Why do firms speculate? Evidence from the gold mining industry

 
 
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                                Why do firms speculate?
                         Evidence from the gold mining industry
                                           Tim R. Adam
                                  MIT Sloan School of Management
                                   50 Memorial Drive, E52-403A
                                      Cambridge, MA 02142
                                        Tel.: (617) 253-5123
                                        Fax: (617) 258-6855
                                      E-mail: tadam@mit.edu

                                         Chitru S. Fernando
                                 Michael F. Price College of Business
                                      University of Oklahoma
                                    307 West Brooks, Room 205
                                     Norman, OK 73019, USA
                                        Tel.: (405) 325-2906
                                        Fax: (405) 325-7688
                                     E-mail: cfernando@ou.edu

                                            Jesus M. Salas
                                 Michael F. Price College of Business
                                      University of Oklahoma
                                    307 West Brooks, Room 205
                                     Norman, OK 73019, USA
                                        Tel.: (405) 325-1775
                                        Fax: (405) 325-7688
                                       E-mail: jsalas@ou.edu



                                              February 2007


JEL Classification: G11; G14; G32; G39

Keywords: Corporate risk management; selective hedging; speculation; managerial
compensation.



 We thank Ted Reeve for providing us with his derivative surveys of gold mining firms, and Sridhar Gogineni
and Leung Kam Ming for excellent research assistance. We are responsible for any remaining errors.
Why do firms speculate?
                      Evidence from the gold mining industry

                                          Abstract


We study the selective hedging puzzle, using data on the speculative activity of a sample of
92 North American gold mining firms, a setting that seems likely to satisfy the conditions
stipulated by Stulz (1996) for shareholder value-maximizing selective hedging. Contrary to
our predictions, we find that smaller firms speculate more than larger firms, although they are
less likely than larger firms to possess the information and financial advantages necessary to
outperform the market through speculation. We also find that a higher probability of financial
distress is linked to a higher likelihood of corporate speculation. Nonetheless, this finding
fails to explain the speculation undertaken by the bulk of the firms in our sample, which are
financially sound and far from bankruptcy. Our findings on the relationship between
speculation and managerial incentives provide no support for (and indeed, contradicts) the
possibility that managers may be speculating in their own self interest. We find that rewarding
managers through stock and options, and also insider ownership of the firm’s shares, actually
work to reduce managerial incentives to speculate. Since neither shareholders nor managers
seem to benefit from selective hedging, our findings are consistent with the remaining
possibility for selective hedging identified by Stulz (1996) – that managers hedge selectively
because they erroneously believe they can outperform the market – which raises many new
questions for future research.




                                              2
1. Introduction

        Recent studies of corporate risk management have documented a considerable

divergence between the theory and practice of hedging. The existing theory of corporate risk

management assumes that firms use derivatives only to hedge risk exposures brought about

during their normal course of business, which adds value by reducing transaction and

contracting costs, taxes, and other market imperfections.1 In contrast, there is growing

evidence that firms incorporate market views into their hedging programs and thus hedge

selectively.2 Firms that hedge selectively vary the size and timing of their derivatives

transactions based on their expectations about future market prices. For selective hedging to

be value increasing, however, firms would need to have information that is not available to

the rest of the market, and the ability to act on this information without jeopardizing their core

business.

        Stulz (1996) argues that in the course of their regular business activity, some firms

may accumulate privileged information about their market, citing as an example the case of a

large copper consumer whose significant market presence provides a unique ability to

aggregate demand and supply information about the copper market and forecast prices more

accurately than the market.3 In such cases, firms may be tempted to hedge selectively using

their proprietary information. However, firms may be misunderstanding the source of their

comparative advantage and thus believe they possess valuable information when in fact they


1
  See, for example, Stulz (1984), Smith and Stulz (1985), Stulz (1990), Froot, Scharfstein and Stein (1993),
DeMarzo and Duffie (1995), and Mello and Parsons (2000) for further discussion on the theoretical motives for
hedging.
2
  See, for example, Dolde (1993), Bodnar, Hayt and Marston (1998), Glaum (2002), Faulkender (2005), Adam
and Fernando (2006), Brown, Crabb and Haushalter (2006), Geczy, Minton and Schrand (2006), Beber and
Fabbri (2006), and Faulkender and Cherchenko (2006).
3
  See, for example, Grossman (1976), Diamond and Verrecchia (1981) and Huberman and Schwert (1985) for
development of the notion of information aggregation in a securities market context.



                                                     3
do not. Moreover, notwithstanding any private information a firm might have, selective

hedging exposes it to considerably more risk relative to the case in which it engages in pure

hedging. Stulz (1996) concludes that a firm that seeks to add shareholder value by selective

hedging must not only have a genuine information advantage but also have the financial

strength to support the extra risk that selective hedging entails.

        In a recent study, Adam and Fernando (2006) find considerable evidence of selective

hedging in a sample of 92 North American gold mining firms. In contrast to the shareholder

value-maximizing outcome that the aforementioned notion of rational selective hedging might

predict, they find no evidence of economically significant cash flow gains arising from

selective hedging for their sample of firms.4 This observed lack of success raises important

questions about the motivations for firms to speculate in this way.

        Stulz (1996) advances three other lines of reasoning that could explain selective

hedging. First, he notes that from an agency-theoretic standpoint, taking gambles on the

market could be a rational strategy for managers of firms that are in financial distress.5

Second, he argues that some incentive compensation schemes could induce managers to

engage in selective hedging even if it does not benefit shareholders. Finally, he raises the

possibility that some managers may engage in selective hedging because they erroneously

believe that they have a comparative advantage in hedging selectively, which in turn might

lead them to overestimate their ability to beat the market.




4
  The evidence in Adam and Fernando (2006) is confirmed by Brown, Crabb and Haushalter (2006), who also
find little evidence of successful selective hedging in their sample of 44 gold producers.
5
  In a somewhat related argument, Campbell and Kracaw (1999) show that speculation may sometimes be
optimal for firms that have minimum-scale projects and meager internal resources, when external financing is
costly.



                                                      4
Using as our frame of reference the Stulz (1996) criteria for a shareholder value-

maximizing selective hedging strategy and employing the data from Adam and Fernando

(2006), we examine cross sectional differences across gold mining firms that hedge

selectively and analyze how these differences relate to the cash flows they earn from selective

hedging. We also examine how managerial compensation and the presence of inside owners

might influence selective hedging activity.

