Empirical Findings on Underreporting

5.3.2.1 Calculating Option Values

In order to determine whether or not companies underreport the option values in their annual reports, I first determine all the necessary input variables as objectively as pos-sible, i.e., strictly according to the guidelines from IFRS 2.⁸⁹ All I require from the annual reports are general information such as the exercise conditions and caps as well as the (expected) maturity. Further, I only include companies that report the fair value either at grant date or at the end of the fiscal year.⁹⁰ This has the advantage that I do not have to eliminate option issues for which not all the parameters are disclosed. This results in 125 observations.

The other inputs are determined as follows. Since the expected dividend yield may only be based on publicly available information, I rely on I/B/E/S consensus estimates for the relevant years. Historical annualized volatilities and correlations with an index, when necessary, are calculated based on the continuously compounded daily returns over a period that corresponds to the expected life of the option or the maximum stock price history, whichever is shorter. Finally, I calculate risk-free interest rates from the term structure based on traded German government bonds.⁹¹

Uncertainty about the exercise of ESO is one of the major difficulties in option valu-ation (e.g., Maris et al., 2003). As stated above, I use the expected time to maturity from annual reports whenever it is available. When companies make no mention of the expected life, I assume the maximum time to maturity is the expected one.⁹² With the time of exercise known, all options are de facto European-style options which simplifies valuation greatly.

To obtain option values, I use a common framework, based on standard no-arbitrage pricing. It assumes that stock prices and, whenever necessary, index levels follow corre-lated geometric Brownian motion processes under the risk-neutral measure. All exercise

89See Section 3.2.2.

90SAR have to be revalued at the end of each fiscal year until they are exercised or expire. In this case I evaluate the underreporting at the end of the year in which they were first issued, since that is the one that is relevant for the income statement.

91The German Bundesbank uses the Svensson method (Svensson, 1994) and publishes daily values for the parameters, available at www.bundesbank.de.

92Five companies state that they model a specific exercise behavior, which I cannot reproduce because of insufficient information. I will, however, account for this in my regression analyses.

conditions and caps are considered, except for the accounting hurdles that exist for two plans. The price computations use Monte Carlo simulations with daily time steps and 100,000 replications. The resulting option values are the ones to be expected under strict adherence to the IFRS rules. Based on these values and the disclosed ones from the financial statements, I measure underreporting as

disclosed value−expected value disclosed value .

This ratio will be below zero when the options are undervalued and above zero when they are overvalued.

5.3.2.2 Underreporting

For those companies that provide enough information to calculate a fair value, I set that expected fair value in relation to the fair value stated in the annual reports. Results are presented in Table 5.4 and values below zero indicate underreporting while values above zero indicate overreporting.

EffectivenessofIFRS291

2005 2006 2007 2008 2009 2010 2011 total

Observations 22 23 20 21 16 12 11 125

Mean −0.512 −0.139 −0.424 −2.469 0.007 −0.278 −0.518 −0.670

Median 0.054 0.007 −0.151 −0.0745 0.082 −0.217 −0.427 −0.052

SD 1.453 0.626 0.714 6.060 0.450 0.892 0.549 2.690

Max 0.777 0.549 0.349 0.372 0.787 0.545 0.307 0.787

Min −4.726 −2.433 −2.074 −21.66 −0.956 −2.819 −1.735 −21.66

T mean (1-sided) 0.057* 0.149 0.008*** 0.038** 0.525 0.152 0.005*** 0.003***

T mean (2-sided) 0.113 0.300 0.016** 0.077* 0.950 0.304 0.011** 0.006***

This table shows the means and medians of the underreporting for each year, calculated as the difference between disclosed value and the expected value, divided by the disclosed value. SD refers to the standard deviation. T-tests were performed with the null hypothesis that the mean is equal to zero and the alternative hypothesis that the mean is below zero (one-sided) and unequal to zero (two-sided). Values are the p-values for said hypothesis tests.

It can be seen that the mean of the underreporting ratio is negative for the complete sample and in every year, except for 2009. Moreover, the years differ quite a bit, both in terms of the standard deviation and in terms of the minimum value (i.e., the maximum underreporting). 2005 and 2008 had the most dispersion of the underreporting values.

The maximum values, that is overreporting, appear to be rather stable over the years. I performed t-tests in order to determine if the underreporting is statistically significant.

The null hypothesis that the mean is equal to zero can be rejected in favor of the alternative that it is below zero (one-sided tests) in four of the seven years and for the overall sample. For the two-sided tests with the alternative hypothesis that the mean is unequal to zero, the p-values for the t-test are only significant in three of the seven years.

In 2008, the low mean and the high standard deviation are caused by two outliers with underreporting ratios of -21.66 and -18.96. Both are cases in which the respective companies reported extremely low fair values. One case can probably be attributed to a data error: the company reports to have used a dividend yield of 18% in estimating the fair value. When I use a dividend yield of 1.8% along all the other parameters used by the company, the result is quite close to the value I have determined with the objective market parameters. For the other outlier there seems to be no apparent reason. Results remain the same, however, even if I leave the two outliers out of the analysis. The underreporting mean in 2008 is then -0.591 with a standard deviation of 1.229. Both the one-sided and the two-sided T-test are still significant at the same confidence level.

The same holds true for the entire sample when the outliers are eliminated; the mean falls to -0.35 but the significance levels remain unchanged. Since it is the objective of this study to identify underreporting regardless of the cause, I will not exclude the outliers from further analysis.

Table 5.5 shows the underreporting broken down by plan category. It can be seen that statistically significant underreporting is limited to plans with absolute performance conditions and those with a combination of different types of hurdles. Those are also the two categories with the worst disclosure performance. It should be noted, though, that the median for the category of absolute performance hurdles is positive, while that for the combined category is also negative. As before the statistical significance does persist even when the two aforementioned outliers are excluded.⁹³

93 The mean underreporting drops to -0.201 in the first column of Table 5.5, yet the significance level for the one-sided t-test remains at 5% and the one for the two-sided test is increased to 5% (p-value of 0.021).

Table 5.5: Underreporting by Plan Category

Performance Condition Absolute Relative Acc.-based Combined

N 81 9 6 29

Mean −0.466 −2.102 −0.200 −0.891

Median 0.017 0.007 −0.259 −0.421

SD 2.503 6.338 0.510 1.326

Max 0.787 0.521 0.549 0.545

Min −21.66 −18.96 −0.690 −4.726

T mean (1-sided) 0.049** 0.175 0.191 0.001***

T mean (2-sided) 0.098* 0.349 0.381 0.001***

This table shows the means and medians of the underreporting for each plan category, calculated as the difference between disclosed value and the expected value, divided by the disclosed value. SD refers to the standard deviation. T-tests were performed with the null hypothesis that the mean is equal to zero and the alternative hypothesis that the mean is below zero (one-sided) and unequal to zero (two-sided).

Values are the p-values for said hypothesis tests.

The findings presented in theses two tables clearly show that underreporting is a sta-tistically significant issue in German executive stock options. Similar to the results in Bechmann and Hjortshøj (2009) not all years show underreporting though. But in con-trast to that study, I use the expected time to maturity and not the contractual time and still find significantly downwardly biased option values.⁹⁴ Thus, underreporting may be of more concern in this setting and potentially caused by the more intricate stock option design elements. It is therefore a logical next step to investigate which companies underreport the value of their ESO.