Corporate hedging and firm value. Can corporate hedging increase firm value?

Corporate hedging and firm value

Can corporate hedging increase firm value?

Muller, K.L.J.

08-30-2016

Corporate hedging and firm value

Can corporate hedging increase firm value?

Masterthesis 2016

Supervisor: Dr. Qiu

Date:

08-30-2016

By:

Keaven Muller, S4140540

Table of contents

1. Introduction...4 2. Literature...5 3. Methodology...8 Data...8 Variable definitions...9 Method...12 4. Results...16

5. Summary and conclusion...24

References...26 Appendices...28 Appendix 1...28 Appendix 2...29 Appendix 3...30 Appendix 4...30 Appendix 5...31

1. Introduction

Hedging is a form of risk management which has become increasingly popular among large corporations. It is supposed to reduce the possibility of negative outcomes and to make the cash flows to and from the company more stable. The central idea behind this form of risk management is that in the end it reduces risks and increases the stock value of a company. The question is: Does it?

Miller and Modigliani(1958) present their view of the classic stock market as a perfect market with unlimited access to capital and information. In this perfect world without transaction costs and information asymmetries hedging, and risk management in general, is irrelevant as investors can choose individually how many risk they want to take at the same cost. This makes the investor indifferent between companies that engage in hedging and those who do not.

However, the perfect world on which the theory of Miller and Modigliani is based seems to be very different to the financial markets we see in practice. The basics of the Miller and Modigliani-world, like the lack of transaction costs and information asymmetry, do exist in the real world. With that in mind risk management suddenly becomes of great potential value. Companies might have cost and informational advantages of private investors which makes the more efficient in managing risk. Hedging is an important way to do so.

Corporate hedging policies can reduce corporate risk in different ways. Mayers and Smith(1982) and Smith and Stulz(1985) advocate that hedging can reduce the probability of financial distress and therefore can greatly reduce the associated expected costs. Smith and Stulz also point out a tax benefit for corporate hedging in case of convex corporate tax structures, due to less volatile results over time. Furthermore, hedging might be able to solve the problem of underinvestment as

companies might be willing to take more risk because of the risk reducing function of hedging. These benefits can increase firm value and reduce stock price return volatility.

The way hedging reduces risk is by reducing the volatility of potential outcomes. It reduces upside potential in favor of reducing downside risk. This makes cash flows to and from the company more stable than in a situation without hedging. This research focusses of the effect of this reduction in volatility of cash flows. As hedging reduces this volatility of cash flows it can reduce the volatility of the overall result of the company. In today’s stock market volatile results will immediately translate to volatility on the stock market as investors have more than ever excess to this information and are

able to trade quickly. As sharpe(1964) explains in the CAPM-model a major determinant of desired return on investment is the risk of the individual stock relative to the risk of the market. A higher relative risk means more required return and therefore lower stock prices. This is where hedging can be of great potential value. Risk in the CAPM-model is determent by the Beta coefficient. This Beta coefficient represents the historic volatility of the stock. Higher volatility means a higher Beta and a higher desired return. The basics of this model show us that company can increase their stock value by reducing volatility of its stocks on the market. Hedging might be able to do so.

This research uses a set of quarterly data for 53 companies over a period of 5 year(2011 to 2015) to investigate the effect of corporate hedging policies on stock return volatility and firm value. Using a set of multiple OLS regressions I investigate the effect of different types of hedging on the stock return volatility, to see whether corporate hedging can reduce stock return volatility, and if so, whether it leads to a higher stock price according to CAPM. The same dataset is used to see whether corporate hedging can increase firm value. The main questions of the thesis are therefore: “Can corporate hedging reduces stock return volatility?” and “Can corporate hedging increase firm value?”

The rest of the thesis structured as follows. Chapter 2 presents an overview of existing literature related to hedging, firm value and stock price return volatility. It provides a theoretical framework in which this thesis should be placed and provides useful insight on the subject. In chapter 3 the methodology is presented. It provides information on the dataset and the variables that are used, combined with a detailed description of the statistical method that is used. Chapter 4 provides the results of the analysis and discusses them in light of literature. Chapter 5 concludes on the findings of chapter 4 and answers the main questions of the thesis. Furthermore, weaknesses and potential improvements of the thesis are discussed in order to improve future research.

2. Literature

Early work in the field of Hedging by Modigliani and Miller(1958, 1961) suggest that hedging does not add to firm value and corporate hedging should therefore be avoided. Their work on capital structure and dividend policy states that without market imperfection hedging does not create additional value for the company. In this scenario of a perfect market investors have perfect insight in the risks associated with the investment. By diversification investors can create their own

activities. Companies should therefore be reluctant to hedge their positions as it would decrease overall efficiency.

For hedging to be beneficial to companies the market should be imperfect. In an imperfect market costs could arise from unhedged risk exposures as it could increase the volatility of earnings. In this case hedging can reduce the costs for companies(Jin and Jorion,2006). These costs elaborated on in the next paragraphs.

Hedging and financial distress

An important reason for companies to hedge their risky position are the costs related to financial distress. Due to risky business transactions companies could be faced with big losses, leading to cash flow or even solvency problems. These problems induce costs like re-financing costs or even

bankruptcy. The expected costs of financial distress is equal to the probability of financial distress multiplied by the costs in case of financial distress(Mayers and Smith, 1982). Smith and Stulz (1985) advocate companies can greatly reduce the probability of encountering financial distress by using hedging strategies. Hedging can reduce the cash flow volatility leading to a more stable company and less risk of encountering financial distress. They also argue that the probability of encountering financial distress becomes greater if the ratio between fixed claims and assets rises. Companies should therefore be more willing to hedge if they face (relatively) larger fixed claims. Warner(1977) also has found that the costs related to financial distress are not proportional to the size of the company, suggesting that small firms are even more likely to hedge. Furthermore, Robicheck and Myers (1966) argue that these costs can increase dramatically if there is more financial distress, even though the company might be able to avoid bankruptcy.