       Despite the fact that the conditions for selective hedging stipulated by Stulz (1996) are

more likely to be satisfied in the gold mining industry than in many other industry settings,

we find no evidence of selective hedging practice that seems consistent with the Stulz (1996)

criteria for rational shareholder value-maximizing speculation. When we examine the

relationship between selective hedging and firm size, we find a negative relationship, which is

the opposite of what we would expect to find if larger firms have a true comparative

advantage in speculation due to information access and creditworthiness. It is possible that

smaller firms are more likely to erroneously believe that they have information the market

does not have. It is also possible that smaller firms may be more constrained in external

capital raising due to asymmetric information and engage in selective hedging to supplement

their smaller internal resources, as predicted by Campbell and Kracaw (1999).

       We also find support for the notion that the probability of financial distress might

affect the likelihood of corporate speculation. We find that the firms in our sample that have

the highest probability of bankruptcy also speculate more, which seems to support the agency-

theoretic notion articulated by Stulz (1996) that shareholders of firms close to bankruptcy may

have incentives to speculate at the cost of bondholders. Nonetheless, as observed by Glaum

(2002), while this argument might explain some of the relative differences in the intensity of




                                               5
speculation across our sample, it fails to explain the speculation undertaken by the bulk of the

firms in our sample, which are financially sound and far from bankruptcy.

       Our findings on the relationship between speculation and managerial incentives

provide no support for (and indeed, contradicts) the possibility raised by Stulz (1996) that

managers may be speculating in their own self interest.          Our finding that speculation

decreases with the vega of option holdings by both CEOs and CFOs directly contradicts the

view that stock option ownership may induce executives to speculate to increase volatility.

Our finding that speculation decreases with the delta of managerial stock and option

ownership suggests that rewarding managers through stock and options actually works to

reduce their incentives to speculate. This conclusion is supported by our finding for insider

ownership. Given that selective hedging adds no value, it is not rational for managers to

speculate even their own self interest, and this is what our insider ownership findings seem to

suggest, that the presence of insiders deters firms from engaging in speculation and reduces

the losses that result from such speculation.

       Overall, it would seem that neither shareholders nor managers benefit from selective

hedging in our sample of firms. Notwithstanding the possibility that the likelihood of

bankruptcy might partially explain some of our findings, our collective results are consistent

with the remaining possibility for selective hedging highlighted by Stulz (1996) that managers

hedge selectively because they erroneously believe that they can outperform the market.

       Two recent papers have examined the question of what firm and managerial

characteristics distinguish firms that hedge selectively. Géczy, Minton and Schrand (2006)

base their study on the firms in the Wharton survey (Bodnar, Hayt and Marston (1998)) and

find that CFO stock price sensitivity (delta) is positively associated with the probability of




                                                6
actively taking positions, while CEO stock price sensitivity is negatively related to

speculation. They argue that these findings are consistent with the CFO being the active

executive in speculation decisions, whose actions are not impeded by the CEO. For a sample

of large U.S. non-financial firms with currency exposure, Beber and Fabbri (2006) examine

the link between CEO compensation and selective hedging. They find no statistically

significant relation between CEO delta and selective hedging, although they find a decrease in

hedging when the sensitivity of CEO compensation to stock price volatility (vega) increases.

They also find that CEO characteristics such as gender, age, tenure and holding the MBA

degree can explain speculative behavior.

       Neither of these studies utilize data sets that permit the authors to determine whether

or not the selective hedging that they document is successful and thereby provide a context for

what the motives for selective hedging might be in their respective samples. In contrast, the

evidence from the gold industry documented by Adam and Fernando (2006) and Brown,

Crabb and Haushalter (2006) clearly show that selective hedging gains in the gold industry

are not economically significant on average. Additionally, both these papers examine

selective hedging in the currency market, an arena in which it is unlikely that any individual

firm would have a comparative advantage in selective hedging as defined by Stulz (1996). In

contrast, the gold mining industry is a more specialized commodity industry and it is easier to

conceive of the possibility that some firms in this industry have a comparative advantage in

selective hedging. Additionally, our data set from the gold mining industry permits us to

undertake a more in-depth examination of selective hedging at the level of individual

transactions and provide new insights by looking at hedging across different maturities.




                                              7
The rest of our paper is organized as follows. In Section 2 we briefly review the

existing evidence on selective hedging and formulate our empirical hypotheses. Section 3

describes our data set. Section 4 examines the relationships between selective hedging, firm

size and other firm characteristics. Section 5 analyzes firms’ cash flows from selective

hedging, differentiated by hedge maturities and in relation to firm characteristics. Section 6

examines the relationship between selective hedging, and managerial compensation and

insider ownership. Section 7 concludes.



2. Corporate speculation

       The existing theory of corporate risk management assumes that firms use derivatives

purely for hedging purposes, and that the benefits of derivatives usage accrue solely from the

alleviation of market imperfections. In contrast, there is considerable survey evidence that

managers’ market views affect the risk management programs of many firms. In a survey of

244 Fortune 500 firms, Dolde (1993) reports that almost 90% of the firms surveyed at least

sometimes based the size of their hedges on their views of future market movements. Bodnar,

Hayt and Marston (1998) survey derivatives usage by 399 U.S. non-financial firms and find

that about 50% of their sample firms admit to sometimes (and 10% frequently) altering the

size and or the timing of a hedge based on their market views. Glaum (2002) surveys the risk

management practices of the major non-financial firms in Germany. He finds that the majority

follows forecast-based, profit-oriented risk management strategies.       Faulkender (2005)

examines whether firms are hedging or timing the market when selecting the interest rate

exposure of their new debt issuances and shows that the interest rate risk management

practices of the firms in his sample are primarily driven by speculation or myopia instead of




                                              8
hedging considerations. In a follow-on paper, Faulkender and Chernenko (2006) further

explore the reasons for the interest rate timing behavior documented by Faulkender (2005).

Their empirical findings suggest that swap usage and the choice of interest rate exposure are

primarily driven by a desire to meet consensus earnings forecasts and to raise managerial pay.

Adam and Fernando (2006) find considerable evidence of selective hedging in their sample of

gold mining firms but find no economically significant cash flow gains on average from

selective hedging. Brown, Crabb, and Haushalter (2006) also study selective hedging in the

gold mining industry and arrive at a similar conclusion. Beber and Fabbri (2006) analyze the

time-series variation of foreign currency derivatives in a sample of large U.S. non-financial

firms and document a substantial time-series variation in currency derivatives holdings in

excess of what can be explained by changes in currency exposure, which they attribute to

selective hedging.

