Dissertation

The Role of Leverage in Explaining the Association

between Interest Rates and the Aggregate Earnings of

Nonfinancial Firms

DAVID THWAITES, University of Edinburgh

Abstract. This study examines whether cross-sectional differences financial leverage influence

the association between unexpected changes in interest rates and unexpected aggregate earnings

of nonfinancial firms listed on the FTSE All-Share Index – with a correction for survivorship

bias. The results show that the aggregate unexpected earnings of highly leveraged firms are more

significantly and positively associated with unexpected changes in interest rates than the rest of

the sample. It is then shown that this is as a result of a positive association with unexpected

operating income and a negative association with unexpected interest rate expense. In both cases,

the associations are stronger and more significant relative to the rest of the sample.

1. INTRODUCTION

The negative association between interest rates and stock market returns is a well-

documented phenomenon (Lintner, 1975; Bodie, 1976; Fama and Schwert, 1977; Hess and Lee

1999). While several studies attempt to explain this relationship by suggesting that it is due to a

negative relationship between interest rates and earnings (Fieldstein, 1980; Fama, 1981; Collins

and Kothari, 1989), more recent studies find a positive relationship between interest rates and

aggregate earnings (Nissim and Penman, 2003; Kothari et al., 2004). There has subsequently

been a lack of research into further understanding the relationship between interest rates and

earnings, because the primary focus in much of the literature is on explaining the relationship

between interest rates and stock returns. Specifically, there is a notable dearth of research into

how cross-sectional differences across firms may alter the nature of the relationship between

interest rates and aggregate earnings.

The purpose of this paper is therefore to investigate whether cross-sectional differences

in financial leverage affect the magnitude of the association between unexpected interest rate

changes and unexpected aggregate earnings. The potential for leverage to explain cross-sectional

differences in this association is primarily twofold: (1) the operating incomes of highly leveraged

firms are likely to be more sensitive to changes in economic activity, and as interest rates should

covary with economic activity, the earnings of highly leveraged firms may be more sensitive to

interest rate changes (2) the net interest expenses of highly leveraged firms are likely to be larger

in proportion to their operating incomes, and therefore any effects of interest rate changes on

prevailing debt market rates would be more strongly felt by firms with higher levels of leverage.

The existing research specifically documents this relationship in the context of US

interest rates and US listed firms. Therefore this study sets out to first establish that a significant

positive association exists between interest rates in the UK and the future aggregate earnings of

UK firms. Next firms are separated into three groups based on their relative levels of leverage in

order to determine if there are any cross-sectional differences in the association between interest

rate changes and the earnings of firms with differing levels of leverage.

The remainder of this paper is organized as follows. Section 2 surveys the existing

literature on the effects of interest rates on earnings and further develops the hypothesis. Section

3 describes the methodology employed, along with potential sources of bias and controls. The

empirical results and a discussion of their implications follow in section 4. Section 5 concludes

the study with a brief summary of the results obtained.

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2. LITERATURE REVIEW

The Fisher hypothesis (Fisher, 1930) states that the nominal interest rate is the sum of the

real interest rate and expected inflation, and that therefore, changes in inflation will impact the

real interest rate unless the nominal interest rate adjusts at the same rate. In economies with

inflation targeting central banks (such as the US and the UK), the express purpose of monetary

policy is to maintain a prescribed level of interest (both the Federal Reserve and the Bank of

England target 2% inflation). Therefore assuming the Fisher hypothesis to be correct, nominal

returns on assets should move in the direction of changes in nominal interest rates. It is then

puzzling that returns on common stocks have consistently been found to be negatively associated

with interest rate changes.

In efficient capital markets, the market price of the firm is the discounted present value of

all anticipated net cash flows, and therefore, there are only two possible means of explanation,

changes in interest rates: (1) dampen expectations of future net cash flows (2) exert a stronger

influence on the discount rate, than the implicit expected inflation exerts on future net cash

flows. In popular valuation models such the residual income model developed by Edwards and

Bell (1961), Ohlson (1995) and Feltham and Ohlson (1995), forecasted earnings are used as a

proxy for expected cash flows. It then follows that an important avenue for future research is

further understanding the relationship between earnings and interest rate changes. Several studies

contradict the expectation upheld in this paper, that earnings are positively associated with

interest rates. Their arguments are as follows.

Fedlstein (1980) finds that an increase in expected inflation (and therefore an increase in

interest rates) reduces real earnings by way of increased corporate taxes. He suggests that

historical cost depreciation and certain inventory accounting methods such as first-in first-out

(FIFO), do not instantaneously adjust to inflation, and therefore in times of inflation, real taxable

earnings increase. Fama (1981) argues that there is a negative relationship between expected

inflation and real economic activity. As interest rates should change in the direction of expected

inflation, this implies a negative association between interest rate changes and earnings. Collins

and Kothari (1989) reason that if the discount rate is the sum of the risk-free rate of return and a

risk premium, then a rise in interest rates should – all else being equal – revise expectations for

future earnings innovations downwards. More specifically, an increase in the discount rate

should reduce the number of potential investments with rates of return above the discount rate,

and as such reduce future investments and earnings. In retrospect, Kothari (2001) acknowledges

that this argument ignores the possibility that the change in interest rates could be solely as a

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result of expected inflation. If this were the case, the expected association between interest rates

and earnings would be negligible, as the firm would pass on the effects of the expected inflation

to its customers. Therefore the presumption in Collins and Kothari (1989) must have been that

either a significant portion of changes in interest in rates is as a result of unexpected inflation,

which has a negative impact on stock prices (Schwert, 1981), or that nominal interest rates

covary positively with real interest rates.

In conflict with the arguments presented above, Nissim and Penman (2003) and Kothari

et al. (2004) find that aggregate earnings are positively related to interest rate changes. As an

aside to their test on the earnings response coefficient, Kothari et al. (2004) find a strong positive

correlation between aggregate earnings and changes in Treasury bill rates. In a more in depth

study, Nissim and Penman (2003) document a positive association between unexpected

aggregate earnings and unexpected changes in interest rates. They then further decompose

unexpected earnings into unexpected operating income and unexpected net interest expense and

find a positive association between both components of unexpected earnings, and unexpected

changes in interest rates. The reported magnitude of the association is larger for operating

income than for net interest expense and they therefore arrive at the conclusion that the effect of

unexpected interest rate changes is stronger on unexpected operating income than it is on

unexpected net interest expense, so that the effect on earnings is ultimately positive.

As noted before, there is a lack of research into cross-sectional differences that could be

driving the relationship between interest rate changes and earnings. A notable exception to this is

the finding in Sweeny and Warga (1986) that the electric utilities sector is more sensitive to

interest rate changes than the wider market. They argue that regulated companies cannot

immediately adjust prices in response to inflation due to constraints imposed by regulators.

However, thus far the potential effect of cross sectional differences in leverage on the association

between earnings and interest rates has not been examined. There are at least two ways in which

leverage may impact on this relationship.

First, higher levels of leverage magnify changes in operating income, such that in times

of increasing economic activity highly leveraged firms can expand their operations faster.

