hedge positions, regardless of the chosen operationalization of IND0= 0. The α-values for the hedge positions varied from 0.004 up to 0.008 with the smallest zero interval for IND0. The latter abnormal return is twice the size of the corresponding value for the base case strategy, implying that modelling mispricing has been almost as important as forecasting mispricing in explaining the excess return to the indicator variable strategy. Also note that the positive α-values for the hedge positions of the latter strategy without exception are caused by strong positive α-values for the long positions (p-values 0.001 or better), while α-values were non-significant for the short positions.

Table 5. 
ABNORMAL (MONTHLY) CAPM RETURNS OVER 36-MONTH HOLDING PERIODS
Investment strategyPositionαβ
  1. Values of α and β have been estimated in accordance with regression (10), where α is the abnormal return and β is the beta value of the position. For the long and the hedge positions, the null hypothesis of a non-positive α is tested against the alternative hypothesis of a positive α. For the short position, the null hypothesis of a non-negative α is tested against the alternative hypothesis of a negative α (p-values in parenthesis, no p-value is reported if the sign of α is inconsistent with the alternative hypothesis). Tests of β-values are two-tailed (p-values within parenthesis).

Base case strategyLong0.0050.818
(0.000)(0.000)
Short0.0010.780
(—)(0.000)
Hedge0.0040.038
(0.002)(0.067)
Indicator variable strategy   
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long0.0090.765
(0.000)(0.000)
Short0.0010.784
(—)(0.000)
Hedge0.008−0.019
(0.002)(0.653)
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
Long0.0060.843
(0.000)(0.000)
Short0.0010.792
(—)(0.000)
Hedge0.0060.051
(0.002)(0.087)
 Zero interval for IND0:
 [−0.4·B0, 0.4·B0]
Long0.0060.887
(0.001)(0.000)
Short0.0020.777
(—)(0.000)
Hedge0.0040.110
(0.008)(0.000)

4.3 Market-Adjusted Returns—the Statistical Return Metric

In this section, a market-adjusted return metric in line with Ou and Penman (1989) is used to evaluate the returns for the investment strategies. The methodology has previously been used in, for example, Stober (1992) and Holthausen and Larcker (1992). The analysis is based on linear regressions with market-adjusted returns for individual stocks over 36-month holding periods as the dependent variable.

The return metric—henceforth denoted the statistical return metric—is helpful in permitting more straightforward comparisons with previous research, and it facilitates the statistical analysis when controlling for risk proxies. The metric corresponds to an investment strategy where a hedge position is held over the full period 1983–2003. Companies that have been delisted before the end of some 36-month holding period are not included in the assessment of the return metric. More precisely, the market-adjusted returns have been calculated as follows:

image(11a)
image(11b)
image(11c)

where

  • inline image= market-adjusted buy-and-hold return at the end of month z= 36

  • (H= hedge position, L= long position, and S= short position),

  • Rj,z= return on stock j in month z,

  • Rm,z= return on market index month z, and

  • inline image= number of stocks in the position over the period 1983–2000 (L= long position and S= short position).

Investment returns in accordance with the statistical return metric are reported in Table 6. For the base case strategy, the return for the hedge position over 36-month holding periods was an impressive 39.96%,17 and for the indicator variable strategy the corresponding return was an even more impressive 86.94% with the smallest zero interval for IND0. Even though these returns can be expected to be positively biased (cf. section 4.4 below), they indicate that forecasting and modelling mispricing can be of about equal importance in explaining the market-adjusted returns.

Table 6. 
MARKET-ADJUSTED BUY-AND-HOLD RETURNS (STATISTICAL RETURN METRIC) FOR 36-MONTH HOLDING PERIODS
Investment strategyPosition 
  1. The return to the hedge position has been calculated as the difference between the market-adjusted return to the long and the short position after 36-month holding periods, in accordance with expressions (11a), (11b) and (11c).

Base case strategyLong0.3194
Short−0.0803
Hedge0.3996
Indicator variable strategy  
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long0.8222
Short−0.0472
Hedge0.8694
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
Long0.5797
Short−0.0414
Hedge0.6211
 Zero interval for IND0:
 [−0.4·B0, 0.4·B0]
Long0.4469
Short−0.0475
Hedge0.4944

The statistical return metric has been further analysed in regression analyses with the market-adjusted return for individual stocks as the dependent variable. In a first step, the independent variable is only a dummy variable indicating whether a stock belongs to the long or the short position:

image(12)

where inline image,

inline image= dummy variable, equal to 1 if the investment strategy Str(.) classified stock j as a short position and 0 otherwise, and

inline image= error term.

The intercept θ0 in (12) corresponds to the average market-adjusted return to the long position (as reported in Table 6), and θ1 is the market-adjusted return to the hedge position multiplied by (−1).

In a second step, independent variables that have been proposed to represent risk proxies in previous research18 have been included in the regressions. Each risk proxy variable has been calculated as an arithmetic average of the variable measured at the investment date, 12 months after the investment date, and 24 months after this date. The following regression has then been estimated:

image(13)

where

  • ln((B/M)j,t) = logarithm of book value divided by market value of owners' equity for company j at time t,

  • (E/P)j,t= earnings per share for period t divided by the stock price at the end of the period for company j,

  • (D/P)j,t= dividend per share for period t divided by the stock price at the end of the period for company j,

  • ln(MVj,t) = logarithm of market value of owners' equity for company j at the investment point in time, and

  • inline image= (denotes) arithmetic average.

