Exchange Rate Risk and Relative Performance Evaluation

Abstract

The relative performance evaluation (RPE) hypothesis posits that executive compensation should not be influenced by uncontrollable exogenous shocks. However, prior studies often find limited empirical support for this hypothesis, partly because identifying peers exposed to the same exogenous shocks is challenging. We propose a new method for identifying peers and testing the RPE hypothesis within the context of exchange rate risk. Specifically, we select peers based on the sensitivity of their stock returns to exchange rate fluctuations. We find evidence that firms respond to significant exchange rate movements by ex post adjusting their peer selection to include peers with similar exchange rate risk exposure. Furthermore, after accounting for ex post peer group adjustments, we find much stronger support for the RPE hypothesis than prior studies.

1. Introduction

Setting Chief Executive Officer (CEO) compensation is one of the most important issues for firms. Paying for performance is crucial to mitigate agency cost, and this is especially important for CEOs whose unobservable efforts and actions can significantly affect the distribution of firm performance. However, it is difficult to accurately measure the degree of firm performance for which CEOs are responsible. Firm performance is associated with both CEO decisions and exogenous shocks that are outside of the CEO’s control. It is well understood that firms should not reward or punish CEOs for performance reflecting exogenous shocks because it would be wasteful and costly. Greater uncertainty in CEO compensation necessitates a greater risk premium for the additional compensation risk (Holmstrom, 1979).

A large stream of literature examines how exogenous shocks can be filtered out from executive compensation. The relative performance evaluation (RPE) hypothesis implies that this can be achieved by making compensation contingent on peer performance (Holmstrom, 1982; Holmstrom & Milgrom, 1987). Despite the theoretical appeal of this hypothesis, prior studies do not find consistent empirical evidence to support it (Murphy, 1999; Abowd & Kaplan, 1999; Prendergast, 1999).

An important difference among the empirical studies of testing RPE is the selection of peer firms. Some use firms covered by the stock market index (Garvey & Milbourn, 2003), others choose firms in the same industry (Aggarwal & Samwick, 1999b; Antle & Smith, 1986), and still others select firms in the same geographic region (Barro & Barro, 1990). Clearly, the choice of peers determines the extent to which exogenous shocks can be filtered out and critically affects tests of the RPE hypothesis. At the same time, it is practically difficult to consider all of the relevant dimensions, such as industry, size, growth, diversification, and financial constraints, that affect the capacity of a peer group to filter out common shocks. Thus, a possible explanation for the failure to obtain consistent empirical results supporting RPE is that prior studies do not identify the appropriate peer group.

Albuquerque (2009) contributes to the literature by showing that peer selection based on both industry and firm size captures many of the important dimensions of risk exposure. Gong et al. (2011) corroborate this finding using data on compensation benchmarking peers from proxy statements. Nevertheless, two important issues remain unaddressed. First, peers are selected ex ante, which is inconsistent with the theory predicting that firms should use all information available to ex post filter out exogenous shocks. For example, major macroeconomic shocks cannot be predicted, and ex ante selected peers may not be effective in the presence of these shocks. Second, the testing power is low because prior studies do not measure the magnitude of exogenous shocks and identify sub-samples where the effect of RPE is most pronounced.1

In this paper, we test relative performance evaluation (RPE) in the context of a specific macroeconomic shock: exchange rate volatility. As the global economy becomes increasingly interconnected, U.S. firms are more closely tied to international markets. Exchange rate fluctuations can influence firm performance by altering the cost of imports and exports, the value of foreign earnings, and the competitiveness of U.S. goods and services abroad (Itagaki, 1981; Dominguez & Tesar, 2006). Prior research also shows that firms differ in how much exchange rate risk they bear, depending on their international operations and financial structures (Allayannis & Ofek, 2001).

Firms with foreign subsidiaries or substantial international transactions are directly exposed to exchange rate movements, which can have immediate financial implications. Moreover, even firms without direct international operations may be indirectly affected if they compete with foreign companies in the U.S. market. In such cases, a strong dollar may benefit foreign competitors by making their goods cheaper, thereby impacting the performance of domestic firms. This context provides a natural setting to examine whether RPE mechanisms account for the varying degrees of exchange rate exposure across firms.

We predict that exposure to exchange rate risk is a criterion in identifying peers and that this criterion is more important for peer selection when large exchange rate movements occur. Our empirical analyses examine whether firms select peers ex ante, as assumed in the prior literature, or whether they adjust their peer selection ex post, depending on the magnitude of exchange rate movements. Moreover, our research design enhances testing power by excluding firm-year observations that have minimal or no exposure to exchange rate fluctuations.

Specifically, we first regress firm stock returns on dollar index returns to compute the sensitivity (exposure) of each firm to exchange rate risk, and then calculate the stock returns of peers with similar exposure to exchange rate risk.2 To test for RPE, we use three methods to select firm-year observations exposed to exchange rate movements. The first sub-sample includes observations in the time periods within which the fluctuation in the dollar index is large; the second sub-sample consists of firms in industries that are sensitive to fluctuations in the dollar index; the third sub-sample comprises observations in the overlap of the first and second sub-samples.

