Why Firms Use Non-Linear Hedging Strategies

Transcription

1 Why Firms Use Non-Linear Hedging Strategies Tim Adam Hong Kong University of Science & Technology January 2003 Abstract This paper examines how firms hedge, what instruments firms use and whether there are systematic differences between firms adopting different risk management strategies. I find that the decision to use non-linear hedging strategies (options strategies) is mostly a function of market conditions and to a lesser extent due to the non-linearity of the exposure. Consistent with Stulz (1996), larger firms are more likely to incorporate a market view in their risk management programs and use asymmetric hedging strategies (buy or sell options). Financially less constrained firms are more likely to buy options, while financially more constrained firms are more likely to sell options. This result is consistent with the hypothesis that financial constraints affect firms discount factors, and hence their hedging decisions. Finally, if market volatility is high firms are less likely to choose option strategies. This is consistent with the fact that option strategies expose a firm to volatility risk, which may be undesirable. JEL Classification:G32 I would like to thank Greg Brown, Kalok Chan, Gunter Dufey, Joseph Fan, Charles Hadlock, David Haushalter, Tim Opler, Peter Tufano and seminar participants at the University of Michigan, the Hong Kong University of Science & Technology, and Nanyang Technological University of Singapore for valuable comments and suggestions. I claim responsibility for any remaining errors and omissions. I am also grateful to Ted Reeve for providing me with his derivatives surveys. Contact information: Department of Finance, HKUST, Clear Water Bay, Kowloon, Hong Kong, Tel.: (+852) , Fax: (+852) , adam@ust.hk 1

2 Why Firms Use Non-Linear Hedging Strategies Abstract This paper examines how firms hedge, what instruments firms use and whether there are systematic differences between firms adopting different risk management strategies. I find that the decision to use non-linear hedging strategies (options strategies) is mostly a function of market conditions and to a lesser extent due to the non-linearity of the exposure. Consistent with Stulz (1996), larger firms are more likely to incorporate a market view in their risk management programs and use asymmetric hedging strategies (buy or sell options). Financially less constrained firms are more likely to buy options, while financially more constrained firms aremorelikelytoselloptions. Thisresultisconsistentwiththehypothesis that financial constraints affect firms discount factors, and hence their hedging decisions. Finally, if market volatility is high firms are less likely to choose option strategies. This is consistent with the fact that option strategies expose a firm to volatility risk, which may be undesirable. 1 Introduction The existing empirical literature on corporate risk management has examined three main questions: Why do firms hedge, 1 what determines the extent of hedging, 2 and what are the effects of hedging? 3 This paper extends this literature by analyzing a fourth question: how do firms hedge? What hedging instruments do firms use and why? In particular, this paper investigates why some firms use linear hedging strategies (e.g. forwards only) while others use non-linear hedging strategies (options), and how firms that rely on non-linear strategies choose between hedging portfolios 1 See Nance, Smith and Smithson (1993), Mian (1996), Dolde (1996), and Géczy, Minton and Schrand (1997). 2 See Tufano (1996), Haushalter (2000), Allayannis and Ofek (2001), and Graham and Rogers (2002). 3 See Tufano (1998), Guay (1999), Barton (2000), Allayannis and Mozumdar (2000), Adam (2002a), and Allayannis and Weston (2001). 2

3 that have convex, concave, or collar payoff profiles. 4 These questions are interesting because understanding how firms structure their hedging portfolios can give clues as to why firms hedge in the first place. A number of theoretical models have been developed to addressed the question of why options are necessary to hedge an exposure optimally. For example, Adler and Detemple (1988), and Moschini and Lapan (1995) show that if hedgeable and non-hedgeable risks are correlated, then the optimal hedging portfolio is non-linear, i.e. contains options. Brown and Toft (2002) extend this result and show that even if hedgeable and non-hedgeable risks are uncorrelated the optimal hedging portfolio can be non-linear. Adler and Detemple (1988) show that borrowing and short-selling constraints also give rise to a demand for options. Moschini and Lapan (1992) consider a firm s option to choose certain production parameters after product prices are observed. Assuming hedging is desirable, hedging this production flexibility option optimally requires non-linear hedging instruments. Froot, Scharfstein and Stein (1993) show that if a firm s future capital requirement is a non-linear function of some risk exposure, then options may be necessary to achieve the value-maximizing hedge. 5 Common to all of these papers is the focus on the decision to use linear versus non-linear hedging strategies, and the insight that if the exposure is non-linear, then non-linear instruments are necessary to obtain the optimal hedge. Franke, Stapleton and Subrahmanyam (1998) extend the literature by explaining 4 For the purpose of this paper a hedging strategy or instrument is said to be linear if the payoff of the strategy/instrument at maturity is a linear function of the underlying asset. A hedging strategy/hedging instrument is said to be non-linear if the payoff of the strategy/instrument at maturity is a non-linear function of the underlying asset. For example, options have non-linear payoff functions and are therefore classified as non-linear instruments. 5 To illustrate this point, consider a gold mining company, which would develop an existing gold reserve only if the gold price were to rise above some threshold. In this case the firm would need to raise capital to build the mining facilities only if the gold price rose above the threshold but would have no financing needs if gold prices remained low. Since the exposure is non-linear, the firm would need a non-linear hedging strategy to hedge the resulting financing risk. 3