       Collectively, this body of evidence suggests that the practice of selective hedging is

widespread in the corporate world. Since it does not appear to generate significant profits, one

wonders why managers devote resources to trying to beat the market. We next develop a

series of hypotheses to guide the empirical analysis of selective hedging in our sample.



2.1 Empirical hypotheses

       In contrast to the theories of corporate hedging, Stulz (1996) has argued that some

firms may have an incentive to speculate if they possess inside information and have a

comparative advantage in risk bearing due to their financial strength. In his example of a large

copper consumer, the firm obtains access to specialized information about the copper market

as a result of its copper purchasing activity. In a more general context, Diamond and




                                               9
Verrecchia (1981) model information aggregation in securities markets, and show that prices

can aggregate diverse sources of information possessed by individual traders.6 In a corporate

setting where individual firms can aggregate information from diverse business transactions,

it is conceivable that they may obtain an advantage in doing so over others in the market. It is

reasonable to assume that the potential for a firm to access specialized information or

aggregate information will increase with its presence in the market and the resources it can

expend on gathering such information, both of which can be proxied by the size of the firm. A

comparative advantage in bearing risk is a function of a firm’s size and the strength and

quality of its balance sheet, which can be measured by the firm’s leverage, liquidity, and other

attributes of creditworthiness. Therefore, we expect to find that large firms are more likely to

engage in selective hedging than small firms. We also expect to find more creditworthy firms

to display a higher propensity to engage in selective hedging than less creditworthy firms.

Additionally, to the extent selective hedging creates shareholder value, we expect to find the

value created by selective hedging to increase with the size of the firm.

          In our sample, firms use derivatives with maturities of up to five years. Since markets

are less efficient at forecasting prices further out into the future, we would expect any relative

informational advantage of larger firms to increase as the time to maturity of derivatives

instruments increases. Additionally, from a creditworthiness standpoint, larger firms are more

likely to have access to long-term derivatives positions than smaller firms. Therefore, we

expect a positive relationship between firm size and the average hedging duration.

Additionally, to the extent that these transactions produce non-zero cash flows, we expect to




6
    See also Grossman (1976) and Huberman and Schwert (1985).



                                                    10
see larger firms being relatively more successful than smaller firms as the duration of hedging

increases.

       Stulz (1996) also notes that financially distressed firms could have an incentive to

speculate regardless of whether or not they believe they can beat the market. In this case,

stockholders would benefit if the speculation is successful but only bondholders would lose if

it is not. If this holds true for our sample, we expect to find an increase in speculation as the

probability of bankruptcy increases. In a somewhat related line of reasoning to Stulz (1996),

Campbell and Kracaw (1999) argue that financially constrained firms may also have

incentives to speculate. If this were true, we expect to find an increase in speculation as

financial constraints increase.

       If selective hedging is driven by managerial incentives, we expect to find an increase

in selective hedging with various incentive compensation features that could make managers

better off if they speculate. Since speculative activity increases stock return volatility, we

would expect to find a monotone relationship between selective hedging and stock option

compensation. Conditional on selective hedging being successful, we expect to find a positive

relationship between selective hedging and stock ownership. And conditional on selective

hedging being unsuccessful, we expect to find a negative relationship between selective

hedging and stock compensation. Similarly, conditional on selective hedging being

successful, we expect to find an increase in selective hedging with insider ownership. In

contrast, if selective hedging is unsuccessful, we expect to find selective hedging activity

decreasing with insider ownership.




                                               11
3. Data

       The sample of firms and their derivatives transactions that we study in this paper is

identical to the sample used by Adam and Fernando (2006). This sample consists of 92 gold

mining firms in North America, encompassing the majority of firms in the gold mining

industry. These firms are included in the Gold and Silver Hedge Outlook, a quarterly survey

conducted by Ted Reeve, an analyst at Scotia McLeod, from 1989 to 1999. Firms not

included in the survey tend to be small or privately held corporations.

       The survey contains information on all outstanding gold derivatives positions, their

size and direction, maturities, and the respective delivery prices for each instrument. The

derivatives portfolios consist of forward instruments (forwards, spot-deferred contracts, and

gold loans) and options (put and call). There are a total of 2,541 firm-quarter observations of

which 1,450 firm-quarters represent nonzero hedging portfolios. Tufano (1996) and Adam

and Fernando (2006) provide further details about this data set.

       Using this data set, together with market data on average gold spot and futures prices,

interest rates, and the gold lease rate, Adam and Fernando (2006) calculate the quarterly net

cash flows associated with each derivatives transaction for each firm. They also separate

hedge ratios and derivatives cash flows into (1) a component attributable to pure hedging and

(2) a component attributable to speculation in the form of selective hedging. Appendix A

provides a summary of this decomposition of hedge ratios and cash flows. A more detailed

description of how these calculations are performed is provided in Adam and Fernando

(2006). We perform our analysis using the hedge ratio components and derivatives cash flows

attributed by Adam and Fernando (2006) to selective hedging.




                                              12
We obtain financial data from Compustat, or from a manual search of firms’ financial

statements if a firm is not covered by Compustat. Stock market return data comes from the

CRSP database and Datastream. We hand collect operational data, e.g., gold production

figures, production costs per ounce of gold, etc., from firms’ financial statements.

       We gather compensation data through ExecuComp or through manual collection if the

firm is not covered by ExecuComp. Specifically, we gather proxy statements for firm-year

observations not available on ExecuComp. We then calculate the stock and option holdings

for CEOs and CFOs and aggregate stock holdings for all insiders (executives and members of

the board of directors). In addition, we estimate the sensitivities of stock and option holdings

to changes in stock price level and volatility following Core and Guay (1999). A detailed

description of the compensation variable estimation is provided in Appendix B.

       Table 1 provides summary statistics of our sample. Figure 1 plots the median selective

hedging levels in our sample (median differentials between actual and predicted hedge ratios,

i.e., hedge ratio residuals) over time for one-year hedge maturities. Similar patterns exist for

longer hedge maturities. As in previous studies, we observe considerable volatility. Figure 2

plots the percentage of selective hedgers in our sample over time for each of the five

maturities contained in our sample, where selective hedgers are defined as firms whose

selective hedging exceeds a threshold level. We observe a general increase in the incidence of

selective hedging over time.