However, if economic activity slows and the firm’s operating income decreases, the ultimate

effect on earnings is magnified by its debt obligations. As interest rates covary with economic

activity, the expected result would be that the earnings of highly leveraged firms are more

positively associated with changes in interest rates. Consistent with this hypothesis, Christie

(1982) finds that taken together, financial leverage and interest rates are positively associated

3

with stock return volatility. As one of the roots of return volatility is earnings volatility, results

from this study will contribute to explain this association.

Second, the interest rate charged on corporate debt is comprised of a measure of the ‘risk-

free’ return on government debt and a risk of default premium. All else being equal, the chance

of a firm defaulting on its debt increases as the firm takes on more debt. Therefore, the default

premium charged on a more highly leveraged firm’s debt should be higher than that of a firm

with low leverage. Furthermore, the default premium has been found to vary over time with the

business cycle (Fama and French, 1989) and time variance in defaults has been found to be

negatively associated with unexpected economic activity and unexpected inflation (Fons, 1987).

Unexpected interest changes are likely to reflect information about unexpected economic activity

and unexpected inflation and therefore the default premium is likely to be negatively associated

with changes in interest rates. This effect is likely to be the strongest for firms with high levels of

leverage and high default premiums priced into their debt expenses. However, as the risk-free

component of the interest rates charged on corporate debt will increase with interest rates, the net

effect on the association is unclear.

These untested hypotheses represent a significant gap in the literature, and offer a basis

with which to revise earnings forecasts – in both a cross-sectional and macroeconomic context –

as new information is revealed regarding changes in interest rates, economic activity and

inflation.

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3. METHODOLOGY

All firm-specific data is collected from Thomson Reuters Datastream database, for the

sample period 1991-2013. The data covers 469 nonfinancial firms listed on the FTSE All-Share

Index as of January 2015 – corrected for dead and delisted firms1 – with a December fiscal year-

end. Financial firms are excluded from the sample as they inherently hold higher levels of

financial assets and liabilities, and as such, their revenues, expenses and ultimately their earnings

are more likely to be more sensitive to changes in interest rates than the population of

nonfinancial firms (Flannery and James 1984; Ewig, Payne, and Forbes 1998; Dinenis and

Stalkouras, 1998). The sample is restricted to December fiscal year ends to allow for cross-

sectional aggregation of firm-specific year-end data. UK government bond (gilt) yields are taken

from the Bank of England’s estimates of the nominal government liability curve (GLC) available

on their website. Values for the UK index of production and the UK consumer price index are

taken from the Office for National Statistics website. 2

3.1 Earnings and Interest rates

In order to first establish that a positive association exists between UK firms’ earnings

and changes in UK interest rates, the two-stage regression methodology of Nissim and Penman

(2003) is employed. The first stage regressions remove much of the expected component of the

change in earnings and the change in interest rates, so that yearly cross-sectional means can be

calculated for each. In the second stage, the yearly cross-sectional mean of the unexpected

change in earnings is regressed on the unexpected interest rate change. With regards to the first

stage, individual regressions are run to determine unexpected earnings in the year of the interest

rate change (t = 0) and in each of the following two years (t = 1 and 2), so that in the second

stage of the regression it is possible to investigate the unexpected interest rate change’s

association with both current, and future unexpected earnings.3 The first stage of the regression is

described as follows.

The firm-specific measure of unexpected earnings is defined as the residual from the

regression of earnings in year t (Et) on the following instruments for expected earnings, available

at the end of the year prior to the interest rate change (t = -1): (1) earnings, or net income after

1 To the extent to which data was available on Datastream (see appendix 1 for details).2 A description of how and when the data was accessed from these sites is included in appendix 1.3 Nissim and Penman (2003) run separate regressions for the subsequent five years but establish that the unexpected change in interest rates is insignificant for the years: t = 2, 3, 4, and 5.

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preferred dividends (E-1); (2) the market value of common equity (MCVE-1); (3) the term-

structure of UK spot interest rates, proxied for using the 1-, 5-, and 10-year yields on the

government liability curve (r1-1, r5-1, and r10-1, respectively); (4) the one-year percent change in

the UK index of production (EA-1); and (5) the rate of inflation defined as the one-year percent

change in the consumer price index (INF-1). The justification for the inclusion of each of these

instruments follows the description of the regression model.4 Additionally, all firm-specific

variables in the regression are divided by the book value of common equity (CE-1) at the end of

the year prior to the interest rate change. To safeguard against the potential for the deflation of

these variables to engender bias, the inverse of the book value (1CE-1) is incorporated in the

regression as a control variable. The firm-specific regression model is therefore:

E t

CE-1 = α0 + α1

E-1

CE-1 + α2

MCVE-1

CE-1 + α3r1-1 + α4r5-1 + α5r10-1 + α6EA-1

+ α7INF-1 + α8 1CE-1

+ ε, (1a)

for t = 0, 1, and 2.

The cross-sectional mean of unexpected earnings (UE[Et]) is subsequently estimated as

the mean value of the regression residual (ε t) across all firms in each sample year. With data

covering the period from 1991-2013 this yields 22 – t observations.5 The purpose of this method

is to improve precision by using firm-specific data to approximate a market-wide value of

unexpected earnings.6 The approximated market-wide measure of unexpected earnings is defined

as:

UE[Et/CE-1] = ε t (1b)

for t = 0, 1, and 2.

4 A detailed explanation of how each variable is calculated is also provided in appendix 1.5 Year-end data from 1991 is used to estimate firm-specific unexpected earnings in 1992, thus reducing the sample period from 23 to 22 years.6 As stipulated by Nissim and Penman (2003, p. 782).

6

The preceding steps are then repeated, this time using the change in the one-year interest

rate in year t = 0 (Δr0) as the independent variable.7 To be precise, the interest rate change is

regressed on the same explanatory variables shown in equation 1a, and the unexpected interest

rate change (UE[Δr0]) is estimated using the mean value of the regression residuals (ε t) for each

sample year. The residuals are determined by the following regression:

Δr0 = α0 + α1 E-1

CE-1 + α2

MCVE-1

CE-1 + α3r1-1 + α4r5-1 + α5r10-1 + α6EA-1

+ α7INF-1 + α8 1CE-1

+ ε, (2a)

The estimated unexpected interest rate change in year t = 0 is defined as:

UE[Δr0] = ε t (2b)

The second stage of the regression is then a time-series regression of the cross-sectional

mean of unexpected earnings in year t (UE[Et/CE-1]), on the unexpected interest rate change in

year t = 0 (UE[Δr0]) for all sample years:

UE[Et/CE-1] = β0 + β1UE[Δr0] + ε (3)

for t = 0, 1, and 2.

The use of a pooled, cross-sectional time-series approach is well established in the

earnings forecast literature (Collins and Kothari, 1989; Ou and Penman, 1989; Basu, 1997).

Fama and French (2000) contend that simple time-series models are too susceptible to

survivorship bias, in that these studies are typically restricted to firms with long earnings

histories (for example, Lev, 1969). Conversely, cross-sectional regressions can be used for larger

samples of firms with minimal survival requirements. In this particular study for example, firms

need only to have two consecutive years of earnings history to be included.

