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									                                                       2~   ~‘ ~‘—

           Graduate School of Business


              Research Paper No. 200


       John G. McDonald and Bruno H. Solnik

                   April 1974

                     GOLD MINING STOCKS:     AN ECONOMIC ANALYSIS, 1968-1974

                             John C. McDonald and Bruno H.    Solnik

       Gold has been a topic of universal interest among institutional and individual
investors in 1973 and 1974.       This paper analyzes the relationship between returns
on common stocks of gold mining companies and changes both in the price of gold
bullion in London and in the level of the stock market in the United States, with
an economic interpretation of the gold production process underlying gold stock
returns.    Since 1933 American citizens have not been permitted to own gold, except
in the form of jewelry and certain numismatic coins minted prior to 1933.1             The
results of this study indicate the extent to which gold mining stocks          ——   which .Amer—
icans may own   ——    represent viable   ~              for gold bullion in investors’
       From 1934 to 1968 the price of gold in dollars remained virtually unchanged
at $35 an ounce.       in March 1968 the “gold pool’s” controls on the market price of
gold were abandoned, as the two~tier price system was introduced, and from March
1968 to March 1974 the price of gold rose from $35 to $173 an ounce.           In April 1973
we examined the relationship of gold mining shares to gold and the stock market,
using the model reported in this paper,          Two sub—periods were analyzed:     1968 to
1971, when the gold price fluctuated in the $35—$44 range, and 1971 to March 1973,
when the gold price increased to $90 an ounce.          Our objective was to investigate
the basic structure of the gold share/gold and gold share/stock market relationships,
to use our empirical estimates as a toQl in predicting gold mining share returns in
the following year (April 1973 to March 1974), and then to wait until April 1974 to
see how well the predicted relationship of gold stocks to gold and the stock market
corresponded to the actual relationship in this one—year period.
       Using data available in April 1973 when the price of gold was approximately
$90 an ounce, we found that the relationship between gold stocks and gold and the
stock market appeared to have been different in the immediately preceding 24—month
period (April 1971 to March 1973) of relatively high and rising gold prices than in

    Graduate School of Business, Stanford University and at C.E.S.A., Paris, respec-
    tively. Support from a grant by the Dean Witter Foundation is gratefully

the 1968—1971 period of relatively low and stable gold prices.     Five months later,
with the price of gold near $100 an ounce in early September, we wrote an analysis
of the economics of gold production and summarized the estimated coefficients in the
model, based on data for the period April 1968 to March 1973.2     We then waited to
measure in “real time” the returns on a portfolio of gold mining stocks over the
year ending March 1974.
     Economists frequently argue about the “significance” of empirical findings,
with the essential issue being whether a model fairly represents a persisting
structural process or whether it is simply an artifact supported by a specific
sample of data.     Harvard political scientist Graham Allison emphasizes the importance
of prediction and action in the real world with     llison’s Pre~p~: “The best
simple—minded test of expertise in a particular area is the ability to win money on
a series of bets on future occurrences in the area.”     While the consistent “winning
of bets” in financial markets is not likely to result from mechanical use of any
model, we did find our model useful in forecasting gold stock returns over the test
year of this experiment, and in understanding the basic determinants of returns on
gold mining shares.
     The principal outcome of the analysis that follows is to show that this two—
variable model of the return—generating process for gold mining stocks was
remarkably robust in predicting the response of gold mining stock returns to the
gold price change (from $90 to $173 an ounce, a 92.2 per cent increase) and the
stock market return (minus 12.5 per cent) that actually materialized in the 12—month
period, April 1973 to March 1974.     The model described in this paper enables one to
make predictions of gold mining stock returns contingent on his forecasts of the
gold price and stock market return, where the latter were made outside the context
of this analysis.     (Our initial set of expectations in April 1973 included a 50
per cent increase in gold price and a 10 per cent return in the stock market in
the year April 1973 to March 1974.     We would stress that it is the structure of the
model and not our specific gold price and stock market forecasts in this instance
which concerns us in this paper.)     The model, together with the economic analysis
that goes with it, appears to provide a promising structure for the prediction of
gold stock returns implied by or consistent with any investor’s expectations of the
future price of gold and the stock market return in a forthcoming period.