Regressions for the whole investment period 1983–2003 are reported in Table 7. The table shows that market-adjusted returns for the long positions and the hedge positions (as assessed by inline imageand inline image), both for the base case strategy and all versions of the indicator variable strategy, were basically unaffected by the inclusion of the risk proxies. Notably, the coefficients for the earnings-to-price ratio and size received the right signs in the regressions, however with weak levels of significance. This means that the observed mispricing appears to be more or less unaffected by the inclusion of the risk proxy variables.

Table 7. 
ESTIMATED COEFFICIENTS FOR REGRESSIONS (12) AND (13)
Investment strategyθ0θ1θ2θ3θ4θ5Adj. R2No. obs.
  1. Regressions (12) and (13) are inline imageandinline imageinline image, respectively. The dependent variable is the market-adjusted buy-and-hold return inline image, where Rj,z is the return on stock j month z and Rm,z is the market return month z. inline imageis the average value of the logarithm of the book value divided by the market value of owners' equity at the end of year t, inline imageis the average value of earnings per share divided by the stock price at the end of year t, inline imageis the average value of the proposed dividend per share divided by the stock price at the end of year t, and inline imageis the average value of the logarithm of the market value of owners' equity at time t. For the intercept, inline imageand inline image, the null hypothesis of a non-positive coefficient is tested against the alternative hypothesis of a positive coefficient. For inline imageand inline imagethe null hypothesis of a non-negative coefficient is tested against the alternative hypothesis of a negative coefficient (p-values in parenthesis; no p-value is reported if the sign of a coefficient is inconsistent with the alternative hypothesis). Tests of inline imageare two-tailed (p-values within parenthesis).

Base case strategy0.319−0.400    1.5%727
(0.000)(0.000)
0.333−0.423−0.1970.126−2.403−0.0652.2%717
(0.000)(0.000)(—)(0.256)(0.456)(0.028)
Indicator variable strategy        
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
0.822−0.869    3.5%363
(0.000)(0.000)
1.051−1.176−0.3540.401−5.437−0.0544.7%358
(0.000)(0.000)(—)(0.178)(0.361)(0.180)
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
0.580−0.621    2.1%427
(0.000)(0.001)
0.724−0.822−0.2860.295−2.518−0.0282.8%423
(0.000)(0.000)(—)(0.186)(0.604)(0.297)
 Zero interval for IND0:
 [−0.4 ·B0, 0.4·B0]
0.447−0.494    1.7%538
(0.000)(0.000)
0.511−0.589−0.2290.236−2.183−0.0502.1%534
(0.000)(0.000)(—)(0.216)(0.593)(0.124)

4.4 Market Adjusted Returns—the Realistic Return Metric

The statistical return metric does not correspond to an implementable investment strategy. First, the exclusion of delisted companies requires foreknowledge of the firms which will be delisted during future 36-month holding periods. Second, the allocation of capital to the long and the short positions in a certain year requires foreknowledge of the total number of firm-specific positions over the period 1983–2003.19 However, in line with Skogsvik (2008) it is possible to define an alternative return metric corresponding to a more implementable investment strategy—the so-called realistic return metric. This metric is solely based on information being available at the investment point in time.

The realistic return metric for the hedge position is specified in (14a), with the corresponding long and short positions in (14b) and (14c), respectively. As can be seen from the latter two expressions, market-adjusted returns for individual stocks have been equally weighted each year, and the yearly return observations have been equally weighted in the assessment of average returns.20

image(14a)
image(14b)
image(14c)

where MJBH(·),36= realistic market-adjusted buy-and-hold return to the position after 36 months (H= hedge position, L= long position, and S= short position), and

N(·),t= number of stocks in the position year t (L= long position and S= short position).

Empirical observations for the realistic return metric over the period 1983–2003 and the two subperiods 1983–94 and 1992–2003 are presented in Table 8. Having eliminated the foreknowledge that was required for the statistical return metric, the observed market-adjusted returns decrease considerably. For the base-case strategy, the average market-adjusted return to the hedge position is now 26.51% (p-value 0.0174)21 over the whole period. As for the indicator variable strategy, the average market-adjusted return for the hedge position varies between 24.46% (p-value 0.0493) with the widest zero interval for the indicator variable, up to 44.69% (p-value 0.0092) with the medium zero interval [−0.2 B0, 0.2 B0]. With a market-adjusted return of 26.51% for the base case strategy, the latter figure implies modelling mispricing of about 18.2% for the Swedish stock market over the period 1983–2003.

Table 8. 
MARKET-ADJUSTED BUY-AND-HOLD RETURNS (REALISTIC RETURN METRIC) FOR 36-MONTH HOLDING PERIODS
Investment strategyPosition1983–941992–20031983–2003
  1. The return to the hedge position has been calculated as the difference between market-adjusted returns for the long and short position after 36-month holding periods, in accordance with expressions (14a), (14b) and (14c) (p-values for one-tailed t-tests for 1983–2003 in parenthesis).