Close to related to the previous point is the notion that companies can increase their debt capacity by hedging. Both Ross(1997) and Leland(1998) argue that if the probability of encountering financial distress is significantly reduced due to hedging the company can increase its debt capacity. Tax benefits of hedging

Another reason for companies to hedge their positions is a possible reduction in the costs of taxes. Smith and Stulz (1985) have argued that for companies in countries with a convex tax structure volatility of taxable income can be costly. Reducing volatility for the taxable income can reduce the expected amount of tax the company has to pay. Their point can best be explained by an example:

In Country One the corporate tax rate is 10% for an income up to €100.000 and 20% for everything above €100.000. A certain company will either have a taxable income of

€50.000(state A) or €150.000(state B), with a 50% probability, depending on the outcome of a transaction. In state A the company has a tax liability of €5.000 and in state B the company has a tax liability of €20.000. The expected tax liability is therefore

€12.500(=0,5*5000+0,5*20000). The company could also use a hedge to transfer the risk and to receive a certain income equal to the expected income of state A and B combined. This income would be €100.000. The tax liability for this income would be €10.000. The expected tax liability is therefore higher if the company decides not to hedge.

As can be seen in the example hedging can be beneficial for companies that face a convex tax structure. However, in case of a linear or concave tax structure hedging is not beneficial or can even be costly. Only a convex tax structure is therefore an incentive to hedge.

Underinvestment

Although standard theory suggests that companies would start projects with a positive Net Present Value(NPV) Meyers(1977) describes a situation in which companies would be reluctant to engage in these projects. This is called underinvestment. According to Meyers(1977) corporate debt is the main reason behind underinvestment. Due to restrains in debt issuance or financial risks related to debt companies might be underinvesting. Bessembinder(1991) argues that hedging might be able to solve these debt related problems and solve the problem of underinvestment. He argues that

companies are reluctant to take investment risks because of the potential downside risk for shareholders. In case of a bankruptcy shareholders are the last in line to claim anything. Debt holders will be compensated first and take therefore less risk. Companies might therefore be reluctant to take on any project with borrowed money because of the large downside potential for shareholders. Hedging can largely eliminate this downside potential making it less risky for the shareholders. The company might invest more in that case using borrowed money because it is now more beneficial for its shareholders.

Stock price volatility and the effect of hedging

The relation between hedging and stock price volatility has yet to be determined in today’s financial literature. In their study, Allen and Rachim(1996) investigate the determinants of stock price volatility and find that size, the payout ratio, the level of debt and the earnings volatility are important influencers of stock price volatility. Especially earnings volatility, size and leverage are important factors that drive stock price volatility. They find that these factors are strongly related to stock price volatility. In the light of this study the relationship between earnings volatility( and the lack thereof) and stock price volatility should especially be interesting. Baskin(1989) elaborates on

the argument of small firms by discussing the effect of size on stock price volatility. According to Baskin relatively small companies are usually less diversified, there are less informed market participants and these companies have usually limited information exposure to the public, all of which can increase volatility of stock prices.

Management incentive to hedging

Corporate management has, obviously, also a large say in the hedging decision of a company. The managerial attitude towards hedging is therefore of great importance for the hedging strategy of a company, regardless of the company’s fundamentals. Stulz(1984) argues that it might be beneficial for the managers personal wealth to change the hedging strategy of the company. If managers have a concave utility function, and therefore declining marginal utility, and receive variable compensation depending on the company’s performance they are better off with less volatile profits, and therefore less volatile compensation. In case of declining marginal utility the managers are in total better off over multiple periods if the results of a company are less volatile. The reasoning behind this is similar to the reasoning behind tax savings for less volatile companies. To create a more stable income managers could also hedge the volatile results of the company personally. It might however be that the managers are unable to effectively hedge or that the company is able to hedge much cheaper(Nance, Smith and Smithson, 1993)

3. Methodology

Data

The dataset used in this thesis is constructed by gathering nominal hedging data from quarterly reports combined with data gathered from the DataStream and Thompson-Reuters databases. The dataset covers quarterly data for five years starting from q1 2011 and ending at q4 2015 and a group of 53 companies belonging to S&P-100 index. Data is gathered for Firm value, daily stock market return, market capitalization, leverage, liquidity, dividend and the nominal amounts of Foreign exchange, Interest rate, Commodity and Equity hedging. These nominal hedging amount are a sum of financial derivatives used, like options and swaps, to hedge certain risks or cash flows. The dataset only includes derivative use designated for hedging purposes, derivative use for speculative purposes is excluded for the dataset. Hedging data comes from quarterly reports provided by the U.S. SEC information database EDGAR.

Variable definitions

Interest rate hedging

(

IRR

)

Nominal amount of outstandinginterest rate hedges

_J

Totaldebt

J

This variable represents the relative amount of debt that has been hedged by the company. Belghitar, Clark and Judge(2008) find that interest rate hedging can have a positive effect on debt capacity and the value of the firm. The variable is a ratio of the nominal amount of outstanding interest rate hedges divided by the total debt of the company. The nominal amount of outstanding interest rate hedges is the sum of all financial derivatives related to interest rate on debt that are designated for hedging purposes. Total debt is the sum of all outstanding short and long term loans the company has. Total debt is measured on a yearly basis. To construct the interest rate hedging ratio yearly data has been used for all quarters in that respective year. Because the total debt does not change dramatically over time I have no suspicion that the amount of total debt fluctuates heavily within the period of a year. The ratio is therefore still a good proxy to measure the relative amount of hedged interest rate risk per quarter.

Commodity hedging

( CoR )

Company

¿ ¿

J

Nominal amount of outstandingcommodity hedges

J

¿

This variable represents the relative amount of commodity price risks that is hedges by the company. Previous papers like Jin and Jorion(2006) and Balcilar, Demirer and Hammoudeh(2016) focus on the role of hedging for different commodity prices. Their papers are relatively narrow and focus on specific markets and commodity risks. However, in general can be concludes that these commodity risks and hedging play an important role for many companies, especially for companies that need these commodities in their production process. A measure for commodity hedging is therefore included.

The variable is a ratio of the nominal amount of outstanding commodity hedges divided by the size of the company. The nominal amount of outstanding commodity hedges is the sum of all financial derivatives related to commodity prices, and designated for hedging purposes. These commodities of include oil, gas, coal or agricultural goods. Many of the companies involved in this type of hedging

use these commodities as raw materials for the production of their products. Company size is measured as the total value of outstanding stocks at the end of the quarter.