                           [Place Table 1 and Figs 1 & 2 about here]




                                               13
4. Hedging, speculation and firm size

       In this section, we examine how selective hedging is related to firm size and other

characteristics. Since selective hedging is undertaken only by firms that use derivatives, we

begin by examining how the likelihood of derivatives use (i.e., a firm being a “hedger”) is

related to a firm’s size and other characteristics. Thereafter we analyze selective hedging for

the firms that are identified as being derivatives users. We also examine how the use of

derivatives and selective hedging varies by hedge maturity.



4.1 The likelihood of being a hedger

       We first analyze the question of the likelihood that a firm is a hedger as a function of

firm size by using a logit model where the dependent variable is equal to one if a firm is

hedging and zero if it is not. As we can see from Table 2, there is a strong positive

relationship between the likelihood of hedging and size. Furthermore, the relationship

between hedging likelihood and size becomes stronger for longer hedging maturities. We also

compute predicted values from the model, which confirm that the predicted likelihood of

hedging drops sharply as the maturity becomes longer. The overall results are consistent with

the general notion in the literature that larger firms are more likely to hedge than smaller

firms, possibly due to their higher levels of expertise and resources, even though the need to

hedge may be greater for smaller firms.

                                  [Place Table 2 about here]

       The regression results in Table 3 show that the magnitude of hedging, as measured by

hedge ratios, is also increasing in firm size. The coefficient on firm size is significant and




                                              14
positive across all hedging maturities. Hedge ratios decline with hedge maturity, indicating

that the percentage of near-term production that firms hedge is higher than the corresponding

percentage of longer-term production.

                                  [Place Table 3 about here]



4.2 Speculation and firm size

       Having identified the firms in our sample that use derivatives, we explore the question

of which of these firms are more likely to speculate. In Table 4, we use the standard deviation

of actual hedge ratios as a measure of speculation to examine how selective hedging is related

to firm size for the sample of firms that hedge. Our regression results show that larger firms

speculate less than smaller firms for all hedging maturities, a finding that stands in stark

contrast to our previous findings reported in Tables 2 and 3, that larger firms are more likely

to hedge and hedge a greater percentage of their production than smaller firms. The

relationship between speculation and size remains robust when we control for the level of

hedging using hedge ratios.

                                  [Place Table 4 about here]

       The argument from hedging theory that hedging decreases expected bankruptcy costs

(e.g., Smith and Stulz (1985)) suggests that firms are more likely to hedge when they are

closer to bankruptcy. As noted by Stulz (1996), it is also the case from agency theory that

stockholders will have more incentive to speculate when firms are closer to bankruptcy. In

Table 5, we present results from our analysis in this regard. Specifically, Panel A of Table 5

presents our findings on the relationship between hedging and the likelihood of bankruptcy

while Panel B presents our findings on the relationship between speculation and the likelihood




                                              15
of bankruptcy. We use Altman’s z-score as a measure of the firm’s likelihood of bankruptcy,

where higher z-scores are associated with a lower chance of bankruptcy. We also allow for

the relationship between hedging and z-scores and between speculation and z-scores to be

non-linear by including the square of z-scores. We find a convex relationship between z-

scores and the likelihood of hedging across all hedging maturities, i.e., firms hedge more both

when they are close to bankruptcy and when they are far from bankruptcy, relative to

intermediately-placed firms. Interestingly, we find a similar convex relationship between z-

scores and selective hedging, i.e., firms also speculate more both when they are close to

bankruptcy and when they are far from bankruptcy, relative to intermediately-placed firms.

We should also note that the previously observed relationships between hedging and size and

between speculation and size remain largely robust when we control for the likelihood of

bankruptcy.

                                  [Place Table 5 about here]

       In Table 6, we test the robustness of the speculation-size relationship by re-running the

speculation-size regressions while controlling for other firm characteristics: market-to-book

(M/B) ratio, Herfindahl Index (measuring each firm’s concentration in gold mining as

determined by books assets allocated to gold mining versus other business segments the firm

may be involved in), dividend dummy (equal to one if the firm pays dividends in year t),

quick ratio, leverage ratio (based on book values) and free cash flow (based on market

values).

                                  [Place Table 6 about here]

       As would be observed from Table 6, the previously identified relationship between

speculation and firm size remains broadly robust, although weaker (perhaps due to the smaller




                                              16
sample size). The significantly negative relationship between speculation and size persists for

one and two-year maturities, but loses significance thereafter.

        Looking at the regression results that link selective hedging to other firm

characteristics, we see several interesting patterns. First, speculation is negatively related

(when statistically significant) to the market-to-book ratio regardless of maturity, suggesting

that firms with higher growth options speculate less. The Herfindahl index is weakly

negatively related to speculation for the five-year-ahead hedging maturity. Since the

Herfindahl index that we use measures the extent to which a firm specializes in gold mining,

it provides another measure of the firm’s potential to have access to specialized information.

In this context, however, the result for the five-year maturity is the opposite of what we would

expect if firms were speculating to exploit an information advantage. The quick ratio is

negatively related to speculation for the three-, four-, and five-year maturities. Perhaps

surprisingly, we found no relationship between speculation and whether or not the firm pays

dividends, between speculation and leverage (with book values)7 and between speculation and

free cash flow. Overall, these results suggest that more liquid and less financially constrained

firms speculate less, which is consistent with the idea in Campbell and Kracaw (1999).



4.3 Discussion

        We find that larger firms are more likely to hedge and that they hedge a higher

percentage of their production when they do hedge, relative to smaller firms. These findings

are not surprising and are consistent with the view that larger firms hedge more than smaller

firms because of their higher financial strength, and higher levels of expertise and other


7
 We also explore using leverage using market values with similar results. However, the number of observations
was much more limited.


                                                     17
resources that they can commit to hedging. In contrast, smaller firms speculate more than

larger firms. This finding is puzzling and is contrary to the notion from Stulz (1996) that to

the extent firms speculate based on an actual or perceived information advantage, larger firms

would have a higher advantage than smaller firms. It is possible that smaller firms are more

likely to erroneously believe that they have information the market does not have. It is also

possible that smaller firms may be more constrained in external capital raising due to

asymmetric information and engage in selective hedging to supplement their smaller internal

resources, as predicted by Campbell and Kracaw (1999).