4 the choice between two non-linear hedging strategies. They show that risk-averse investors who are exposed to both hedgeable and non-hedgeable risks, buy options (a convex hedging strategy), while investors who are only exposed to hedgeable risk, sell options (a concave hedging strategy). The intuition is similar to Leland (1980), who shows that agents whose risk tolerance increases with income, purchase portfolio insurance from agents whose risk tolerance increases less rapidly. Brown and Toft (2002) show that firms use convex hedging strategies if price and quantity risks are negatively correlated while they use concave hedging strategies if price and quantity risks are positively correlated. Finally, Adam (2002a) extends Froot, Scharfstein and Stein s (1993) theory of corporate risk management, and demonstrates that the cost differential between internal and external capital, a measure of the magnitude of a firm s financial constraints, affects its choice between convex, concave, and collar hedging strategies. If the cost differential is small, a firm hedges primarily to reduce the likelihood of a cash shortfall in the future. This can be achieved by buying options (a convex strategy). If the cost differential is large, a firm focuses mostly on raising cash to meet current financing needs. The firm sells financial contracts that minimize credit risk. This can be achieved by selling options (a concave strategy). Firms in between these two extremes use hedging strategies that have both convex and concave elements, e.g. collar strategies. The purpose of this paper is to document how firms hedge, and to determine whether there are systematic differences between firms that use linear, convex, concave, or collar hedging strategies. Is the choice of hedging strategy driven primarily by firm fundamentals or by market conditions? To determine the payoff profiles of the hedging portfolios one needs to know the types of instruments used, the size and direction of the taken positions, and the respective delivery prices. Such detailed information about derivatives positions is usually not available, which may be the 4

5 reason why the question of how firms hedge has so far not been evaluated empirically. An exception is the gold mining industry. Gold mining firms publish sufficient details about their hedging portfolios in their annual reports. The unprecedented detail of this data is why the gold mining industry has been chosen for this study. A further advantage of this industry is that the sample consists of a relatively homogeneous group of firms with similar risk exposures. Differences in hedging strategies are therefore less likely simply the result of differences in exposures but more likely due to differences in certain firm characteristics. There are several other studies that have evaluated risk management strategies in the gold mining industry. Tufano (1996) and Adam (2002b) both analyze the determinants of the decision and the extent of hedging. Tufano assumes that firms hedge their future gold production and findsthathedgeratiosarehigheramongfirms that keep less liquidity, and are lower among firms that reward their executives with more stock options but with less shares of the company. Adam (2002b) finds that gold mining firms on average hedge their future capital expenditures, and that the extent of hedging depends positively on measures of financial constraints. In a second paper, Tufano (1998) studies the gold price exposure of a cross-section of gold mining firms, and finds that hedging has only a marginal effect on a firm s stock price sensitivity to gold prices. Petersen and Thiagarajan (2000) show that differences in operating cost structures can lead some firms to use financial hedges while it leads others to use operational hedges to mitigate gold price exposure. Finally, Brown, Crabb and Haushalter (2002) examine whether gold mining firms adjust their hedge ratios due to their expectations about future gold prices. The results in this paper show that the choice of hedging instrument is driven partly by firm fundamentals and partly by market conditions. For example, the decision to use non-linear hedging strategies appears to be mostly a function of market 5

6 conditions, i.e. the level of gold prices and gold price volatility, and to a lesser extent a function of firm fundamentals. Consistent with Stulz (1996), I find that large firms are more likely to incorporate a market view in their hedging programs and use asymmetric hedges. 6 Given the particular hedging problem of the sample firms the market view implicit in an asymmetric hedge is "The gold price will rise (will not fall) in the future." 7 I find that if the gold price is low firms are more likely to choose an asymmetric hedge. This result is consistent with the findings of Brown, Crabb and Haushalter (2002) that gold mining firms have superior forecasting ability with respect to the future gold price. Thus when the gold price is low they correctly anticipate on average that it will rise in the future. Furthermore, if market volatility is high firms are less likely to choose non-linear or asymmetric hedges. This is consistent with the fact that options strategies expose a firm to volatility risk, which may be undesirable. Regarding the questions who buys options (a convex hedging strategy) and who sells options (a concave hedging strategy), I find that firms that are more diversified, more highly levered, and pay dividends are more likely to use convex than concave strategies. In fact, the descriptive statistics show that convex hedgers are among the most creditworthy of firms and concave hedgers are among the least creditworthy of firms. These results are consistent with the hypothesis that the least financially constrained firms are mostly concerned with hedging the risk of a future cash shortfall (they buy options), while the most financially constrained firms are mostly concerned with raising funds to make up a current cash shortfall (they sell options). The remainder of the paper is organized as follows. Section 2 describes the data 6 A hedging strategy is said to be asymmetric if the payoff of the strategy at maturity is an asymmetric function of the underlying asset. For example, an option has an asymmetric payoff profile, while a collar has a symmetric payoff profile. 7 This statement will be explained in more detail in Section