Using peers with comparable exposure to exchange rate risk, we provide robust evidence supporting the RPE hypothesis through both aggregate and firm-specific regressions. Our findings demonstrate that these peers are particularly effective at filtering out shocks during periods of significant exchange rate fluctuations. This suggests that firms adjust their peer selection ex post following an exchange rate shock. In additional analyses, we find similar results for oil price risk.

This paper contributes to the literature in three ways. First, it provides evidence that exposure to a specific macroeconomic shock is an important criterion in selecting peers. Second, this paper shows that firms adjust peer selection for optimal risk sharing purposes when large macroeconomic shocks occur. This finding casts doubt on the common assumption in the prior literature that peers are selected ex ante and/or that peer selection remains mostly constant over time. Third, this paper introduces a new research design that considerably increases the statistical power when testing the RPE hypothesis.

The rest of this paper is organized as follows. Section 2 reviews the prior literature and states hypotheses; Section 3 discusses the research design; Section 4 presents the empirical results; Section 5 shows additional analysis; and Section 6 concludes this paper.

2. Literature and Hypotheses

2.1. Theoretical Background

There is a moral hazard problem in setting a CEO compensation contract because CEOs’ unobservable efforts and actions can significantly affect the distribution of firm performance. Holmstrom (1979) shows that the CEO compensation contract can be improved by including any ex post available information signal even if it is imperfectly reflective of CEO’s actions. Based on this theory, the RPE hypothesis argues that firms can filter out the effect of exogenous shocks by making compensation contingent on the performance of peer firms (Holmstrom, 1982; Holmstrom & Milgrom, 1987).

Several studies caution that the RPE argument only holds in the absence of strategic interaction among peer firms (Vrettos, 2013; Aggarwal & Samwick, 1999a, 1999b; Fumas, 1992), e.g., in the absence of collusion among peers. Also, RPE may lead to excessive risk-taking if the CEO anticipates that exogenous risks will always be fully filtered out. For example, RPE may reduce incentives to engage in hedging activities, to purchase insurance, or to exercise prudence when entering risky foreign countries.

2.2. Literature Review

Many empirical studies examine whether firms use RPE to filter out the effects of external shocks on firm performance. The results of existing empirical studies are mixed. Some find evidence to support RPE, while others fail to do so. Aggarwal and Samwick (1999a) identify peer firms within the same industry and find evidence supporting RPE in analyses of compensation levels. However, they do not observe the same support when examining changes in compensation levels. Garvey and Milbourn (2003) find evidence to support RPE for firms with younger and less wealthy managers, but the results do not support RPE for average firms. Antle and Smith (1986) identify peer firms as those in the same industry and use stock return to measure firm performance, and they find that only 16 out of 39 firms support RPE. The results of Gibbons and Murphy (1990) support RPE when firm performance is measured by stock return. With the same sample of Gibbons and Murphy (1990), but different measures of compensation and performance, Jensen and Murphy (1990) do not find evidence to support RPE. The results of Janakiraman et al. (1992) support RPE when peer firms are identified as those in the same industry and when firm performance is measured by stock return. Barro and Barro (1990) do not find evidence to support RPE with peer firm identification of the US largest commercial banks within the same geographical region. Bertrand and Mullainathan (2001) find that CEOs are paid for luck when peer firms are identified by industry, and this is more likely in poorly governed firms.

One main difference among the above studies is the criterion to choose peer firms, and it is also a significant challenge to implement (Gibbons & Murphy, 1990; Baker, 2002) or test (Parrino, 1997) RPE. The most popular and easy way is to use stock market index or firms in the same industry as peer firms, assuming that they have similar exposure to exogenous shocks. However, there are many more factors that contribute to similar exposure, such as the cost to respond to shocks (Thomas, 1990), the financial and borrowing credit constraint (Fazzari et al., 1988; Gertler & Gilchrist, 1994), the degree of diversification (Kogut & Kulatilaka, 1994), operating leverage, growth options, firm disclosure (Chen et al., 2025a), and investment decisions (Chen et al., 2025c). Additional factors include institutional investors and their behavior (e.g., Yang & Kazemi, 2020; Yang et al., 2021; Yang & Chen, 2021; Yan & Yang, 2022; Chen et al., 2025b). There are two challenges if we include all these characteristics in selecting peer firms. First, accurately measuring certain characteristics, such as the cost of responding to shocks and growth options, is challenging. Second, considering all these characteristics may result in identifying too few peer firms, leading to noisy results when attempting to filter out external shocks.

Even though these characteristics capture different aspects of firms, they are dependent on each other. For example, they are usually related to firm size (Albuquerque, 2009). Small firms tend to have lower diversification, larger financial and borrowing credit constraints, and smaller operating leverage. Albuquerque (2009) implicitly shows that firm size is monotonically associated with these firm characteristics and is a good indicator to identify peer firms in testing RPE. In addition, Gong et al. (2011) explicitly demonstrate that firms select peers within the same industry and the same firm size quartile.

Albuquerque (2009) contributes to the literature by arguing that peer firms should be identified based on both industry and firm size, suggesting that varying peer selection criteria may explain the inconsistent findings in previous RPE studies. However, the industry-size criterion is not the sole method for selecting peers and does not eliminate the possibility of other relevant criteria. Furthermore, it remains unclear whether firms adjust their peer selection ex post in response to a macroeconomic shock.