Base case strategyLong0.27960.13320.2064
(0.0570)
Short−0.0298−0.0876−0.0587
(0.1277)
Hedge0.30940.22080.2651
(0.0174)
Indicator variable strategy    
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long0.55300.27130.4121
(0.0220)
Short−0.02910.0129−0.0081
(0.4365)
Hedge0.58210.25840.4202
(0.0271)
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
Long0.42710.19200.3096
(0.0524)
Short−0.0366−0.2381−0.1373
(0.0497)
Hedge0.46370.43010.4469
(0.0092)
 Zero interval for IND0:
 [−0.4·B0, 0.4·B0]
Long0.31660.14530.2310
(0.0586)
Short−0.0158−0.0114−0.0136
(0.3813)
Hedge0.33230.15680.2446
(0.0493)

Consistent with the abnormal CAPM returns (cf. Table 5) and the buy-and-hold returns based on the statistical return metric (Table 6), most of the returns in Table 8 are due to the long positions. The table also shows that for all investment strategies the returns to the hedge and the long positions in general have been considerably lower in the second subperiod. Notably, the market-adjusted returns to the long positions for the subperiod 1992–2003 are about half as large as the corresponding returns for the first subperiod 1983–94. Hence, the observed mispricing appears to be decreasing over time, an issue that will be further analysed in section 5.3 below.

5: THE ISSUE OF MARKET MISPRICING

Taken at face value, the empirical results in the previous section indicate non-trivial forecasting and modelling mispricing in the Swedish stock market over the period 1983–2003. Values of Jensen's alpha were positive and significant for the hedge and the long positions of all investment strategies, and observed excess returns based on the statistical return metric were more or less unaffected by the risk proxy variables. As measured by the realistic return metric, market adjusted hedge returns over 36-month holding periods of about 26.5% for the base case strategy and about 42.0% for the indicator variable strategy (with the smallest zero interval for IND0) have been observed. Roughly speaking, this corresponds to non-trivial monthly excess returns of 0.66% and 0.98%,22 respectively. A legitimate question is then whether these observations really indicate a persistent deviation from market efficiency in the semi-strong sense.

5.1 Results Due to Statistical Overfitting?

Since the long and short positions for the 36-month holding periods have been formed each year over the period 1983–2000, typically three positions of each type have been held simultaneously.23 Hence, returns have been overlapping in calendar time, meaning that levels of significance can be exaggerated (cf. Frankel and Lee, 1998). To address this concern, the sample has been divided into three subsamples with non-overlapping data, where the first subsample included every third year starting from 1983, the second subsample every third year from 1984, and the third subsample every third year from 1985. Jensen's alpha, regression (13), and buy-and-hold returns according to the realistic return metric have subsequently been re-calculated for these subsamples.

Abnormal CAPM returns for the non-overlapping subsamples are reported in Table 9. The base case strategy now generated positive values of Jensen's alpha for the hedge positions in the first and the third subsample (p-values 0.046 and 0.003, respectively). All specifications of the indicator variable strategy also generated positive α-values for the hedge position in the first and the third subsample (p-values between 0.007 and 0.139). For the second subsample, α-values for the hedge positions were positive, but with weak statistical significance (p-values 0.212 for the base case strategy, and between 0.052 and 0.221 for the indicator variable strategy). The abnormal returns to the hedge and the long positions for the indicator variable strategy with the smallest zero interval for IND0 still dominated the corresponding returns for the base case strategy in all three subsamples.

Table 9. 
ABNORMAL CAPM RETURNS FOR 36-MONTH HOLDING PERIODS WITH NON-OVERLAPPING SUBSAMPLES
Investment strategyPositionSubsample ISubsample IISubsample III
αβαβαβ
  1. In subsample I positions were formed in 1983, 1986, 1989, 1992, 1995 and 1998; in subsample II positions were formed in 1984, 1987, 1990, 1993, 1996 and 1999; and in subsample III positions were formed in 1985, 1988, 1991, 1994, 1997 and 2000. Values of α and β have been estimated in accordance with regression (10), where α is the abnormal return and β is the beta value of the position. For the long position, the null hypothesis of a non-positive α is tested against the alternative hypothesis of a positive α. For the short position, the null hypothesis of a non-negative α is tested against the alternative hypothesis of a negative α (p-values in parenthesis, no p-value is reported if the sign of α is inconsistent with the alternative hypothesis). Tests of β-values are two-tailed (p-values within parenthesis).