                             I.   MODEL OF GOLD STOCK RETURNS

     This model relates the expected return on gold mining stocks to the return
(percentage price change) on gold and to the total return in the stock market.      In
reality it is obvious that the market return on an individual gold mining stock is a
complex function of many factors in the company, industry, nation, and the general
world economy.    Our model simply states that the return on gold mining equities
(the return—generating process) is a positive function of two variables:      the
change in the price of gold as it affects the value of mine output and existing ore
bodies, and the return on the stock market as it reflects the changes in the market
value of all other assets in the aggregate portfolio of risky assets:

                                   R   BG(RGI + Bs(RsI   ,                           (1)

where R is the total return (dividend yield plus capital gain) on a gold mining
stock or portfolio over one time period such as a quarter, RG is the return on gold

(percentage change in gold price), R5 is the return on the stock market return

(dividend yield plus percentage change in a market index).
     The coefficients B~and B5 represent the volatility or sensitivity of a gold

stock or portfolio with respect to gold prices and the stock market as a whole;
these coefficients are fundamentally related to the economics of gold mining in each
country~ as shown later in this paper.     The key point is that gold stock returns are
seen in this model to be ~             related not only to gold price changes but also
to stock market returns, once the gold price effect is accounted for in the model by
the R0 term.     Traditionally, discussions of gold mining stocks have emphasized the

negative correlation coefficient sometimes observed between price changes of gold
stocks and changes in the stock market index, as suggested in the following statement
published in 1972:     “When the trend of the market as a whole is definitely up, gold
stocks generally are weak and declining.     But during rapidly falling or ‘bear’
market conditions, the gold group usually makes strong gains.       •T1iis model and the
estimates of the coefficients demonstrate that this common impression was fostered
by the historically negative correlation between gold price changes and stock market
returns.   We would choose to emphasize that, once the impact of changes in the price
of gold has been explicitly recognized, gold mining stocks have been positively
related to the stock market.

     The evidence for 1968—1973, presented in the next section, shows that estimates
of these coefficients BG and B5 are indeed positive and correspond well to the

magnitudes expected after fundamental economic analysis of gold production and the
reaction of mining company earnings to changes in the price of gold.       As a result
we felt in 1973 that the model and the estimates of the coefficients reported here
provided a plausible initial basis for prediction of gold stock returns contingent
upon expectations   of gold price   changes and the stock market return   in 1973—1974.

                       II.   THE EMPIRICAL EVIDENCE AS OF 1973

Returns on Gold
     The nominal return on holdings of gold, denominated in dollars, was zero from
1934 to 1968, when the dollar—gold price was maintained at $35 an ounce; the nominal
return realized by actual investors in gold was negative, of course, after adjust-
ment for storage and insurance costs.      From 1968 to 1973 the nominal internal rate
of return on gold holdings was approximately 25 per cent a year, as the gold price
in dollars increased three—fold following the removal of controls by the “gold pool”
on the market price of gold.     The nominal internal rate of return on gold holdings
over the entire 1934—March 1973 period was approximately 2.5 per cent a year, as
gold rose from $35 to $90 an ounce.  The average short—term interest rate on U.S.
Treasury bills in the 1934—1973 period was 2.2 per cent.4 The realized mean return
on gold thus was slightly higher than the mean risk—free rate in the 1934—1973
period.   Comparing gold to commodities in general,we find that the average (com-
pounded) annual increase in the price of gold in the period 1934—1973 was approxi—
mately equal to the average increase in consumer prices     ——   on the order of 3 per
cent a year in the United States.      Obviously, the entire increase in gold price came
in the last 5 years of this long period, but the price of $9O.an ounce in 1973 was
roughly that which would have been attained if gold had increased in price at a
little less than 3 per cent per year every year for 4 decades, from an initial base
of $35 an ounce in 1934.
     Gold is viewed by individuals in many countries as an extraordinary hedge or
“store of value” because of its traditional ease of exchange for goods and services
in those relatively infrequent but unhappy states of the world (domestic war,
economic crisis, political upheaval) when financial claims such as common stocks
often have relatively less value or liquidity.5 In a general portfolio context,

