Gold options, an attractive investment instrument for the
non-U.S. investor : the case of the Belgian and Dutch investor
Citation for published version (APA):Beckers, S., & Soenen, L. A. (1983). Gold options, an attractive investment instrument for the non-U.S. investor : the case of the Belgian and Dutch investor. De Economist, 131(1), 80-87.
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DE ECONOMIST 131,NR. 1, 1983
G O L D O P T I O N S , AN A T T R A C T I V E I N V E S T M E N T I N S T R U M E N T F O R T H E NON-U.S. I N V E S T O R - T H E C A S E
OF T H E B E L G I A N A N D D U T C H I N V E S T O R
BY
STAN BECKERS* AND LUC A. SOENEN**
1 INTRODUCTION
Gold has always been an investment instrument whose popularity is closely linked to economic and political instability. In addition, every well-diversified portfolio will contain gold under some form or another (gold bars, Kruger- rands, stock in gold mining companies, gold indexed bonds, gold options,
etc.).
The value of these instruments is essentially linked to the spot price o f gold as set on the major commodity exchanges (London, Zurich, Chicago, Tokyo). The majority o f the transactions on these exchanges occur in U.S. dollars and it is probably fair to state that the gold price is determined by investors who use dollars as their base currency. This also means that, at least theoretically, the fate o f the U.S. dollar on the foreign exchange market and the gold price are closely linked. Any investor who manages his portfolio with a non-U.S, dollar base currency, therefore, has to take into account this linkage between the dollar and the gold price. In this article we empirically investigate the relationship between the strength o f the dollar and the gold price. The implications for (non-U.S. dollar denominated) portfolio manage- ment are studied. Special attention is given to the gold options market which recently opened up additional investment opportunities.2 THE GOLD PRICE AND THE STRENGTH OF THE DOLLAR
Since the price o f gold on the world market is set in U.S. dollars, its fate has been linked closely to the strength of the dollar on the foreign exchange market. It is usually argued that high U.S. dollar interest rates account for
* Barr Rosenberg and Associates, Berkeley, California.
** Eindhoven University of Technology, DePartment of Industrial Engineering and Management Science, Eindhoven, Holland.
GOLD OPTIONS 81
a strong dollar as investors bid up the dollar exchange rate to take advantage of much higher interest rates. At the same time, however, gold becomes less interesting as an alternative investment instrument since it has a zero yield. Following this argument a strong negative correlation should be observed between the return on gold and the strength o f the dollar. 1 Table 1 does in- deed show that the return on gold (in $) has on average a negative correlation of about -.40 with the U.S. dollar expressed in Belgian francs (BF) or Dutch guilders (FL). Foreign exchange losses therefore will alternate with all the gains a (non-dollar denominated) investor makes on gold investments (and vice versa). The effect is quite strong and persisted almost constantly from
1975 through 1981.
Given this strong negative correlation one would however also expect gold prices expressed in local currency (for instance Belgian francs or Dutch guilders) to behave more smoothly than gold prices expressed in U.S. dollars. Indeed any extreme up or down movement would be compensated by an opposite move in the exchange rate. It is therefore expected that the gold return distribution will read differently depending on the currency in which it is expressed. Table 2 verifies to what extent the distribution conforms to a
TABLE 1 - CORRELATION BETWEEN THE WEEKLY RETURN ON GOLD (IN $) AND THE WEEKLY RETURN ON THE U.S. $ EXPRESSED IN BF OR FL
Correlation coefficient Correlation coefficient gold - U$/BF gold - U$/FL
1 9 7 5 - . 4 8 3 * * * - . 4 4 1 * * * 1 9 7 6 - . 1 1 1 - A 4 1 1 9 7 7 - . 2 1 1 - . 3 4 7 * * 1 9 7 8 - . 5 3 2 * * * - . 8 5 9 * * * 1 9 7 9 - . 3 9 6 * * * - . 5 2 7 * * * 1 9 8 0 - . 3 9 4 * * * - . 4 4 2 * * * 1981 - . 5 2 4 * * * - . 5 4 9 * * * m e a n - . 3 7 9 - . 4 7 2
Note: * * * : significantly different from 0 at 99% level. ** : significantly different from 0 at 95% level.
