Gold Prices And Real Interest Rates, Part I | Seeking Alpha

Gold Prices And Real Interest Rates, Part I | Seeking Alpha
Gold Prices And Real Interest Rates, Part II | Seeking Alpha
This is the scariest gold price chart - News 2 Gold - Blogger

Posted: 05 May 2014 01:33 PM PDT

Summary

The real price of gold is defined as the Nominal Price divided by the preceding month's CPI index for each July starting in 1975.
The real interest rate is defined as the 3-month T-bill rate minus the inflation rate for the preceding month.
An argument is made why gold prices should be related to real interest rates since the price of gold is fixed by the market.
The relationships of the real gold price, and annual changes in the real gold price with real interest rates and the annual change in real interest rates are strong.

This analysis was inspired by Jeffrey Dow Jones' article, entitled, "A Brief History Of Gold And Why It's Overvalued By A Factor of 2," which appeared on Seeking Alpha, Feb. 13, 2014.

The article crystallized a lot of things for me.

If gold is money (and it was the standard for the US dollar until 1971), then its price should be equal to the real value of the dollar; that is, the value of the dollar discounted for consumer price inflation. And, he showed, that despite some large deviations from the CPI trend, this was, in fact, the case, both when the price of gold was fixed, and when it was traded on open markets. Therefore, I realized that this perspective made it much easier to analyze other influences on the gold price, because those influences account for the deviations from the inflation adjusted gold price.

Two things fascinated me about Jeffrey's graph showing the price of gold versus inflation. After the inflation of WWI, there was no consumer price inflation in the 1920s, and then there was severe deflation, with no change in the gold price (set at $20.67), until 1934. Then, the Treasury (or was it the Federal Reserve?) devalued the US dollar to $34.57 per oz. Jeffrey wrote, "I have no idea how the Treasury determined that $35 was the right price." But, it was reset to what it should have been at, given the inflation that had occurred since 1900. The effect was probably substantial. Our government demanded that US citizens turn their gold into the banks, which presumably they were not reluctant to do, given that they could get $34.57 per oz, when the previous day they could only get $20.67, and these were dollars that had been rapidly increasing in value because of the deflation of the previous three years. Also, gold was no longer accepted as money, so they redeemed it for money, and deflation ended! There wasn't much inflation, but deflation stopped for the next 4 years.

Gold could still be demanded for settling international transactions; that is, be transferred between central banks. But, where a US$100 debt brought a foreign country 4.84 oz of gold before, now they only got 2.89 oz. By resetting the price of gold, the US had devalued its currency relative to other countries, which should have served to increase exports and decrease imports until such time that the other countries devalued their currencies with respect to gold, and so created inflation. Inflation is a good thing, at least relative to deflation. So I hadn't appreciated until now, how significant the revaluation of gold was (and its demise as a medium of exchange within the US) for getting us out of the Depression.

The second thing that struck me about Jeffrey's graph was that when the countries of the world decided to drop the gold standard, and US citizens were free to own gold, "the free market managed to carry the price almost immediately to where it should have been priced had gold simply appreciated over the years at the same rate as the CPI" (as Jeffrey wrote). The gold price hit its inflation-adjusted price in about 1975, overshot, and then undershot, before rallying again. It then stayed above its inflation trend except for several years in the 1990s.

The Data

So, I will begin my analysis in 1975, when the market price had returned the price of gold to its long-term inflation trend. My unit of observation is the first trading day of July each year, with the gold price taken from the Perth mint. I tried working with monthly variations in the inflation-adjusted gold price, but the variations were just too noisy to extract worthwhile relationships. I used the CPI provided by Shiller in his CAPE Excel data sheet. His numbers don't exactly correspond to the bls.gov numbers, but they're close enough. The historical three-month Treasury bill rate and the ten-year T-bond yield were acquired from finance.yahoo. The statistical analyses were performed in Excel.

Jeffrey received a lot of comments complaining that the CPI does not correctly measure inflation. My response is: Yes, it does! What else would you use? And it's not relevant to the analysis. He showed a high degree of correspondence of the gold price to the CPI, and how well it measures consumer price inflation doesn't matter in the least. I think it does an excellent job, and almost all financial professionals accept it as the measure of consumer price inflation. The fact that the way it is calculated has changed over the years doesn't matter either.

The BLS provides a CPI index that is calculated using the 1970's methodology, and it's not very different from the current CPI. I think that in the past it was calculated wrongly, and probably overstated inflation in the past, rather than understating it now.

My dependent variable then, is the July gold price divided by the CPI for that month. This is my inflation-adjusted gold price (real gold price) variable, and I have now controlled for the effect of dollar inflation on the gold price. The average real price of gold over the 40 years since 1975 was 3.31. It's an index, not a dollar amount. It's the variation in this measure that matters, and you can get back to the nominal dollar price of gold by multiplying the real price by the CPI value for the appropriate month and year.

The Independent Variables

So what influences the real gold price? Well, it's all about demand and supply. The problem is you can't directly measure either of these, much less gauge their influence on past prices.

Grant Williams (Things that Make You Go Hmmm), has argued that last year there was a shortage of physical gold relative to the demand. I found the argument quite compelling. China is supposedly buying all new annual production. The Comex, Williams suggests, will not be able to meet demands for physical delivery on their futures' contracts. Yet the gold price kept dropping until the end of 2013. William Kaye argues that the Asian demand is being met by Western central banks leasing the gold to bullion banks, which sell it, but the bullion banks don't have to replace the gold from the deposit from whence they leased it. The central bank keeps the gold on its balance sheet. Kaye and Williams think this arrangement must eventually fail. But, I think the mechanism for satisfying the Asian gold demand is irrelevant to the gold price.