gold’s attractiveness is associated with the relatively low correlation of returns
(percentage price changes in a series of periods) on gold to returns on other risky
assets in the world’s markets.    In the case of the United States, the correlation
coefficient between monthly returns on Standard and Poor’s 500 stock index and
monthly percentage changes in the price of gold in London was —0.08 in the period
1968—1973.    At a gold price of approximately $100 an ounce, the estimated value of
all gold bullion and coins held by individuals, corporations and national treasuries
was $165 billion.6 By comparison the market value of all publicly traded common
stocks was on the order of 10 times larger than this gold stock (approximately
$1,100 billion in total U.S. equities and $500 billion in other markets.)
        In terms of variability of monthly returns in 1968—1973, gold bullion return
fluctuations were roughly 31 per cent greater than stock market return fluctuations.
The standard deviation of monthly returns on Standard and Poor’s 500 stock index
was 3.87 per cent, and the standard deviation of London gold price changes was 5.07
per cent per month.     To the extent that total variability provides a measure of
risk, gold holdings were “riskier”    than the market portfolio of stocks reflected by
Standard and Poor’s 500 stock index.

Returns on Gold Mining Stocks
     Market returns to investors in gold mining equities were investigated in the
seminal work of S. H. Prankel of Oxford University.7 He estimated the average
annual return on shares of South African gold mining companies, which produce two—
thirds of the world’s total gold output, to be 4.0 per cent in the period 1935—
1963.  For the same period in the United States, Fisher and Lone estimated the
average annual return on New York Stock Exchange stocks to be 13.6 per cent.8 The
mean annual risk—free rate on U.S. Treasury bills in this 1935—1963 period was 1.3
per cent.  Note that the average annual return on long—term high—grade bonds in
the United States was 3.1 per cent in the 1935—1963 period of Frankel’s study.9
For this era of governmental controls on gold prices, these data suggest that the
long—run return to investors in gold mining stocks was higher than the risk—free
interest rate (and higher than realized returns on high—quality bonds), but ret4urns
on gold mining shares were lower than average returns on common stocks listed on
the New York Stock Exchange.     We judge these estimates to be representative of long—
term return relationships in the 1934—1968 era of controlled gold prices near $35
an ounce.     Our results for 1971—1973 suggest that the latter period differed sub-
stantially from these past long—term returns on gold equities.

Estimates from Model, 1968—1973
    We computed quarterly returns, including dividEnds and capital gains, for each
of 15 “gold stocks” in the sample, including 6 South African, 1 American and 7
Canadian mining companies, in addition to one closed—end investment company (ASA
Ltd.) with primary holdings of South African gold mining shares)° A “gold mining
share portfolio” was constructed, assuming equal dollar investment in each of these
15 stocks during 20 quarters in the period April 1968 to March 1973.       April 1968 was
chosen as the initial month of the analysis, following the end of direct governmental
controls on the market price of gold by the United States and other “gold pool”
nations in March 1968.     We divided our data into 2 subperiods:    April 1968 to March
1971, when the London gold price fluctuated between $35 and $44 an ounce; and April
1971 to March 1973, when the London gold price increased $90 an ounce.       The basic
motivation for splitting the 1968—1973 period was to examine the relationships under
the “old regime” of gold prices of $35—$44 an ounce and under the ~         regime” of
higher, freely--fluctuating gold prices.    Using these data, we estimated the coeffi-
cients in equation (2) which represents a regression form of the basic model in
equation (1), to which subscripts have been added to indicate the stock or portfolio
i and the time period t:

                             Ri1   a1 + BGIRGt + BSjRSt + u1~    .                   (2)