       Our finding of non-linear relationships between both hedging and speculation with the

likelihood of bankruptcy seems interesting and provides new insights. On the one hand, our

finding that the firms in our sample that have the lowest probability of bankruptcy hedge and

speculate more is not surprising. Both these findings can be explained by the firms in question

having the deep pockets to engage in hedging or speculation, despite the fact that in the latter

case the merits of what they are doing may be questionable. Our finding that the firms in our

sample that have the highest probability of bankruptcy also hedge more provides further

support for the theoretical argument that hedging reduces bankruptcy costs (Smith and Stulz,

1985). Our finding that the firms in our sample that have the highest probability of bankruptcy

also speculate more seems to support the agency-theoretic notion articulated by Stulz (1996),

that shareholders of firms close to bankruptcy may have incentives to speculate at the cost of

bondholders. Nonetheless, as observed by Glaum (2002), while this argument might explain

some of the relative differences in the intensity of speculation across our sample, it fails to

explain the speculation undertaken by the bulk of the firms in our sample, which are

financially sound and far from bankruptcy.




                                              18
5. Cash Flow Effects of Speculation

       In this section, we examine the cash flows from selective hedging activities and how

these cash flows vary across firms. Our cash flow measure is the difference between the total

derivatives cash flows and the predicted hedge cash flows, i.e., the selective hedging or

speculative cash flows. Adam and Fernando (2006) find no conclusive evidence based on

their analysis of selective hedge cash flows that firms are systematically successful at

speculating on changes in their market views. We explore this question further by examining

how selective hedging cash flows vary with firm size and hedge maturities.



5.1 Selective hedging cash flows and firm size

       In this section we analyze how selective hedging cash flows are related to hedge

maturity and firm size. Table 7 summarizes the results of the analysis of cash flow gains from

speculation, using quarterly observations.

                                   [Place Table 7 about here]

       We test whether cash flows from selective hedging are related to size, which would be

the case if larger firms have a true comparative advantage in speculation due to information

access and creditworthiness. Surprisingly, we find a significant negative relationship between

selective hedging cash flows and size for the aggregate selective hedging cash flows and

(weakly) for the one-year maturity. The negative coefficient on the aggregate cash flows is

quite surprising and contrary to what we would expect based on a rational theory of

speculation as in Stulz (1996). Our results provide no evidence that the conditions for

successful speculation stipulated by Stulz (1996) exist in the gold market or if they do, that




                                                 19
firms are able to successfully exploit them. The extent of hedging (hedge ratio) and

speculation (volatility of hedge ratio) are not significantly related to selective hedging cash

flows.



6. Managerial compensation, insider ownership, and speculation

         We now turn to the second alternative hypothesis proposed by Stulz (1996), that

managers speculate as a rational response to the way in which they are incentivised through

compensation and ownership of the firm. As noted previously, managers are more likely to

speculate when their wealth increases with stock volatility, which would be the case when

they own stock options. A commonly used measure of the sensitivity of executive stock

option holdings to changes in volatility is the aggregate vega of the option holdings. In this

section we examine whether corporate speculation is positively related to the aggregate vega

of option holdings for both the CEO and the CFO. On the other hand, especially given the

findings in the literature that selective hedging does not have a beneficial impact on

shareholder wealth, it is possible that the ownership of shares in the firm might attenuate any

incentive for managers to speculate. Thus, we also examine the relation between selective

hedging and the delta of stock and option holdings by the CEO and CFO. Along similar lines,

we also examine the relation between selective hedging and insider stock holdings.

         We present results from our analysis of speculation and executive compensation in

Table 8 (for CEOs) and Table 9 (for CFOs). After controlling for firm size, we find that the

relationship between speculation and vega is consistently negative for both CEOs and CFOs,

which directly contradicts the view that stock option ownership may induce executives to

speculate to increase volatility. In contrast, the relationship between speculation and delta is




                                              20
also consistently negative for both CEOs and CFOs, which suggests that the ownership of

stock does reduce the incentive for these executives to engage in speculation.

                               [Place Tables 8 & 9 about here]

       We present our findings of the relationship between speculation and insider ownership

in Table 10. We find a significant negative relationship between insider ownership and

speculation for one-year hedge maturities, which persists when we control for firm size and

hedge ratio. Given that selective hedging adds no value, this finding is consistent with the

notion that insider ownership attenuates the incentive for speculation. A similar but weaker

result holds for the two-year maturity. In contrast, we find a weakly positive relation between

speculation and insider ownership for four-year hedge maturities.

                                  [Place Table 10 about here]

       While speculative cash flows are not a perfect measure of speculation (since they arise

from the product of speculation and price), they have the benefit of allowing us to obtain an

aggregate measure across the five hedging maturities. Using selective hedging cash flows as a

measure of aggregate speculation by our sample firms, we repeat our analysis of the

relationship between speculation and compensation, and speculation and insider ownership.

The results are reported in Table 11.

                                  [Place Table 11 about here]

       We find no significant relationship between selective hedging cash flows and

managerial compensation measures. In contrast, we find a positive relationship between

selective hedging cash flows and insider ownership after controlling for size. This finding is

interesting, especially when viewed in conjunction with our finding in Table 10 of a

significant negative relationship between insider ownership and speculation for one- and two-




                                              21
year hedge maturities. Noting that the bulk of speculation occurs at the one-year maturity, this

finding suggests that the presence of insiders deters firms from engaging in speculation and

reduces the losses that result from such speculation.



6.1 Discussion

       Overall, our findings on the relationship between speculation and managerial

incentives provide no support for (and indeed, contradicts) the notion that managers may be

speculating in their own self interest. Our finding that speculation decreases with the vega of

option holdings by both CEOs and CFOs directly contradicts the view that stock option

ownership may induce executives to speculate to increase volatility. Our finding that

speculation decreases with the delta of managerial stock and option ownership actually

suggests that rewarding managers through stock and options actually work to reduce their

incentives to speculate. This conclusion is supported by our finding for insider ownership.

Given that selective hedging adds no value, it is not rational for managers to speculate even in

their own self interest, and this is what our findings seem to suggest, that the presence of

insiders deters firms from engaging in speculation and reduces the losses that result from such

speculation.