The problem with supply and demand includes the fact that most futures contracts are settled in cash (US dollars). Gold has been sold from GLD's vaults because large holders of GLD have redeemed their shares for cash. If they want to buy GLD again, then State Street will charge them the price it takes to buy the physical gold to put back in their vaults.

Many discussions of gold supply seem to think in terms of annual production, and try to equate annual demand with annual supply. But, although annual production of gold is measurable, it is not a measure of gold supply. The supply of gold is all that there is, and annual production is a pretty small increment of that. The issue is how much gold will be offered for sale as a function of price. We don't know that function. One potential or actual source of supply is the western central banks, which have purchased no gold that I know of since 1971, but have sold some (near the market bottom in the late 1990s). Their huge holdings are a major hangover for the gold market, because with floating exchange rates, and with the US dollar as the global currency reserve, the central banks actually have no use for that gold.

Some other central banks have been buying gold, but there is no reason to assume that they will continue to do so, and when conditions are right, they can just as easily turn around and sell the stuff. What conditions? That is the question. What changes the DEMAND for gold, and for its derivatives, by investors and central banks? I think, the demand for gold is a trade-off. Either you buy the US dollar or you buy gold.

The comments on Jeffrey's article brought up the issue of global inflation, and global demand for gold. Nearly all analyses of gold prices view prices from the perspective of what's happening in the US. I think that's the correct approach. If you have high inflation in your country, your alternative to buying gold is to buy the US dollar. If you buy the US dollar, your currency will devalue relative to the US dollar. The point is that the floating currency exchange rates will take care of differences in global inflation, and the US dollar index should have an influence on gold prices. If the index declines, the dollar is devaluing. Presumably, people prefer to purchase gold rather than the US dollar.

I will look at the US dollar price in another article, but in the meantime let's return to China. Why has their central bank been accumulating gold, when it is not accepted for international transactions? Perhaps they're not rational. After all, isn't a capitalistic economy directed by a Communist government an oxymoron? Let's assume the Chinese government is rational. There is a good reason to buy gold instead of interest-bearing Treasury bonds, and that reason is negative real interest rates.

Assume that gold is a substitute for money, and that it therefore may be expected to rise in dollar terms at a rate equal to the US inflation rate. Assume that the interest rate on the 1-year Treasury note is 1% and that US consumer prices have inflated at 2% last year, and they will probably do so again next year. If you invest in $100 of 1-year T-notes, then you will have a nominal value of $101 after one year, but the real value is $99 because of the inflation. If gold keeps pace with inflation it will be worth $102 after one year, a real value of $100. The gold investment wins. Remember, however, that gold is riskier than T-notes; so many investors will want a bigger premium (a more negative real interest rate) in order to buy gold. This is the only rational reason why US investors and foreign investors should buy gold as an investment.

But, if the Chinese are rational, they should sell that gold in a heartbeat if US real interest rates become positive. I am of the opinion that focusing on demand, on the presumption that Asian gold demand will continue regardless of its price, and regardless of the determinants of that demand, is silly. I was greatly influenced, in forming that opinion, by the fact that gold prices fell so much in 2013. The idea that western central banks are suppressing the price of gold in the face of that Asian demand is too conspiratorial for me.

Now, you might note that the gold price soared in 1933, when real interest rates were very positive because of deflation, which should negate my thesis. But, the market did not determine gold prices in 1933. They were set by the Fed, which belatedly corrected their error of not raising the gold price after the high inflation of WWI.

Real Interest Rates

Exploration of the relationship between interest rates and gold prices must be in the academic literature, but I no longer have the resources or inclination to look for it. Rudarakanchana has an excellent graph showing the history of inflation-adjusted gold prices and real interest rates. Jeff Clark, writing for Seeking Alpha on April 4, 2012 did not use an inflation adjusted gold price, but he also pointed out that the relationship does exist, and thought that gold would continue to rise at that time. It didn't.

The graphs below show the scatters for inflation adjusted gold prices plotted against 3-month real interest rates, and 10-year real interest rates. I simply deducted the annual inflation rate (%) for the 12 months preceding July from the 3-month T-bill yield (%) and from the 10-year T-bond yield to get my variables.

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Pearson's r for the first graph is -.36, and for the second graph it is -.31. The graphs are fairly similar, and the relationships are not strong, but they are in the right direction. Higher real interest rates are associated with lower inflation-adjusted gold prices. There is a curvilinear relationship apparent as a result of the years 1983 and 1984 when real interest rates were very high, and the inflation-adjusted gold price was about average.

Can we infer causality from the relationships?

The Scientific Method, the Dismal Science, and Statistical Inference

The deductive scientific method postulates theories as explanations of phenomena, whereby X causes Y, W causes V etc. If X causes Y then they must be empirically related (correlated), and so scientists check to see if the correlations exist. They cannot prove the theory by finding the correlation because there may be a data set, which does not exhibit the correlation. They can disprove the theory, or a portion of it by failing to find the hypothesized relationship. Note that scientists may discover relationships, which lead to theories to account for those relationships. That's the inductive method. The theory should then generate other hypothesized relationships, which must be tested from the deductive mode.