Foreign Exchange hedging

(

FXR

)

Nominal amount of outstandingforeign exchange hedges

_J

International sales

J

This variable represents the relative amount of currency exchange rate risk that is hedged by the company. Hagelin and Pramborg(2003) and Allayannis and Weston(2001)find that hedging foreign exchange exposure can reduce exchange rate exposures and can increase firm value. A company that hedges a high amount of foreign exchange risk relative to its exposure can benefit from hedging. The variable is a ratio of the nominal amount of outstanding foreign exchange hedges divided by the amount of international sales of the company. The nominal amount of outstanding foreign exchange hedges is the sum of all financial derivatives related to foreign exchange and currency transactions, that are designated for hedging purposes. International sales is a measure of the turn-over of the company generated outside its domestic borders, on an annual basis. To turn the data into quarterly data the annual amount of international sales was divided by four and spread out over the four quarters of the respective year. This data transformation holds the assumption that the sales are spread equally over the year. Over a small timeframe of a year I argue that this is a plausible assumption and that the resulting Foreign Exchange Hedging ratio is not jeopardized.

Stock return volatility

( RVol )

A dependent variable in this research is stock return volatility. It measure the volatility of the returns of a particular stock. It is calculated as the volatility of daily stock returns over a period of one quarter of a year. First the daily return of the stocks is calculated as the percentile change in the closing price between today and yesterday. The stock return volatility is then calculated as the standard deviation of all daily returns within one quarter of a year.

Firm value- Tobin’s Q(Q)

The second dependent variable in this research is firm value, measured as a version of Tobin’s Q. Tobin’s Q is often used as a measure of firm value. It is defined as the market value of the company divided by the book value of its assets. I use the price-to-book ratio to express Tobin’s Q, similar the paper of Jin and Jorion(2006).

Dummy financial sector

Regarding the use of derivatives there might be a factor that is different between the companies in the dataset. Pramborg (2004) suggest that financial firm might have different motivations and information regarding hedging. Companies active in the financial sector might react differently to certain events and their hedging strategies might have different effect on the stock return volatility. Because these companies are more familiar with the use of financial derivatives they might be able to respond differently to market events. Even though the hedging data has been cleared from speculative derivative use, companies in the financial sector still might react differently. To find out whether this is indeed the case an extra dummy variable is created for financial sector companies, i.e. banks and insurers. This dummy is used in an interaction effect with the variables Foreign exchange( dFXR ), Commodity( dC∨¿ ) and Interest rate( dIRR ) hedging to find out

whether de effect of these variables differs between financial sector and non-financial sector companies.

Control variables for Stock price return volatility

Stock return volatility can be influenced by volatile cash flows to and from the company. Hedging can reduce the volatility of these cash flows and might therefore have an effect on stock return volatility. There are however other factors that might also influence these cash flows and subsequently the stock return volatility. Allen and Rachim (1996) argue that leverage, the relative amount of debt to common equity, can have an effect on stock return volatility as it increases the risk for the company. Due to interest rate payments highly leveraged companies are faced with high costs and are

therefore even more vulnerable to shocks on the income side. In this research the ratio of total debt to common equity is used as a measure of leverage( Lev ).

Company size(

¿ ¿

) could be of influence for stock return volatility. The argument here is that

smaller companies are usually less diversified and are less actively monitored by investors. A less diversified business model potentially increase the possibility of negative events and increases the risk. Furthermore, if a company is less actively monitored investors are more likely to be surprised causing large and rapid stock price changes. Market capitalization is used as a measure of company size.

The last control variable is lagged stock return volatility. Although in a perfect market current stock return should not be related to previous stock returns, this kind of momentum does seem to exist. If

stock returns are related over time, so can stock return volatility be, as it is directly linked. The last control variable is therefore the measure of stock return volatility lagged by one quarter of a year. Control variables for Firm value

When assessing the relationship between firm value and hedging it is again important to control for other factors that might influence firm value. The control variables used are similar to those used in the paper of Pramborg(2004).

The first control variable is again company size(Size), equal to the variable used for the analysis of stock return volatility. Allayannis and Weston(2001) have found a negative relation between company size and Tobin’s.

The second control variable is leverage(Lev). Again this variable is equal to the variable used for the analysis of stock return volatility. Allayannis and Weston(2001) have found again a negative relation between leverage and Tobin’s Q.

The third control variable is liquidity(Liq). Pramborg(2004) argues that companies that have cash constrains are likely to have a higher Tobin’s Q because they are more likely to invest in projects that offer a relatively high NPV. The Current Ratio is used as a measure of liquidity.

The last control variable is dividends(Div). Dividends can be used by companies to signal expected future profits. A dummy is used to control for dividends, which is set to one in case a company pays out dividends.

Method

As mentioned before the dataset contains quarterly data for 53 companies over a period of 5 years. This panel data set will be analyzed using an OLS regression. To make sure this method can be properly used the data must follow the assumptions regarding multicollinearity, homoscedasticity and normality.

To test multicollinearity a VIF-test is used to assess collinearity between the variables. With VIF values less than 2 there is no sign of serious multicollinearity in both the data for the stock price return volatility analysis and the data for the firm value analysis. The was some multicollinearity for the analysis of the “Financials’’ dummy’s. This has been solved by dropping one of these variables. The data does violate the assumption of homoscedasticity and displays a degree of

heteroscedasticity. To address this issue the analysis was performed using the option to calculate robust standard errors.

The assumption of normality of the residuals was also violated for the analysis. However, Lumley et al.(2002) argue that the normality assumptions become less important when the sample size becomes bigger. They argue that with a sample size of 100 observations or more moderate non-normality is no longer an issue. For samples with roughly 500 observations or more even extreme non-normality is no longer an issue, and the normality assumption itself no longer plays an

important role for statistical analysis. So, although the dataset in this paper shows non-normality of the residuals the data is still used because the size of the sample is sufficient to overcome potential problems of non-normality.

Analysis of stock price return volatility

The method that will be used is to research the effect of hedging on the volatility of stock price return will be an Ordinary Least Squares(OLS) regression, similar to the method used by Allen and Rachim(1996). The regression is based on panel data containing multiple time-points.