Many studies document that past earnings, book value and market value of equity contain

information regarding future earnings incremental to each other (Peasnell, 1982; Collins et al.,

1997; Penman, 1997; Fama and French, 2000). Nevertheless, it remains difficult to empirically

7 The interest rate change in year t = 0 (Δr0), is defined as the difference between the nominal one-year rate at the end of the year, t = 0, and at the end of the prior year, t = -1 (i.e. Δr0 = r10 – r1-1).

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separate the expected and unexpected components of earnings. The use of current earnings to

forecast future earnings, presumes a component of earnings to be persistent (Kormendi and Lipe,

1987; Collins and Kothari, 1989; Easton and Zmijewski, 1989). Under the maintained hypothesis

of efficient capital markets, market value is defined as the discounted present value of expected

future net cash flows, and as such should inherently contain additional information about future

earnings, beyond that contained in past earnings (Collins et al., 1987; Kothari and Sloan, 1992).

While the use of book value as a deflator, allows for cross-sectional earnings to be measured

relative to firm size, and for future earnings to be measured relative to the base period t = -1.

Though this step is not without its own potential sources of error (see Christie, 1987).

Operating under the assumption that future earnings are associated with changes in

interest rates, it is necessary to control for interest rates at the start of the period. Although this

study only examines earnings up to three years in the future, the 5- and 10-year interests rates are

included in addition to the 1-year rate, owing to association found by Fama (1984) between the

current term-structure of interest rates and future business conditions. The index of production is

selected as the proxy for economic growth, as the gross production proxies (i.e. GDP or GNP)

include the output of all industries – including financial firms, which are excluded from this

study. The use of this proxy is in keeping with previous studies (Fons, 1987; Fama, 1990) and

subsequent studies that find a strong correlation between the index of production and aggregate

earnings (Kothari et al., 2004). Finally, as earnings are measured in nominal terms, the growth

rate in the consume price index is included as a proxy for expected inflation.8

With regards to the instruments used to remove the expected component of short-term

interest rate changes, Nissim and Penman (2003) are relatively brief. As such, the following

justifications are presented as informed presumptions on the matter. It is also necessary to

preface this section by acknowledging the difficulties associated with determining expected

short-term interest rates (see Fama, 1990, and Chan et al., 1992, for short-term US yields; and

Evans, 2003, for short-term UK yields).

The use of spot rates, over forward rates, is supported by the work of Fama (1976) who

finds that forward rates contain about as much information as past spot rates, regarding future

spot rates. Similarly, this study finds that over the period examined, the 1-year spot rate

marginally outperforms the 1-year forward rate in explaining the subsequent one-year interest

rate change – although neither is significant. This finding holds true for the addition of the 5-,

and 10-year forward and spot rates into the regression, although notably their addition

8 Table 8 in appendix 2 shows the explanatory power of the firm-specific regression as each of the instruments is added into the regression.

8

substantially reduces the adjusted R-squared of both models.9 The growth rate in the consumer

price index is used here to proxy for expected inflation because, as mentioned in section 2,

expectations for future changes in interest rates will rely heavily on expected inflation. Similarly,

the growth rate in the index of production is included as a proxy for expected economic activity,

as expectations for future economic activity will influence expected inflation and ultimately the

expected change in interest rates (Geske and Roll, 1983). The firm-specific variables used in

equation 1a, are also included so as to orthoganlize the residuals from the regression with respect

to all the instruments employed in the firm-specific regression.

Admittedly, the individual regression residuals from the interest rate change regression

(equation 2a) lack a clear interpretation. However, Nissim and Penman (2003) speculate that the

alternative approach – which entails inserting the proxy for the change in interest rates into the

first stage earnings regression (equation 1a) – is likely to inflate the t-statistic. Additionally, they

assert that, because the residuals from the interest rate change regression are orthoganalized on

the instruments used in the earnings regression, the two-stage approach is virtually equivalent to

the alternative approach. Indeed, upon conducting the one-step alternative approach, they

describe the t-statistics as “substantially larger than those reported”, and find little difference in

the coefficient of the interest rate change (Nissim and Penman, 2003, p782).

3.2 Decomposing Earnings

For further context with which to interpret the results, and in keeping with the

methodology of Nissim and Penman (2003), the regressions outlined in the previous section are

then rerun substituting earnings with operating income and net interest expense. Specifically, the

firm-specific first-stage regression (equation 1a) is rerun using the same predictors, but with the

value of the components at time t and t = -1, substituted for earnings at time t and t = -1 (Et and

E-1). Separate first-stage interest rate regressions (equation 2a) are run using each component, so

that the residuals used in calculating the measure for unexpected interest rate changes are

orthoganalized with respect to the instruments used in the corresponding firm-specific

regression. The effect this has on the yearly mean residuals from the interest rate regression is

negligible, and the results are unaffected by the use of the same yearly mean residuals in each

regression. The second-stage regression is then rerun to determine if unexpected interest rate

9 For a more thorough examination of the explanatory variables used in the interest rate regression, and for specific values see tables 9 and 10 in appendix 2.

9

changes are associated with unexpected operating income and unexpected net interest expense in

year t.

It is necessary to highlight that Nissim and Penman (2003) briefly explain this step in

their empirical results and not in their methodology. They state that they “decompose earnings

into the related operating and financing components” (Nissim and Penman, 2003, p784) however

make no mention of the procedure used. Furthermore, the reported results of the regression show

the unexpected measure of each component to be deflated by the same book value variable as

earnings (CE-1), and the table notes describe the deflator as the book value of common equity. In

the interest of maintaining consistency and simplicity across the regressions, the methodology in

this study uses the book value of equity to deflate all of the firms specific variables, including the

components of earnings. I

However in a separate paper, Nissim and Penman (2005) define net operating assets to be

the sum of the book value of equity, and net financial debt. So as to not completely overlook the

potential implications on the results, the operating income regressions are rerun substituting all

occurrences of the book value of equity with net operating assets (as defined above), and the net

interest expense regressions are rerun substituting the book value of equity with net financial

debt. The results are reported in Table 13, appendix 1. For both components, the sign of the

association remains the same as it was when the book value of common equity was used, but the

results are not identical.

3.3 Leverage, Earnings and Interest rates

In order to assess if cross-sectional differences in leverage affect the relationship between

earnings and interest rates, the sample firms are separated in each year based on their ratio of net

financial debt to market value of common equity at the end of the year prior to the interest rate

change. The separation is performed by first ranking the firms in each sample year on their level

of leverage and then dividing them into three groups: High-ND firms (highest 30%), Med-ND

firms (middle 40%), and Low-ND firms (lowest 30%). The regressions described above are then

rerun for each of the firm groups. The use of financial leverage is in keeping with the intent of

this study to examine potential differences on the cross-sectional net interest expense

regressions. Operating liabilities (i.e. trade payables, pension liabilities) would not contribute to

these cross-sectional differences, as they do not carry interest charges.