Science uses a variable language, because you must have multiple observations of something to establish a relationship. The multiple observations of a characteristic constitute a variable. In economics, the most common unit of observation is a point in time, although they can look for geographic relationships by using a geographic unit of observation.

To establish causation, the rules are simple. The cause (X) must precede the effect (Y) in time. X and Y must be correlated. There is no alternative explanation for the correlation other than that X causes Y. The rules are simple. The game is not. Proper experimental protocols require that everything about two groups is identical except for X and Y. One group is then subjected to the stimulus X, and then the effect on Y is measured to see if it is different from Y in the group that did not get the stimulus. Particularly in the case of human groups, it is very hard (impossible) to prevent contamination of the experiment in some way. Since you can't make all humans identical, you want the averages for the control variables in the two groups to be similar.

The social sciences cannot engage in experiments. That's why they are the soft sciences. They also have a habit of misusing statistics. So, to establish correlations we measure the characteristics of observations drawn via random samples. With historical data, however, we don't have random samples. We only have the recent past, which may be assumed to be a random sample from all of history and the future. But, in fact, it isn't a random sample. The result is that many of the correlations we find vary over time. They are unstable. A good illustration is the correlation between monthly variations in T-bond yields and the S&P 500. Over a range of years, you may have a positive correlation between the variables. Over a different range of years, you may have no correlation, and over another range, you may get an inverse correlation. My point is that there is no reason to engage in statistical inference with this sample of data. Besides, the assumptions for statistical inference are not met in the case of the real gold price versus real interest rates.

A meaningful correlation requires several things. One is that each of the variables is relatively symmetric in its distribution, and another is that there are no outliers. The real price variable has some right skew (a few exceptionally large values, with no exceptionally low values), but it's not a big problem. There are outliers. A correlation coefficient compares the variation in values around a regression line with the variation around the mean of a dependent variable. Outliers are a few values or one value that pulls the regression line toward that/those value(s), although the line may still be far away from the point, reducing the correlation coefficient. In the scatter above, the two years with the highest real interest rates are outliers. They make the relationship look U-shaped, and so they are actually weakening the linear relationship and the correlation coefficient, because Pearson's correlation coefficient describes the closeness of a linear relationship between two variables.

Another problem with relationships in a non-experimental setting is that the relationship may be spurious. This is where both variables are caused by another variable such that they exhibit a close relationship, which is not causal. A spurious relationship is different from a coincidental relationship. Spurious relationships are very common where a point in time is the unit of observation. If two things both increase steadily over time, they will exhibit a close positive relationship. Time is the cause of both. Most of you will have seen the correlation between the Fed's balance sheet and the S&P 500 index. They show it from 2008 on. It is not evidence of causality, because the correlation results from the steady increase of both variables over time since early 2009.

Time may not be the real common cause of the relationship, but there could be other factors that create the relationship, or alternatively suppress it. I will include some in Part II, but first I want to ask the question, is it real rates or nominal rates that affect gold prices?

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Pearson's correlation coefficient for the above scatter is -.06, and the r for the graph below is -.03. This means there is no linear relationship between the two variables in both cases.

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Again, the U-shaped relationship is even more evident in these graphs, and that is what causes the correlation coefficient to be almost zero, because r describes the closeness of a linear relationship. Perhaps, the higher real gold prices at times of very high nominal yields is because inflation is accelerating, causing the high yields on Treasury paper to arrest that trend. I will look at that, but first I want to address the last assumption/problem that may be influencing the relationship between real interest rates and real gold prices. That problem is the fact that the observations are not independent of each other.

Independence means that the value of one observation does not affect the value of another. The best single determinant of the price of gold in 1977 is the price of gold in 1976. The same is also probably true of the real price of gold. Let's have a look.

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Pearson's correlation coefficient for the above scatter is .77. That's an r-square of .59. 59% of the total variation (total variation is measured as the sum of the squared deviations around the mean) in the real price of gold is explained by the previous year's real price. Also, the correlation coefficient is .55 when the 3-month T-bill real interest rate is regressed against the previous year's 3-month T-bill real interest rate.

This problem is called serial correlation or auto-correlation. It is very common in econometrics. And the nature of the problem is the fact that we actually have only 3 lengthy episodes of negative, or very low positive real rates (1975-80, 1991-94, 2001-13) and two episodes of high real rates.

The auto-correlation problem can be ameliorated via auto-regression, in which the previous year's value (and perhaps the year before that) is used as an independent variable in a multiple regression model. We should also be able to make the observations independent of each other by using annual percentage change variables, although the change variables could be auto-correlated also. Here are the scatters of annual change in the real price of gold versus annual change in the real interest rates. I tried percentage change, but the variability in the percentages was too great creating a skew problem in the real gold price, and you can't calculate a percentage change when the real interest rate goes from negative to positive or vice-versa.

I checked for auto-correlation in the variables and there was none in the change of the real gold price. The change in the 3-month real interest rate had an inverse correlation of -.41 with the previous year's change, which should be expected. If the real rate becomes increasingly negative one year, you would expect it to become less negative the following year.

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R = -.54

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R = -.49.