Some prior studies test RPE implicitly by determining peers ex ante with a rule, such as being in the same industry or in the same industry and same firm size quartile. Other studies test RPE explicitly by analyzing the actual selected peers released in-firm proxy statements (Gong et al., 2011). Even for these actual selected peers, they are chosen ex ante. Black et al. (2012) argue that firms may use peers which are not disclosed in their proxy statements. It is difficult for firms to predict future macroeconomic shocks before peer selection released in firm proxy statements. However, firms may have the intention to adjust peer selection ex post after a macroeconomic shock. Our paper seeks to find evidence to support this argument.

There is another branch of the literature that explains why RPE does not hold in empirical tests. One possible reason is the peer selection issue (Albuquerque, 2009). The other potential reason is firm’s ability to find peers. Albuquerque (2014) argues that high-growth firms do not use RPE to filter out the effects of exogenous shocks because each of them has some unique characteristics and, thus, it is difficult to find appropriate peers.

2.3. Hypotheses

To solve the moral hazard problem in setting CEO compensation, firms need to filter out the effect of exogenous shocks on firm performance by the performance of peer firms. The desirable peers should have similar exposure to and ability to deal with exogenous shocks, and the peer selection determines the extent to which the effect of exogenous shocks can be filtered out. Ideal peer firms should be similar in several aspects, such as industry, size, diversification, financial constraints, etc. Albuquerque (2009) argues that industry and size can seize most of these aspects. Thus, we propose the following hypothesis:

H1: 

There is a negative relationship between CEO compensation and the performance of industry peers with similar sizes.

However, the industry-size criterion cannot rule out other possible peer selection criteria. Another way to select peer firms is to calculate the effect of a macroeconomic shock on firm performance and then identify peers with similar exposure to that shock. A good candidate of macroeconomic shock is an exchange rate shock. Firms in the US are more likely to operate in international markets either directly or indirectly with the growth of global economy, and exchange rate volatility can affect firm performance (Itagaki, 1981; Dominguez & Tesar, 2006). This argument leads to the next hypothesis:

H2: 

There is a negative relationship between CEO compensation and the performance of peers with similar exposure to exchange rate risk.

Prior studies test RPE in the context that peers are selected ex ante. Even for the selected peers released in proxy statements, they are chosen ex ante. However, the theoretical foundation of RPE (Holmstrom, 1979) argues that firms should choose peers ex post. In practice, firms could adjust peer selection ex post when exchange rate shock occurs, and the newly included peer firms should have similar exposure to the exchange rate shock. Since it is difficult to predict exchange rate shock, firms cannot identify the desirable peers in advance. If they want to use RPE, they must adjust peer selection ex post. In addition, this type of peer adjustment is for effective risk-sharing, while not for self-service to justify high CEO payment. This motivates our final hypothesis:

H3: 

The relationship in H2 will be stronger when the fluctuation in exchange rate is high.

3. Research Design

3.1. Data and Sample Selection

We obtain CEO compensation data from ExecuComp, financial measures from Compustat, monthly stock returns from the Center for Research in Security Price (CRSP), inflation measure from the CRSP-US Treasure and Inflation Indexes, the dollar index (Trade Weighted U.S. Dollar Index: Broad—TWEXB, end of period monthly) from the Federal Reserve Bank of St. Louis, and crude oil monthly price from the website of Index Mundi.

Our sample period spans from January 1995, when dollar index data first became available, to December 2015.3 We limit our sample to observations available in both CRSP and ExecuComp, ensuring all variables required for this study have valid values. Firms with total assets below USD 10 million and those with fewer than 10 years of data are excluded.

Table 1. Sample selection.

	Number of Observations
Observations from Compustat	233,868
Less observations not covered by CRSP or observations without valid stock returns	77,302
Less observations with less than $10M total asset	33,709
Less observations not covered by ExecuComp	85,082
Less observations with negative CEO compensation, sale, market value, or equity	6040
Less observations with missing variables	998
Less firms with less than 10 years of observations	9907
Final sample	20,830

Table 1 outlines the sample selection procedure. The sample period is from 1995 to 2015.

outlines the sample selection procedure. The final sample comprises 20,830 firm-year observations spanning 1334 firms.

3.2. Variables

The dependent variable ${(CEOPay}_{it})$ is the natural log of inflation-adjusted total CEO annual compensation in January 1992 dollars. Stock return is used to measure firm and peer performance. Following the prior literature, the real, inflation-adjusted, firm stock return is calculated as $log\left({\displaystyle \frac{1+annual stock return/100}{1+annual inflation rate calculated by CPI}}\right)$. We follow Albuquerque (2009) to calculate industry-size peer return $\left({PeerRetIS}_{it}\right)$. Specifically, we first merge CRSP and Compustat and exclude small firms whose total assets are less than USD 10M. Then, we calculate the quartile of firm market value at the beginning of the year based on all firms in the merged dataset for each year. This approach ensures that relevant peer firms are included, even if they are not covered by ExecuComp. For each firm, the industry-size peer stock return is calculated as the equal-weight average of stock returns of the peer firms that are in the same industry (two-digits SIC) and same firm size quartile in that year, excluding the firm itself. If the number of peer firms is less than two, the industry-size peer stock return is calculated as the industry average.