1 The data for this study consisted o f the Friday closing gold price as q u o t e d on the International Money Market at the Chicago Mercantile Exchange. Exchange rates o f the U.S. dollar versus the Belgian franc and the Dutch guilder were provided by the Krediet- bank and the A m r o b a n k respectively. Our sample covers the period 1/1/75 through 12/31/81.
82 S. B E C K E R S A N D L.A. S O E N E N
T A B L E 2 - W E E K L Y R E T U R N D I S T R I B U T I O N O F G O L D E X P R E S S E D IN D I F F E R E N T C U R R E N C I E S
Ho : return distribution is normal - X 2 test used
$ FL BF
1975 *** *** accept
1976 *** accept ***
1977 accept accept accept 1978 accept accept accept 1979 accept accept accept
1980 *** ** accept
1981 ** accept accept
Note: *** reject H o at .5% level. ** reject H o at 1% level.
standard normal. It is immediately obvious that b o t h the gold return dis- tribution in F L and BF approached the normal more closely than the gold returns in dollars. It m a y therefore be concluded that the exchange rate c o m p o n e n t imbedded in the gold return distribution in non-dollar currency contributes to a m o r e ' n o r m a l ' behaviour.
Along the same lines it would also be expected that the variance o f the return distribution in F L and BF would be different from the variance o f the dollar denominated distribution. Table 3 compares the variances over time. The differences in the variances are statistically different at the 99% level. In addition, on average for a n y given year the variance o f the return in BF or F L is 10% less than the variance o f the return in dollars. Gold investments in BF or F L therefore tend to be less risky than gold investments in dollars.
T A B L E 3 -- V A R I A N C E O F W E E K L Y G O L D R E T U R N D I S T R I B U T I O N ( I N %) E X P R E S S E D IN D I F F E R E N T C U R R E N C I E S $ FL BF 1975 2.2402 2.049 1.9837 1976 2.4691 2.4418 2.6910 1977 2.2368 2.0998 1.6619 1978 2.9986 2.2236 2.1847 1979 3.7116 3.3627 3.0296 1980 7.6129 7.1892 7.4025 1981 3.3828 2.9318 3.049
G O L D O P T I O N S 8 3
A foreign investor who buys gold in his local currency implicitly assumes an exchange risk since the price of gold is determined in U.S. dollars. How- ever, the increased risk he implicitly assumes is more than compensated by the negative correlation between the dollar gold price and the exchange rate. His overall risk exposure is therefore smaller than that of an investor who uses the dollar as his base currency. In addition, at least historically, the gold price in foreign currency has behaved more 'normally' than the dollar gold price. In the next paragraph we briefly look into the problem of market efficiency.
3 E F F I C I E N C Y O F T H E G O L D M A R K E T
The efficiency of the gold market was studied in detail by Solt and Swanson (1981). They did not find any evidence that investors, before or after trans- action costs, could profitably exploit serial dependence in the return dis- tributions. Hence, if the dollar gold return distribution passes the weak form test, we would expect the BF and FL denominated distributions to pass the test as well unless the foreign-exchange market component introduces a pattern on which can be traded. Inspection of table 4 however confirms the hypothesis that all the return distributions essentially exhibit zero auto- correlation. There is therefore no evidence that a simple trading strategy based on autocorrelation in the return process may yield extraordinary returns. T A B L E 4 -- A U T O C O R R E L A T I O N C O E F F I C I E N T S O F T H E W E E K L Y G O L D R E T U R N D I S T R I B U T I O N E X P R E S S E D I N D I F F E R E N T C U R R E N C I E S $ FL BF 1975 .084 . 1 9 8 .145 1976 .214 .159 .211 1977 .191 -.114 .212 1978 .089 -.170 .044 1979 -.123 -.025 -.091 1980 -.306** -.245 -.370** 1981 -.016 -.090 -.062 Note: **significantly different from 0 at 95% level.