An r of -.54 means 29% of the total variation in the change of the real gold price is explained by the concurrent change in the 3-month real rate (r-sq = .29). On average, a substantial increase in the 3-month real rate is associated with a substantial decrease in the real gold price. Pretty awesome, although a lot of that correlation is because of three years. In 1980, the real interest rate went from -2.08 to -4.51 (remember this is all end of June), and the gold price soared. In 1981, Volcker tightened the screws and the real rate went from -4.51 to +4.11 (a change of +8.62) as nominal rates soared, and inflation quickly subsided. The nominal price of gold fell from $644 to $409 from July 1980 to July 1981. I remember it well. In July 2008, inflation had remained fairly high as the Fed rapidly lowered interest rates, and the nominal gold price went from $665 in 2007 to $940 in 2008. Then in 2009, there was actually a brief period of deflation such that there was a big increase in real interest rates and the nominal price (and real price) of gold was largely unchanged from July to July. It did plummet and rally in between.

Do nominal interest rates account for this relationship? No. The correlation of the real price of gold with the nominal 3-month T-bill rate was -.06. That is, there was no relationship. The change in the real price of gold had a -.22 correlation with the change in the nominal 3-month T-bill rate, mostly because of 1981. It's the real rate of interest that matters.

There is not a good theoretical reason to use the real 10-year bond yield, because the 10-year bond is not equivalent to cash or money. It is a risk asset, vulnerable to interest-rate risk, and therefore not a plausible alternative to gold. Also, the correlation of the real 10-year rate with real gold prices is not as strong as that with the real 3-month rate. I was curious if the yield spread had an effect on the gold price, however. If the yield spread is large, it is in the investor's interest to borrow cheaply short term, and buy long-term bonds with a much higher interest rate. This should diminish the demand for gold, and so I would expect the real price of gold to diminish as the yield spread increases.

My measure of yield spread is to subtract the real 3-month T-bill yield from the real 10-year T-bond yield. When I correlated the spread with the real gold price, the correlation was +.11. This is tantamount to no correlation. For change in the spread versus the change in the real gold price, the correlation was .17, which is almost zero also. The positive sign indicates that when the yield spread increased the real gold price increased, but this was only because of two years. In 1980, short-term rates were lowered when inflation was not yet under control, and the real price of gold soared, and in 1981, short-term rates were dramatically raised with the real rate going from -4 to +4, as we have previously seen. The 10-year yield also rose a lot but not as much as the short-term rate. So the yield spread narrowed and gold prices tanked. It appears that the high real interest rates caused the decline in gold prices, and so the spread variable is superfluous, but I will keep the yield spread variable in my multivariate analysis, in case there is an independent relationship between it and the real gold price, one which is being suppressed by failure to control for other variables in these simple relationships.

The Multivariate Model

Multiple regression tries to separate the effect of various factors on the real gold price from each other, and the technique controls for the fact that the contributing factors to the gold price are correlated with each other. If you have three variables, gold prices, real interest rates and last year's gold prices, multiple regression will take the variation in gold prices, which is unrelated to the variation in real interest rates, and correlate that independent variation with the variation in last year's gold prices, which is also unrelated to the variation in real interest rates. And it simultaneously relates the variation in gold prices that is independent of the variation in last year's gold prices with the variation in real interest rates that is independent of the variation in last year's gold prices. Another way of saying this is that we see how gold prices and real interest rates co-vary, while last year's gold prices do not change (it's held constant).

A big problem in multiple regression is multi-collinearity, when two independent variables are highly correlated with each other, and the technique cannot sort out which one of them accounts for the variation in the dependent variable. Other problems with multiple regression are as I described them in the case of simple relationships (asymmetry in the distribution of one or more variables, outliers, etc.).

Multiple regressions generate equations that describe the independent effect that each independent variable has on the dependent variable. By plugging the values of the independent variables for a year into the equation you can calculate a predicted value for the dependent variable (Yhat), and then subtract that from the actual value of the dependent variable (Y minus Yhat), and that gives you the error (also called the residual). The sum of the squared errors divided by the sum of the squared deviations around the mean of the dependent variable (called the total variation) generates the multiple coefficient of determination (r-squared), which is the proportion of the total variation in Y explained by the equation. The total variation of Y is defined as the sum of the squared deviations of Y around its mean.

My two models are:

1. The real price of gold regressed against last year's real gold price, the real interest rate of the 3-month Treasury bill, and the spread between 3 month and 10 year T-bond rates.

2. The annual change in the real price of gold regressed against last years' changes in the real price of gold, the 3-month real rate of interest at the beginning of the period that precedes the annual change, and the change in the 3-month real rate of interest. The changes are not in percentages, but actual changes.

Model 1

The initial model returned an r-sq of .72, primarily because of the variable, last year's real gold price. The t-statistic is used in statistical inference to help decide whether a relationship found in a sample could have been the result of sampling error. That is, it calculates the probability that the sample could have been drawn from a population of observations in which there was no relationship between the two variables. My data did not satisfy the assumptions required of statistical inference, and 40 consecutive years is not a random sample of the population of all possible years. But the t-value is a good descriptor of the strength of the relationship between two variables in a particular data set, and so I used it to dump the interest rate spread variable, which did not add to the multiple r-sq for the regression.

My final version of model 1, as a result, was

Predicted real price of gold = 1.00 + .781(last year's real gold price) - .211(the real 3-month interest rate).

The r-sq was .72. Last year's real gold price had the greatest effect on the real gold price by far, and the relationship with the real interest rate was very strong (t=4.02).

Model 2

In model 2, my dependent variable is the annual change in the real gold price regressed against the three variables listed above. The initial r-sq was .39. Again, I used the t-value to remove the previous year's change in the real price of gold variable. It had no independent effect on the next year's change in real gold price. So there was no auto-correlation in the changes from year to year, which surprised me.