To calculate the stock return of peers with similar exposure to exchange rate risk $\left({PeerRetEX}_{it}\right)$, we first regress real firm stock return on real dollar index return for each firm. The estimated coefficient is a measure of the firm’s sensitivity to exchange rate risk. We then rank these coefficients, categorizing them into seven groups.4 Firms in the same group are considered to have similar exposure to exchange rate risk. The stock return of peers with similar exposure to exchange rate risk is calculated as the average annual stock returns of observations in the same group, excluding the firm itself. These returns are computed at the end of each peer’s fiscal year.

According to the prior literature, the following control variables are included in the regressions: firm size is measured as the natural log of sales, growth options is measured as the ratio of the firm market value to the book value of assets at the beginning of a year, CEO tenure is measured as the natural log of the length of years of serving as CEO,5 idiosyncratic variance is measured as the difference between the variance in firm stock return and the variance in industry stock return over the past 35 months, CEO chair dummy (whether the CEO also serves as the board chair), CEO ownership dummy (whether the CEO ownership share is smaller than the sample median in the year), and interlock dummy (whether the CEO is involved in a interlock relationship). Variables are winsorized at the top and bottom 1 percent.

Table 2. Description statistics.

	Num of Obs	Mean	Std. Dev.	Min	Max
Ln (CEO Compensation)	20,830	7.684	1.010	5.361	10.021
FirmRet	20,830	0.061	0.420	−3.219	3.349
PeerRetIS	20,825	0.080	0.285	−1.840	2.098
PeerRetEX	20,830	0.133	0.181	−0.569	0.613
Ln (Sale)	20,830	7.082	1.601	−2.765	12.543
GrowOption	20,830	1.946	1.811	0.401	105.090
CeoTenure	20,830	8.864	7.717	1.000	61.789
IndVar	20,830	0.012	0.083	−0.022	6.289
ChairD	20,830	0.628	0.483	0.000	1.000
CeoEquityOwnD	20,830	0.526	0.499	0.000	1.000
InterlockD	20,830	0.042	0.201	0.000	1.000

Table 2 presents the summary statistics of the variables used in the analysis. See Table 1 for sample selection procedure and Appendix A for variable definitions.

shows the descriptive statistics. The mean values of the variables align closely with those reported in Albuquerque (2009).

3.3. Selection of Specific Shocks

The purpose of this paper is not to find a universal method to select peers that can filter out exogenous shocks. We aim to find an easy way to select peers under a specific macroeconomic shock. The selection of the shock is a crucial part of the research design. An ideal shock for RPE testing should satisfy three key criteria. First, it must be measurable in terms of its impact on firm performance, with a clear identification of when and which firms are affected. Second, the shock should significantly impact firm performance to motivate firms to use RPE to filter out its effects. Third, it should impact firms differently, making peer selection a meaningful and non-trivial task.

For RPE testing in this paper, we choose exchange rate risk (the primary test) and oil price fluctuations, which are intuitively significant and common shocks that firms typically encounter. Given that observable measures exist for exchange rates and oil prices, and their effects on firm performance can be calculated, the first criterion is fulfilled. While these shocks intuitively satisfy the second criterion, we quantitatively demonstrated their impact on firm performance in

Table 3. Sensitivity measurement.

Panel A: Macro Shocks
	Dollar Return		Oil Price Return			S&P 500 Return
Mean of monthly return	−0.0007		0.0007			0.0036
Stdev of monthly return	0.0154		0.0785			0.0419
Number of observations	252		288			288
Aggregate Level
Elasticity	−0.2375		0.0904			1.0161
Abs (Elasticity * Stdev)	0.0037		0.0071			0.0426
Number of Observations	1,551,942		1,799,101			1,799,101
Firm Level
Elasticity (absolute value)	1.4159		0.3141			1.1496
Abs (Elasticity * Stdev)	0.0218		0.0247			0.0482
Number of Observations	15,757		17,115			17,115
Panel B: Specific Currencies
	Euro Return	CNY Return		GBP Return	JPY Return		CHF Return
Mean of monthly return	−0.0015	−0.0013		−0.0012	−0.0021		−0.003
Stdev of monthly return	0.0257	0.0246		0.0229	0.0261		0.0269
Number of observations	203	288		288	288		288
Aggregate Level
Elasticity	−0.5446	0.1009		−0.2671	0.1031		−0.0605
Abs (Elasticity * Stdev)	0.0140	0.0025		0.0061	0.0027		0.0016
Number of Observations	1,160,781	1,799,101		1,799,101	1,799,101		1,799,101
Firm Level
Elasticity (absolute value)	1.0278	4.1935		0.9669	0.7347		0.7257
Abs (Elasticity * Stdev)	0.0264	0.1032		0.0221	0.0192		0.0195
Number of Observations	12,559	17,115		17,115	17,115		17,115

Table 3 presents the sensitivity of each macro index (panel A) and currency (panel B). The mean of monthly return is calculated as the average monthly return of each macro index or currency. The stdev of monthly return is calculated as the standard deviation of monthly return of each macro index or currency in the sample. Elasticity is the estimated coefficient (${\widehat{\alpha }}_1$) of the regression, ${FrimRet}_{it}={\alpha }_0+{\alpha }_1{IndexRet}_{it}+{ϵ}_{it}$. In panel B, CNY indicates Chinese Yuan, GBP denotes British Pound, JPY represents Japanese Yen, and CHF refers to Swiss Franc.