In this equation R11 is the total return on gold mining stock or portfolio I in

quarter t; R01 is the quarterly percentage change in London gold price; Rs~Is the

quarterly return on Standard and Poor’s 500 stock index including dividends; ui~is

a random error term; a1 is a constant; and B01 and Bsi represent the volatility

coefficients of returns on gold mining share or portfolio i with respect to gold
and stock market returns.     Quarterly periods were used rather than monthly, after
careful consideration of the loss of “degrees of freedom” occasioned by using so
few data points.   Monthly data in preliminary tests generally gave less significant
results than quarterly data.
     Estimates of the volatility coefficients for the gold mining share portfolio
and examples of two individual mining stocks are shown in Table 1.      Returns on the
gold mining share portfolio were found to be related to gold returns in both sub—
periods; estimates of       of 1.97 and 1.44 for the gold mining share portfolio

                                                     TABLE 1

                              Estimates of Volatility Coefficients, 1968—1973

                                            Model:       Equation (2)

                                 Period April 1968—March 1971    Period April 1971—March 1973
                               (Gold Price in $35 to $44 Range) (Gold Price in $40 to $90 Range)
                                          a      B0    Bs   R2 Average*
                               Average                                    a   B0     B5
                               Return                —       — Return

Gold Mining Stock Portfolio        .7     .00     1.97       0.04 .53     6.5    —.14 1.44     1.58   .82
                                         (,l0)**(3.O)        (.12)              (1.9) (4.3)   (1.2)


     Cginpbeil Red Lake           1.8     .02     2.61       —.16 .62     8.3    —.21 1.88     3.29   .67
     (Canadian mine)                     (.53)   (3.7)       (.41)              (1.6) (3.1)   (1.3)

     Free State Geduld            1.2     .01    1.11          .04 .52    3.8    —.11   .87   1.98   .70
     (South African mine)                (,%~). (1.7)        (.10)              (1,9) (3.4)   (~‘98)

Basic Variables in Model

     Gold Bullion (London)         .1                                    11,8

     Standard & Poor’s 500        2.1                                     2.2
          (New York)

     Arithmetic average, per cent per quarter.

**   Numbers in parentheses are t—ratios.

indicate that gold stocks tended to be more volatile than gold in both subperiods.
Returns on gold mining shares displayed no systematic relationship with the stock
market in the earlier period of gold prices in the $35 to $44—an—ounce range; how-
ever, gold mining share returns were systematically related to the stock market in
the 1971—1973 period, when the estimate      of Bs for our gold mining share portfolio

was 1.58.    All of the signs of the coefficients are positive, as expected, indicating
support for the relationship posited in equation (1).      The volatility estimates of
B0, but not B5, are significant In the usual statistical sense at the 95 per cent

level of confidence.
     The findings suggest that at higher gold prices and gold mine profitability,
gold mining share returns were positively related to stock market returns after
movements associated with changes in gold price were taken into account.        Casual
observation during this period led one to perceive a negative relationship between
gold mining shares and the stock market, as indicated by the bivariate correlation
coefficient between monthly returns on our gold mining share portfolio and Standard
and Poor’s 500 stock index of —0.177 in 1971—1973.      States of the world (current and
anticipated) which have had negative implications for the economy and the stock
market have often had positive implications for the gold price in dollars.
     The portion of the total variance in returns on the gold mining share portfolio
explained by returns on gold and the stock market was 53 per cent in 1968—19 71 and
82 per cent in l97l-~l973, as indicated in Table 1,     All of the estimates of vola—
1-ility with respect to gold price BG are higher for the earlier period of smaller

movements in gold price than for the latter period of large increases in gold price.
Three reasons for this finding,     to be explored below, are the effect of gold price
increases on mind production decisions as to ore grade extracted; gold stock
investors’ expectations     that part of the large increase in gold price was    transitory
rather than permanent; and the increasing significance     of the stock market factor.