The final model was: predicted real price change = .22 - .287(change in the real interest rate) -.156(the 3-month real interest rate at the start of the time change). The r-sq was .39, which is pretty awesome, until you recognize that to predict the change in the real gold price, you need to be able to predict the change in the inflation, and the change in interest rates, because these are all concurrent changes.

The equation indicates that on average if the real interest rate (this is called ceteris paribus), a negative real interest rate at the start of the year (July to July in this study) was associated with a rise in the real price of gold. A positive real interest rate was associated with a decline in the real price of gold. The higher the real interest rate the bigger the decline. If real interest rates rose during the one-year period, ceteris paribus, the real price of gold declined over that time period. So if the real rate was negative but became less negative, the gold price declined. If the real rate was positive but declined, the price of gold rose. The change in the real interest rate had the greatest individual effect on the real gold price (t=4.76). The previous year's real interest rate had a t = 2.4.

So I have argued why real short-term interest rates should influence the demand for gold, and therefore the price of gold. And, I have shown that, over the last 40 years real interest rates explained why gold prices would race well ahead of inflation in some years, and in other years why they would lag behind inflation. In my next article, I will add the influence of the value of the dollar, and changes in the US inflation rate to the model, on gold prices.

Disclosure: I am long TLT, NLY, REM. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article. (More...)

Gold Prices And Real Interest Rates, Part II | Seeking Alpha

Posted: 06 May 2014 08:14 AM PDT

Summary

Simple relationships are shown for the dollar index and changes in the inflation rate versus the real gold price and annual changes in the real gold price.
These variables are then included in a multiple regression with real interest rates and annual changes in the real interest rate for 1975-2013.
Real interest rates and changes in those rates have a dominant influence on real gold prices and annual changes in real gold prices.
Changes in the inflation rate have only a minor effect, because the Fed appears to be late in changing interest rates in response to changes in the inflation rate.

In Part I of this treatise, I found a strong relationship between the real price of gold (the July gold price divided by the CPI for the preceding month), the real interest rate as measured by the 3-month Treasury bill rate minus the inflation rate, and changes in that real interest rate. Annual changes in the real gold price were also closely related to these two variables. Here, in Part II, I will add two more variables that should influence the real price of gold.

The Value of the Dollar

In Part I, I argued that we didn't have to worry about inflation in other countries affecting their demand for gold, because the value of their currencies should reflect differential geographic inflation rates. If a country has inflation higher than that in the US, its currency should be under pressure, and so its investors should be inclined to purchase US assets. In the case of buying US T-notes, they have a choice. They may buy the US dollar (Treasury bills) or gold. They should therefore respond just like rational US investors. They should buy T-bills if the real interest rates are positive. If I control for real interest rates, the value of the US dollar relative to other currencies shouldn't have an effect on the price of gold. That is, if real interest rates are high in the US, that should increase the value of the US dollar, and lower the price of gold at the same time. Let's look at the simple relationship first.

My independent variable is the adjusted major currencies dollar index, which I got from the Atlanta Federal Reserve. In the first scatter below, the linear correlation coefficient is -.32, although a negative exponential curve would describe the scatter much better. As the dollar index increased the real price of gold decreased, as anticipated. When the dollar is in demand, presumably people are responding to higher interest rates available in the US, rather than gold. We will see if real interest rates are the primary influence when both variables are tried in a multivariate model.

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The next scatter has a correlation coefficient of r = -.40. When the dollar went down, the real price of gold went up. The pattern is there even if you remove the outliers. In fact, the outliers weaken the relationship. The outliers are 1986, when the dollar fell a lot and the real price of gold was unchanged, 1980 when the dollar was unchanged but gold rose a lot (the year of low real interest rates), and 1981 when the dollar rose a lot in association with a large increase in real rates and gold fell.

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Changes in the Inflation Rate

Inflation is a rate of change. It is the rate at which money loses value relative to the things that money can purchase. On average, the rate of increase in the price of gold should be correlated with the inflation rate, and Jeffrey Jones shows that it is, but with large deviations, that may last for many years. Erb and Harvey show this also. In addition to real interest rates, it should be expected that the rate of change in the real gold price will accelerate if the inflation rate accelerates; that is, if the rate of inflation is getting worse. Real gold prices should increase, in that case.

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R = .25 in the above graph. The correlation coefficient indicates that when the annual inflation rate is high in any given year, the real gold price tends to be higher than average. But, the r-square is only .06, which is very weak, and much of the relationship is because of one year with very high inflation, 1980. The real price of gold was also above average in 2009, when we briefly had deflation.

The next graph looks at the effect of a change in the inflation rate.

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R = .11. Curiously, this graph shows no relationship between the real gold price and whether inflation was higher or lower than the previous year. But, when I relate the annual change in the real gold price to the annual change in the inflation rate, I do get a positive relationship of r = .41 (below). The strength of this relationship is greatly influenced by just two years: 1980, when the inflation rate was already high and jumped some more, and real gold prices jumped, and 1981, when the inflation rate declined from a very high level to a still high level (10%), and the real price of gold plummeted. 1981 was also the year when real interest rates jumped from very negative to very positive.

The other notable year in the graph below is 2009, when inflation went from 5.6% to -2.1%, but the real price of gold was virtually unchanged from July 2008 to July 2009. Remember that the price of gold did plummet in 2008, and rallied in 2009.