. The top section of panel A in Table 3 shows the mean real monthly returns of dollar index, oil price index, and S&P500 index, as well as their standard deviations in our sample period. In the aggregate-level analysis, we regress real monthly firm return on real monthly return of each index:

$${FirmRet}_{it}={\alpha }_0+{\alpha }_1{IndexRet}_{it}+{ϵ}_{it}$$

(1)

where ${\widehat{\alpha }}_1$ is the index elasticity of stock price. It measures the percentage change in stock price for 1% change in the index. The results are shown in the middle section of panel A in Table 3. The minimum absolute value of elasticity is 0.09 for oil price index, which is roughly 10% of the S&P 500 index elasticity (1.02). Since the volatility of each index may be quite different, we also calculate the absolute value of the product of each elasticity and the standard deviation of monthly return for each index, which measures the effect on firm return for the change of one standard deviation. The minimum value (0.0037 for dollar index) is roughly 10% of the value for S&P 500 index (0.0426).

Since some firms respond positively, while other firms respond negatively, to the change in the index, certain effects are canceled out in the aggregate level analysis. To solve this issue, we estimate regression (1) for each firm, and then calculate the mean absolute value of elasticity across firms. The results are reported in the bottom section of panel A in Table 3. The minimum value of the product of the elasticity and standard deviation (0.0218 for dollar index) is roughly 40% of the value for S&P 500 index. These results show that the selected shocks have significant effects on firm performance. In addition, the large difference between the aggregate level and firm level analysis indicates that these shocks affect some firms positively and others negatively. This provides support for the third criterion of an appropriate shock in RPE testing. Panel B of Table 3 shows the result of sensitivity analysis for certain major world currencies. Some sensitivities are greater than that of the dollar index, while others are smaller. To capture the overall effect, we use the dollar index in this paper.

3.4. Models

Following Albuquerque (2009), we use the following model to test H1:

$${CEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{ControlVariables}_{it}+{ϵ}_{it}$$

(2)

where CEOPay is the natural log of inflation-adjusted total CEO annual compensation in January 1992 dollars, FirmRet is the real firm stock return, and PeerRetIS is the real stock return of peers in the same industry and size quartile, excluding the firm itself. If H1 is true, we expect ${\alpha }_2<0$, which suggests that firms use industry-size peer performance to filter out external shocks.

We test H2 with the following model:

$$\begin{gathered} {CEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{PeerRetEX}_{it} \\ +{\alpha }_4{ControlVariables}_{it}+{ϵ}_{it} \end{gathered}$$

(3)

where PeerRetEX is real stock return of peers in the same exchange rate risk exposure group, excluding the firm itself. H2 predicts that ${\alpha }_3<0$, which indicates that the performance of peers with similar exposure to exchange rate risk can filter out the effect of external shocks. This test is conservative because some peers with similar exposure to exchange rate risk are already included in the industry-size peer group. To mitigate this effect, we also estimate model (3) without industry-size peer performance.

To test H3, we estimate model (3) using three sub-samples where the impact of exchange rate risk is more pronounced. The first sub-sample includes observations from periods of significant dollar index fluctuations. The second sub-sample consists of firms operating in industries sensitive to dollar index changes. The third sub-sample comprises observations that fall within both prior groups. Additionally, we conduct a full-sample regression, incorporating sub-sample indicators.

4. Empirical Results

4.1. Full Sample Analysis

Table 4. Full sample analyses of CEO total compensation.

	CEO Total Compensation
	(1)	(2)	(3)
Intercept	4.860 ***	4.856 ***	4.865 ***
	(1.26)	(1.26)	(1.26)
FirmRet	0.221 ***	0.206 ***	0.224 ***
	(0.02)	(0.02)	(0.02)
PeerRetIS	−0.084 ***		−0.082 ***
	(0.02)		(0.02)
PeerRetEX		−0.063 *	−0.055 *
		(0.03)	(0.03)
Ln (Sale)	0.278 ***	0.277 ***	0.278 ***
	(0.03)	(0.03)	(0.03)
GrowOption	0.048 *	0.048 *	0.048 *
	(0.02)	(0.02)	(0.02)
CeoTenure	0.124	0.127	0.123
	(0.39)	(0.39)	(0.39)
IndVar	−0.037	−0.038	−0.035
	(0.06)	(0.05)	(0.06)
ChairD	0.034	0.033	0.034
	(0.02)	(0.02)	(0.02)
CeoEquityOwnD	−0.034 *	−0.034 *	−0.034 *
	(0.02)	(0.02)	(0.02)
InterlockD	0.025	0.024	0.025
	(0.04)	(0.04)	(0.04)
Year dummies	Yes	Yes	Yes
Industry dummies	Yes	Yes	Yes
CEO-fixed effects	Yes	Yes	Yes
Adjusted  $R^2$	0.753	0.752	0.753
Number of observations	20,825	20,830	20,825