7 sample and discusses the major risk management strategies used by gold mining companies in North America. Section 3 derives testable hypotheses, and contains the descriptions of variables used in this study. Section 4 presents the empirical results, and Section 5 concludes. 2 Risk Management Strategies in the Gold Mining Industry The sample firms are those firms that are included in the Gold & Silver Hedge Outlook from 1989 to The Gold & Silver Hedge Outlook is a quarterly survey conducted by Ted Reeve since December 1989, and published by Scotia Capital. The survey contains information on the derivatives positions of 118 gold mining companies and covers most firmsinthenorthamericangoldmining industry. Firms that are not included tend to be small and privately held corporations. Appendix A provides an example of the raw data. The industry focus implies that the sample firms share similar risk exposures. This turns out to be an advantage because differences in the observed hedging strategies should not be a mere reflection of differences in exposures, but are more likely a result of differences in certain firm-specific characteristics. In order to create a homogeneous group of firms that face similar risk exposures, firms whose primary business segment is not gold mining (SIC code 1040) are excluded. This exclusion applies only to FMC Corp. Appendix B lists all firms included in this study. Most financial data are obtained from the active, Canadian, and research tapes of the Compustat database. Financial data for firms included in the survey but not covered by Compustat are collected by hand from firms annual reports and 10-K forms. Operational data, such as production and reserve statistics, cash costs, etc. are also collected by hand from firms annual reports and 10-K forms. Financial 7

8 market data, such as gold spot and futures prices, interest rates, etc. are obtained from Datastream. Gold mining companies face two principal risk exposures: Price risk, which mostly consists of the exposure to gold prices, and production risk. In contrast to price risk, production risk can usually not be hedged or insured due to moral hazard or adverse selection. Gold price risk can be hedged, however, and the hedging of it is widespread. Between 1989 and 1998, on average only 35% of gold mining companies did not hedge (see last column in Table 1). Despite relatively similar risk exposures hedging strategies differ tremendously. To manage gold price risk mining firms have been using forwards and spot-deferred contracts, put and call options, and gold loans. 8 The resulting risk management portfolios have provided firms with payoff profiles that are linear, concave or convex functions of the future gold price, or payoff profiles that are neither convex nor concave (collars). Table 1 shows the relative importance of each strategy and how the distribution of hedging strategies evolved over time. In 1989, 63% of firms used linear strategies, but that number has converged to about 20% in more recent years. Since 1994, the majority of firmsthathedgeusenonlinear strategies. A collar, consisting of a put (long) and a call (short), is the most widespread hedging strategy using options, used by about 21% of firms. About 10% of firms use convex hedging strategies, while the remaining 7% use concave strategies. Until 1994, convex and concave hedging strategies played only a minor role, but have became more prevalent since In 1989, only 6% of firms used asymmetric hedging strategies, i.e. portfolios that contain either long puts or short calls (but not both), but this number has gradually increased to almost 30% in A spot-deferred contract is like a forward contract except that delivery can be deferred for several years at the discretion of the deliverer. If delivery is deferred, the new delivery price is set at the prior contract price plus the current contango premium. A gold loan is essentially a structured debt contract in which the borrower commits to repay the loan in ounces of gold. The cash flows of a gold loan can be replicated by a standard debt contract and a portfolio of forward contracts. 8

9 Firms did not usually adopt just one hedging strategy during the sample period, but switched strategies (ignoring no hedging) on average 1.6 times over the 10-year period, or once every 3 years. On average firms used 2 different hedging strategies over the sample period. Table 2 presents descriptive statistics on other hedging parameters such as the extent of hedging, 9 the average maturity of the hedging portfolio, the use of spotdeferred contracts, and the market value of the hedging portfolio. The average hedge ratio differs significantly depending on the hedging horizon. Firms that hedge, hedge on average 46% of their expected future gold production in the next fiscal year, 23% of their expected gold production 2 years ahead, and 11% of expected gold production 3 years ahead. The hedging horizon varies between one and up to ten years, but most firms hedge their gold production of the next 1 or 2 years only. The average maturity of the hedging portfolio is about 1.6 years and relatively stable over time. The use of spot-deferred contracts was relatively uncommon in the late 1980s and early 1990s. Their use peaked in 1993 and has since stabilized at about 40% of all linear hedge positions (excluding gold loans). The average market value of the hedging portfolio over the sample period is $2.87 per ounce of gold reserves. It tends to be positive if gold prices are falling and negative if gold prices are rising, implying that on average gold mining firms hedge rather than speculate. Given the average price of an ounce of gold of $356, or the average profit margin 10 of about $82, the market value of the hedging portfolio is relatively small, and is consistent with Tufano s (1998) finding that hedging does not materially affect the gold price exposure of gold mining stocks. 9 The hedge ratio is defined as the fraction of future gold production that has been hedged. 10 The profit margin is defined as the difference between the gold spot price and a firm s cash extraction costs per ounce of gold. 9