Base case strategyLong0.0050.7890.0030.8730.0070.795
(0.010)(0.000)(0.124)(0.000)(0.002)(0.000)
Short0.0010.7400.0010.7850.0010.810
(—)(0.000)(—)(0.000)(—)(0.000)
Hedge0.0040.0490.0020.0880.006−0.016
(0.046)(0.187)(0.212)(0.029)(0.003)(0.617)
Indicator variable strategy
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long0.0080.7590.0060.9860.0140.568
(0.002)(0.000)(0.072)(0.000)(0.013)(0.000)
Short0.0010.7360.0010.8240.0020.789
(—)(0.000)(—)(0.000)(—)(0.000)
Hedge0.0080.0230.0050.1620.012−0.222
(0.007)(0.625)(0.122)(0.019)(0.032)(0.017)
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
Long0.0050.7630.0060.8780.0080.884
(0.016)(0.000)(0.046)(0.000)(0.006)(0.000)
Short−0.0000.771−0.0000.8310.0020.775
(0.494)(0.000)(0.494)(0.000)(—)(0.000)
Hedge0.005−0.0080.0060.0470.0060.108
(0.049)(0.871)(0.052)(0.415)(0.032)(0.022)
 Zero interval for IND0:
 [−0.4·B0, 0.4·B0]
Long0.0050.9320.0050.8960.0080.838
(0.054)(0.000)(0.075)(0.000)(0.000)(0.000)
Short0.0010.7260.0020.8010.0020.801
(—)(0.000)(—)(0.000)(—)(0.000)
Hedge0.0040.2070.0020.0950.0070.037
(0.139)(0.000)(0.221)(0.045)(0.007)(0.351)

Re-estimated coefficients for regression (13) are reported in Table 10. Regarding the base case strategy, abnormal returns remained significant (p-values between 0.002 and 0.050) in all subsamples, with reasonably stable estimates of θ0 and θ1. The return performance of the indicator variable strategy was more negatively affected though, with a strong variation in estimated values of θ0 and θ1, and with poor levels of significance for the second subsample. Partly this can be explained by the smaller number of observations for the indicator variable strategy in the three subsamples, but nevertheless the estimated coefficients appear to lack stability.

Table 10. 
ESTIMATED COEFFICIENTS ON NON-OVERLAPPING SUBSAMPLES FOR REGRESSION (13)
Investment strategySub-sampleθ0θ1θ2θ3θ4θ5No. obs.
  1. In subsample I positions were formed in 1983, 1986, 1989, 1992, 1995 and 1998; in subsample II positions were formed in 1984, 1987, 1990, 1993, 1996 and 1999; and in subsample III positions were formed in 1985, 1988, 1991, 1994, 1997 and 2000. Regression (13) is specified as inline image.

  2. MJBHj,36 is the market-adjusted buy-and-hold return defined as inline image, where Rj,z is the return on stock j month z and Rm,z is the market return month z. The independent variables are explained in Table 7. For the intercept, inline image and inline image, the null hypothesis of a non-positive coefficient is tested against the alternative hypothesis of a positive coefficient. For inline image and inline image, the null hypothesis of a non-negative coefficient is tested against the alternative hypothesis of a negative coefficient (p-values in parenthesis; no p-value is reported if the sign of a coefficient is inconsistent with the alternative hypothesis). Tests of inline imageare two-tailed (p-values within parenthesis).

Base case strategyI0.386−0.490−0.2180.045−3.876−0.174248
(0.024)(0.026)(—)(0.446)(0.600)(0.011)
II0.350−0.387−0.2970.2091.074−0.048242
(0.002)(0.007)(—)(0.216)(0.781)(0.126) 
III0.263−0.403−0.0540.182−5.7760.035227
(0.050)(0.022)(—)(0.362)(0.275)(—)
Indicator variable strategy        
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
I2.005−2.230−0.4701.557−2.363−0.283117
(0.000)(0.000)(—)(0.104)(0.141)(0.032)
II0.154−0.162−0.1470.2540.9510.025132
(0.228)(0.254)(—)(0.205)(0.877)(—)
III0.929−1.055−0.307−1.820−1.1390.121109
(0.014)(0.015)(—)(—)(0.900)(—)
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
I1.556−1.714−0.4441.324−6.151−0.191142
(0.000)(0.000)(—)(0.099)(0.208)(0.070)
II0.078−0.084−0.1380.1432.5070.029153
(0.321)(0.340)(—)(0.292)(0.579)(—)
III0.594−0.753−0.1960.005−2.6120.116128
(0.032)(0.022)(—)(0.497)(0.738)(—)
 Zero interval for IND0:
 [−0.4·B0, 0.4·B0]
I0.872−0.991−0.3890.719−8.487−0.228178
(0.002)(0.004)(—)(0.212)(0.415)(0.015)
II0.174−0.176−0.1610.1721.508−0.006190
(0.112)(0.159)(—)(0.249)(0.722)(0.442)
III0.457−0.587−0.0970.030−3.5480.071166
(0.028)(0.018)(—)(0.480)(0.582)(—)

Market-adjusted buy-and-hold returns according to the realistic return metric are presented in Table 11. In particular for the indicator variable strategy, the returns show a fair amount of variation over the subperiods, revealing a lack of robustness of the profitability of the strategy. Looking at market-adjusted returns to the long positions, most of the statistical significance has evaporated for both the base case strategy and the indicator variable strategy. However, it must be noted that these statistical tests are severely hampered by the small number of observations in the three subsamples.