Table 4 reports the full sample results of the following regression. ${CEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{PeerRetEx}_{it}+{\alpha }_4{ControlVariables}_{it}+{ϵ}_{it}$. Standard errors are reported in parentheses below coefficient estimates. *, and *** denote statistical significance at 10%, and 1%, respectively. See Appendix A for variable definitions.

shows the regression results for the full sample. The dependent variable is the CEO total compensation. Consistent with Albuquerque (2009), the estimated coefficient on industry-size peer return is significantly negative at 1% level in column (1). This provides support for H1. The estimated coefficient on stock return of peers with similar exposure to exchange rate risk is also significantly negative at 10% level in columns (2) and (3). Thus, the performance of peers with similar exposure to exchange rate risk has additional power to filter out the effect of external shocks in RPE testing, which is consistent with H2. In this sense, we document another important dimension in identifying peers in RPE testing.6

4.2. Sub-Sample Analysis

In this section, we test H3 using sub-samples with which the effect of exchange rate risk is more pronounced. We create three sub-samples for analysis. The Variance sub-sample consists of observations from periods with high dollar index volatility, defined as a 12-month variance exceeding 5. The Industry sub-sample includes observations from the 36 industries most sensitive to dollar index changes. The Variance–Industry sub-sample comprises observations that appear in both the Variance and Industry sub-samples.

The results are shown in

Table 5. Sub-sample analyses of CEO total compensation.

	CEO Total Compensation
	Variance	Industry	Var–Industry	Full Sample
Intercept	4.964 ***	3.358 **	2.878 ***	4.842 ***
	(0.91)	(1.70)	(0.94)	(1.27)
FirmRet	0.216 ***	0.208 ***	0.197 ***	0.225 ***
	(0.03)	(0.03)	(0.04)	(0.02)
PeerRetIS	−0.088 **	−0.039	−0.053	−0.077 ***
	(0.04)	(0.03)	(0.05)	(0.02)
PeerRetEX	−0.114 **	−0.085 *	−0.162 **	0.005
	(0.05)	(0.05)	(0.06)	(0.04)
Interaction				−0.140 ***
				(0.05)
Indicator				0.034 *
				(0.02)
Ln (Sale)	0.245 ***	0.347 ***	0.309 ***	0.277 ***
	(0.03)	(0.04)	(0.05)	(0.03)
GrowOption	0.070 ***	0.034	0.059 ***	0.047 *
	(0.02)	(0.02)	(0.02)	(0.02)
CeoTenure	−0.020	−0.305	−1.680 ***	0.121
	(0.50)	(0.53)	(0.44)	(0.39)
IndVar	0.059	−0.006	0.123 ***	−0.032
	(0.06)	(0.05)	(0.04)	(0.05)
ChairD	0.037	0.025	−0.003	0.034
	(0.03)	(0.03)	(0.06)	(0.02)
CeoEquityOwnD	−0.041	−0.031	−0.073 **	−0.034 *
	(0.03)	(0.03)	(0.04)	(0.02)
InterlockD	0.118	0.083	0.224 *	0.025
	(0.08)	(0.06)	(0.12)	(0.04)
Year dummies	Yes	Yes	Yes	Yes
Industry dummies	Yes	Yes	Yes	Yes
CEO-fixed effects	Yes	Yes	Yes	Yes
Adjusted  $R^2$	0.758	0.721	0.733	0.753
Number of observations	10,011	10,265	4884	20,825

Table 5 presents the sub-sample results of the following regression. ${CEOPay}_{it}={\alpha }_0+{\alpha }_1{FrimRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{PeerRetEX}_{it}+{\alpha }_4{ControlVariables}_{it}+{ϵ}_{it}$. The Variance sub-sample includes observations in the time periods within which the fluctuation in the dollar index is large; the Industry sub-sample consists of firms in industries that are sensitive to the fluctuation in the dollar index; the Var–Industry sub-sample comprises observations in the overlap of the Variance and Industry sub-samples. Standard errors are reported in parentheses below coefficient estimates. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively. See Appendix A for variable definitions.

. There are three interesting findings in this table. First, for the Variance and Variance–Industry sub-samples, both the magnitude and significance level of the estimated coefficient for the exchange rate peers are larger compared to the result in the full sample. Additionally, the magnitude is larger in the Industry sub-samples. These results suggest that the effect is more pronounced in the sub-samples and that firms adjust CEO compensation ex post when the exchange rate risk is high.

Second, the estimated coefficients for industry-size peers are smaller and insignificant in the Industry and Variance–Industry sub-samples compared to the result in the full sample. The significance level in the Variance sub-sample is also lower. Third, the estimated coefficient for exchange rate peers is larger than that for industry-size peers in all three sub-samples. These results indicate that firms use the performance of peers with similar exposure to exchange rate risk, not industry-size peers, to filter out the effect of exchange rate fluctuations when such shocks occur.7 More generally, we argue that firms may use different criteria to identify peers to filter out the effect of different shocks. The results for oil price shock discussed in Section 5 provide support to this argument.