84 S. BECKERS AND L.A. SOENEN 4 IMPLICATIONS FOR THE GOLD OPTIONS MARKET
The European Options Exchange in Amsterdam started trading in listed options on gold on April 2, 1981. Both puts and calls are traded, and each contract covers 10 troy ounces of gold. The option prices are quoted in U.S. dollars and decimals per troy ounce. Following the traditional standardization procedures, the options expire at 2:00 p.m. (local time) on the third Friday of the expiration month (February, May, August, November). The striking prices are usually set at $25 intervals and the possibility to exercise is guaran- teed by the European Gold Options Clearing Corporation. Transaction costs amount to $10 per contract (round-trip) for orders of more than 10 contracts. If fewer than 10 contracts are traded, the round-trip cost may increase to $13 per contract.
The price of the gold option is directly determined by the spot price for gold (where the London fixing is used as the point of reference). Black and Scholes (1973) developed a seminal call option pricing formula under the assumption that the return distribution of the underlying asset follows an lognormal distribution. On the other hand no closed form solutions for the pricing of American puts are available. In general, however, the value of a call (put) will increase (decrease) with the price of the underlying asset. Since both the puts and calls are priced in U.S. dollars, an investor who used the FL or BF as a base currency will have to take into account the negative correlation between gold prices and the dollar exchange rate in evaluating his positions.
Specifically one would expect the return on a call in BF to be less than the return in dollars. The dollar call price increases with the price of gold but at the same time the dollar will tend to weaken on the foreign exchange market. Alternatively one expects the return on a put in FL to exceed the return in dollars since the dollar value of the put decreases with an increase in the gold price. The same line of reasoning can be applied to the riskiness of the option return depending on the currency in which it is expressed. Following the same argument the variance of the call return in BF or FL should be less than the variance in dollars. Similarly, the put expressed in BF or FL will be more risky than the put in dollars.
These hypotheses are tested in table 52 where the mean weekly returns and their standard deviations were computed for all options quoted on the European Option Exchange during the period 4/2/81 through 12/31/81.
2 The data for the gold options were collected from the European Options Exchange's daily official list.
G O L D O P T I O N S
T A B L E 5 -- W E E K L Y R E T U R N S O N C A L L S A N D P U T S E X P R E S S E D I N D I F F E R E N T D E N O M I N A T I O N S
8 5
CaUs
Exercise Mean Mean Mean St.Dv. St.Dv. St.Dv. Price Return Return Return
$ FL BF $ FL BF 375 - . 0 2 1 6 - . 0 2 6 8 - . 0 2 4 2 .1470 .1410 .1381 400 - . 0 2 8 0 - . 0 3 0 6 - . 0 3 5 6 .2534 .2456 .2421 425 - . 0 3 1 8 - . 0 9 2 2 - . 0 6 0 2 .2500 .2635 .2457 450 - . 1 0 6 8 - . 1 2 1 4 - . 1 1 7 0 .2862 .2763 .2732 475 - . 1 1 6 0 - . 1 2 5 8 - . 1 2 3 4 .2576 .2560 .2454 500 - . 1 4 8 0 - . 1 1 2 5 - . 1 1 0 2 .3096 .3491 .3494 525 - . 2 4 0 6 - . 1 8 8 5 - . 1 8 0 4 .3732 .3131 .3030 550 -.1700 - . 1 5 7 9 -.1705 .3595 .3722 .3409 Puts
Exercise Mean Mean Mean St.Dv. St.Dv. St.Dv. Price Return Return Return
$ FL BF $ FL BF 375 - . 0 2 7 0 - . 0 2 2 2 - . 0 2 8 7 .2854 .2551 .2872 400 - . 0 4 6 2 - . 0 5 1 7 - . 0 4 5 3 .2689 .2698 .2682 425 .0232 .0205 .0232 .2830 .2876 .2783 450 .0619 .0741 .0905 .2649 .2727 .2735 475 .0410 .0327 .0434 .2463 .2463 .2515 500 .0547 .0642 .0683 .2177 .2134 .2196 525 .0611 .0670 .0715 .1568 .1653 .1695 550 .0665 .0665 .0659 .1452 .1586 .1629
Since on average the gold price declined during this period it is not sur- prising that puts yielded positive returns whereas calls lost money. In general one can readily infer that indeed calls (puts) denominated in FL or BF had a lower (higher) return than their dollar denominated counterpart. Similarly, the corresponding standard deviation tended to be lower (higher). Table 5 convincingly shows that a put investor who does not use the dollar as his base currency incurs a greater risk (and a corresponding higher return potential) than his counterpart who has a dollar base. Alternatively a call investor will have a lower risk exposure (and lower return potential).