     Returns on gold mining shares, either individually     or collectively   in our
industry portfolio   ,   generally had greater total variability than returns on gold
in London.   An indication of the relative variability of returns is given by the
standard deviations of monthly returns, which we computed for the two subperiods,
1968—1971 and 1971—1973 (in per cent per month):      London gold, 3.20 and 7.28;

Standard and Poor’s 500 stock index, 4.19 and 3.13; our gold mining share portfolio,
8.26 and 11.45; and Campbell      Red Lake Mines, 11.90 and 16.57.       In the 1968—1971
period of gold prices in the $35—$44 an ounce range, gold mining shares were signi-
ficantly related to gold with volatility greater than 1, however, mining equities
were not significantly related to the stock market in 1968—1971.        In this period
these gold mining stocks produced an average return higher than that on gold but
lower than that on the stock market index    ——    consistent with the long—run results
of Frankel discussed above.    For the period 1971—1973 in which gold prioe rose from
$40 to $90 ~nounce, gold mining share returns exh.~biteda positiye ~e1ationsh~p
both to gold returns and to stock market returns~ The average quarterly
returns in the latter period were 6.5 per cent for the gold mining share portfolio,
11.8 per cent for gold, and 2.2 per cent for the stock market index.

Gold Price, Mine Production, and Investor Expectations
     Financial interpretation of the coefficients may be made in the light 9f tradi-
tional valuation theory, where stock price is a function of expected future earnings
and dividends and a market rate of discount which is a function of risk.        One impli-
cation of this interpretation for equation (1) is that gold prices primarily affect
expected earnings, and that the stock market return primarily reflects the required
discount rate for gold mining shares.    With the dramatic increase in gold price in
1971—1973 many marginal high--cost mines became profitable, and many mining operations
supported by government subsidy in Canada, Australia, Rhodesia, Philippines and
Ghana, became viable business enterprises.        Many ore bodies which could not be mined
profitably at $35 an ounce became potentially profitable at higher gold prices.
With this increase in the profitability of gold mines above the break—even points,
the “similarity” of these common stocks with those of most manufacturing and service
companies was generally greater; hence we find it plausible that the stock market
factor was relatively more important in explaining gold mining share returns in 19 71—
1973 than in 1968—19 71.
     As the price of gold increased, the value of all gold ore bodies increased as
well; however, the impact on current and expected future earnings from gold mines
depended on the effect of gold price changes on production decisions.       For example,
in the case of the Canadian gold producer, Campbell Red Lake, we observed that the
elasticity of earnings per share with respect to gold price12 was 1.69 in the peri6d
1966—1972, reflecting the “operating leverage” that output price increases (relative
to labor costs) normally have on corporate earnings.        The volatility of share return
                                         —   10   —

with respect to gold price BG in Table 1 was 2.88 and 1.88 for Campbell Red Lake,

so that earnings volatility   and share price volatility      with respect to gold price
appeared to have roughly the same magnitude,          For the world’s major gold producers
in South Africa,   the response of corporate earnings to an increase       in gold price
is smaller, as South African companies are required by law to “mine to the average
grade.”13 In calculating the average grade of gold ore, these companies must
include the lowest grade ore that can be treated profitably at current output prices
and production costs, so that an increase in gold price leads to a decline in the
average grade assigned to an ore body, to the extraction of ore bearing less gold
per ton, and hence to lower gold output in the short run.14 Using one major South
African gold mine as an example, we estimated the elasticity of earnings per share
with respect to gold price for Free State Geduld to be 0.15, positive but less than
one, and statistically less significant than that of Campbell Red Lake)5 Corres-
pondingly, the volatility of share price with respect to gold price of Free State
Geduld, 1.11 in 1968—1971 and 0.88 in 1971—1973, was less than that of the Canadian
producer and less than one in the latter period.          Aggregate time series data by
country show that the output of gold from South Africa has generally varied inversely
with gold price, whereas gold output from the rest of the world has varied directly
with gold price.
     The finding that all estimates of BG were smaller in the 1971—1973 period than

In 1968—1971 in part reflects these production decisions and the increased importance
of the market factor, but it may also imply that investors viewed a portion of large
movements in gold price as transitory.       The relative (percentage) response of gold
mining share prices to large movements in gold price appeared to be smaller than
that observed for small increases in. gold price, evidence that investors may not
revalue proportionately the entire stream of expected earnings of gold producers
when gold price rises to historic highs.      A number of public statements by gold
mining company executives indicated their expectation that gold prices would decline
when the level reached $120 an ounce late in 1973.17          The term structure   of interest
rate provides a crude analogy, in the case where current short—term rate increases
exceed long—term rate increases.    Each gold mine has an expected life (e.g., 6 to
20 years for Free State Geduld), and gold mining share prices reflect implicitly a
                                                               life~ On occasions
stream of investors’ expected future gold prices over the mine~~
when large movements in gold price lead mining company officials and investors to
doubt that prices will be maintained at current levels over this expected life, one
                                           —   11   —

might expect to observe that gold mining share prices move proportionately less in
response to big changes than to small changes in current gold price.