The last column in Table 5 shows the regression results for the full sample with an indicator variable for the Variance–Industry sub-sample and an interaction variable that is the product of the indicator variable and the stock return of peers with similar exposure to exchange rate risk. Consistent with the above results, the estimated coefficient of the interaction is significantly negative. As a robustness check, we perform a similar analysis using the change in CEO total compensation as the dependent variable, representing the variable component of CEO pay. The results, shown in

Table 6. Sub-sample analyses of the change in CEO total compensation.

	The Change in CEO Total Compensation
	Variance	Industry	Var–Industry	Full Sample
Intercept	0.590	0.065	−0.526	7.670 *
	(0.64)	(0.84)	(1.49)	(4.29)
FirmRet	0.311 ***	0.332 ***	0.295 ***	0.343 ***
	(0.03)	(0.04)	(0.05)	(0.03)
PeerRetIS	−0.080	−0.025	−0.032	−0.068 *
	(0.06)	(0.05)	(0.08)	(0.03)
PeerRetEX	−0.179 **	−0.087	−0.217 *	−0.015
	(0.07)	(0.08)	(0.11)	(0.06)
Interaction				−0.167 **
				(0.07)
Indicator				0.042
				(0.03)
Ln (Sale)	−0.072 **	−0.128 ***	−0.133 **	−0.101 ***
	(0.04)	(0.03)	(0.06)	(0.02)
GrowOption	−0.005	0.000	−0.013	0.005
	(0.03)	(0.02)	(0.03)	(0.02)
CeoTenure	−0.679	−0.324	−1.175	−0.325
	(0.42)	(0.39)	(1.18)	(0.21)
IndVar	0.508	−0.057	0.387	−0.042
	(0.34)	(0.04)	(0.34)	(0.05)
ChairD	−0.008	−0.064	−0.073	−0.038
	(0.05)	(0.04)	(0.08)	(0.02)
CeoEquityOwnD	0.026	0.012	−0.003	0.017
	(0.04)	(0.03)	(0.05)	(0.02)
InterlockD	0.082	0.042	0.172	0.036
	(0.10)	(0.07)	(0.18)	(0.04)
Year dummies	Yes	Yes	Yes	Yes
Industry dummies	Yes	Yes	Yes	Yes
CEO-fixed effects	Yes	Yes	Yes	Yes
Adjusted  $R^2$	0.254	0.122	0.252	0.118
Number of observations	8789	8693	4284	17,655

Table 6 presents the sub-sample results of the following regression. ${ChgCEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{PeerRetEX}_{it}+{\alpha }_4{ControlVariables}_{it}+{ϵ}_{it}$. The Variance sub-sample includes observations in the time periods within which the fluctuation in the dollar index is large; the Industry sub-sample consists of firms in industries that are sensitive to the fluctuation in the dollar index; the Var–Industry sub-sample comprises observations in the overlap of the Variance and Industry sub-samples. Standard errors are reported in parentheses below coefficient estimates. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively. See Appendix A for variable definitions.

, align with those reported in Table 5.

4.3. Firm-Specific Analyses

We next conduct firm-specific analyses, recognizing that RPE coefficients may vary across firms. We estimate regressions individually for each firm, including only the constant, firm performance, and peer performance as independent variables.

Table 7. Firm-specific regressions.

Estimated Coefficients	Median	Mean	Std. Dev.	N	t-Stat.
Panel A: with single peer return
FirmRet	0.114	0.146	0.759	1334	7.015
PeerRetIS	−0.062	−0.103	0.943	1334	−3.993
Adjusted  $R^2$	0.102	0.150
FirmRet	0.149	0.190	0.700	1334	9.904
PeerRetEX	−0.266	−0.290	1.325	1334	−7.999
Adjusted  $R^2$	0.116	0.163
Panel B: with both peer returns
FirmRet	0.160	0.199	0.822	1334	8.845
PeerRetIS	0.017	0.011	1.218	1334	0.336
PeerRetEX	−0.245	−0.312	1.671	1334	−6.816
Adjusted  $R^2$	0.193	0.237

Table 7 summarizes the statistics for the coefficients of the following regressions, estimated for each firm. Panel A: ${CEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{ϵ}_{it}$. ${CEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetEX}_{it}+{ϵ}_{it}$. Panel B: ${CEOPay}_{it}={\alpha }_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{PeerRetEX}_{it}+{ϵ}_{it}$. See Appendix A for variable definitions.

reports the mean and median of the estimated coefficients, along with the t-statistics for testing whether the mean of the estimated coefficients differs significantly from zero.

Panel A shows the results when only a single peer return (i.e., either PeerRetIS or PeerRetEX) is included in the regression. Consistent with the results in Table 4, the mean estimated RPE coefficient is significantly negative when peer performance is measured by the industry-size peer stock return or exchange rate peer stock return. This indicates that the exchange rate peer stock return is effective in filtering out external shocks. Panel B exhibits the results when both peer returns are included in the regression. The mean estimated RPE coefficient is significantly negative when peer performance is measured as the exchange rate peer stock return, but is insignificant when peer performance is measured as the industry-size peer stock return. This shows that the effect of shocks is more likely to be filtered out by the performance of exchange rate peer firms than by the performance of industry-size peer firms.