7. Conclusions

       There is considerable evidence that firms use derivatives to speculate, but the gains

from speculation appear to be small at best. This raises the puzzle of why managers commit

time and resources to an activity that does not appear to increase shareholder value. We

examine this puzzle by studying the North American gold mining industry. This industry is




                                               22
likely to satisfy the conditions stipulated by Stulz (1996) for rational selective hedging that

maximizes shareholder value. However, we find that small firms are more active speculators

than large firms. This is surprising because small firms are less likely than large firms to have

an information advantage and thus be able to beat the market. Furthermore, small firms are

less able to bear the additional risks of selective hedging than large firms. We find a positive

relation between the probability of financial distress and the likelihood of speculation,

consistent with an agency-theoretic explanation of corporate speculation. Nonetheless, this

finding fails to explain the speculation undertaken by the bulk of the firms in our sample,

which are financially sound and far from bankruptcy. Our findings on the relationship

between speculation and managerial incentives provide no support for (and indeed,

contradicts) the possibility that managers may be speculating in their own self interest. We

find that rewarding managers through stock and options, and also insider ownership of the

firm’s shares actually work to reduce managerial incentives to speculate.

       Since our findings show that neither shareholders nor managers benefit from selective

hedging, our study renews the challenge of explaining this behavior from a rational value-

maximizing standpoint. Our overall results point to the remaining possibility for selective

hedging highlighted by Stulz (1996) that managers hedge selectively because they

erroneously believe that they can outperform the market. Our findings in support of this

possibility also raise many new questions that have relevance for both academics and

practitioners, especially from the standpoint of corporate governance and behavioral finance.




                                               23
Appendix A: Identifying hedge ratio components and cash flows attributable selective
hedging8


           Consider a commodity producing firm that sells a fraction (the “hedge ratio”) of its

expected future production forward at the forward price of F(t,T). The hedge ratio for

production sold x years forward can be expressed as:

                                                Portfolio delta ( x  year contracts )
                   x  year hedge ratio                                                ,
                                               Expected production ( x years ahead )

where portfolio delta is the weighted sum of the deltas of the individual derivatives positions.9

           In our gold sample, x = 1, 2, 3, 4, 5.

           The firm will be considered a “pure hedger” if it changes its hedge ratios only in

response to changes in fundamental drivers of hedging, such as leverage or liquidity.

Alternatively or in addition to hedging due to fundamental reasons, it is also possible for a

firm to hedge “selectively” by varying its hedge ratios over time due to changes in its

expectation of the future spot price relative to the forward price that is currently observed in

the market. Such a firm would reduce its hedge ratio if it increases its estimate of the future

spot price relative to the forward price and vice versa.

           Hedge ratios and cash flows attributable to a firm’s derivatives positions can be

separated into two components:

           i.      a component attributable to pure hedging.

           ii.     a component attributable to selective hedging.

           Adam and Fernando (2006) utilize a Cragg (1971) two-stage regression model to

identify the hedge ratio component that is attributable to a pure hedging rationale. The


8
    Based on Adam and Fernando (2006).
9
    See Tufano (1996) and Adam and Fernando (2006) for further details.


                                                       24
predicted values from these regressions provide estimates of hedge ratios that firms would

maintain under a pure hedging strategy. The differentials between the actual hedge ratios

maintained by the firm and the predicted hedge ratios from the regression model provide an

estimate of the hedge ratio “residual” that can be attributed to selective hedging.

       The predicted hedge cash flow, i.e., the cash flow that the would have accrued to the

firm had it maintain the hedge ratios predicted by the regression model, is calculated by using

a firm’s actual derivatives portfolio but adjusting the number of contracts outstanding for each

instrument using

                                                       predicted hedge ratio
                            N predicted  N actual                          ,
                                                        actual hedge ratio

where N actual equals the actual number of contracts outstanding for each contract type while

N predicted is the number of predicted contracts for the corresponding contract type. The

predicted hedge cash flow is calculated using exactly the same procedure used to calculate the

total derivatives cash flow based on the actual number of contracts, described in Allen and

Fernando (2006). The selective hedge cash flow is the difference between the total derivatives

cash flow and the predicted hedge cash flow.




                                                       25
Appendix B: Estimation of compensation measures10



We compute the delta - sensitivity of the option value to a one percent change in the stock price

and the vega - sensitivity of the option value to a one percent change in the stock return volatility

- using the Black-Scholes option pricing model, as modified by Merton to account for dividend

payouts:

Call = Se-dT N(Z) – Ke-dT N(Z – σT 0.5 )                                             (A.1)

Delta = 0.01e-dT N(Z) S                                                              (A.2)

Vega = 0.01e-dT N’ (Z) ST 0.5                                                        (A.3)



where:

Z = (ln (S/K) + T (r - d + 0.5))/( σT 0.5 )

S = price of the underlying stock.

K = exercise price of the option.

T = time to maturity of the option (number of years).

d = dividend yield on the underlying stock.

r = risk-free interest rate.

σ = expected stock return volatility over the life of the option (annualized).

N( ) = standard normal cumulative density function.

N( )’ = standard normal probability density function.



We hand collect option holdings and in the money value of options from proxy statements for

gold producing firms for each year between 1989 and 1999. We compute the delta and vega

10
     Based on Core and Guay (1999)

                                                 26
measures for option holdings by CEOs and CFOs. We obtain S from Compustat as the end of

year stock price. We follow the methodology of Core and Guay (1999) to obtain K and T. More

specifically, we compute K in two steps: first, we divide the potential realizable value of options

by the number of options held at year-end, obtaining an average difference between the stock

price and the strike price. Then, we subtract this ratio from the stock price to get an average

strike price. We set T to 7.5 as suggested by Core and Guay (1999) for cases in which option

maturity is unavailable. We obtain dividends paid by the firm through Compustat. r is the

Treasury bond yield to maturity, from CRSP as quoted at the firm's fiscal year end. Since we set

T to 7.5, the closest available bond maturity is the seven-year bond. We compute stock return

volatility with weekly returns from Compustat and Datastream adjusted for distributions and

stock splits. We compute delta and vega for the average option grant using equations (A.2) and

(A.3) and then multiply them by the number of options held by the executive. We compute the

delta of the executive shareholdings as the number of owned shares multiplied by one percent of

the stock price at the end of the fiscal year. The vega of the shareholdings is assumed immaterial,

consistent with Coles et al. (2003). We obtain the delta of the executive compensation as the sum

of the delta of the options and the delta of the shareholdings. We obtain the vega of the executive

compensation as the sum of the vega of the option holdings of the executive. For speculation in

year t we use compensation data from proxies issued in year t, which correspond to

compensation data on t-1.