10 3 Hypotheses and Construction of Variables This section develops testable hypotheses, and discusses the construction of variables used in this study. The empirical analysis focuses on three questions: First, why do some firms use linear hedging strategies while others use non-linear strategies? Second, why do some firms use symmetric hedging strategies while others use asymmetric strategies? Third, among non-linear hedgers, why do some firms use convex strategies while others rely on concave or collar strategies? 3.1 The Choice Between Linear and Non-linear Strategies The papers mentioned in the introduction have shown that the optimal hedging strategy is non-linear if the risk exposure to be hedged is non-linear. A variety of factors can cause the risk exposure to be non-linear: borrowing or short-selling constraints, production flexibility, non-linear capital requirements, or the existence of non-hedgeable risks. Unfortunately, not all of these theories are testable because of data limitations. However, I will develop two main hypotheses: one based on Froot, Scharfstein, and Stein (1993), the other based on Brown and Toft (2002). Froot, Scharfstein, and Stein (1993) show that if external capital is costly firms have an incentive to match their cash inflows (internal cash) with their cash outflows (e.g. capital expenditures). If capital expenditures are a non-linear function of some underlying risk factor, then a non-linear hedging strategy would be necessary to obtain the optimal hedge. Capital expenditures in the mining industry are mostly caused by new mine developments and mine expansions. These expenditures are typically step functions, i.e. a firm will develop a new mine only if the gold price is above a certain threshold, and postpone or abandon the development if the gold price is below the threshold. 10

11 The larger a firm s investment program, the more likely is a mismatch between inflows and outflows, and the more likely does the non-linearity in expenditures matter. Thus, firms with relatively large investment programs should be more likely to use non-linear hedging strategies than firms with relatively small investment programs. Hypothesis 1: Firms with relatively large investment programs use nonlinear hedging strategies, while firms with relatively small investment programs use linear hedging strategies. I measure the relative size of a firm s investment program by two variables: the ratio of capital expenditures over net sales, and the ratio of capital expenditures over net plant, property and equipment. 11 If it is the case that firms effectively hedge their future capital expenditures then the size of a hedge should increase with a firm s future capital expenditures. Since high capital expenditures are most effectively hedged with non-linear strategies, the decision to use non-linear strategies should be correlated with generally higher hedge ratios. Thus, estimating the correlation between the decision to use non-linear versus linear hedging strategies and the size of the hedge (measured by a hedge ratio) can serve as a consistency check, even though it is not a direct determinant of the decision to use linear versus non-linear hedging strategies. 11 In 2000, I sent a survey to 120 mining and exploration companies in North America, of which 32 returned the survey. Among the respondents were 18 firms that did not use derivatives (mostly exploration companies), while 14 did use derivatives. Those firms cited "options offer more flexibility than forwards in designing an optimal hedge" as the second most important reason for using options. This statement is consistent with the hypothesis that firms use options to approximate some optimal non-linear hedging strategy. The survey also revealed firms hedging objectives. The majority of firms stated that (i) reducing volatility in cash flows, (ii) ensuring that internal cash is sufficient to finance capital expenditures, (iii) reducing the probability of financial distress, and (iv) ensuring that operations remain profitable even if metal prices decline were their primary or secondary hedging objectives. The majority of firms achieve those objectives by reducing the volatility in operating net cash flows or free cash flows. Thus, the survey indicates that cash-flow hedging, as suggested by Froot, Scharfstein and Stein (1993), is common in the mining industry. 11

12 Brown and Toft (2002) show that in the presence of non-hedgeable risks, or risks that for some reason are not hedged, a firm s total risk exposure is non-linear, so that the optimal hedging strategy is also non-linear. There are several risk exposures which gold mining companies face in addition to gold price risk: production risk, foreign currency risk, price risk due to the production of metals other than gold (silver, copper, zinc, etc.), and the risk of bankruptcy. Each one of these additional risk exposures potentially increases the non-linearity of a firm s total risk exposure and should therefore increase the likelihood that a firm adopts a non-linear hedging strategy. Hypothesis 2: Firms that face high levels of (additional) non-gold risk exposures are more likely to use non-linear hedging strategies, while firms that face low levels of non-gold risk exposures are more likely to use linear strategies. I use four variables to proxy for non-gold risk exposures. (i) Production risk is measured by the mean squared production forecast error defined by kx 2 µŷt,t+i y t+i, MSE t = 1 k i=1 y t+i where ŷ t,t+i denotes the production forecast of year t + i at time t, andy t+i denotes the actual gold production in year t + i. 12 (ii) Foreign currency exposure is measured by a dummy variable which equals one if the functional currency of a firm is not the U.S. dollar and zero otherwise. Firms which report their financial statements in say the Canadian dollar view the majority of their costs to be denominated in Canadian dollars. These firms are subject to foreign currency exposure because the gold price 12 Gold mining companies report these production forecasts in the derivatives surveys that are conducted by Ted Reeve from Scotia Capital. There are up to k production forecasts available at each point in time (k max =4). 12