5. Additional Analysis: Oil Price Shock

Another common macroeconomic shock is oil price fluctuations. We investigate whether firms leverage the performance of peers with similar exposure to oil price risk to filter out the effects of these shocks ex post. We adopt a research design similar to our exchange rate risk analysis in Section 4. In this context, we calculate the stock returns of peers with similar exposure to oil price risk. The Variance sub-sample comprises observations from periods of high oil price volatility, defined as a 12-month variance exceeding 20. The Industry sub-sample includes observations in the 36 industries most sensitive to oil price changes. We predict that firms use peer performance to mitigate the impact of oil price shocks, and the findings reported in

Table 8. Oil price risk analyses.

	CEO Total Compensation
	Full Sample	Variance	Industry	Var–Industry	Full Sample
Intercept	4.863 ***	6.411 ***	3.730 ***	5.561 ***	4.860 ***
	(1.26)	(0.30)	(1.30)	(0.43)	(1.27)
FirmRet	0.224 ***	0.194 ***	0.211 ***	0.180 ***	0.224 ***
	(0.02)	(0.03)	(0.02)	(0.04)	(0.02)
PeerRetIS	−0.083 ***	0.010	−0.077 **	0.013	−0.079 ***
	(0.02)	(0.04)	(0.03)	(0.05)	(0.02)
PeerRetOP	−0.035	−0.130 ***	−0.034	−0.110 **	0.016
	(0.03)	(0.04)	(0.04)	(0.05)	(0.04)
Interaction					−0.118 **
					(0.05)
Indicator					0.014
					(0.02)
Ln (Sale)	0.278 ***	0.237 ***	0.303 ***	0.241 ***	0.278 ***
	(0.03)	(0.04)	(0.04)	(0.05)	(0.03)
GrowOption	0.048 *	0.015	0.039 *	0.008	0.048 *
	(0.02)	(0.04)	(0.02)	(0.03)	(0.02)
CeoTenure	0.123	−0.378	−0.308	−1.166 **	0.126
	(0.39)	(0.51)	(0.39)	(0.52)	(0.40)
IndVar	−0.035	−0.076 *	0.011	−0.043	−0.033
	(0.06)	(0.04)	(0.06)	(0.04)	(0.05)
ChairD	0.034	0.047 *	0.035	0.067 *	0.034
	(0.02)	(0.03)	(0.03)	(0.04)	(0.02)
CeoEquityOwnD	−0.034 *	−0.049 **	−0.033	−0.059 *	−0.035 *
	(0.02)	(0.02)	(0.03)	(0.03)	(0.02)
InterlockD	0.024	0.010	0.096	0.015	0.024
	(0.04)	(0.10)	(0.06)	(0.13)	(0.04)
Year dummies	Yes	Yes	Yes	Yes	Yes
Industry dummies	Yes	Yes	Yes	Yes	Yes
CEO-fixed effects	Yes	Yes	Yes	Yes	Yes
Adjusted  $R^2$	0.753	0.780	0.741	0.782	0.753
Number of Obs	20,825	10,625	12,407	6361	20,825

Table 8 reports the results of the following regression, ${CEOPay}_{it}=C_0+{\alpha }_1{FirmRet}_{it}+{\alpha }_2{PeerRetIS}_{it}+{\alpha }_3{PeerRetOP}_{it}+{\alpha }_4{ControlVariables}_{it}+{ϵ}_{it}$, where PeerRetOP indicates the real stock return of peers in the same oil price risk exposure group, excluding the firm itself. The Variance sub-sample includes observations in the time periods within which the fluctuation of oil price is large; the Industry sub-sample consists of firms in industries that are sensitive to the fluctuation of oil price; the Var–Industry sub-sample comprises observations in the overlap of the Variance and Industry sub-samples. Standard errors are reported in parentheses below coefficient estimates. *, **, and *** denote statistical significance at 10%, 5%, and 1%, respectively. See Appendix A for variable definitions.

are consistent with this prediction.

For the full sample analysis, the estimated coefficient for oil price peers is not significant, even though it is negative. But it is significantly negative, and the magnitude is much larger, in the Variance and Variance–Industry sub-samples. Interestingly, the estimated coefficient for industry-size peers is insignificant in the Variance and Variance–Industry sub-samples. These findings suggest that firms are more likely to rely on the performance of peers with similar exposure to oil price risk to mitigate the impact of oil price shocks.

6. Conclusions

This paper tests RPE in the context of macroeconomic shocks, where peers with similar exposure to such shocks can be readily identified. We then investigate whether firms adjust their peer selection ex post, following the occurrence of macroeconomic shocks. Furthermore, our research design enables us to focus on observations directly impacted by these shocks.

This paper presents three main findings. First, we highlight an important dimension in identifying appropriate peers—those with similar exposure to macroeconomic shocks. This approach enhances the ability to filter out the effects of external shocks in general RPE testing, as outlined in Albuquerque (2009). Second, our results indicate that firms adjust their peer selection ex post following macroeconomic shocks. Unlike prior studies, which typically select peers ex ante and in an arbitrary manner (including those peers disclosed in proxy statements), our findings suggest that firms actively modify their peer selection after macroeconomic shocks occur. Third, we show that firms use different criteria to identify peers for filtering out the effects of various shocks. This study focuses solely on exchange rate risk and oil price risk. Future research could expand on this by investigating other macroeconomic shocks, such as those related to employment and consumer confidence.