3.4 Further Data Specifications

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The methodology employed here differs from that of Nissim and Penman (2003) in two

regards. First, for each of the two-stage regressions they run (earnings, operating income, etc.),

they remove observations for which any of the firm-specific variables lie outside the 1 to 99

percent range of the pooled distribution. This study takes a more conservative approach. For a

single dataset, encompassing the data used in all of the two-stage regressions, observations are

removed only if the firm-specific explanatory variables at the start of the period (t = -1) lie

outside the 0.5 to 99.5 percent range of the pooled distribution.10 Second, several of the firm-

specific variables used are calculated differently to the specifications in Nissim and Penman

(2003). This is either because of issues with data availability on Datastream or to facilitate a

more straightforward interpretation of the results.11 Without further detailed guidance from

Nissim and Penman (2003) on their methodology, the following is presented in order to acquaint

the reader with the specific steps taken to construct the datasets used in the two-stage

regressions.

Following the removal of observations containing explanatory variables outside the

imposed acceptable range, the data is separated into three individual datasets, such that the first

set contains the firm-specific dependent variables (Et , OIt , and NIEt) at time t = 0, the second set

contains the dependent variables at time t = 1, and the third contains the dependent variables at

time t = 2. Observations are removed if Et is exactly equal to zero, as it is assumed that the

company has either died, been delisted, or been removed from the dataset due to a change in its

fiscal year-end from December.12

Observations with OIt and NIEt equal to zero remain in the sample for two reasons. First,

firms that report zero operating income will still report earnings figures (typically negative) and

net interest expense figures, and will typically show a change from the preceding or in the

proceeding year. Similar reasoning follows for firms with zero net interest expense. In other

words, these zero-values have a practical interpretation in the context of the income statement, as

a firm can hold zero interest generating assets and liabilities, or currently not be generating

operating income in a given year (for example, oil and gas exploration companies). Second, by

maintaining the use of the same dataset in the earnings regression, as well as the operating

income and net interest expense regressions, the results represent a true dissection of earnings

10 This is of course excluding the inverse of the book value of common equity (1CE-1), which is only

added as a control variable.11 For example, operating income in Nissim in Penman (2003) is defined as the sum of net interest expense and earnings, whereas here it is the reported operating income figure as provided by Datastream. See appendix 1 for how each of the variables was calculated. 12 As all firm data is set equal to zero if this is the case.

11

into its respective components. Furthermore, these observations make-up less than 0.001% of

each dataset and the reported results are not significantly affected by their exclusion.13

3.5 Potential Sources of Bias and Controls

In equations 1b and 2b, the cross-sectional means of the regression residuals from the

first-stage regressions are calculated on an equally weighted basis. In a similar vein to Nissim

and Penman (2003), the strength of the results from this approach are assessed by rerunning the

second-stage regressions using the cross-sectional mean of the first-stage residuals weighted on

both market and book value. Such that the weight assigned to each residual is based on a firm’s

market or book value in proportion to the sum of all firms’ market or book values in that

particular sample year. Results obtained from these different approaches are similar to those

reported and are included in appendix 1.

The use of the index of production over the gross domestic product as a measure of

economic activity has already been justified. Nonetheless the explanatory power of both

variables – with regards to future earnings – are compared, and the index of production proves

superior. Additionally, the one-year percent change in the index of production and the consumer

price index, is more specially defined as the change in the yearly index from year t = -2, to t = -1.

However, both indices are reported quarterly, and upon closer examination the yearly figures are

determined to be mean of the four quarterly figures reported in a given year. To ensure that the

particular definition of a one-year change has no bearing on the results, the regressions are rerun

using the one-year, fourth quarter to fourth quarter, change in both indices. The results remain

effectively identical.

As mentioned above, issues with data availability constrain the ability of certain variables

to be calculated exactly as they are in Nissim and Penman (2003). A variable of particular

concern is earnings – defined in their study as comprehensive net income, inclusive of the

change in the marketable securities adjustment and the change in the cumulative translation

adjustment. The equivalent of the cumulative translation adjustment found on Datastream, the

unrealized foreign exchange gain/loss, is unavailable for almost a quarter of all firms in the

sample (primarily from the earlier half of the sample period). To this end, firm earnings in this

study are defined as net income after preferred dividends.

The exclusion of the change in the unrealized foreign exchange gain/loss is worth noting,

as a change in the interest rate differential between the UK and other economies will impact the

13 Both the significance and sign of the estimated coefficients reported remain unchanged.

12

respective exchange rates. Therefore, the change in the unrealized foreign exchange gain/loss is

likely to contain important information regarding the effect of changes in interest rates on firms’

expected future payoffs. The findings presented below are sensitive to the definition of earnings,

in that the association between unexpected comprehensive income and the unexpected interest

rate change is statistically insignificant, whilst the association between unexpected net income

after preferred dividends and the unexpected interest rate change is statistically significant. This

is deemed attributable to the inconsistency in data availability.

4. EMPIRICAL RESULTS

The descriptive statistics for each of the datasets used for the regressions is provided in

Table 1. The mean number of firms included in the yearly cross-sectional aggregation is

13

decreasing in time because, as previously mentioned, dead and delisted firms without more than

two or three years of consecutive data are excluded from the datasets at time t = 1, and 2. In spite

of this, the variables measured at time t = -1 prove to relatively consistent across time intervals.

As would be expected with nominal financial measures, almost all of the mean variables are

increasing with time. The only two exceptions being the full sample (panel A) mean earnings

from time t = 1 (0.168) to t = 2 (0.130) and the High-ND (panel B) mean net interest expense

from time t = 0 (0.078) to t = 1 (0.074). Similarly, and as expected, the standard deviations of the

variables are also increasing across time periods. This is because the variables measured at time

t, are being deflated by the book value of equity at t = -1, and as earnings (and therefore its

components) directly impact current book value, it would stand to reason that measuring

variables with respect to the book value of equity, one, two, and three years prior would yield

increasingly varied results across firms.

It is interesting to note the differences in the mean values of the variables across high,

medium, and low net financial debt firms in the sample (panel B, C, and D respectively).

Beginning with earnings, it appears the most profitable firms are those with a medium level of

leverage, followed by the least leveraged firms, whilst the most highly leverage firms appear to

be significantly underperforming. Further decomposing earnings into operating income and net

interest expense, it appears that highly leveraged firms earn more operating income than the least

leveraged firms, but that this is offset by a substantially higher net interest expense. In line with

the conclusions drawn, each set’s mean market-book value ratio follows the ranking of

profitability. Although the mean book value of the most leveraged firms is only marginally less

than those of the least leveraged firms, taking the standard deviation into consideration it appears

the most leveraged firms are consistently the smallest firms in our sample. Firms with a medium

level of leverage are typically the largest.