The first and most basic test is a regression of dependent variable RVol in relation with the independent variables

CoR , FXR∧IRR

. This test provides crude information on the relation between the Stock return volatily and the hedging varibles. e_j is the error term. The regression equation 1 is as follows:

RVol=a+a

₂

IRR+a

₃

FXR +a

₄

CoR+e

_j

Although the previous equation can indicate a relation it does not provide solid evidence to be able to conclude that there is or isn’t a relation between the variables. The first test will therefore be extended with the use of the control variables, to control for other important influences that were not measured in the first test. The variables are leverage(Lev), Size(Size) and stock return volatility lagged with one period(

L

₁

Rvol

). The regression equation 2 is as follows:

RVol=a+a

₂

IRR+a

₃

FXR +a

₄

CoR+a

₅

Lev +a

₆

¿

a

¿

₇

L

₁

RVol+e

_j

The regression above shows the potential relation between RVol and the hedging variables at the same moment in time. It is however arguable that the market might react slowly to cash flow news, or that some information is only transferred to investors on a monthly or quarterly basis at stockholder meetings. This would result in a much slower reaction of the market to changes in cash flows. The result is might be that the effect of hedging policies only becomes apparent after some

time. To gain insight in this potential effect multiple time lags are used to adjust the previous regression equation. The regression equation 3 is as follows:

RVol=a+a₂L_nIRR+a₃L_nFXR +a₄L_nCoR+a₅Lev+a₆¿a¿₇L₁RVol+e_j

L

_n expresses a time lagged variable, where n indicates the number of lags. For completeness I have chosen to use time lags n= 1 up to 4, so the effect of hedging policies on stock return volatility up to one year later will be researched.

As discussed before there might be a difference between companies active in the financial sector, hereafter called “Financials”, and non-financials. To assess that potential difference dummy-interaction variables are used. Again, to assess the crude relation a modified version of the first regression is used. However, because of serious multicollinearity between the variables

FXR

and

dFXR the latter variable was dropped from the regression equation. The resulting equation 7 is as follows:

RVol=a+a

₂

IRR+a

₃

FXR +a

₄

CoR+a

₅

dIRR +a

₆

dCoR+e

_j

As the previous regression equation is only able to expose a crude relation, again control variables are added. The control variables are the same as used in the earlier regressions. The new regression equation can provide an insight in the relation between hedging policies and stock return volatility for both Financials and non-financials. The regression equation 8 is as follows:

RVol=a+a₂IRR+a₃FXR +a₄CoR+a₅dIRR +a₆dCoR+a₇Lev +a₈¿a¿₉L₁RVol +e_j

Analysis of firm value

The method that will be used is to research the effect of hedging on the firm value will again be an Ordinary Least Squares(OLS) regression, similar to the method used by Allen and Rachim(1996) and Pramborg(2004).

The first and most basic test is a regression of dependent variable Tobin’s

Q

in relation with the independent hedging variables CoR , FXR∧IRR . This test provides crude information on the relation between the firm value and the hedging varibles.

e

_j is the error term. The regression equation 9 is as follows:

Although the previous equation can indicate a relation it does not provide solid evidence to be able to conclude that there is or isn’t a relation between the variables. The first test will therefore be extended with the use of the control variables, to control for other important influences that were not measured in the first test. The control variables are leverage(Lev), Size(Size), liquidity(Liq) and a dummy for dividend(Div). The regression equation 10 is as follows:

Q=a+a

₂

IRR+a

₃

FXR+a

₄

CoR+a

₅

Lev +a

₆

¿

a

¿

₇

Liq+a

₈

÷+

e

_j

The regression above shows the potential relation between Tobin’s Q and the hedging variables at the same moment in time. As discussed previously it is arguable that the market might react slowly to cash flow news, or that some information is only transferred to investors on a monthly or quarterly basis at stockholder meetings. This would result in a much slower reaction of the market to changes in cash flows. The result is might be that the effect of hedging policies only becomes apparent after some time. To gain insight in this potential effect multiple time lags are used to adjust the previous regression equation. The regression equation 11 is as follows:

Q=a+a₂L_nIRR+ a₃L_nFXR+a₄L_nCoR+a₅Lev+a₆¿a¿₇Liq+ a₈÷+e_j

L

_n expresses a time lagged variable, where n indicates the number of lags. Again I have chosen to use time lags n= 1 up to 4, so the effect of hedging policies on firm value up to one year later will be researched.

As with stock price return volatility there might be a difference between companies active in the financial sector and non-financial companies for the relation between firm value and hedging as well. To assess that potential difference dummy-interaction variables are used. Again, to assess the crude relation a modified version of the first regression is used. Because of serious multicollinearity between the variables FXR and dFXR the latter variable was dropped from the regression equation. The resulting equation 15 is as follows:

Q=a+a

₂

IRR+a

₃

FXR+a

₄

CoR+a

₅

dIRR+a

₆

dCoR+e

_j

As the previous regression equation is only able to expose a crude relation, again control variables are added. The control variables are the same as used in the earlier regressions. The new regression equation can provide an insight in the relation between hedging policies and stock return volatility for both Financials and non-financials. The regression equation 16 is as follows:

4. Results

Results on stock price return volatility

The correlations between the variables are presented in table 1. As can be seen there is a significant correlation between stock price return volatility( RVol) and foreign exchange hedging(FXR), interest rate hedging(IRR) and Size(Size), foreign exchange hedging and commodity hedging(CoR),

commodity hedging(CoR) and Size, and leverage(Lev) and size.. These correlations vary between minus 17,32% and 9,96%. Although these correlations do not strongly indicate multicollinearity a VIF-test is conducted to test for multicollinearity between the variables(see Appendix 1). With average VIF scores of 1,03 and no big outliers multicollinearity is not an issue for this set of variables. There is no need to change the set of independent variables.

Table 1: Cross-correlation between the variables

RVol IRR FXR CoR Lev Size

RVol 1 IRR 0.0321 1 (0.4621) FXR 0.0996* 0.0818 1 (0.0223) (0.0609) CoR -0.0409 -0.0273 -0.0501 1 (0.3486) (0.5318) (0.2510) Lev 0.0542 0.0617 0.0931* -0.0557 1 (0.2147) (0.1577) (0.0328) (0.2020) Size -0.0768 -0.0902* 0.0430 -0.1732* -0.1064* 1 (0.0785) (0.0387) (0.3254) (0.0001) (0.0146) Note: P-values between parentheses, (*) indicates significance at the 5% level.

Table 2 shows the results of equation 1. Equation 1 is used to assess a crude relation between the dependent variable and the explanatory variables. The results show that there is no significant relation between the dependent variable and the explanatory variables. All P-values are insignificant at the 5% level. The coefficient for foreign exchange hedging(FXR) is however significant at the 10% with a positive coefficient. This result seems counterintuitive as it would mean that foreign exchange hedging would cause more stock return volatility. Previous literature has no explanation for this result. However, because this is only a crude regression we have to be careful when drawing conclusions from this result.