                                                27
References

Adam, T.R. and C.S. Fernando, 2006, “Hedging, Speculation and Shareholder Value,” Journal
of Financial Economics 81, 283-309.

Beber, Alessandro and Daniela Fabbri, 2006, Who times the Foreign Exchange Market?
Corporate Speculation and CEO Characteristics. University of Lausanne and FAME Working
Paper.

Bodnar, G.M., G.S. Hayt and R.C. Marston, 1998 Wharton Survey of Derivatives Usage by U.S.
Non-Financial Firms, Financial Management 27(4), 70-91.

Brown, G.W., P.R. Crabb, and D. Haushalter, 2006, Are Firms Successful at Selective Hedging?
Journal of Business, forthcoming.

Campbell, T. and W. A. Kracaw, 1999, Optimal Speculation in the Presence of Costly External
Financing. In “Corporate Risk: Strategies and Management,” G. Brown and D. Chew, editors,
Risk Publications, London.

Core, John and Wayne Guay, 1999, The use of Equity Grants to Manage Optimal Equity
Incentive Levels, Journal of Accounting and Economics 28, 151-184.

Cragg, J., 1971, Some Statistical Models for Limited Dependent Variables with Application to
the Demand for Durable Goods, Econometrica 39, 829-844.

DeMarzo, P. and D. Duffie, 1995, Corporate Incentives for Hedging and Hedge Accounting,
Review of Financial Studies 8, 743-772.

Diamond, D.W. and R.E. Verrecchia, 1981, Information Aggregation in a Noisy Rational
Expectations Economy, Journal of Financial Economics 9, 221-235.

Dolde, W., 1993, The Trajectory of Corporate Financial Risk Management, Journal of Applied
Corporate Finance 6, 33-41.

Faulkender, Michael W., 2005, Hedging or Market Timing? Selecting the Interest Rate Exposure
of Corporate Debt, Journal of Finance 60, 931-962.

Faulkender, Michael W. and S. Chernenko, 2006, Why are Firms using Interest Rate Swaps to
Time the Yield Curve? Washington University at St. Louis Working Paper.

Froot, K.A., D.S. Scharfstein and J.C. Stein, 1993, Risk Management: Coordinating Corporate
Investment and Financing Policies, Journal of Finance 48, 1629-1658.

Géczy, Christopher, Bernadette A. Minton, and Catherine M. Schrand, 2006, Taking a View:
Corporate Speculation, Governance, and Compensation, Journal of Finance, forthcoming.




                                             28
Glaum, M., 2002, The Determinants of Selective Exchange Risk Management – Evidence from
German Non-Financial Corporations, Journal of Applied Corporate Finance, 14, 108-121.

Grossman, S., 1976, On the Efficiency of Competitive Stock Markets When Traders have
Diverse Information, Journal of Finance, 31, 573-585.

Huberman, G. and G. W. Schwert, 1985, Information Aggregation, Inflation and the Pricing of
Indexed Bonds, Journal of Political Economy, 93, 92-114.

Mello, A. and J. Parsons, 2000, Hedging and Liquidity, Review of Financial Studies 13, 127-153.

Smith, C., and R.M. Stulz, 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.

Stulz, R.M., 1990, Managerial Discretion and Optimal Financing Policies, Journal of Financial
Economics 26, 3-27.

Stulz, R.M., 1996, Rethinking Risk Management, Journal of Applied Corporate Finance 9, 8-24.

Tufano, P., 1996, Who Manages Risk? An Empirical Examination of Risk Management
Practices in the Gold Mining Industry, Journal of Finance 51, 1097-1137.




                                              29
Figure 1: Median Differentials between Actual and Predicted Hedge Ratios, 1989-1999
                                                             (One-year hedge maturity)




                          0.2

                        0.15

                          0.1
Hedge Ratio Residuals




                        0.05

                           0

                        -0.05

                         -0.1

                        -0.15

                         -0.2
                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12

                              06

                              12
                           89

                           90

                           90

                           91

                           91

                           92

                           92

                           93

                           93

                           94

                           94

                           95

                           95

                           96

                           96

                           97

                           97

                           98

                           98

                           99

                           99
                         19

                         19

                         19

                         19

                         19

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                         19

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                         19

                         19

                         19

                         19

                         19

                         19

                         19

                         19

                         19

                         19

                         19

                         19

                         19
                                                                         Time




                                                                    30
Figure 2: Percentage of Selective Hedgers, 1989-1999



                                  60%



                                  50%
Percentage of Selective Hedgers




                                  40%



                                  30%



                                  20%



                                  10%



                                  0%




                                                                                                                                                           1997
                                                                                                                                                                   1998
                                                                                                                                                                          1998
                                                                                                                                                                                 1999
                                                                                                                                                                                        1999
                                         1989
                                                1990
                                                       1990
                                                              1991
                                                                     1991
                                                                            1992
                                                                                   1992
                                                                                          1993
                                                                                                 1993
                                                                                                         1994
                                                                                                                 1994
                                                                                                                        1995
                                                                                                                               1995
                                                                                                                                      1996
                                                                                                                                             1996
                                                                                                                Year                                1997

                                        Maturity 1                   Maturity 2                   Maturity 3                      Maturity 4                      Maturity 5




                                                                                                        31
Table 1. Summary Statistics of Firm, Hedging, and Executive Compensation Characteristics.


This table presents summary statistics for firm, hedging, and executive compensation characteristics. Panel A
presents statistics for firm characteristics. Log (firm size) is the log of the market value of assets. Herfindahl
Index measures each firm’s concentration in gold mining as determined by books assets allocated to gold
mining versus other business segments the firm may be involved in. Dividend dummy is a dummy variable that
is equal to one if the firm paid dividends in year t and zero otherwise. Leverage is the leverage of a firm using
book values. Panel B presents statistics for hedging characteristics. Hedge ratio is the percentage of production
hedged into the future. Speculation is the absolute value of the actual hedge ratio minus the predicted value
(using the Cragg model). Panel C presents statistics for measures of executive compensation. Log (Delta of
compensation of CEO/CFO) is the log of aggregate delta of option and stock holdings for CEOs/ CFOs. Vega
CEO (CFO) is the aggregate vega of option holdings for CEOs (CFOs). Log (insider) is the log of the value of
stock holdings of insiders as a group, i.e., executives and board directors.