                     IV.   ACTUAL VERSUS PREDICTED RETURNS, 1973—1974

     In the year April 1973 to March 1974 the return on gold was 92.2 per cent, as
the price of bullion increased from $90 to $173 an ounce, and the total return on
Standard and Poor’s 500 stock index was —12.5 per cent.           At the end of this 12—month
period, on March 31, 1974, we compared actual versus predicted returns (dividend
year plus capital gain) on the gold mining stock portfolio which comprised our
sample   .   Predicted returns were based on our estimates of volatility coefficients
which related the return on gold stocks to returns on gold bullion and the stock
market; these estimated had been made at the beginning of the year based on data for
the preceding period April 1971—March 1973.
     The actual return on the gold mining stock portfolio in the year ended March 31,
1974 was 124.0 per cent, as indicated in Table 2.            There are two interpretations
and values of “predicted return” based on the model.            First, given perfect informa-
tion about the returns on the two independent variables           ——   92.2 per cent on gold and
—12.5 per cent on the stock market    ——   the model and estimated coefficients would
have led to a “predicted return” on the gold mining stock portfolio of 113.1 per cent.
Second, our initial forecasts of the independent variables             ——   50 per cent return on
gold and 10 per cent return on the stock market         ——   led to a predicted return of 87.8
per cent on the gold mining stock portfolio, using the volatility coefficients
available at the beginning of April 1973.           Similarly, any other investor could have
utilized his own forecasts of the two independent variables in the model at the
beginning of this year to determine the expected gold stock portfolio return con               -~

sistent with his expectations of gold bullion price and the stock market return.
     Three caveats.should be stressed in this analysis.            The aggregation of returns
of 15 gold mining stocks in this portfolio leads to the averaging of prediction
errors, so that the model tends to produce a somewhat greater ~                   for a portfolio
of gold mining shares, ~s investIgated in this analysis, than for individual gold
mining stocks.     Individual gold mining companies differ with respect to production
costs, operating “leverage” of profits ~refative gold price changes,, and other
characteristics which are only partially reflected in the coefficient B0 when the

model is estimated with data on an individual gold mining stock.               In addition, the
actual return on the gold stock portfolio was closer to the predicted return in this
                                                   —    12   —

                                                       TABLE 2

                           Returns on Gold Mining Stock Portfolio, 1973—1974
                                    Period: April 1973—March 1974

                                                                                   Predicted Returns
                                     Actual Returns*                            Gold Stock Portfolio **
                                                                               Contingent    Contingent
                                                                                   On           On
                          Gold      Standard & Poor’s             Gold Stock     Actual     Forecasts of
                         Bullion       500 Stock                  Portfolio
                                                                               RG and R5   RG5O% RSlO%
                        in London        Index                   (15 issues)


 June 1973                 36.9%        —    .6%                    23.4%        52.2%

 September 1973          —18.9              4.8                    —1.4%        —19.6

 December l9?3             12.2         —9.2                        41.0           3.0

 March 1974                54.1         —2.7                        58.1          73.6


     April 1973—
     March 1974            92.2%       —12.5%                      124.0%        113.1%        87.8%

 *    All returns include dividend yield and capital gain or loss.

**    Based on the model in equation (1) and estimated volatility coefficients in Table 1
      for the period April 1971—March 1973.

experiment over the entire year of this experiment than for individual quarters (as
shown in Table 2) or shorter holding periods.    Finally, estimates of the coeffi-
cients B0 and Bs were obtained by ordinary least—squares regression using quarterly

data over the previous two years; the method of estimating these coefficients and
the assessment of their stability obviously require further investigation when more
data are available for the post—1971 era of gold prices.