13 is denominated in U.S. dollars. (iii) A firm s exposure to metal prices other than gold is measured by a Herfindahl index based on the values of the various metals a firm produces. This index is defined as follows. nx µ 2 si P n i=1 s, i i=1 where s i is the revenue contribution of each metal, and n is the total number of metals produced by the firm. A low index value indicates that a firm produces a variety of different metals, and hence is exposed to a variety of different metal prices. (iv) Finally, the risk of bankruptcy is measured by Altman s z-score (see Altman, 1968). Lower values indicate a higher risk of bankruptcy than higher values. The choice to use a non-linear hedging strategy may also be a function of market conditions such as the gold price and the gold price volatility. 13 For example, if the gold price is low firms cash inflows are low relative to their planned capital expenditures. This potentially increases the mismatch between cash inflows and outflows, and hence increases the likelihood that a firm will adopt a non-linear hedging strategy. 14 Hypothesis 3: When the gold price is low firms tend to use non-linear hedging strategies, while when the gold price is high firms tend to use linear hedging strategies. Non-linear hedging strategies expose firms to volatility risk, because the value of options depends on the volatility of the underlying asset. This additional risk exposure may be undesirable, and if sufficiently large, could cause firms to refrain from using options strategies. 13 The survey mentioned in Footnote 11 revealed that after "size of exposure" the most important determinants of instrument choice are market conditions, such as volatility, expected future spot prices, and liquidity of contracts. 14 Brown, Crabb and Haushalter (2002) also test for the effects of market conditions on hedging strategies. 13

14 Hypothesis 4: When the gold price volatility is high firms tend to use linear hedging strategies, but when the gold price volatility is low firms tend to use non-linear hedging strategies. 3.2 The Choice Between Symmetric and Asymmetric Hedging Strategies Symmetric hedging strategies are associated with risk management portfolios that have symmetric payoff functions (forwards and collars), while asymmetric strategies are associated with portfolios that have asymmetric payoff functions (long puts or short calls). Both types of strategies can provide effective hedges. The interesting feature about asymmetric strategies, however, is that they incorporate an implicit market view with respect to the future gold price. Suppose a gold mining firm wants to hedge its downside risk, and has to decide between shorting a forward and buying a put. Both strategies would satisfy the firm s hedging objective. The difference is that buying the put protects the downside at a fixed cost, while shorting the forward protects the downside at a contingent cost which increases as the gold price increases. If the firm s managers had no particular market view, and in the absence of any market frictions, the firm would be indifferent between the two contracts. However, if the firm s managers believed that the gold price were likely to rise, then shorting the forward would appear expensive, since the loss on the forward increases as the gold price rises. Therefore, the firm would prefer to lock in a fixed cost and hedge using the put (an asymmetric strategy). Thus, when a manager believes that gold prices are likely to rise in the future he/she should be more likely to use an asymmetric hedge Similarly, a manager who believes that gold prices are unlikely to fall in the future would prefer to sell calls rather than to short forwards, because the call option premium is larger than the expected gain on the forward contract. See Figure 1 for a graphical comparison between symmetric and asymmetric hedging strategies. 14

15 Hypothesis 5: When the gold price is expected to rise firms are more likely to use asymmetric hedging strategies. In addition to taking a directional view, asymmetric hedging strategies expose a firm to volatility risk because volatility affects the value of options. To the extent that this volatility risk is undesirable, high volatility would make asymmetric hedges less desirable or more costly. Hypothesis 6: When gold price volatility is high firms are less likely to use asymmetric hedging strategies. Stulz(1996)arguesthatlargeandhighlyprofitable firms have a comparative advantage in risk-taking, because of their greater capacity to bear risks. It follows from this argument that larger and more profitable firms are more likely to speculate, i.e. incorporate a market view in their hedging programs, and hence use asymmetric hedging strategies. Hypothesis 7: Larger and more profitable firms are more likely to use asymmetric hedging strategies. Firm size is measured by the log of the market value of assets and the log of the value of gold reserves, while profitability is measured by a firm s profit margin. 3.3 The Choice Between Non-Linear Hedging Strategies The three non-linear hedging strategies used in the gold mining industry are convex, concave and collar strategies. Convex strategies contain long positions of put options. They will generally lead to cash inflows if gold prices decline, but require the firm to pay the option premium. Thus, convex strategies not only shift cash flows across 15

16 states of nature but also across time - from the present to future periods. 16 Concave strategies contain short positions in call options, and hence have completely opposite cash flow effects. They will generally lead to cash outflows if gold prices rise, but lead to cash inflows in the present because the firm collects the option premium from selling the calls. Thus, concave strategies shift cash flows from future periods to the present. Collar strategies, which consist of long puts and short calls, represent a mix of these two strategies. Since convex and concave hedging strategies have completely opposite cash flow implications, both in the present and in the future, firms that adopt either strategy should differ systematically in their hedging objectives and possibly other firm characteristics as well. For example, selling gold forward or purchasing put options on gold both hedge a mining firm s downside risk. Selling gold in the forward market, however, implies that the firmgivesupitsupsidepotential,whichmanyfirmsviewasacost.thus,if a firm can afford it, i.e. if the firm has sufficient cash resources or is not financially constrained, it will at least partially hedge by purchasing puts. 17 If the financial condition is less strong, firms may finance the purchase of the puts by selling call options, and thus hedge using zero-cost collars. This strategy is still preferable to hedging with only forwards because the firm can retain some upside potential (for gold prices in between the strike prices of the puts and the calls). If a firm s financial condition is sufficiently weak it may be willing to give up much of its upside potential and raise cash by selling calls. 18 Selling call options on 16 In contrast, forward contracts shift cash flowsonlyacrossstatesofnaturebutnotacrosstime. 17 Firms that participated in the survey (see Footnote 11) cited that the most important reason for them to use options was that options allow one to protect the downside while maintaining some upside potential. 18 For example, in 1998, Kinross Gold Corp sold call options worth $2.1 million to partially pay for the acquisitions costs for Amax Gold. The following year, another year of major acquisitions, Kinross sold further calls worth $4.5 million. Other firms that have sold substantial call option positions include Cambior and IAM Gold. 16