Table 2: results of the regression: RVol=a+a₂IRR+a₃FXR +a₄CoR+e_j

Coef. Std. Err. T-statistic P-value

IRR .2540454 .268232 0.95 0.344 FXR .0784446 .0403244 1.95 0.052 CoR -.0371526 .0377748 -0.98 0.326 Cons .0126608* .0002505 50.55 0.000

R

2 : 0.0118 F-stat: 1.75 F-prob.= 0.1551 Note: (*) indicates significance at the 5% level.

Table 3 shows the results of equation 2. Control variables are now added to equation 1. The regression shows no significant relation between stock price return volatility(RVol) and the variables for hedging(IRR, FXR, CoR). There is a significant relation between the control variable lagged stock price return volatility (L1.RVol) and stock price return volatility . Stock price return volatility can be predicted based on the stock return volatility of the previous period.

Table 3: results of the regression: RVol=a+a₂IRR+a₃FXR +a₄CoR+a₅Lev +a₆¿a¿₇L₁RVol+e_j

Coef. Std. Err. T-statistic P-value

IRR -.1459905 .2962177 -0.49 0.622

FXR .0338644 .0323143 1.05 0.295

CoR -.0257069 .031187 -0.82 0.410

Lev 1.21e-06 9.92e-07 1.22 0.224

Size -2.60e 09 -1.30 0.193 L1.Rvol .5232898* .0471822 11.09 0.000 Cons .0063489* .0006623 9.59 0.000 R2 _: 0.2908 F-stat: 21.26 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

Table 4 shows the results of equation 3. Compared with equation 2 I now use one period time lag for variables the hedging variables interest rate(IRR), foreign exchange(FXR) and commodity

hedging(CoR). Again the relation between stock price return volatility and the hedging variables is not significant. There is no indication that one time lag can better represent the relation between stock price return volatility and the hedging variables. The relation between stock price return volatility and lagged stock price return volatility is positive and significant.

Table 4: results of the regression:

RVol=a+a2L1IRR+a3L1FXR+a4L1CoR+a5Lev +a6¿a¿7L1RVol+ej

Coef. Std. Err. T-statistic P-value

L1.IRR .2993979 .371779 0.81 0.421

L1.FXR .0427553 .0350945 1.22 0.224

L1.CoR -.0303866 .0363894 -0.84 0.404

Lev 9.81e-07 8.05e-07 1.22 0.224

Size -1.53e-09 2.08e-09 -0.73 0.463

L1.Rvol .5313492* .0471302 11.27 0.000

Cons .0060996* .0006576 9.28 0.000

R

2 : 0.2955

F-stat: 22.23 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

The results for equation 4, 5 and 6, with respectively 2, 3, and 4 periods time lag, are presented in Appendix 2. The results for all three equations are similar to the results of equation 3. There is no significant effect for the hedging variables IRR, FXR and CoR over the different time periods. The relation between the control variable lagged stock price return volatility (L1.RVol) and stock price return volatility remains positive and significant. The result suggests that hedging does not have an effect over time. With information traveling quickly through the market nowadays a time lag of more than one year is not expected to add any additional value to the analysis.

Table 5 shows the results of equation 7. In this analysis an interaction for so-called Financials(for definition, see Chapter 3 Methodology) is added to equation 1. First I ran a crude test to provide insight in the relation between RVol and the set of explanatory variables. The first interesting finding is that the interaction dummy for interest rate hedging(dIRR) has a significant effect with a P-value of 0,001. The coefficient for dIRR is positive however, which goes against the expectation that (Interest rate) hedging decreases stock return volatility. A possible explanation could be that Financials react significantly different than other companies and therefore should be treated differently when it comes to hedging. The literature provides no other explanation for these results. We therefore have to treat the results with caution, especially if we keep in mind that this regression equation is only used as a crude test of the basic relation between the dependent and independent variables. The interaction dummy for commodity hedging(dCoR) is significant at a 10% level. The negative coefficient suggest a negative relation between stock price return volatility and commodity hedging for Financials, as expected based on previous literature. However, as this is a crude test we also have to treat this result with caution.

Table 5: results of the regression: RVol=a+a₂IRR+a₃FXR +a₄CoR+a₅dIRR +a₆dCoR +e_j

Coef. Std. Err. T-statistic P-value

IRR -.1198756 .3196868 -0.37 0.708 FXR .0164363 .0461379 0.36 0.722 CoR -.0178924 .0377554 -0.47 0.636 dIRR 7.630239* 2.236556 3.41 0.001 dCoR -.5426501 .3199628 -1.70 0.090 Cons .0126013* .0002546 49.50 0.000

R

2 : 0.0523 F-stat: 2.73 F-prob.= 0.0191 Note: (*) indicates significance at the 5% level.

Table 6 shows the results of equation 8. This test adds the control variables to the crude test of equation 7 and makes the results more meaningful. Again the interaction variable for interest rate hedging(dIRR) has a relation with stock price return volatility(RVol) which is significant at a 5% level. The P-value of the coefficient is 0,045. The coefficient of dIRR again points to a positive relation, although the coefficient is smaller in equation 8 than it is for equation 7. Nevertheless the result goes against expectation. There is a lack of theoretical support in current literature for this finding. The result should therefore be treated with a lot of caution. It does seem to indicate that there is a difference between Financials and non-financials in their responds to corporate hedging strategies.

Table 6: results of the regression:

RVol=a+a

2

IRR+a

3

FXR +a

4

CoR+a

5

dIRR +a

6

dCoR+a

7

Lev +a

8

¿

a

¿

9

L

1

RVol +e

j

Coef. Std. Err. T-statistic P-value

IRR -.2891617 .3044035 -0.95 0.343

FXR .0024598 .0340875 0.07 0.943

CoR -.0149241 .0312926 -0.48 0.634

dIRR 3.627979* 1.804383 2.01 0.045

dCoR -.1945899 .3271804 -0.59 0.552

Lev 1.31e-06 9.98e-07 1.31 0.191

Size -1.65e-09 1.96e-09 -0.84 0.401

L1.Rvol .5059108* .0469496 10.78 0.000

Cons .0064193* .0006636 9.67 0.000

R2 _:

0.2988

F-stat: 16.43 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level, (**) indicates significance at the10% level.