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The Multivariate Models

These simple relationships have shown that certain critical years have muddied or highlighted the relationship between the real gold price and its primary determinants. In 1979-1980, the nominal and real price of gold were in a 4-year uptrend and jumped to exceptional levels in association with a high inflation rate, an increase in that inflation rate, a very negative real interest rate, a decline in that real interest rate, and a cheap dollar which was largely unchanged from the previous year. In 1981, gold collapsed, reversing its uptrend, in association with a high, but decreased inflation rate, a sharp increase in the real interest rate to a large positive level, and a sharp increase in the value of the US dollar. 1981 was also the year that the Hunt brothers' attempt to corner the silver market went awry. Did that affect the gold price, or did these other factors cause the price of silver to collapse?

Can we separate the role of the various factors from each other, and control for the fact that the contributing factors to the gold price are correlated with each other? The answer is, yes. Multiple regression attempts to do that. I explained it in Part I. In sum, multiple regression tries to find the co-variation between two variables, while the other variables do not vary.

Model 1

My first model is the real price of gold regressed against last year's real gold price, the dollar index, the real interest rate of the 3-month Treasury bill, the spread between 3-month and 10-year T-bond rates, the inflation rate, and the annual change in the inflation rate.

The initial model returned an r-sq of .738, primarily because of the variable, last year's real gold price. The t-statistic is a good descriptor of the strength of the relationship between two variables in a particular data set, and so I used it to dump independent variables, which were adding little to the multiple r-sq for the regression.

My final version of model 1, as a result, was:

Predicted real price of gold = .922 + .81 (last year's real gold price) - .183 (the real 3 month interest rate) + .07 (change in the inflation rate).

The r-sq was .729; so deleting the other variables changed nothing, and the r-squared is little different from the model in Part I, which had only last year's real gold price and the real interest rate as the independent variables. So change in the inflation rate does not add much explanation to the variation in real gold prices.

The previous year's real gold price had the greatest effect on the real gold price by far, and the relationship with the real interest rate was strong. The change in the inflation rate had only a minor independent influence on the real gold price. It was the change in the real interest rate that mattered. Yes, if inflation accelerated by 1 percentage point (from 10% to 11% say), the independent effect was to increase the real price of gold by .07 (the plus .07 coefficient), but that's not a big effect.

Remember, the real price of gold is measured as the nominal price in dollars divided by the CPI index value for that month. So in July of 1980, the nominal gold price was $644, the CPI index was 82.70, and therefore, the real price of gold was 7.79, its all-time high in this 40-year time span. In July of 1981, the CPI was at 91.60, a 10.76% inflation rate, down some from the 13.13% rate of the previous 12 months. So the real price of gold should have gone down a little, but not by as much as it did, given that inflation was still very high. Volcker hiked interest rates from 8.62% to 14.87% to combat the inflation. The real rate of interest went from -4.51% to +4.11%, and this change overwhelmed the effect of still-high inflation on the real gold price. The nominal price fell to $409.28, and the real price dropped to 4.47.

The relationships in the multiple regression are quite dependent on just a few years, but I think those occasions matter. Most years, gold prices, real interest rates, and the inflation rate didn't vary much, but in a few years, interest rates and inflation moved a lot, and the response of gold prices was major and obvious. So I can explain variation in real gold prices to some extent, at least for the past 40 years, but can I predict the future movement in real gold prices?

By plugging the values for each year into the equation, I can get a predicted value (Yhat) for the real gold price for each year. I then subtract Yhat from the actual real gold price each year, and get the prediction error or residual. If the residual is positive, then the actual price was higher than the predicted price (i.e. gold was overpriced), and if the residual is negative, the actual price was less than the predicted price (i.e. underpriced). The question then is, if gold is overpriced, does it tend to be underpriced the next year, and vice-versa. Correlation of the residuals with next year's real gold price should generate an inverse correlation.

Dang. No inverse correlation. Actually, the correlation was positive (r = .47). Overpriced gold tended to stay overpriced, and vice-versa. There was also no correlation between the residuals and the real gold price 5 years in the future. So there was no indication of when the overpriced trend or underpriced trend would change.

The residuals were highly auto-correlated, reflecting the 3 major trends in gold prices during those 40 years. The residuals were generally negative from 1989 to 2005, meaning gold was underpriced according to the equation, but the real price of gold kept falling until 2001. After that, it rose every year, and the residuals became positive from 2005 until 2012. The average real price of gold over the 40 years was 3.31. In 2013, it was 5.51 ($1287 nominal price), down from 6.96 the previous year. The equation indicates the real price should have been 6.89, because a negative real interest rate became more negative. So the residual was negative. Gold is underpriced currently, but as I have just indicated, it tends to stay underpriced or overpriced for many years in a row.

Notice, however, that I didn't actually look at the annual change in price. Gold can remain overpriced, but the real price might still decrease. So I should correlate the residuals with next year's change in the real gold price, rather than the price itself. If gold is overpriced, according to the equation, then we should expect a drop in its real price, i.e. an inverse correlation. Well, the correlation coefficient between the residuals and the change in real price was minus .149, which essentially means no linear correlation. Was it Yogi Berra who said, prediction is very hard, especially when it's about the future?

Model 2

The second model regressed the annual change in the real price of gold against last year's changes in the real price of gold, the 3-month real rate of interest preceding the annual change, the change in the 3-month real rate of interest, the change in the inflation rate, the change in the spread, and the change in the dollar index. The changes are not in percentages, but actual changes, and they are concurrent.