17 gold is a cheaper way of raising cash than issuing regular debt in the presence of financial distress costs. This is because the call options that a mining firm writes contain less credit risk (due to the mining firm s inherent long position in gold) than a standard bond that raises an equivalent amount of cash. This discussion motivates the following hypothesis. Hypothesis 8: Firms use convex strategies if their financial constraints are relatively low. Firms use concave strategies if their financial constraints are relatively high. Firms with average financial constraints use collar strategies. Hypothesis 8 is also consistent with Adam (2002a) who showed that if financial constraints are binding then the payoff profile of the optimal hedging portfolio (convex, concave, or collar) is a function of a firm s cost differential between internal and external funds. This cost differential can be interpreted as a measure of the magnitude of a firm s financial constraints. To test this hypothesis it is necessary to construct measures of the magnitude of a firms financial constraints or its cost differential between internal and external capital. I use the following variables to proxy for a firm s cost differential between internal and external funds. Firm size: Gertler and Hubbard (1988), Whited (1992), and Fazzari and Petersen (1993) have argued that small firms are more likely to face borrowing constraints and hence face higher credit risk premia than large firms. 19 According to Myers and Majluf (1984) larger firms are also less likely to be subject to information asymmetries, and thus have a lower cost of external financing. Size is measured by two variables: the market value of assets and the value of a firm s gold reserves. The value of a firm s 19 For example, if there are fixed costs associated with security issuance then larger firms face lower issuance costs due to scale economies. 17

18 gold reserves also represents its maximum collateral value, and hence should have a direct relation with a firm s credit risk premium. Investment opportunity set: Growth and investment opportunities are more difficult to value than assets in place. Firms with a relatively high proportion of growth opportunities face more information asymmetries, and hence a higher cost of external capital than firms with fewer growth opportunities. In addition, asset substitution is an important issue at firms with many investment opportunities, which should cause lenders to demand a higher credit risk premium from borrowers. The market-to-book ratio of assets is widely used as a proxy for Myers (1977) notion of the mix of assets in place versus growth opportunities. 20 Onthenegativeside,the market-to-book ratio is also used as a performance measure, which might obscure its use as a proxy for information asymmetries. Diversification: Diversification measures a firm s access to a reliable internal capital market. According to Weston (1970), more diversified firms enjoy a larger internal capital market. Lewellen (1971) further argues that diversification increases a firm s debt capacity and hence reduces its financial constraints. In contrast, Jensen (1986) and Stulz (1990) discuss the costs of diversification, but Rumelt (1974) argues that the positive aspects dominate in related diversification. Thus, diversification should be negatively related to a firm s financial constraints. Diversification is measured by two Herfindahl indices: one based on the distribution of business-segment assets, the other based on the distribution of the values of metals produced. Firms that produce a variety of different metals enjoy more stable income streams than firms that produce only one metal. Multi-metal producers should therefore be able 20 Ialsoconsideredafirm s expensed and capitalized exploration expenditures (similar to R&D) as an alternative measure of growth opportunities. These expenditures, however, proved to be uncorrelated with the market-to-book ratio of assets and the real option measures used by Adam and Goyal (2002). Hence, exploration expenditures appear to be a poor proxy for acquired growth opportunities. 18

19 to attract better financing terms than single-metal producers (see also Lammont, 1997). Dividends: According to Lang and Stulz (1994) and Pratap and Rendon (1998) dividends proxy for current financial constraints because firms that pay dividends are less likely to face capital shortages than firms that do not pay dividends. Dividends are measured by a dummy variable that equals 1 if a firm paid cash dividends during the fiscal year and zero otherwise. A second variable, the dividend payout ratio, is defined by the ratio of cash dividends over net income. This variable has been used by Fazzari, Hubbard and Petersen (1988) to proxy for financial constraints. Profit margin:afirm s profit margin measures the relative difference between thegoldspotpriceandafirm s unit production costs (cash costs). It is calculated by (spot price - cash costs) / cash costs. The smaller this mark-up the less profitable are a firm s mining operations. Since profitability is one factor in lenders credit evaluations, a lower profit margin should be associated with a higher credit risk premium. Liquidity: Opler, Pinkowitz, Stulz and Williamson (1999) find that firms that have the greatest access to the capital markets, such as large firms and those with credit ratings, tend to hold lower ratios of cash to total non-cash assets. Kim, Mauer and Sherman (1998) show that the optimal level of liquidity increases with the cost of external financing. John (1993) argues that firms that are subject to higher financial distress costs hold greater amounts of cash. I therefore expect a positive relation between a firm s liquidity and its cost differential between internal and external capital. Liquidity is measured by a firm s quick ratio, which is defined as the ratio of cash and cash equivalents over short-term liabilities. Leverage: Kaplan and Zingales (1997) argue that the likelihood that a firm is financially constrained depends positively on its leverage. The gold mining industry, 19