In addition to the previous test an extra test was conducted with one time lag for the variables IRR, FXR, CoR, dIRR and dCoR. The results of this test are presented in Appendix 3. The results show no significant relation between stock price return volatility and the explanatory variables of interest. A further analysis with more time lags is therefore not conducted.

Firm value

The correlations between the variables are presented in table 7. As can be seen there is a significant correlation between firm value(Q) and commodity hedging(CoR), leverage(Lev) and Size(Size), between interest rate hedging(FXR) and dividends(Div), between commodity hedging(CoR) ,Size and liquidity(liq), between leverage(Lev), size and liquidity, and between liquidity and dividends. These correlations vary between minus 38,46% and 72,29%. The correlation of 72,29 is between firm value(Q) and leverage(Lev). The correlation between the explanatory variables do not strongly indicate multicollinearity. However, to be sure a VIF-test is conducted to test for multicollinearity between the variables(see Appendix 4). With average VIF scores of 1,11 and no big outliers multicollinearity is not an issue for this set of variables. There is no need to change the set of independent variables.

Table 7: Cross-correlation between the variables

Q IRR FXR CoR Lev Size Liq Div

Q 1 IRR 0.0086 1 0.8525 FXR -0.0798 -0.0095 1 0.0851 0.8375 CoR -0.1101* -0.0181 -0.1155* 1 0.0173 0.6969 0.0125 Lev 0.7229* 0.0883 -0.0162 -0.0582 1 0.0000 0.0567 0.7266 0.2094 Size -0.1047* -0.0646 0.1010* -0.2046* -0.1347* 1 0.0237 0.1632 0.0290 0.0000 0.0035 Liq -0.0684 0.0170 -0.0350 -0.1034* -0.1054* -0.0865 1 0.1397 0.7133 0.4501 0.0254 0.0227 0.0619 Div 0.0037 -0.1988* -0.0328 0.0856 0.0679 0.0157 -0.3846* 1 0.9364 0.0000 0.4795 0.0645 0.1428 0.7349 0.0000 Note: P-values between parentheses, (*) indicates significance at the 5% level.

relation between the dependent variable and foreign exchange(FXR) and commodity(CoR) hedging. The results show a negative relation. This would indicate that (foreign exchange and

commodity)hedging would reduce firm value. This result goes against intuition and previous literature. Previous studies have no explanations as to why hedging would reduce firm value. This regression is however a crude relation. The results should therefore be treated with caution.

Table 8: results of the regression:

Q=a+a

₂

IRR+a

₃

FXR+a

₄

CoR+e

_j

Coef. Std. Err. T-statistic P-value

IRR -135.8507 652.844 -0.21 0.835 FXR -234.7416* 30.33591 -7.74 0.000 CoR -168.5955* 33.68356 -5.01 0.000 Cons 7.113172 .4581791 15.52 0.000 R2 _: 0.0390 F-stat: 20.67 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

Table 9 shows the results of equation 10. Control variables are now added to equation 9. Again, the explanatory variables for hedging (IRR, FXR and CoR) now all indicate a negative relation with the dependent variable. These relations are statistically significant and the coefficients are high. These results go against economic theory and expectations. Previous paper are also not able to provide economic explanation for these results. The results should therefore be treated with caution.

Table 9: results of the regression:

Q=a+a

₂

IRR+a

₃

FXR+a

₄

CoR+a

₅

Lev +a

₆

¿

a

¿

₇

Liq+a

₈

÷+

e

_j

Coef. Std. Err. T-statistic P-value

IRR -1235.709* 612.5465 -2.02 0.044

FXR -192.5858* 37.73243 -5.10 0.000

CoR -137.5256* 32.3833 -4.25 0.000

Lev .0486204* .0062831 7.74 0.000

Size -1.83e-06 1.64e-06 -1.12 0.263

Liq -.3514544 .2697242 -1.30 0.193 Div -2.195863* .5102931 -4.30 0.000 Cons 5.809918* .9092489 6.39 0.000 R2 _: 0.5403 F-stat: 14.24 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

Table 10 shows the results of equation 11. Compared with equation 10 I now use one period time lag for hedging variables (IRR, FXR and CoR). Again we see statistically significant negative relations

for the hedging variables with one time lag. As hedging is expected to increase firm value, the results are counterintuitive and contradict the previous literature. The results should therefore be treated with caution.

Table 10: results of the regression:

Q=a+a

2

L

1

IRR+a

3

L

1

FXR +a

4

L

1

CoR+a

5

Lev +a

6

¿

a

¿

7

Liq+a

8

÷+

e

j

Coef. Std. Err. T-statistic P-value

L1.IRR -1496.067* 556.4742 -2.69 0.007

L1.FXR -215.5178* 34.59885 -6.23 0.000

L1.CoR -142.8319* 35.84643 -3.98 0.000

Lev .0497638* .0066305 7.51 0.000

Size -1.99e-06 1.68e-06 -1.19 0.235

Liq -.372659 .2446989 -1.52 0.128 Div -2.056976* .5817803 -3.54 0.000 Cons 5.836083* 1.006272 5.80 0.000 R2 : 0.5538 F-stat: 14.65 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

The results for equation 12, 13 and 14, with respectively 2, 3, and 4 periods time lag, are presented in Appendix 5. The results for all three equations are similar to the results of equation 11. The hedging variables are statistically significant but the lack of economic theory backing up the results makes that they should be treated with caution.

Table 11 shows the results of equation 15. In this analysis an interaction for so-called Financials(for definition, see Chapter 3 Methodology) is added to equation 9. First I ran a crude test to provide insight in the relation between Firm value(Q) and the set of explanatory variables. Foreign exchange and commodity hedging have a statistically significant negative relation to firm value, as does the interaction variable for Financials with interest rate hedging. The economic foundation for these results are however very weak. The interaction variable for Financials with commodity hedging is statistically significant and has a positive relation. This is in line with economic theory and previous literature, which expects (commodity) hedging to have a positive(increasing) effect on firm value. This is however a crude regression equation used to indicate a possible effect. Equation 16 should be used to further investigate the relation.