Panel A: Firm Characteristics
                                                     No. Obs.        Mean          Median           Std. Dev
log (firm size)                                        534           5.5867         5.4581           1.7537
Market to Book Ratio                                   534           1.8586         1.5641           1.1234
Herfindahl Index                                       578           0.9486         1.0000           0.1594
Dividend dummy                                         539           0.4323         0.0000           0.4959
Quick Ratio                                            531           3.6598         1.6178           8.5898
Leverage (based on book value)                         534           0.4039         0.1671           3.4906
Free Cash Flow                                         513          -0.0571        -0.0270           0.1343

Panel B: Hedging Characteristics
                                                     No. Obs.       Mean           Median           Std. Dev
Hedge ratio of production 1 year ahead                2000          0.3474         0.2295            0.4406
Hedge ratio of production 2 years ahead               2002          0.1875         0.0300            0.2859
Hedge ratio of production 3 years ahead               2020          0.0924         0.0000            0.1901
Hedge ratio of production 4 years ahead               2058          0.0423         0.0000            0.1221
Hedge ratio of production 5 years ahead               2077          0.0349         0.0000            0.1432
Speculation 1 year ahead                              1121          0.1018         0.0076            0.2373
Speculation 2 years ahead                             1270          0.0557         0.0000            0.1332
Speculation 3 years ahead                             1521          0.0331         0.0000            0.0865
Speculation 4 years ahead                             1741          0.0196         0.0000            0.0674
Speculation 5 years ahead                             1890          0.0185         0.0000            0.0904

Panel C: Compensation Characteristics
                                                     No. Obs.        Mean         Median            Std. Dev
Log (Delta of compensation of CEO)                     274          10.2445       10.0302            1.9721
Log (Delta of compensation of CFO)                     139           9.1782        9.5058            3.0420
Log (Vega of compensation of CEO)                      293           8.4939        8.9066            2.9067
Log (Vega of compensation of CFO)                      202           7.2826        8.0123            2.8142
Log (dollar value of insider ownership )               205          15.7774       15.6146            2.0597




                                                    32
Table 2: Likelihood of Hedging and Firm Size


Panel A presents the logit regression results of the likelihood that a firm is a hedger. The
dependent variable is a dummy variable that is equal to one if the firm hedges at time t.
Figures in parentheses denote t-statistics. In Panel B, the predicted likelihood that a firm is a
hedger is estimated and summary statistics are presented.

Panel A: Logit regression results
                      1-year          2-year          3-year         4-year           5-year
                     Hedging         Hedging         Hedging        Hedging          Hedging
                     Dummy           Dummy           Dummy          Dummy            Dummy
                    0.3218***       0.4163***       0.3974***      0.4557***        0.4402***
Log (firm size)
                      (5.06)          (6.99)          (6.89)         (7.20)           (6.20)
Pseudo R2             0.0475          0.0821          0.0778         0.095            0.0843
Chi sq.-value          27.91           56.24          53.43          59.39            43.07
N                       498             502             504           515               518
*** denotes significance at the 1% level.

Panel B: Predicted likelihood of hedging
                      1-year          2-year          3-year         4-year           5-year
                     Hedge           Hedge           Hedge           Hedge           Hedge
                     Dummy           Dummy           Dummy           Dummy           Dummy
Mean                   0.72            0.57            0.42            0.3             0.19
Median                 0.73            0.57             0.4           0.26             0.16
Std. deviation         0.11            0.16            0.16           0.15             0.12
N                      498             502             504            515              518




                                               33
Table 3: Magnitude of Hedging and Firm Size


Panel A presents the regression results of hedging activity as a function of firm size. We estimate the
following regressions: hedge ratio = a + b*X + e. The dependent variable is the percentage of production that
a firm hedges at time t. Figures in parentheses denote t-statistics. In Panel B, the predicted percentage of gold
hedged is estimated and summary statistics are presented.

Panel A: OLS regression results
                        1-year              2-year            3-year              4-year             5-year
                     Hedge ratio         Hedge ratio        Hedge ratio        Hedge ratio        Hedge ratio
                      0.0365***          0.0359***          0.0205***           0.0092***          0.015***
Log (firm size)
                        (4.00)             (4.95)             (4.77)              (3.48)             (4.93)
R2                      0.0313             0.0448             0.0433              0.023              0.045
F-value                  16.03              24.47              22.73              12.14              24.29
N                         498                502                504                515                518
*** denotes significance at the 1% level.

Panel B: Predicted hedge ratios
                        1-year              2-year            3-year              4-year             5-year
                     Hedge ratio         Hedge ratio        Hedge ratio        Hedge ratio        Hedge ratio
Mean                    0.296               0.155              0.078              0.034              0.029
Median                  0.292               0.151              0.076              0.033              0.027
Std. deviation          0.063               0.063              0.036              0.016              0.026
N                        498                 502                504                515                518




                                                       34
Table 4: Speculation and Firm Size


This table presents the OLS regression results of speculatve activity as a function of firm characteristics. We estimate the
following regressions: Speculation = a + b*X + e if firm is a hedger in period t where speculation is measured by the
standard deviation of actual hedge ratios. The dependent variable is the percentage of production that a firm speculates at
time t. Figures in parentheses denote t-statistics.



                          1-year               2-year                3-year             4-year               5-year
                        Speculation          Speculation           Speculation        Speculation          Speculation
Log (firm size)     -0.03*** -0.035*** -0.027*** -0.035*** -0.01*** -0.02*** -0.006 -0.01***            -0.006    -0.009
                     (-3.35) (-4.94)     (-5.30)   (-7.86) (-3.25) (-5.03) (-1.08) (-2.88)              (0.52)    (-1.28)
4-quarter average
Hedge ratio                   0.474***               0.281***             0.23***            0.564***            0.626***
                               (14.96)                (10.67)              (8.54)             (12.35)             (12.36)
R2                   0.0311    0.4104     0.0858      0.3385     0.0472   0.2903    0.0079    0.5130    0.0029    0.6277
F-value               11.20    121.10      28.04       76.26      10.59   43.56      1.17     77.41      0.27     76.72
N                      351       351        301         301        216      216       150       150       94        94
*** and ** denote significance at the 1% and 5% level respectively.




                                                            35
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