The initial r-sq was .443. Again, I used t-values to remove independent variables that seemed to have little independent effect on the real gold price changes. The previous year's change in the real gold price had no effect on the next year's change in real gold price. So, there was no auto-correlation in the changes from year to year, which surprised me.

I was also surprised to see that the independent effect of an increase in the inflation rate was to decrease the real gold price. It was a very weak effect, so the variable was deleted, but it appeared to make sense until I looked at the simple relationship between the change in the inflation rate and the change in the real interest rate. That correlation was -.705. Note that this is an inverse correlation. When inflation accelerated, real interest rates decreased (and went or were negative). My interpretation is that the Fed was usually late in raising interest rates when the inflation rate was increasing, and late in lowering interest rates when there was disinflation. What I was seeing was that in a few critical years, the market anticipated that the Fed would have to greatly increase rates to address inflation, and therefore sold gold, as inflation was still rising. This may be the reason why gold prices fell a lot in 2013. By the time real interest rates started to dramatically rise, gold was already well down, and so we see a good relationship between real interest rates, the change in real interest rates, and the change in real gold prices, but not with the change in inflation rates. And that is probably why other studies have found little relationship between annual inflation rates and gold price changes. They did not control for interest rates, and so they could not see that when inflation is high, gold will be sold in anticipation of higher real interest rates, and that when inflation is low, gold will be bought in anticipation of lower real interest rates, as in 2001. It wasn't the 9/11 event itself, it was the lower interest rates because of 9/11 which raised gold prices.

The final model was:

Predicted real price change = .202 - .2605 (change in the real interest rate) - .0309 (change in the dollar index) - .1286 (the 3-month real interest rate at the start of the time change).

The r-sq was .437, which is pretty awesome until you recognize that to predict the change in the real gold price, you need to be able to predict the change in the inflation rate, the change in interest rates, and the change in the dollar index, because these are all concurrent changes. Economists are renown for their lack of foresight. How many predicted that long-term interest rates would fall when the Fed started tapering QE this year? So don't rely on anyone's predictions; you are better off just using last year's values to predict next year's values.

I tried correlating the residuals against the next year's price change. The idea was that if the equation under-predicted the price change of gold, there would be reversion to the mean. If the gold price growth were much faster than predicted in one year, would it be lower in the next? No such luck. The correlation was very weak (r = -.22, r-sq = .05).

Would previous year changes in the dollar index and in the real interest rate help predict the gold price change the following year? Nope! Curiously, when I regressed the real gold price change against the concurrent changes in real interest rates and the dollar index, the level of real interest rates at the start of the change period had a strong inverse effect on the change in real gold prices. But, the same variable, when coupled with the previous year's changes in real interest rates and the dollar index, did not have a strong effect on the change in real gold prices, although its effect was still negative (high real interest rates were associated with smaller increases or decreases in real gold prices).

Returning to the equation above, what does it tell us? On average, if the real interest rate and the dollar index do not change (this is called ceteris paribus), a negative real interest rate at the start of the year (July to July in this study) was associated with a rise in the real price of gold. A positive real interest rate was associated with a decline in the real price of gold. The higher the real interest rate, the bigger the decline. If real interest rates rose during the one-year period, ceteris paribus, the real price of gold declined over that time period. So if the real rate was negative but became less negative, the gold price declined. If the real rate was positive but declined, the price of gold rose. The change in the real interest rate had the greatest individual effect on the change in the real gold price. If the real interest rate did not change, an increase in the value of the dollar was associated with a decline in the real price of gold, and a decline in the value of the dollar raised the price of gold. Presumably, if the dollar rose, that reflected a desire by foreigners to own the US dollar, rather than gold or their own currency. If the dollar fell, presumably people would rather own gold or a foreign currency in preference to the US currency. Of the three independent variables, the change in the dollar index had the weakest effect on gold prices.

An r-sq of .44 is pretty impressive. I found only 3 years where the model's error was somewhat large and got the direction of the real price change wrong. The worst was last year, 2012-13. The model predicted a small increase in the real price of gold because real rates were negative, and became more so as a result of a slight increase in inflation. The nominal price of gold fell $307 per oz. Perhaps it was a reaction to very high real prices of gold in the previous two years. Curiously, this was the year the Asians were supposedly accumulating gold. Clearly, some people/institutions were very eager to sell it to them.

In 1982-83, the model predicted a significant decline in real gold prices associated with a high real interest rate, which increased a lot. But the nominal price of gold rose from $339 to $423. Perhaps, this was an oversold bounce, because gold had declined from $644 in 1980 to $339 in 1982. Gold did continue its decline after that to $317 in 1985. A substantial decline for gold was predicted for 2008-9, because the brief deflation caused real interest rates to jump. In fact, nominal gold prices were largely unchanged.

So, what do we do with this model, which still requires that you predict inflation rates and interest rates to predict gold prices? Well, perhaps it could be used in conjunction with Jeffrey Jones' 12-month moving average model. For example, in 1983, Jeffrey's model probably had gold moving above its 12-month MA, but real interest rates were high and rising, and so the buy could have been ignored.