Table 11: results of the regression: Q=a+a₂IRR+a₃FXR+a₄CoR+a₅dIRR+a₆dCoR+e_j

Coef. Std. Err. T-statistic P-value

IRR 235.0457 725.0385 0.32 0.746 FXR -186.3526* 37.44396 -4.98 0.000 CoR -191.5573* 36.49355 -5.25 0.000 dIRR -7553.258* 1002.782 -7.53 0.000 dCoR 737.3919* 189.1209 3.90 0.000 Cons 7.203916* .4745964 15.18 0.000

R

2 : 0.0552 F-stat: 51.41 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

Table 12 shows the results of equation 16. This test adds the control variables to the crude test of equation 15 and makes the results more meaningful. The results show that the hedging variables for foreign exchange hedging(FXR), commodity hedging(CoR) and the interaction variable for Financials with interest rate hedging(dIRR) have a statistically significant relation with firm value. Their negative coefficients contradict economic theory. Previous literature has no explanation for these results. The meaning of the results is therefore very doubtful, and they should be treated with caution. The interaction variable for Financials with commodity hedging(dCoR) is significant at a 10% confidence level. The positive coefficient suggest a positive relation, where (commodity) hedging would increase firm value. This is in line with economic theory.

Table 12: results of the regression:

Q=a+a

2

IRR+a

3

FXR+a

4

CoR+a

5

dIRR+a

6

dCoR+a

7

Lev +a

8

¿

a

¿

9

Liq+a

10

÷+

e

j

Coef. Std. Err. T-statistic P-value

IRR -923.1614 606.2134 -1.52 0.128 FXR -308.9022* 51.82648 -5.96 0.000 CoR -130.9705* 29.80121 -4.39 0.000 dIRR -7491.352* 1232.507 -6.08 0.000 dCoR 511.699 264.93 1.93 0.054 Lev .0459585* .0057347 8.01 0.000

Size -1.64e-06 1.51e-06 -1.08 0.280

Div -1.49449* .6436528 -2.32 0.021

Cons 4.713201* .6605822 7.13 0.000

R2 _:

0.5199

F-stat: 20.36 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level, (**) indicates significance at the10% level.

5. Summary and conclusion

This paper investigate the effect of corporate hedging on stock return volatility and firm value for a group of 53 company presented in the S&P-100 index for the period of 2011 to 2015 using quarterly data. I test for a difference in stock return volatility and firm value for companies that use different levels of corporate hedging relative to their company and business size.

The results suggest that there is no significant relation between the hedging variables and stock return volatility. Analysis shows no significant results for both the basic regression and the

regressions with time lag. Only the control variable of lagged stock return volatility seems to have a significant effect. These result are in line with the theory of Miller and Modigliani(1958, 1961) that hedging does not add value to the company as private investor can reach similar results in their portfolio by means of diversification. The results do not support the idea that hedging can improve cash flow stability resulting in more stable stock returns. My research therefore indicates that corporate hedging has no significant effect on stock return volatility.

An important determinant of stock return volatility seems to previous stock return volatility. The results suggest that stock return volatility in the previous quarter can explain current stock return volatility. This suggest that there is sort of a momentum in the market. The effect of previous stock return volatility is an interesting effect to take into account when analyzing stock return volatility. Our knowledge regarding this relation is still open for further research.

For companies active in the financial sector the results do suggest an effect of hedging on stock price return volatility. More specific, interest rate hedging seems to have an positive effect on stock return volatility. This means stock return volatility is expected to go up if companies active in the financial sector chose to actively hedge their interest rate positions and risks. This result is controversial as it goes against the conclusion that can be drawn from previous scientific literature. Previous literature suggest that either hedging has no effect, or it will reduce cash flow volatility and consequently stock return volatility. The economic significance of this finding is therefore very doubtful. Further

research would be needed to (in)validate this relation.

The relation between firm value and hedging is still vague. Although the analysis overall suggest a negative relation between hedging and firm value, this finding is economically very hard to explain. Previous literature has no explanation as to why hedging would reduce firm value. Intuitively this finding is very contradictory to what we would expect when hedging and to what hedging in is

essence used for in practice. It is therefore not possible to draw any solid conclusions from the analysis without further research and information on this relation between hedging and firm value. The analysis provides a basic insight into the relation between corporate hedging ,and stock price return volatility and firm value. Due to limitations in freely available data the dataset present a rather small timeframe and a limited number of companies. Furthermore, again due to data

limitation the ratio’s used as proxies for corporate hedging are not perfect and will therefore always cause a small error in the results. I argue that these proxies are close estimates that can adequately describe the real explanatory variable, without compromising the results of the analysis. A small error will however persist. The results would certainly have a higher validity if the tests would have been done with a more extensive dataset. Potential replication studies would be of value if they would address this is issue and use more extensive datasets.

References

 Allayannis, G., & Weston, J. P. (2001). The Use of Foreign Currency Derivatives and

Firm Market Value. Review Of Financial Studies, 14(1), 243-276.

 Allen, D. E., & Rachim, V. S. (1996). Dividend Policy and Stock Price Volatility:

Australian Evidence. Applied Financial Economics, 6(2), 175-188.

 Balcilar, M., Demirer, R., Hammoudeh, S., & Nguyen, D. K. (2016). Risk Spillovers

across the Energy and Carbon Markets and Hedging Strategies for Carbon

Risk. Energy Economics, 54159-172.

 Baskin, J. (1989). Dividend Policy and the Volatility of Common Stock. Journal of

Portfolio Management, 15 (3), 19-25.

 Belghitar, Y., Clark, E., & Judge, A. (2008). The Value Effects of Foreign Currency and

Interest Rate Hedging: The UK Evidence. International Journal Of Business, 13(1),

43-60.

 Bessembinder, H., (1991), Forward contracts and firm value: Investment incentive

and contracting effects, Journal of Financial and Quantitative Analysis 26, 519-r532.

 Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical

Work. Journal Of Finance, 25(2), 383-417.

 Jin, Y., & Jorion, P. (2006). Firm Value and Hedging: Evidence from U.S. Oil and Gas

Producers. Journal Of Finance, 61(2), 893-919.

 Leland, H.E., (1998), Agency costs, risk management, and capital structure, Journal of

Finance 53, 1213- 1243.

 Lumley, T.,

Diehr, P., Emerson, S., Chen, L.(2002). The importance of the normality

assumption in large public health data sets. Annual Review of Public Health 23,

151-169.

 Mayers, D., & Smith, C. (1982). On the Corporate Demand for Insurance. The Journal

of Business, 55(2), 281-296.