Table 11. 
MARKET-ADJUSTED BUY-AND-HOLD RETURNS (REALISTIC RETURN METRIC) FOR 36-MONTH HOLDING PERIODS WITH NON-OVERLAPPING SUBSAMPLES
Investment strategyPositionSubsample ISubsample IISubsample III
  1. In subsample I positions were formed in 1983, 1986, 1989, 1992, 1995 and 1998; in subsample II positions were formed in 1984, 1987, 1990, 1993, 1996 and 1999; and in subsample III positions were formed in 1985, 1988, 1991, 1994, 1997 and 2000. The return to the hedge position has been calculated as the difference between market-adjusted returns for the long and short position, in accordance with (14a), (14b) and (14c) (p-values for one-tailed t-tests in parenthesis, no p-value is reported if the sign of the return is inconsistent with the alternative hypothesis).

Base case strategyLong0.26400.14670.2086
(0.1955)(0.2143)(0.1904)
Short−0.11010.0205−0.0865
(0.1103)(—)(0.2594)
Hedge0.37410.12620.2951
(0.1053)(0.2593)(0.0711)
Indicator variable strategy    
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long0.64290.19510.3985
(0.1164)(0.1592)(0.1216)
Short−0.10380.01340.0662
(0.1006)(—)(—)
Hedge0.74670.18170.3323
(0.0902)(0.2196)(0.1814)
 Zero interval for IND0:
 [−0.2·B0, 0.2·B0]
Long0.45320.18620.2893
(0.1977)(0.0484)(0.1763)
Short−0.1943−0.0858−0.1319
(0.1433)(0.2597)(0.1983)
Hedge0.64750.27200.4212
(0.1102)(0.0357)(0.0689)
 Zero interval for IND0:
 [−0.4·B0, 0.4·B0]
Long0.33520.12690.2308
(0.1920)(0.2162)(0.1742)
Short−0.07620.0580−0.0228
(0.1430)(—)(0.4190)
Hedge0.41140.06890.2536
(0.1406)(0.3654)(0.1199)

5.2 Why Only Mispricing for the Long Positions?

As noted previously, the positive hedge returns are almost solely due to the return performance of the long positions. This is somewhat surprising, as one might expect that market mispricing should generate a more symmetrical return distribution for the long and short positions.

A legitimate objection might hence be that the asymmetric return distribution could be explained by a size effect. To address this issue, Table 12 reports the average and median values of inline imagefor the long and the short positions of the indicator variable strategy with the smallest zero interval for IND0.24 Indeed, both the mean and median market values of owners' equity for the short positions exceed the corresponding values for the long positions in thirteen out of eighteen years. The mean and median differences in size (short minus long position) appear to increase over time, implying that—if the returns to the investment strategies were due to a size effect—the market-adjusted returns would be increasing over time. However, as shown in Table 8 above and further elaborated in section 5.3 below, the returns to the strategies rather tend to decrease over time. Furthermore, when controlling for size in regression (13) above, the returns could not be explained by differences in company size.25

Table 12. 
MEAN-ADJUSTED MARKET VALUES OF OWNERS' EQUITY FOR STOCKS BELONGING TO THE INDICATOR VARIABLE STRATEGY, WITH THE UNCERTAINTY INTERVAL FOR IND0∈[−0.1·B0, 0.1·B0]
YearLong positionShort positionDifference in means (Short–Long)Difference in medians (Short–Long)
MeanMedianMeanMedian
  • Average values and medians of mean-adjusted values of the logarithm of market values of owners' equity at the end of the third month in the financial year. The mean-adjustment is made each year for individual years, and for all years in the total sample.

  • a

    No long positions were formed in 1989.

1983−0.6174−0.74490.21800.24740.83530.9924
19840.21460.2146−0.0165−0.1435−0.2311−0.3581
1985−0.2131−0.33080.04440.01280.25740.3436
19861.01371.0137−0.0461−0.0153−1.0598−1.0290
19871.00581.0058−0.03350.1298−1.0394−0.8760
19881.52451.5245−0.0663−0.2923−1.5908−1.8168
1989a0.00000.1999
1990−1.2040−1.20400.10470.30581.30871.5098
1991−1.5051−1.91290.70240.87212.20752.7850
1992−0.7483−1.52102.54412.50303.29244.0241
1993−0.1364−0.21372.31852.31852.45482.5321
1994−1.3620−1.36202.72392.72394.08594.0859
1995−0.3242−1.45580.40520.07670.72941.5326
1996−1.6596−3.00670.63831.01842.29784.0251
1997−0.7090−0.70900.0886−0.03220.79770.6768
1998−3.0405−3.04050.43440.39303.47493.4335
1999−0.81270.14960.81270.69041.62540.5409
2000−0.9789−0.11470.61180.26371.59070.3785
All years−0.7956−1.07210.25150.35591.04711.4280

Since the asymmetric returns might only be partly attributable to differences in company size, another question is whether the observed results might be caused by the probabilistic ROE prediction models having been more accurate for the long positions. Or alternatively, if stock prices just have been more inclined to go up when there was ‘good’ news than to go down when there was ‘bad’ news. A positive market sentiment bias of this kind will in the longer run cause overpricing, which in turn would reduce the potential of replicating the abnormal return performance of the long positions in out-of-sample evaluations.