20 however, is characterized by generally low leverage levels. The non-existence of debt at many smaller firms most likely signals that debt capital is too costly or even unavailable. The existence of debt at larger, more diversified firms signals that these firms are sufficiently creditworthy. 21 Therefore, I consider low leverage as a signal of a potentially high credit risk premium. Leverage is measured by the ratio of the book value of all liabilities over the market value of assets. 22 Credit rating: Barclay and Smith (1995) argue that firms with credit ratings are more likely to have access to the corporate bond market than non-rated firms. Furthermore, rated firms suffer from fewer information asymmetries than non-rated firms due to the rating process. Hence, the credit risk premium should be higher at non-rated firms relative to rated firms. Unfortunately, only 15% of the sample firms actually have a credit rating. Thus, a credit rating dummy is unlikely to provide much statistical power. In addition, credit ratings in the mining industry tend to be below investment grade. It is therefore not certain that having a credit rating implies better financing terms than having no rating. I nevertheless include a dummy variable in the analysis that equals one if a firm has a S&P senior-debt rating and zero otherwise. Table 3 summarizes all variables and the respective data sources. 4 Results Table 4 provides descriptive statistics of the 101 sample firms for which financial data was available. The two size measures, the market value of assets and the value of gold reserves, show that the gold mining industry consists of mostly small firms and a few 21 Zaheer H. Khan, from CBRS Inc., writes in Establishing Credit Ratings for Mining Companies, While senior companies could arrange financing through the issuance of bonds, debentures, notes or preferred shares, junior and medium sized companies are quite restricted in their ability to issue corporate IOUs. 22 Alternatively, leverage could be defined by the ratio of the book value of long-term debt over the book values of long-term debt and equity, or by the debt-equity ratio. The empirical results were virtually identical, no matter what definition of leverage was used. 20

21 large producers. For example, firms market values of assets range from $5 million to about $11 billion. The median firm has a market value of $290 million and owns gold reserves valued at $47 million, while the mean values are $1,015 million and $401 million respectively. The two Herfindahl indices indicate that most gold mining firms are focused on gold mining activities only. The mean Herfindahl index based on asset segments is 0.96, while the mean Herfindahl index based on metals production is Profit margins are slim. The average profit margin over production costs (excluding noncash items such as depreciation, amortization and depletion) is 29%. Some companies are not even able to recover their cash production costs. Most gold producers maintain relatively low leverage levels, relatively high cash balances and pay no dividends, suggesting that many firms in the mining industry are financially constrained. The median debt-equity ratio is 0.18, while the median quick ratio is Furthermore, most gold mining firms have no credit rating (85%), and if they do their ratings tend to be below investment grade. However, reflecting the generally conservative financing policies, Altman s z-score indicates that most firms face a remote probability of bankruptcy in the short-term. Firms investment programs are substantial. The average firm spends 50% of its sales on capital expenditures. Finally, 45% of firms are subject to foreign currency risk because their functional currency is not the U.S. dollar. In summary, a typical gold mining firm is a fairly small enterprise, which focuses exclusively on gold mining and operates under a slim profit margin. To support its investment program it must raise external financing, mostly in form of equity. The average firm pursues a conservative financial policy, has no public debt outstanding, and pays no dividends. Table 5 provides descriptive statistics for firms grouped by the hedging strategy 21

22 they follow: no hedging, linear, convex, collar, or concave strategies. The firms that stand out most clearly at either end of the spectrum are convex and concave hedgers. Firms that use convex hedging strategies tend be the largest firms in the gold mining industry (as measured by the market value of assets) and own substantial gold reserves. They are among the most diversified firms, maintain the highest debt and lowest liquidity levels, are the most likely to have a credit rating and pay dividends. They also operate under the highest profit margins in the industry. In contrast, firms that use concave hedging strategies are among the least diversified firms in the industry, maintain the lowest debt and highest liquidity levels. They are among the least likely to pay dividends, and if they do pay dividends offer the lowest dividend payout ratios among firms that hedge. Firms that use collar or linear strategies do not distinguish themselves a lot. In fact, in many respects collar hedgers are similar to convex hedgers. Finally, firms that do not hedge tend to be the smallest firms in the industry. They are the least likely to have a credit rating, operate under the lowest profit margins, but are the most diversified in terms of the metals they produce. 4.1 The Choice Between Linear and Non-linear Strategies Section 3 hypothesizes that the choice between linear and non-linear strategies is affected by the magnitude of a firm s capital expenditures, as well as the existence of additional non-gold risk exposures. Each of these factors can cause the total risk exposure to be non-linear. Tables 6 and 7 contain the univariate and multivariate analyses One caveat in this study is that the sample is relatively small. Therefore the results are potentially more sensitive to changes in the sample size than in large sample studies. I address this problem in three ways. (i) All tests are performed with and without outliers. Outliers are defined as the extreme 1% of values for each variable. (ii) Variables that reduce the sample size significantly are excluded in robustness checks. (iii) All tests are performed on the full sample and the subsample which excludes marginal hedgers, i.e. firms that hedge less than 10% of output. Whenever a change in the sample size significantly affected the results, all results are reported. 22