 Miller, M.H., Modigliani, F., (1961), Dividend policy, growth, and the valuation of

shares, Journal of Business 34, 411-433.

 Modigliani, F., Miller, M.H., (1958), The cost of capital, corporation finance and the

theory of investment, American Economic Review 48, 261-297.

 Myers, S.C., (1977), Determinants of corporate borrowing, Journal of Financial

Economics 5, 147-175

 Nance, D. R., Smith, C. J., & Smithson, C. W. (1993). On the Determinants of Corporate

Hedging. Journal Of Finance, 48(1), 267-284.

 Pramborg, B. (2004). Derivatives Hedging, Geographical Diversification, and Firm

Market Value. Journal Of Multinational Financial Management, 14(2), 117-133.

 Robichek, A., & Myers, S. (1966). Problems in the Theory of Optimal Capital

Structure. The Journal of Financial and Quantitative Analysis, 1(2), 1-35.

 Ross, M.P., (1997), Corporate hedging: What, why and how?, Walter A. Haas School of

Business, University of California, Berkeley.

 Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under

conditions of risk. Journal Of Finance, 19425-442.

 Smith, C.W., Jr., Stulz, R.M., (1985), The determinants of firms’ hedging policies,

Journal of Financial and Quantitative Analysis 20, 391-405

 Stulz, R.M., (1984), Optimal hedging policies, Journal of Financial and Quantitative

Analysis 19, 127-140.

 Warner, J. (1977). Bankruptcy Costs: Some Evidence. The Journal of Finance, 32(2),

337-347

Appendices

Appendix 1

Appendix 1: VIF-test for multicolinearity

Variable VIF 1/VIF

Size 1.06 0.941549 FXR 1.03 0.973791 CoR 1.04 0.959521 IRR 1.02 0.979345 L1.RVol 1.02 0.982385 Lev 1.03 0.971966 Mean VIF 1.03

Appendix 2

Appendix 2: summary of the results of the regressions:

Equation 4: RVol=a+a₂L₂IRR+a₃L₂FXR+a₄L₂CoR+a₅Lev +a₆¿a¿₇L₁RVol +e_j Equation 5:

RVol=a+a

2

L

3

IRR+a

3

L

3

FXR+a

4

L

3

CoR+a

5

Lev +a

6

¿

a

¿

7

L

1

RVol+e

j

Equation 6: RVol=a+a₂L₄IRR+a₃L₄FXR+a₄L₄CoR+a₅Lev +a₆¿a¿₇L₁RVol+e_j

Equation 4 Equation 5 Equation 6

RVol RVol RVol

L2.IRR 0.0615 (0.19) L3.IRR 0.126 (0.40) L4.IRR 0.0753 (0.21) L2.FXR 0.0442 (1.26) L3.FXR 0.0284 (1.05) L4.FXR 0.0236 (0.83) L2.CoR -0.0318 (-1.03) L3.CoR -0.00655 (-0.22) L4.CoR 0.00400 (0.13) Lev 0.00000143* 0.00000110 0.00000133 (2.04) (1.10) (1.44)

Size -1.72e-09 7.41e-10 1.40e-09

(-0.83) (0.40) (0.73) L.RVol 0.536*** 0.531*** 0.430*** (11.04) (11.04) (10.54) _cons 0.00615*** 0.00535*** 0.00640*** (9.39) (8.22) (12.38) t statistics in parentheses * p<0.05, ** p<0.01, *** p<0.001

Appendix 3

Appendix 3: the result of regression:

RVol=a+a₂L₁IRR+a₃L₁FXR+ a₄L₁CoR+a₅L₁dIRR+a₆L₁dCoR+a₇Lev+a₈¿a¿₉L₁RVol+ e_j

Coef. Std. Err. T-statistic P-value

L1.IRR .1864012 .3910536 0.48 0.634

L1.FXR .0169367 .0429081 0.39 0.693

L1.CoR -.0229525 .0364603 -0.63 0.529

L1.dIRR 2.610606 1.620058 1.61 0.108

L1.dCoR -.1103079 .3154666 -0.35 0.727

Lev 1.03e-06 8.09e-07 1.27 0.205

Size -8.64e-10 2.07e-09 -0.42 0.677

L1.Rvol .5184299* .0474235 10.93 0.000

Cons .0061649* .0006633 9.29 0.000

R

2 : 0.2996

F-stat: 17.20 F-prob.= 0.0000 Note: (*) indicates significance at the 5% level.

Appendix 4

Appendix 4: VIF-test for multicolinearity

Variable VIF 1/VIF

Div 1.24 0.809076 Liq 1.22 0.821773 Size 1.09 0.913314 CoR 1.09 0.921108 IRR 1.06 0.943707 Lev 1.05 0.948774 FXR 1.02 0.976587 Mean VIF 1.11

Appendix 5

Appendix 5: summary of the results of the regressions:

Equation 12: Q=a+a₂L₂IRR+a₃L₂FXR+a₄L₂CoR+a₅Lev +a₆¿a¿₇Liq+a₈÷+e_j Equation 13:

Q=a+a

2

L

3

IRR+a

3

L

3

FXR+a

4

L

3

CoR+a

5

Lev +a

6

¿

a¿

7

Liq+a

8

÷+

e

j

Equation 14: Q=a+a₂L₄IRR +a₃L₄FXR+a₄L₄CoR+a₅Lev+a₆¿a¿₇Liq+a₈÷+e_j

Equation 12 Equation 13 Equation 14

Q Q Q L2.IRR -1292.1* (-2.08) L3.IRR -1437.3* (-2.24) L4.IRR -1440.7* (-2.14) L2.FXR -224.4*** (-6.89) L3.FXR -227.8*** (-6.15) L4.FXR -223.6*** (-5.80) L2.CoR -141.8*** (-3.74) L3.CoR -151.4*** (-3.54) L4.CoR -134.4** (-3.08) Lev 0.0497*** 0.0498*** 0.0496*** (7.27) (7.01) (6.65) Size -0.00000211 -0.00000243 -0.00000256 (-1.22) (-1.34) (-1.36) Liq -0.441 -0.330 -0.134 (-1.56) (-1.07) (-0.34) Div -1.681* -1.609 -1.238 (-2.28) (-1.83) (-1.08) _cons 5.629*** 5.563*** 4.974** (4.51) (3.78) (2.74) t statistics in parentheses * p<0.05, ** p<0.01, *** p<0.001