86 S. B E C K E R S A N D L.A. S O E N E N
5 C O N C L U S I O N
Although gold maintains its attractiveness as a 'safe' investment in periods of international turmoil, a potential buyer should seriously consider its return potential before committing himself. It turns out that the base currency he uses is a nonnegligible decision variable. Indeed, the gold price has historical- ly been showfi to vary inversely with the strength of the dollar on the foreign exchange market. In this article we investigate how this affects an investor whose base currency is the Belgian franc or the Dutch guilder. We show that the return distribution for gold in BF or FL behaves less erratically and con- forms closer to the normal distribution than the dollar returns. Somewhat surprisingly, a BF or FL investor also incurs less risk when investing in gold than his dollar counterpart.
Given that the recently established gold options market opens new op- portunities for investors to take levered positions in gold we also briefly looked into the implications of the negative correlation for option investors. It turns out that a BF or FL call investor will incur less risk (and has a lower return potential) than the corresponding dollar call investor. The reverse, however, is true for the puts.
Every BF or FL investor implicitly takes a foreign exchange position when he invests in gold. This article makes explicit the extent to which this add- itional foreign exchange risk should influence his decision process. It turns out that by ignoring this implicit exposure, the investor can seriously mis- judge the total risk he takes on.
6 S U M M I N G UP
Empirical evidence is given that the gold price has historically varied in- versely with" the strength of the U.S. dollar. The implication for the investor whose base currency is not the dollar, i.e. the Belgian franc or Dutch guilder, is that he incurs less risk when investing in gold than his dollar counterpart. For the recently established gold options market, the negative correlation between the return on gold and the strength of the dollar implies that a BF or FL call investor will incur less risk (and a lower return potential) than the corresponding dollar call investor. The reverse also holds for the put investor. This article makes explicit the extent to which the additional foreign ex- change risk should influence the decision to invest in gold (-options).
G O L D O P T I O N S 87
R E F E R E N C E S
Black, F., and M. Sch01es, ~The Pricing of Options and Corporate Liabilities,' Journal of Political Economy, 81 (1973) pp. 637-659.
Snedecor, G.W., and W.G. Cochran, 'Statistical Methods,' Ames, Iowa, U.S.A., 1968. Solt, M.E. and P.J. Swanson, 'On the Efficiency of the Markets for Gold and Silver,'
Journal of Business, 54 (1981) pp. 413-478.
Summary
G O L D O P T I O N S , A N A T T R A C T I V E I N V E S T M E N T I N S T R U M E N T F O R T H E NON-U.S. I N V E S T O R - T H E C A S E O F T H E B E L G I A N A N D D U T C H I N V E S T O R
Gold has always been an investment instrument whose popularity is closely linked to economic and political instability. Since gold transactions occur in U.S. dollars any investor with a non-U.S, dollar base currency will therefore assume exchange risk exposure. Empirical evidence is given that the gold price has historically varied inversely with the strength of the U.S. dollar. The investor whose base currency is n o t the dollar, i.e. the Belgian franc or Dutch guilder, incurs less risk when investing in gold than his dollar counterpart.