                                  V.   CONCLUSIONS

     As the price of gold bullion changes, the value of gold ore bodies changes as
well; with the operating leverage of output price on corporate earnings, a one per
cent increase in gold price is generally associated with an increase of more than
one per cent in the return of the average gold mining share.     As expected, the
results indicate that gold mining share returns were significantly positively related
to returns on gold in the period 1968—1973.     Our estimate of 1.44 for the volatility
of gold mining stock portfolio returns with respect to gold bullion returns implies
that a return of 50 per cent on London gold is associated with an expected return of
72 per cent on the gold stock portfolio, contingent on a zerb return in the stock
market,   This volatility coefficient depends fundamentally on the elasticity of
mining company earnings with respect to gold price.     The volatility of gold mining
stock portfolio returns with respect to Standard and Poor’s 500 stock index was
positive in 1971—1973, whereas it had been near zero in the previous three—year
period.   Total variability of the gold mining stock portfolio as measured by standard
deviation of monthly returns was higher than that of gold bullion in 1968—1971 (8.26
vs. 3.20 per cent) and in 1971—1973 (11.45 vs. 7.28 per cent).     American investors
who own gold mining shares as a “substitute” for gold bullion should be aware that
these shares are generally riskier than gold; gold stocks are likely to increase or
decrease in market price by a greater percentage than. gold.
     Following the estimation of the volatility coefficients in the model using data
available in April 1973, we waited one year to measure actual returns on the gold
stock portfolio of 15 mining issues.   The actual return of 124.0 per cent on the gold
mining stock portfolio in the year ending March 31, 1974 was slightly higher than
the predicted return of 113.1 per cent contingent on perfect forecasts of a 92.2 per
cent return on gold and a —12.5 per cent return on the stock market.     The structural
relationship of gold stocks with gold bullion and the stock market suggested in this
model and estimated with data for .1968—1973 was generally supported by the subsequent
                                      —   14   —

behavior of gold stock returns over a 12—month period in 1973—1974.   Accordingly,
the model indicates a two—factor relationship which should be useful in assessing
expected gold share portfolio returns in the future, contingent on an investor’s
independent forecasts of gold bullion price and the stock market return.
                                     —   15   —


1.   Late in 1973 the Secretary of the Treasury   indicated that Americans might be
     allowed to buy or sell gold at some future   date, not specified; see “The
     Shifting Role of Gold,” The New York Times   (November 21, 1973), p. 51.
     Citizens of certain other countries, e.g.,   The United Kingdom and South Africa,
     also are not permitted to own gold bullion   (uncoined gold in bars or ingots).
     Since 1961 Americans have not been allowed   to own gold held outside the United

2.   The analysis and estimates based on the 1968—March 1973 data were first
     reported in the J. 0. McDonald and B. H. Solnik, “Gold Mining Shares, Gold
     and the Stock Market,” Research Paper No. 182, Stanford Graduate School of
     Business, September 3, 1973. Our model is essentially a “two beta” model
     related to the capital asset pricing model of William F. Sharpe and John Lint—
     her, as demonstrated in the previous paper.

3.   See Donald J. Hoppe, How To Invest in Gold Stocks (New Rochelle, New York:
     Arlington House) 1972: 305.

4.   This mean interest rate reflects the government Treasury hill annual rate on
     new issues, 1941—1973; for 1934—1940, the rate on prime bankers’ acceptances
     was used, as the Federal Reserve Bulletin reported tax—exempt bill rates prior
     to March 1941.

5.   Gold bullion and coins have had desirable characteristics as state—contingent
     claims on consumption goods for at least several thousand years. The “hoarding”
     of gold is relatively common in Europe, Latin America, Africa, and the Orient.
     The teaching of alchemy persists in modern India. See Idries Shah, Oriental
     Magic (London: Octagon Press), 1968: 128—137.

6.   Our estimate of the world stock of monetary gold is derived from the gold stock
     estimate of $58 billion at $35 an ounce developed by Fritz Machlup, “The Price
     of Gold,” The Banker, 118 (September 1968): 782—91.