The first-stage time-series regressions are then run using the full sample, for earnings

(Table 2), operating income (Table 3), and net interest expense (Table 4) to remove the expected

component of each, and assess the quality of the instruments measured at time t = -1. In all three

regressions, and across all three subsequent years, the current values of the dependent variables

(E-1, OI-1, and NIE-1) are significant at the 0.1% level with correspondingly large t-statistics that

decrease through the subsequent years. Future earnings are consistently the hardest to explain,

TABLE 1

Descriptive Statistics

Variables

14

E t

CE-1

E-1

CE-1

OI t

CE-1

OI-1

CE-1

¿E t

CE-1

¿ E-1

CE-1

MCVE-1

CE-1

CE-1

Mean firms in

each year

Panel A: Full Sample

t = 0Mean 0.136 0.116 0.294 0.254 0.035 0.032 3.378 842,071

206Std. Dev. 0.523 0.325 0.405 0.320 0.079 0.074 4.196 3,576,881

t = 1Mean 0.168 0.119 0.341 0.256 0.039 0.032 3.439 827,789

195Std. Dev. 0.613 0.324 0.604 0.318 0.099 0.073 4.286 3,490,965

t = 2Mean 0.130 0.119 0.389 0.257 0.048 0.032 3.467 808,963

184Std. Dev. 2.919 0.325 1.014 0.312 0.167 0.073 4.209 3,366,364

Panel B: High-ND

t = 0Mean 0.061 0.035 0.274 0.248 0.078 0.077 2.083 610,063

62Std. Dev. 0.400 0.374 0.327 0.301 0.096 0.095 2.252 1,839,306

t = 1Mean 0.094 0.036 0.310 0.249 0.074 0.076 2.104 577,483

59Std. Dev. 0.420 0.366 0.360 0.293 0.100 0.091 2.235 1,545,470

Panel C: Med-ND

t = 0Mean 0.198 0.181 0.365 0.318 0.034 0.030 4.180 1,103,116

82Std. Dev. 0.633 0.283 0.314 0.314 0.055 0.041 5.137 4,074,029

t = 1Mean 0.223 0.181 0.417 0.319 0.043 0.031 4.277 1,063,177

78Std. Dev. 0.684 0.294 0.590 0.325 0.089 0.047 5.365 3,814,579

Panel D: Low-ND

t = 0Mean 0.130 0.111 0.218 0.174 -0.009 -0.011 3.606 726,532

62Std. Dev. 0.454 0.305 0.455 0.329 0.063 0.054 3.984 4,124,808

t = 1Mean 0.170 0.119 0.271 0.179 -0.001 -0.010 3.659 764,837

58Std. Dev. 0.665 0.298 0.780 0.316 0.097 0.051 3.890 4,328,357

Where Mean firms in each year refers to the mean number of firms used to calculate cross-sectional averages for the second-stage regressions, in each of the 22 – t years.

with an Adj. R2 of 40.4% for earnings one-year in the future, t = 0, that decreases to 3.5% for

earnings three-years into the future, t = 2. Both earnings and market-to-book value at time t = -1

are significantly, and positively associated with future earnings for all three years – though the

t-statistics is seen to be gradually decreasing. Notably, the R2 of 26.2% reported in Nissim and

Penman (2003) for year t = 0, is substantially lower than the Adj. R2 reported here. While the R2

of 10.1% that they report in year t = 2 is noticeably higher than the Adj. R2, found in Table 2. The

relative volatility of the results obtained in this study is most likely due to the smaller firm

sample and short time period examined.

15

Furthermore, they find all of the instruments significant in the first year – in particular the

growth rate in the index of production and the consumer price index are highly significant in all

three years. Whereas out of all the macroeconomic instruments, only the 1- and 10-year interest

rates at the beginning of the period prove to be significant. Notably, the estimated coefficient on

the 1-year rate (α3) is negative and its corresponding t-statistic gradually increases becoming

significant in year t = 2, while the estimated coefficient on the 10-year interest rate (α5) is

positive, and its associated t-statistic gradually decreases becoming insignificant in year t = 2.

This implies a positive association between the current 10-year rate and near-future earnings, and

a negative association between the current 1-year rate and distant-future earnings – though the

TABLE 2

Earnings at time t regressed on instruments for expected earnings

E t

CE-1 = α0 + α1

E-1

CE-1 + α2

MCVE-1

CE-1 + α3r1-1 + α4r5-1 + α5r10-1 + α6EA-1 + α7INF-1 + α8

1CE-1

+ ε

t 0 1 2α0 -0.057** -0.006 -0.054

t(α0) -2.567 -0.169 -0.292

α1 0.325*** 0.301*** 0.090***t(α1) 26.387 19.230 5.183

α2 0.182*** 0.059*** -0.040*t(α2) 14.378 3.677 -2.221

α3 -0.004 -0.067 -0.177*t(α3) -0.068 -0.936 -2.386

α4 -0.205 -0.201 0.282t(α4) -1.495 -1.207 1.659

α5 0.255** 0.265* -0.097t(α5) 2.692 2.292 -0.810

α6 -0.010 -0.023 -0.004t(α6) -0.702 1.318 -0.224

α7 0.005 -0.002 -0.097t(α7) 0.333 -0.074 0.075

α8 -0.515*** 0.084*** -0.154***t(α8) -43.300 5.503 -9.162

Adj. R2 0.404 0.123 0.035n 4,533 4,100 3,683

Where α is the standardized beta coefficient, t(α) is the corresponding t-statistic, R2 is adjusted for

degrees of freedom, n is the number of observations in the time-series regression. * Significant at the 5% level. ** Significant at the 1% level. *** Significant at the 0.1% level.

associated Adj. R2 is sufficiently small in year t = 2 that the later implication is less conclusive.

The signs on the estimated coefficients for the firm-specific variables (α1 and α1) are positive as

16

expected. In that a portion of current earnings persists in subsequent years and that a high current

market-to-book value indicates that the market is anticipating high future earnings. Due to the

instruments’ inability to satisfactorily explain earnings three years into the future, and the

volatility of these earnings (see panel A in Table 1), results of the second stage regression in year

t = 2 (Table 5) are interpreted with a healthy degree of skepticism. Moreover, when the firms are

separated by net financial debt (Tables 6 and 7) the regressions are only run for two years into

the future (t = 0, and 1). Nonetheless, the shorter time period should be more than adequate to

observe any cross-sectional differences.

TABLE 3

Operating income at time t regressed on instruments for expected operating income

OI t

CE-1 = α0 + α1

OI-1

CE-1 + α2

MCVE-1


1CE-1

+ ε

t 0 1 2α0 0.009 0.019 -0.012

t(α0) 0.783 0.729 -0.203

α1 0.759*** 0.581*** 0.372***t(α1) 80.439 43.274 20.817

α2 0.079*** 0.001 0.039*t(α2) 8.163 0.049 2.108

α3 -0.41 -0.098 -0.170*t(α3) -1.028 -1.778 -2.482

α4 -0.104 -0.002 0.165t(α4) -1.095 -0.015 1.052

α5 0.128 0.080 -0.011t(α5) 1.953 0.904 -0.098

α6 0.003 -0.007 0.006t(α6) 0.321 -0.512 0.346

α7 -0.021 -0.018 -0.010t(α7) -1.899 -1.125 -0.422

α8 0.235*** 0.362*** 0.137***t(α8) 28.492 30.733 8.785

Adj. R2 0.716 0.477 0.179n 4,533 4,100 3,683


degrees of freedom, n is the number of observations in the time-series regression. *Significant at the 5% level. **Significant at the 1% level. ***Significant at the 0.1% level.