My thoughts on the next few years include the observation that the decline of the last two years is so large that we must entertain the possibility/probability that a new multi-year declining trend is underway. But, how can real interest rates possibly become positive again, especially since it will be very difficult for the Fed to raise interest rates given all those excess bank reserves. They have to start selling their Treasuries in great quantities to raise rates. If they did that, a recession would be swift and deflationary. If they don't sell their Treasury holdings, we might have deflation anyway, which would cause positive real interest rates. Unlike the last deflation of the 1930s, when gold rose because the government fixed the price, deflation in a free market should lower the price of gold substantially.

If inflation returns and the Fed doesn't raise rates to fix it, then gold prices will rise. But, I think the odds of rising inflation are lousy. You need much higher aggregate demand to increase inflation, and where is that demand going to come from with monetary stimulus and fiscal stimulus declining, populations aging, and workers not being rewarded (via pay increases) for their higher productivity.

As of the beginning of April (2014), the model for the real price of gold indicates it should be at 6.69 (nominal = $1581) versus an actual price of 5.42 ($1280 nominal). The model for the annual change in real price indicates that from April to April, the nominal price should have increased by $112, whereas it in fact, fell by $320 (-25%). So gold is underpriced. But as I showed above, whether the model indicated that gold was over- or underpriced, it didn't help predict the price one year later. My speculation is that you have to respect the trend; that the drop in price since 2012 is so large that it marks a change in the multi-year trend. Gold may not change much in price for a while, because we do have negative real interest rates, and they are likely to persist unless we have deflation. Then, gold prices should go down because the situation is different from 1934, when gold prices were fixed and had not been adjusted to reflect the inflation that had occurred since the early 1900s.

Remember, my regressions are for July to July. Using a different month will change the parameter values, but I would neither expect a change in the direction of the relationships nor a major change in the strength of the relationships. I welcome any attempt to test the stability of the parameters by testing the relationship on other months, but it's too much work for me, given that I expect little reward from the exercise.

I have not been long or short on gold or its derivatives this year. There are more remunerative investments, in my opinion.

This is the scariest gold price chart - News 2 Gold - Blogger

Posted: 03 May 2014 04:42 PM PDT

In this article we look at gold from different angles: the money supply, the physical gold market and technical gold indicators. Ten long term charts point to a healty condition in the gold market amid the price drop of 2013. We have always advocated to look at gold in a holistic way; the following charts offer a wide perspective. The charts were created and presented by Frank Holmes (USFunds.com) during the recent World Money Show.

Monetary conditions

In the first month of 2014, the M2 money supply, which is a measure of money supply that includes cash, savings and checking deposits, grew faster than the previous two years. In 2012, M2 grew 7.6 percent and in 2013, money supply rose 4.7 percent; at an annualized rate, January's money supply growth "reached an annualized rate of increase of 8.75 percent," according to Bloomberg's Precious Metal Mining team. This may mean "the U.S. Federal Reserve is trying to resurrect inflation, thus increasing the appeal of gold, the supply of which can only increase about 1.5 percent to 2.5 percent annually," says Bloomberg.

The first two charts show the historic correlation between the money supply and the price of gold. The global money supply has clearly driven gold prices, although 2013 was the year in which a significant disconnect occurred. The odds favor an upward revision of the gold price, re-establishing the long term correlation.

As Jim Rickards argues in his book, the price of gold would be well above $3,000 if there was some sort of tie between gold and the money supply. Jim Rickards still expects that the central banks will be forced by market forces to re-establish a tie with gold at some point in the future.

US Money supply vs gold price 1934 2014 price

Physical gold market

2013 was the year of a massive liquidation in physical metal backing gold ETF's. The following chart presents the exceptional outflow of gold out of primarily the GLD . The key question, in our opinion, is not the outlfow, but what happened with that gold. The most common answer is that it went East. Is this positive or negative for gold? We believe it's extremely positive, because the metal is now in strong hands which will keep it for several years or decades. The key point in all this is that much less physical gold will be available once the Western investment demand will pick up again, leading to a potential shortage in the gold market.

The East loves gold. The explosive demand for gold in China is supported by an increase in incomes, a trend that is significantly different compared to the West. This trends favors the affordability of the yellow metal among the biggest gold consumer in the world.

China's investment and jewelry demand has exploded in the last two years. The lower the price of gold went, the higher the demand for the metal. The following chart present an interesting insight: the average grams of gold consumed per inhabitant. Simple math learns that additional 0.1 gram of gold per capita results in an additional 130 tonnes gold demand (which is 5% of the current gold year supply).

Technical picture

From a technical point of view, gold is extremely oversold. Any historic measure shows that the current situation is extreme. One of those measures is the gold oscillator, measuring year-on-year change. A correction to the mean is long overdue.

The successful retest of the June 2013 bottom is a very powerful technical signal.

A short squeeze could be an important technical driver to drive short term gold prices. The chart shows how the gold price tends to rise with extreme short positions by COMEX speculators (non-commercials).

What is tremendously powerful for gold stock investors is this chart: in the last 3 decades, there were only 3 times that gold stocks only saw a consecutive 3-year loss.

Gold Prices And Real Interest Rates, Part I | Seeking Alpha

<b>Gold Prices</b> And Real Interest Rates, Part I | Seeking Alpha

Summary

The Data

The Independent Variables

Real Interest Rates

The Scientific Method, the Dismal Science, and Statistical Inference

The Multivariate Model

Model 1

Model 2

Summary

The Value of the Dollar

Changes in the Inflation Rate

The Multivariate Models

Model 1

Model 2

Monetary conditions

Physical gold market

Technical picture

Full presentation

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