In order to address these two issues, a subsample only including observations for which the future medium-term ROE and investment returns could be observed was identified.26 The subsample included a total of 696 firm-year observations, with 47.0% non-negative and 53.0% negative changes in medium-term ROE. The indicator variable implied non-negative changes in inline imagefor 68.4% and decreases in inline imagefor the remaining 31.6% of the observations. According to the indicator variable strategy with the smallest zero interval for IND0, the subsample included 82 long positions and 263 short positions. The accuracy of the ROE prediction model was very similar for these positions; 62.2% correct predictions for the long positions and 62.4% correct predictions for the short positions. Hence, the asymmetric return distribution can hardly be explained by an asymmetric prediction accuracy on behalf of the ROE prediction model. However, if the indicator variable implied non-positive changes of inline imagebut the book return actually increased, the average market-adjusted return (statistical return metric) to the long positions was a strong +144.7%. On the other hand, if the indicator variable implied non-negative changes of inline imagebut the book return actually decreased, the average market-adjusted return to the short positions was a more modest −23.1%.27

The observations corroborate the idea that market prices have been positively biased during the sample period. Stock prices have (on average) implied too optimistic expectations about future inline image, and they have been more inclined to increase as positive inline imagesurprises have materialized than to decrease in the presence of negative inline imagesurprises. This clearly weakens the validity of out-of-sample inferences for the observed mispricing.

5.3 Returns to Realistic Investment Strategies?

Whether the proposed investment strategies would have been implementable, a distinction can first be made between the statistical return metric and the realistic return metric. As noted previously, the first metric requires foreknowledge of delisted firms and the number of investment signals at future points in time, implying that returns are likely to be positively biased. However, the realistic return metric is not affected by this deficiency.

Another concern is related to the feasibility of the investment positions. Taking short positions in quoted stocks was formally not allowed until 1992 in Sweden, even though one cannot preclude that this type of trading had taken place earlier. On the other hand, the short positions have been of minor importance for the observed mispricing. Focusing on the return performance of the long positions separately, the realistic return metric for the base case strategy was 20.64% and the corresponding value for the indicator variable strategy (with the smallest zero interval for the indicator variable) was 41.21% (cf. Table 8 above). Even if these returns are somewhat lower than the returns to the corresponding hedge positions, they still provide support for the existence of both forecasting and modelling mispricing.

An additional feasibility issue is, however, related to the analysis and valuation modelling that would have been required in order to implement the specified investment strategies. Getting access to the necessary financial statement information and stock market data for the sample companies in the beginning of the 1980s would clearly have required a non-trivial effort. No commercial financial data base was publicly available at that time in Sweden. Also, the necessary data processing and statistical analyses would have been prohibitively costly in the 1980s. Furthermore, one might note that seminal research contributions for the operationalization of the investment strategies were first published in the late 1980s and onwards (Ou and Penman, 1989; Penman, 1991; Ohlson, 1995; Runsten, 1998). Given that investor learning is costly and that the processing of financial statement information and stock market data have been substantially facilitated over time, one might expect that the mispricing of the Swedish stock market has decreased over time.

To evaluate the idea of investor learning, year-by-year market adjusted returns (realistic return metric) are shown for the hedge positions in Figure 2. The graph shows that the base case strategy and the indicator variable strategy (with the smallest zero interval for IND0) generated positive abnormal returns in 14 and 13, respectively, investment periods out of a total of eighteen periods. However, the graph also shows that the market-adjusted returns appear to be minor—or even negative—from 1993 and onwards.

Figure 2.


MARKET-ADJUSTED BUY-AND-HOLD RETURNS TO THE HEDGE POSITION (REALISTIC RETURN METRIC)
MJBH(H) is the difference between the market-adjusted return for the long position and the short position over 36-month holding periods corresponding to investment positions formed in 1983, 1984, . . .  , 2000. The smallest zero interval for IND0 ([−0.1·B0, 0.1·B0]) has been chosen for the indicator variable strategy.

In order to further investigate whether the observed mispricing has decreased over time, buy-and-hold returns for the realistic return metric have been calculated for the subperiods 1983–91, 1989–97, and 1995–2003. The results are presented in Table 13, clearly supporting the idea that investor learning has taken place over time. Average buy-and-hold returns were positive and significant (p-values 0.026 or better) both for the base case strategy and the indicator variable strategy (with the smallest zero interval for IND0) for all investment positions over the first subperiod 1983–91. During the second subperiod 1989–97 only the long position for the indicator variable strategy attains a reasonable level of significance (p-value 0.0901), and there is no evidence of any mispricing over the last subperiod 1995–2003. This means that the observed mispricing for the whole investment period 1983–2003 in the main is attributed to the first third of this period.

Table 13. 
MARKET-ADJUSTED 36-MONTH BUY-AND-HOLD RETURNS (REALISTIC RETURN METRIC) FOR THE SUBPERIODS 1983–91, 1989–97 AND 1995–2003
Investment strategyPosition1983–911989–971995–2003
  1. The return to the hedge position has been calculated as the difference between market-adjusted returns to the long and short position, in accordance with expressions (14a), (14b) and (14c) (p-values for one-tailed t-tests in parenthesis).