As previously mentioned, Nissim and Penman (2003) do not report results for the first-

stage regressions run on future operating income or net interest expense. Nevertheless, they are

reported here in Tables 3 and 4 to provide the reader with additional context to interpret the

results of the second-stage regressions. Both operating income and net interest expense are better

17

explained by the instruments used, showing an Adj. R2 of 71.6%, and 68.2% in year t = 0,

respectively. In addition they both appear to be more persistent – in particular future net interest

expense is highly persistent with 50.1% of its variation being explained three years into the

future, t = 2. This finding is consistent with the fact that bottom-line earnings (proxied for here

using net-income after preferred dividends) include non-recurring items and are therefore likely

to be considerably less persistent.

TABLE 4

Net interest expense at time t regressed on instruments for expected net interest expense

¿E t

CE-1 = α0 + α1

¿ E-1

CE-1 + α2

MCVE-1


1CE-1

+ ε

t 0 1 2

α0 0.004 0.007 0.009t(α0) 1.489 1.551 1.138

α1 0.817*** 0.625*** 0.388***t(α1) 96.238 52.509 32.926

α2 0.058*** 0.093*** 0.068***t(α2) 6.605 7.529 5.604

α3 0.082 0.159* 0.125*t(α3) 1.925 2.771 2.346

α4 -0.095 -0.214 -0.289**t(α4) -0.943 -1.604 -2.368

α5 0.034 0.075 0.155t(α5) 0.486 0.881 1.801

α6 -0.004 -0.003 0.003t(α6) -0.358 -0.218 0.224

α7 -0.012 -0.026 -0.033t(α7) -1.004 -1.541 -1.787

α8 -0.096*** 0.080*** 0.546***t(α8) -11.123 6.565 45.303

Adj. R2 0.682 0.434 0.501n 4,533 4,100 3,683



As with earnings, both current operating income and net interest expense are significant

at the 0.1% level, and positively associated with future values across all three years. For

operating income, market-to-book value is significant except in year t = 2, while for net interest

expense, it remains significant across all three years. Interestingly, the 1-year rate is also

18

negatively associated with future operating income with a gradually increasing t-statistic,

becoming significant year t = 1 and 2. However the 10-year rate, and in fact all of the other

macro variables included in the regression, remain insignificant across all years. In the net

interest expense regressions, the 1-year is almost significant one year into the future, but is

significant at the 5% level two and three years into the future. The corresponding beta

coefficients are positive, and, subsequent to year t = 0, gradually decreasing – as would be

expected. The current 5-year rate is significantly, and negatively, associated (at the 1% level)

with net interest rate expense three years into the future.

Next, using the residuals from the first stage regressions, the yearly cross-sectional means

are calculated for each of the variables at time t. along with the yearly cross-sectional means of

the residuals from each of the corresponding interest rate regressions.14 The aggregate measures

of unexpected earnings, operating income, and net interest expense are then regressed on the

unexpected change in interest rates, for the 22 – t years examined (Table 5, panel A, B and C,

respectively). Panel A shows unexpected earnings at time t = 0, to be significantly, and

positively associated with unexpected changes in the 1-year yield on UK government yields.

This appears to be as a result of a positive association between unexpected interest rate changes

and unexpected operating income, and a negative association with unexpected net interest

expense, although both associations are insignificant. Notably, the estimated coefficient on

UE[Δr0] in the earnings regression, and the corresponding t-statistic in year t = 0, are both almost

half of those reported in Nissim and Penman (2003). However, with regards to the explanatory

power of UE[Δr0], the R2 reported here is only marginally smaller (35.1%) than that reported in

their study (43.6%). Methodological differences aside, this implies that unexpected interest rate

changes should adjust the outlook for current earnings in the direction of the interest rate change,

but to a smaller degree in the UK than in the US. This conclusion is of course subject to the

differences in the calculation of certain variables (see section 3.5), along with differences in the

size of the firm sample, and the length of the sample period.

In panel A, year t = 1, the estimated coefficient on UE[Δr0] remains positive but is

considerably smaller, and its association with unexpected earnings is no longer significant. For

TABLE 5

Unexpected earnings, operating income, and net interest expense regressed on unexpected changes in interest rates

Panel A: Unexpected earnings, UE[Et/CE-1] = β0 + β1UE[Δr0] + ε

14 This is in order to orthoganlize the residuals in each panel regression with regards to the instruments used in the firm-specific first-stage regressions (see section 3.1)

19

t 0 1 2

β0 0.002 0.002 0.005t(β0) 0.241 0.118 0.078

β1 0.593** 0.253 -0.189t(β1) 3.292 1.138 -0.818

R2 0.351 0.064 0.036

n 22 21 20

Panel B: Unexpected operating income, UE[OIt/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.001 0.001 0.000t(β0) 0.217 0.115 0.019

β1 0.237 0.209 0.127t(β1) 1.091 0.934 0.545

R2 0.056 0.044 0.016

n 22 21 20

Panel C: Unexpected Net Interest Expense, UE[NIEt/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.001 0.000 0.000t(β0) 0.046 0.129 0.212

β1 -0.162 0.164 0.301t(β1) -0.735 0.726 1.337

R2 0.026 0.027 0.090

n 22 21 20

Where β is the standardized beta coefficient, t(β) is the corresponding t-statistic, n is the number of observations in the time-series regression. *Significant at the 5% level. **Significant at the 1% level. ***Significant at the 0.1% level.

the unexpected operating income regression (panel B) in year t = 1, the estimated coefficient on

UE[Δr0] remains positive and is roughly the same magnitude as in time t = 0. Interestingly, the

estimated coefficient on UE[Δr0] in the net interest expense regression (panel C) turns positive

and is of almost identical magnitude as in time t = 0. This affords two possible inferences. First,

the expected negative association between interest rates and default premiums is large enough to

offset the increase in the contemporaneous increase in the risk-free component of the debt

market rates. Second, there is in fact a positive association between unexpected changes in

interest rates and unexpected net interest expense but it is delayed, by either the successful

hedging of interest risk (the negative association at time t = 0, thereby potentially being

TABLE 6Unexpected earnings regressed on unexpected changes in interest rates for firms with high,

medium, and low levels of net financial debt

Unexpected earnings, UE[Et/CE-1] = β0 + β1UE[Δr0] + ε

20

t = 0 High-ND Med-ND Low-ND

β0 0.001 0.002 0.002t(β0) 0.179 0.220 0.120

β1 0.518* 0.473* 0.167t(β1) 2.709 2.399 0.755

R2 0.268 0.223 0.028n 22 22 22

t = 1

β0 0.001 0.003 0.001t(β0) 0.061 0.146 0.056

β1 0.391 0.112 0.133t(β1) 1.852 0.490 0.585

R2 0.153 0.012 0.018n 21 21 21


explained by income from these derivatives), or a lag in the time taken for interest rate changes

on government securities to be reflected in the interest rates charged on corporate debt.

Interestingly, the results reported in Nissim and Penman (2003) show the estimated coefficient in

the net interest expense regression, to be marginally larger than zero in year t = 0, before

substantially increasing in years t = 1 and 2.