7.   S. Herbert Frankel, Investment and the Return to Equity Capital in the South
     African Gold Nining Industry, 1889—1965 (Cambridge, Massachusetts: Harvard
     University Press), 1967.

8.   Each stock in Frankel’s averages was weighted by its total market value, in
     contrast to the Fisher—Lone averages for New York Stock Exchange stocks which
     reflect equal weighting of all stocks. Lawrence Fisher and James Ii. Lone,
     “Rates of Return on Investments in Common Stocks: The Year—by—Year Record,
     1926—65,” Journal of Business 41 (July 1968): 291—316.
                                            —   16   —

 9.   Lawrence Fisher and Roman L. Weil, “Coping with the Risk of Interest Rate
      Fluctuations: Returns to Bondholders from Naive and Optimal Strategies,”
      Journal of Business 44 (October 1971): 408—31.

10.   The following companies (and exchanges from which prices were taken) comprise
      the sample: ASA, Ltd. (NYSE), a closed—end investment company primarily
      invested in South African gold mining equities; Blyvooruitzicht Gold, Ameri-
      can Depository Receipt (ADR) (OTC); Campbell Red Lake Mines (NYSE): Dome
      Mines (NYSE): Dickenson Mines (Toronto); Free State Geduld, ADR (OTC); Giant
      Yellow Knife Mines (ASE); Hoinestake Mining (NYSE); Kerr Addison Mines
       (Toronto); Pato Consolidated Gold (ASE); President Brand, ADR (OTC): Presi-
      dent Steyn, ADR (OTC); Western Deep Levels, ADR (OTC); Western Holdings, ADR
       (OTC): and Wright Hargreaves (ASE).

11.   The anticipated value of the regression constant for the gold mining share
      portfolio in the latter period was zero in equation (2), whereas the esti-
      mated constant shown in Table 1 was —0.14; that is, actual returns were 14
      per cent per quarter less than expected in the model contingent on BG, Bs,
      and actual returns on gold and the stock market. This estimated constant
      might be interpreted in terms of investor expectations of future changes in
      gold price or of non—recurring adverse information events during the period.
      An alternative statistical explanation may be that the true relationship
      between returns on gold mining shares and gold was non—linear (in such a
      way as to produce a negative constant in a linear model), as reflected in
      lower values of BG found in the second subperiod of large returns on gold,
      and as explained in terms of mine production decisions and investor expecta-
      tions of transitory gold price movements.

12.   Elasticity of earnings with respect to gold price was estimated by regressing
      percentage changes in earnings per share (PCE) on percentage changes in
      London gold price (PCGt) using annual data in 1966—1972. The results for
      Campbell Red Lake Mines are as follows (t—ratios are shown in parentheses):

              PCE       =.     —0.34 + 1.69 PCGt         +    u       (R2   =   0.94)
                    t         (—0.07)  (7,66)                     t

13.   Fred Hirsch, “Influences on Gold Production,” International Monetary Fund
      Staff Papers 15 (November 1968): 405—88.

14.   If sustained in the longer run, higher gold prices will result in new explora-
      tion, the mining of previously unprofitable (often deeper) gold ore bodies,
      and increased gold output.

15.   The elasticity of earnings of Free State Geduld with respect to gold price,
      based on data described in footnote 12,. was estimated to be 0.15 in the
      following equation:

              PCE       =     0.33     0.15
                             (0.77) + (0.75) PCG +
                                                         Ut           (R~       0.12)
                                          —   17   —

16.   Hirsch, 415—23.

17.   For example, the executive     director of mines of Anglo—Transvaal Consolidated
      Investment Company stated,     “Even with the (gold) price at $120 an ounce, we
      can’t claim that a $90—an—ounce price is safe.” The director of mines of
      Union Corporation said, “What goes up fast may come down just as fast. .We.

      don’t know where the (gold) price floor is.” An official of Anglo—American
      Corporation of South Africa said they were planning operations in its old
      mines on the assumption of a $90—an—ounce price of gold. Wall Street
      Journal   (July 24,   1973): 22.

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