Base case strategyLong0.37260.3742−0.1276
(0.0217)(0.1052)(—)
Short−0.09330.0054−0.0882
(0.0260)(—)(0.2768)
Hedge0.46590.3688−0.0394
(0.0112)(0.1166)(—)
Indicator variable strategy    
 Zero interval for IND0:
 [−0.1·B0, 0.1·B0]
Long0.64290.6628−0.0692
(0.0222)(0.0901)(—)
Short−0.13170.07970.0277
(0.0060)(—)(—)
Hedge0.77460.5830−0.0969
(0.0117)(0.1364)(—)

6: CONCLUDING REMARKS

An important purpose of accounting-based valuation modelling is to identify mispriced stocks through the analysis of financial statement information. In the seminal article Ou and Penman (1989) this idea was exploited using published accounting information to make probabilistic predictions of next year's earnings changes, and then using these predictions to form investment positions. A strategy of this kind provides for a test of forecasting mispricing. The present study contributes by formulating investment strategies that allow for testing both forecasting and modelling mispricing. The forecasting mispricing has been evaluated through an investment strategy of the same kind as in Ou and Penman (1989), Setiono and Strong (1998), and Skogsvik (2008). To address modelling mispricing, an indicator variable strategy based on the RIV model has been operationalized. According to this strategy, investment positions have been taken when accounting-based probabilistic predictions and stock market expectations about future changes in medium-term ROE differ.

With a sample of manufacturing companies quoted on the Swedish stock market (968 firm-year observations) and market data for the period 1983–2003, the main results were as follows. For holding periods of 36 months, both the base case strategy and the indicator variable strategy generated excess returns in standard CAPM tests (i.e., positive values of Jensen's alpha) over the whole period 1983–2003. Both forecasting mispricing and modelling mispricing contributed to explain the abnormal returns generated by the indicator variable strategy. Investment returns were also measured as market-adjusted returns. A statistical return metric was used in order to enhance comparability with previous research and to facilitate control for conventional risk proxies (E/P, book-to-market, size and dividend yield). The statistical return metric indicated that investment returns were substantial and that they could not be explained by the risk proxies. However, as the return metric is based on non-trivial foreknowledge (information about delisted companies and number of investment signals), an alternative return metric has been evaluated. This metric—the realistic return metric—only uses information available at the investment date. Market-adjusted returns based on this metric were found to be smaller than the corresponding returns for the statistical return metric, but nevertheless still quite strong. However, further investigations have shown that the issue of mispricing is more elusive than these results suggest.

First, the performed tests might have been biased due to overlapping sample data in the formation of investment positions. In tests on subsamples with non-overlapping observations, it was found that the abnormal CAPM returns remained fairly intact but that the market-adjusted returns became markedly less significant. However, the latter result was hampered by a substantial reduction of the number of observations in these tests. Second, over the period 1983–2003 the Swedish stock market appears to have been affected by a non-trivial positive sentiment bias (i.e., stock prices going up more strongly with unexpected increases in medium-term ROE, than going down with unexpected decreases in medium-term ROE). It cannot be ruled out that the observed investment returns are specific for this type of market sentiment, and that out-of sample inferences hence might be weak. Third, most of the observed mispricing appears to have taken place over the first third of the investment period 1983–2003. One could expect that costs of data collection and information processing would have been high during this early subperiod. Also, important research-based knowledge instrumental for the specification of the accounting-based investment strategies, was not publicly available until about the mid-1990s.

Overall, the biased significance levels due to overlapping data in the statistical tests of mispricing, the positive sentiment bias of the Swedish stock market over the period 1983–2003, and the instability of the excess returns over shorter subperiods cast doubts on the empirical evidence of mispricing. A reasonable interpretation of the investigation is rather that non-trivial information and data processing costs have prevented investors from taking advantage of the observed forecasting and modelling mispricing up to around 1995, meaning that the mispricing is more hypothetical than being evidence of any market inefficiency. It appears that both types of mispricing have vanished by the mid-1990s. This might be due to investors having gained more knowledge about the statistical properties of medium-term ROE and having become more sophisticated in their fundamental valuation modelling over time.

Footnotes

  • 1

    Historically Swedish accounting principles have been influenced by a German tradition of conservative accounting. Being a member of the European Union, Sweden adopted the requirements of the European Fourth and Seventh Directives in the Swedish Annual Accounts Act of 1995.

  • 2

    The RIV model—originally proposed in Preinreich (1938), Edwards and Bell (1961) and Peasnell (1982), and elaborated in Ohlson (1995) and Feltham and Ohlson (1995, 1999)—is based on the following assumptions: (a) the value of owners' equity is equal to the present value of future expected (net-)dividends, (b) future deviations from the ‘clean surplus relation of accounting’ are expected to be zero, and (c) market values are used in the accounting for (net-) dividends. Consistent with for example Feltham and Ohlson (1999), the model in (1) is written with a year-specific discount rate.

  • 3

    In a few cases where fewer than 48 months of market data were available, the average betas of all other stocks at the portfolio formation dates have been used.