In year t = 2, the estimated coefficient on UE[Δr0] in the earnings regression, turns

negative. This appears to be as a result of a substantially smaller coefficient on UE[Δr0] in the

operating income regression, coupled with a substantially larger coefficient on UE[Δr0] in the net

interest expense regression. Further supporting the notion that the association between

unexpected changes in interest rates is negative in the current year, but both positive and

increasing in magnitude in subsequent years. However any conclusive inferences are hindered by

the fact that only the association between unexpected earnings and unexpected interest rate

changes at time t = 0 is significant, throughout all three panel regressions, and all three years into

the future. Furthermore, unexpected changes in interest rates explain at most, 5.6% and 9% of

the variation in unexpected operating income and unexpected interest expense, respectively.

Therefore it is with considerable caution that these results are interpreted – beyond establishing a

TABLE 7Unexpected operating income and net interest expense regressed on unexpected changes in

interest rates for firms with high, medium, and low levels of net financial debt

Panel A: Unexpected operating income, UE[OIt/CE-1] = β0 + β1UE[Δr0] + ε

21

t = 0 High-ND Med-ND Low-ND

β0 0.000 0.002 0.001t(β0) 0.096 0.250 0.116

β1 0.348 0.112 0.146t(β1) 1.662 0.505 0.661

R2 0.121 0.013 0.021n 22 22 22

t = 1

β0 0.000 0.002 0.001t(β0) 0.009 0.150 0.056

β1 0.426* 0.039 0.060t(β1) 2.053 0.170 0.261

R2 0.182 0.002 0.004n 21 21 21

Panel B: Unexpected net interest expense, UE[NIEt/CE-1] = β0 + β1UE[Δr0] + ε

t = 0 High-ND Mid-ND Low-ND

β0 0.000 0.000 0.000t(β0) -0.92 0.068 0.023

β1 -0.501* -0.396* 0.206t(β1) -2.586 -1.927 0.943

R2 0.251 0.157 0.043n 22 22 22

t = 1

β0 0.000 0.000 0.000t(β0) 0.044 0.139 0.039

β1 0.314 0.028 -0.031t(β1) 1.444 0.124 -0.134

R2 0.099 0.001 0.001n 21 21 21


significant positive association between unexpected earnings and unexpected interest rate

changes.

Nevertheless, having established this result, the firms in the sample are ranked within

each sample year, on their ratio of net financial debt to market value of common equity at the

end of the year prior to the interest rate change, and divided into three groups: High-ND, Med-

ND and Low-ND. The first-stage regressions are then rerun for each group for reasons outlined

in section 3.3 (results not reported), along with the second-stage regressions. The results in Table

6 show that there is a significant positive association between the unexpected earnings of High-,

and Med-ND firms and unexpected changes in interest rates in year t = 0. However, the

22

unexpected earnings of firms in the Low-ND sample are not significantly associated with

unexpected changes in interest rates. Consistent with this, unexpected interest rate changes can

explain 26.8% and 22.3% of the variation in the unexpected earnings of High-, and Med-ND

firms, while only explaining 2.8% of the variation of Low-ND unexpected earnings.

Similar to the results from the full sample second-stage regressions, this significant

positive association for High-, and Med-ND firms seems to be induced by the unexpected

interest rate changes’ positive association (significant for High-ND in year t = 1) with

unexpected operating income (Table 7, panel A) and a significant negative association with

unexpected net interest expense (Table 7, panel B). Focusing on unexpected interest rate expense

regressions, the estimated beta coefficients for High-, and Med-ND firms are substantially larger

than that reported in the full sample regression (Table 5, panel C, t = 0). This is particularly

noteworthy, as the significant negative relationship is only present in the more highly leverage

firms in the sample. Furthermore, the size of the negative coefficient on UE[Δr0] makes the

association far less likely to be explained by income on interest rate risk hedging instruments.

There is however, a possibility that this is due to the tendency for unexpected interest rate

changes to alternate, from one year to the next, between being positive and negative, over the

period examined. Figure 1 shows the variation in the unexpected change in interest rates, and

shows its sign to be almost consistently shifting from negative to positive from one year to the

FIGURE 1

The measure of unexpected changes in interest rates over the sample period

23

next. This adds considerable confusion to the matter, as both the negative and positive estimated

coefficients on UE[Δr0] in the net interest expense regression in the years t = 0, and 1 could then

be a result of a delayed positive association.

However this line of reasoning puts all of the results into question, and the entire

methodology of Nissim and Penman (2003). This is entirely outside the scope of this paper, and

as the results have been found to be in keeping with the prior research used to develop the

examined hypothesis, it is concluded that there is a significant negative association between

unexpected interest rate changes, and the unexpected net interest expenses of firms with

relatively high levels of financial debt. In addition to the delayed but significantly positive

association found between unexpected interest rate changes and the unexpected operating

income. Furthermore, both the magnitude and the significance of these associations are the

greatest for firms with the highest levels of financial debt.

It is also important to stress that Low-ND unexpected earnings are not significantly

associated with unexpected interest rate changes. Neither are Low-ND unexpected operating

income nor Low-ND unexpected net interest expenses. In all cases, the portion of the unexpected

component that can be explained by the regressions is less than 5%. Put differently, the

unexpected earnings of Low-ND firms appear to be almost completely unrelated to unexpected

interest rate changes. The most suitable explanation for this is that, unexpected interest rate

changes will likely reflect unexpected revelations about the state of the economy. If these

unexpected revelations have to do with economy-wide demand, then on the average, more highly

leveraged firms would be in the better (worse) position to deal with excess demand (supply) than

would firms with low levels of leverage.

5. CONCLUSION

24

The results in this study indicate that there is a significant and positive association

between the unexpected aggregate earnings of UK firms and unexpected changes in the one-year

yield on UK government bonds. A further decomposition of earnings into operating income and

net interest expense provides inconclusive evidence on the specific nature of this effect for the

full sample of firms. However, upon separating the firms based on their ratio of net financial

debt to market value of common equity, it is found that the unexpected earnings of the most

leveraged firms are the most significantly and positively associated with unexpected interest rate

changes. This is as a result of a significant positive association between the unexpected operating

income of highly leveraged firms and unexpected interest rate changes, and a significantly

between unexpected net interest expense and unexpected interest rate changes. When using all

three measures, the most highly leverage firms are the most sensitive to interest rate changes,

while the least leveraged firms are appear to be almost completely unaffected by changes in

interest rates.

These findings are most likely due to a positive association between unexpected earnings

and unexpected changes in economic activity and inflation. Therefore earnings forecasts should

be revised by a larger degree for firms with higher levels of net financial debt, in the direction of

the unexpected changes in inflation and economic activity.

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APPENDIX 1

27

The variables used in this study are calculated using the following procedure, and data types

from Datastream:

Earnings (E) =

Market value of common equity = (MCVE)

Book value of common equity = (CE) Financial liabilities =

Financial assets =

Net financial debt (ND) =

Net interest expense (NIE) =

Operating income =

Net income After Preferred dividends [WC01706] + Unrealized Gain/Loss on Marketable Securities [WC03498] + Unrealized Gain/Loss on Foreign Exchange [WC03499]

Market Capitalisation [WC08001]

Common Equity [WC03501]

Short Term Debt & Current Portion Of Long Term Debt [WC03501] + Long Term Debt [WC03251] + Preferred Stock [WC03451] + Minority Interest (Balance Sheet) [WC03426]

Cash and Short-term Investments [WC02001] + Investments in Associated Companies [WC02256] + Other Investments [WC02250]

Financial liabilities – Financial assets

Interest expense [WC01251] – Non-operating interest income [WC01266]

Operating income [WC01250]

1. With regards to the correction for survivorship bias, Datastream provides lists for the

FTSE-All share constituents in the years 1994, 1995, 1996, 1997, and 1998, 1999, 2000.