23 Both the CAPX/sales and the CAPX/PPE ratios appear to be positively correlated with the decision to use non-linear strategies. However, in the univariate tests the difference between linear and non-linear hedgers is not statistically significant, and in the multivariate analysis the relation is not robust. On the other hand, firms that use non-linear hedging strategies hedge more, indicated by the higher hedge ratios. This is consistent with the view that firms hedge their future capital expenditures, as predicted by Froot, Scharfstein and Stein (1993), and that the size of the hedge increases with those expenditures. 24 The presence of non-gold risk exposures does not appear to increase the likelihood that firms use non-linear hedging strategies. Production uncertainty, non-gold metal price exposures (measured by the Herfindahl index), and the risk of bankruptcy (measured by Altman s z-score) are not correlated with the decision to use non-linear hedging strategies. Surprisingly, firms that are exposed to foreign currency risk are less likely to use non-linear strategies. One possible explanation for this result is that many firms hedge their foreign currency exposure separately, so that the dummy variable mostly picks up institutional differences between American and Canadian firms. Firms, which primarily operate in Canada are less likely to use more complex, non-linear hedging strategies. The two factors that have a significant impact on the decision to use non-linear hedging strategies are the gold price and the gold price volatility. If the gold price is low firms are more likely to choose non-linear strategies. At low prices firms cash inflows are low as well, which increases the difficulty of matching cash inflows with cash outflows. In this situation non-linear strategies may be preferable because they 24 The hedge ratio may be endogenous to a firm s decision to use linear versus non-linear hedging strategies. The regressions in Table 7 have therefore been re-estimated excluding the hedge ratio. No significant change in the results was observed. Unfortunately, the data set is too small to estimate a simultaneous equations model. 23

24 can be tailored to a company s hedging needs, and in particular avoid the generation of additional cash inflows in states in which additional cash is not necessary. Finally, gold price volatility has a negative impact on the decision to use non-linear strategies. This is consistent with the view that volatility risk is an undesirable side effect of using non-linear strategies. 4.2 The Choice Between Symmetric and Asymmetric Hedging Strategies Section 3 explained that using an asymmetric hedge implies that a firm incorporates a specific market view in its hedging program. Stulz (1996) hypothesizes that large and highly profitable companies are the most likely to speculate in this fashion. The results, presented in Table 8 and 9, support this hypothesis. Larger firms, especially if measured by the value of a firm s gold reserves, are indeed more likely to employ asymmetric hedges than smaller firms. The coefficient on profit margin is insignificant, however. A further important determinant of the decision to use an asymmetric hedge are market conditions. Specifically, when the gold price and the gold price volatility are low, firms are more likely to use asymmetric hedges. Brown, Crabb and Haushalter (2002) found that gold mining firms have some forecasting ability with respect to future gold prices. If a relatively low gold price indicates that gold mining firms expect gold prices to rise in the future, then firms should prefer asymmetric hedges. The empirical results are consistent with this prediction. Thenegativecoefficient on the gold price volatility again suggests that volatility risk reduces the attractiveness of using options strategies in general. Therefore, if volatility is high firms are less likely to use asymmetric hedges. 24

25 4.3 The Choice Between Non-linear Hedging Strategies Section 3 hypothesizes that the choice between convex, collar and concave hedging strategies is a function of the cost differential between internal and external funds. In particular, firms that use convex strategies have a lower cost differentials than firms that use concave strategies. Firms that use collar strategies are somewhere in the middle. Table 10 contains the multivariate results of ordered probit regressions of the hedging strategy variable which is coded as follows: convex strategy (2), collar strategy (3), and concave strategy (4). One problem with the multivariate analysis is that many regressors are highly correlated with each other, as evidenced in Table 12. Such correlations can significantly and unpredictably bias the regressions results. To reduce this problem I perform the estimation on various subsets of the regressors. Since regressions (3) and (6) contain almost all regressors the results should be interpreted with caution. Overall, the most important determinants of a firm s choice of non-linear hedging strategies appear to be its dividend policy, capital structure and the level of diversification. Firms that pay cash dividends and firms that are highly levered are more likely to use convex than concave hedging strategies. The same holds for diversified firms, i.e., firms that operate in non-mining business segments. If dividend policy, capital structure and diversification adequately proxy for financial constraints in the mining industry, then the multivariate results support the hypothesis that firms that are financially constrained and thus face a larger cost differential between internal and external financing tend to adopt concave hedging strategies, while firms that are less financially constrained and hence face a smaller cost differential tend to adopt convex hedging strategies. All regressions in Table 10 were also estimated including 25