  • 4

    At the future point in time t = Tx, inline imagefor τ≥ 1 where gss= yearly steady state growth of owners' equity (cf. Skogsvik, 1998; Zhang, 2000). Rewriting this expression, the relative measurement bias isinline imageinline image. Given the cost of equity capital and the steady state growth, the cost matching bias on the RHS of (6) can hence be rewritten as a function of the steady state book return inline image. Note, however, that inline imagehas been estimated independently of inline imageand inline imagein the assessment of inline imageand P0, respectively, in this study, as there is no a priori reason for neither inline imagenor inline imageto be equal (or even close) to inline image.

  • 5

    The average cost matching bias was based on the following industries (value of cost matching bias in parenthesis): consumer goods (0.72), pulp and paper (0.67), chemical industry (0.44), engineering (0.33), and other production (0.31).

  • 6

    Extra-ordinary or transitory items have been included in the calculation of ROEt.

  • 7

    The following industries were included: engineering, production, pulp and paper, building and construction, chemical industry, conglomerates, consumer goods, office equipment, pharmaceutical, medical engineering, raw materials, and electric utility.

  • 8

    A non-classified company was included in the sample if the ratios (Fixed assets)t/(Total assets)t, Revenuest/(Total assets)t−1 and Revenuest/Inventoryt−1 were between the minimum and maximum values for the classified manufacturing companies. No trading, retail, or financial companies were among the additional companies. The additional companies were only included during the period 1970–93; from 1994 and onwards all additional companies were classified as manufacturing by the business magazine. The inclusion of the non-classified companies is not likely to have had any disturbing effect on the empirical results.

  • 9

    For example, the change in medium-term ROE for 1979 is the difference between the average value of ROEt for 1980–82 and the average value of ROEt for 1977–79.

  • 10

    For instance, the ROE prediction model for 1972–79 was based on financial statement data up to 1982. At the first investment point in time (end of March 1983) the data were assumed to be publicly available. In a Swedish institutional context this is a realistic assumption.

  • 11

    The results are consistent with, for example, Freeman et al. (1982) on U.S. data, and Skogsvik (2008) on Swedish data.

  • 12

    The proportion of increases in inline image(prop) in the estimation periods was 0.482, 0.519, 0.564, 0.515, 0.376 and 0.485, respectively.

  • 13

    Based on unadjusted probabilities (inline image), 70.3% predictions were correct with a probability cut-off value of 0.5. The calibration formula in (9) hence provided a clear improvement of the prediction performance for the logit models.

  • 14

    Despite a high overall value of correct predictions, the χ2-value for the third holdout period is low. In a technical sense this is caused by the weak prediction performance with regard to increases in inline imagefor this period.

  • 15

    Both inline imageand P0 were calculated ex dividend, that is, excluding dividends that in general would be paid during the first six months after the investment date. Dividends have then been discounted with the risk free rate in the adjustment of the cum dividend stock price.

  • 16

    The abnormal CAPM returns have been assessed for December year-end companies only, each regression including 648 (18 investment dates times 36 months) observations. Any receipts from securities being delisted were reinvested in the market index for the remainder of the 36-month holding periods.

  • 17

    A similarly calculated return metric over 24-month holding periods was 12.5% in Ou and Penman (1989).

  • 18

    Going back to the seminal paper by Fama and French (1992).

  • 19

    Note that the purpose of regressions (12) and (13) was not really to assess the magnitude of the abnormal returns, but rather to investigate to what extent the intercept θ0 and the coefficient θ1 of the dummy variable were affected by the risk proxies.

  • 20

    Only December year-end companies have been included in the realistic return metric, since all positions for a certain year had to be taken at the same point in time. Money received from stocks that were delisted during a holding period has been reinvested in the market index. Any rebalancing of the remaining stocks was then not required and investments in the market index do not create any excess returns.

  • 21

    Reported p-values are based on t-tests with portfolio returns for each investment year as underlying observations.

  • 22

    (1.26511/36− 1) = 0.66% and (1.42021/36− 1) = 0.98%, respectively.

  • 23

    With the exceptions that one portfolio of each type was formed in 1983 and 2003, and two of each type were formed in 1984 and 2002.

  • 24

    In calculating annual average and median values, the market values of owners' equity have been mean-adjusted each year. For all years, the mean-adjustment is based on the average market value of owners' equity in the total sample.

  • 25

    As a further check to investigate whether the investment returns might be driven by a size effect, the regression inline image (where inline image has been mean-adjusted each individual year) was run annually for the indicator variable strategy with the smallest uncertainty interval for IND0. The market-adjusted returns could not be explained by the size variable in any year.

  • 26

    Buy-and-hold returns according to the statistical return metric for the base case and the indicator variable strategy for this subsample were almost identical to the returns for the total sample.

  • 27

    With the indicator variable implying non-positive changes in inline image, the average 48-month beta-value at the investment date was 0.879 for stocks with future increases in inline image. With the indicator variable implying non-negative changes in inline image, the average beta-value was 0.988 for stocks with future decreases in inline image. Hence, the difference in beta-values would rather imply a higher expected return for the short positions than for the long positions.

Ancillary