Therefore dead and delisted companies that were added to the index prior after the year

2000, are not included in the correction.

2. The Bank of England’s estimates of the nominal government liability curve (GLC) were

accessed using the following domain (01/02/2015):

28

http://www.bankofengland.co.uk/statistics/Pages/yieldcurve/archive.aspx

The specific file selected was the GLC Monthly Data from 1970-present.

3. The values for the UK production index and the UK consumer price index were taken

from the Office for National Statistics website via the following domain (01/02/2015):

http://www.ons.gov.uk/ons/site-information/using-the-website/time-series/index.html

The Series ID for the production index is L2KQ, and the for the consumer price index,

D7BT.

29

http://www.ons.gov.uk/ons/site-information/using-the-website/time-series/index.html

http://www.bankofengland.co.uk/statistics/Pages/yieldcurve/archive.aspx

APPENDIX 2

TABLE 8

Earnings at time t regressed on instruments for expected earnings

E t

CE-1

= α0 + α1 E-1

CE-1

+ α2 MCVE-1

CE-1

+ α3r1-1 + α4r5-1 + α5r10-1 + α6EA-1 + α7INF-1 + α8 1CE-1

+ ε

Predictors Adj. R2 n

E-1

CE-1

0.152 4.533

E-1

CE-1

, MCVE-1

CE-1

0.155 4,533

E-1

CE-1

, MCVE-1

CE-1

, 1CE-1

0.400 4,533

E-1

CE-1

, MCVE-1

CE-1

, 1CE-1

, r1-1 , r5-1 , r10-1 0.404 4,533

E-1

CE-1

+ α2 MCVE-1

CE-1

, 1CE-1

, r1-1 , r5-1 , r10-1 , EA-1 0.404 4,533

E-1

CE-1

+ α2 MCVE-1

CE-1

, 1CE-1

, r1-1 , r5-1 , r10-1 , EA-1 , INF-1 0.404 4,533

Where R2 is adjusted for degrees of freedom, and n is the number of observations in the time-series

regression.

30

TABLE 9Comparison of the spot and forward rates being added into the regression model

individually

Spot Rates, Δr0 = α0 + α1r1-1 + α2r5-1 + α3r10-1 + α4EA-1 + α5INF-1 + ε


r1-1 0.119 22

r1-1 , r5-1 , r10-1 0.029 22

r1-1 , r5-1 , r10-1 , INF-1 0.175 22

r1-1 , r5-1 , r10-1 , INF-1 , EA 0.134 22

Forward Rates, Δr0 = α0 + α1Fr1-1 + α2Fr5-1 + α3Fr10-1 + α4EA-1 + α5INF-1 + ε


Fr1-1 0.078 22

Fr1-1 , Fr5-1 , Fr10-1 0.015 22

Fr1-1 , Fr5-1 , Fr10-1 , INF-1 0.216 22

Fr1-1 , Fr5-1 , Fr10-1 , INF-1 , EA 0.168 22

Where R2 is adjusted for degrees of freedom, and n is the number of observations in the time-series

regression.

31

TABLE 10

Comparison of the regressions of interest rate change at time t = 0, on spot and forward rate

Spot Rates, Δr0 = α0 + α1r1-1 + α2r5-1 + α3r10-1 + α4EA-1 + α5INF-1 + ε

α0 0.647t(α0) 0.659

α1 -0.220t(α1) -0.198

α2 -1.299t(α2) -0.507

α3 1.237t(α3) 0.718

α4 0.106t(α4) 0.446

α5 -0.457t(α5) -1.690

R2 0.340n 22

Forward Rates: Δr0 = α0 + α1Fr1-1 + α2Fr5-1 + α3Fr10-1 + α4EA-1 + α5INF-1 + εα0 0.491

t(α0) 0.536

α1 -0.056t(α1) -0.081

α2 -1.212t(α2) -0.897

α3 1.192t(α3) 1.287

α4 0.041t(α4) 0.174

α5 -0.532*t(α5) -2.131R2 0.366n 22



32

TABLE 11Unexpected earnings, operating income and interest expense calculated using the market-value

weighted residuals

Unexpected Earnings, UE[Et/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.000 0.000 0.000t(β0) -1.625 1.651 1.079

β1 0.145 0.145 -0.048t(β1) 0.657 0.641 -0.204

R2 0.021 0.021 0.002n 22 21 20

Unexpected Operating Income, UE[OIt/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.000 0.000 0.000t(β0) 0.526 0.267 -1.664

β1 -0.219 0.089 -0.057t(β1) -1.004 0.388 -0.243

R2 0.048 0.008 0.003n 22 21 20

Unexpected Net Interest Expense, UE[NIEt/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.000** 0.000 0.000t(β0) -3.076 -1.304 1.673

β1 -0.351 -0.057 0.155t(β1) -1.674 -0.247 0.664

R2 0.123 0.003 0.024n 22 21 20


33

TABLE 12Unexpected earnings, operating income and interest expense calculated using the book-value

weighted residuals

Unexpected Earnings: UE[Et/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.000** 0.000 0.000t(β0) -2.907 0.837 -1.266

β1 0.272 0.562** -0.042t(β1) 1.265 2.962 -0.176

R2 0.074 0.316 0.002n 22 21 20

Unexpected Operating Income: UE[OIt/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.000* 0.000 0.000t(β0) -2.664 1.018 -0.987

β1 0.237 0.325 0.022t(β1) 1.089 1.497 0.095

R2 0.056 0.106 0.001n 22 21 20

Unexpected Net Interest Expense: UE[NIEt/CE-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.000 0.000 0.000**t(β0) 0.211 -1.406 3.777

β1 -0.168 0.380 0.181t(β1) -0.762 1.788 0.781

R2 0.028 0.144 0.033n 22 21 20


TABLE 13

34

Unexpected operating income and interest expense calculated using the decomposed book value as a deflator for the firm-specific variables

Unexpected Operating Income, UE[OIt/NOA-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 0.017 0.022 -0.042t(β0) 0.079 0.054 -0.082

β1 0.526* 0.391 0.221t(β1) 2.767 1.852 0.962

R2 0.277 0.153 0.049n 22 21 20

Unexpected Net Interest Expense, UE[NIEt/ND-1] = β0 + β1UE[Δr0] + ε

t 0 1 2

β0 -0.001 -0.002 0.001t(β0) -0.147 -0.096 0.026

β1 -0.060 -0.206 -0.229t(β1) -0.269 -0.917 -0.998

R2 0.004 0.042 0.052n 22 21 20


35

Dissertation

Documents

aggregate unexpected

leveraged firms

unexpected changes

aggregate earnings nissim

earnings fieldstein

negative association

rate changes

us listed firms