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The price of gold depends on many variables, among them the real federal funds rate, which is the federal funds rate adjusted for inflation. But the real federal funds rate, or RFFR, alone does not explain variation in gold prices. One must also look at the change in the RFFR for a full understanding.
A recent commentary by Frank Holmes of U.S. Global Investors, argues that is predictive of year-over-year returns for gold: “Gold has experienced positive higher year-over-year returns whenever the real interest rate tipped below 2%,” Holmes wrote. “And the lower the rates drop, the stronger gold tends to perform.” The chart below, taken from this commentary, illustrates his point.
Analysts at Deutsche Bank, the originators of the chart, shared a similar view in a recent commentary of their own: "On our analysis, since 1970 whenever U.S. real interest rates have fallen below -3 percent, gold prices have typically been able to rise by an average of 40 percent year-on-year. On this basis, if real rates remain at current depressed levels, it would imply a move above $2,000/oz is only a matter of time."
Figure 1
Presently the RFFR is about – 3.9%. According to figure 1 an investment in gold one year ago should have provided a return of almost 50% to date. The actual return was about 35% – not too far from what the chart predicts.
The results of my own analysis support this conclusion. The average year-over-year returns for gold corresponding to various RFFRs are listed in table 1 below. (Table 1 uses slightly different data than figure 1, which is for the time period 1970 to 2010. Table 1 covers returns from 1966 to 2011.) For a RFFR of -3.9%, the average year-over-year return for gold was about 48%, when interpolating between the listed values corresponding to the RFFR of -3% and -4%.
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Table 1
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Gold - year-over-year returns when Real Fed Funds Rate is as shown, from 1966 - 2011 |
Real Fed
Funds Rate
+0.5% & -0.5%
|
Real Fed Fund
Rate 1-yr ago
% |
number
of occurrences
days |
average
of all
occurrences |
maximum
of all
occurrences |
minimum
of all
occurrences |
-5% |
any |
30 |
14% |
110% |
2% |
-4% |
any |
158 |
50% |
123% |
2% |
-3% |
any |
247 |
31% |
116% |
-14% |
-2% |
any |
563 |
17% |
105% |
-29% |
-1% |
any |
1091 |
16% |
117% |
-29% |
0% |
any |
1635 |
19% |
278% |
-36% |
1% |
any |
1728 |
16% |
246% |
-15% |
2% |
any |
1521 |
13% |
110% |
-18% |
3% |
any |
2077 |
8% |
163% |
-37% |
4% |
any |
1004 |
-4% |
103% |
-36% |
5% |
any |
734 |
2% |
105% |
-41% |
6% |
any |
218 |
-3% |
61% |
-28% |
7% |
any |
257 |
-12% |
40% |
-38% |
8% |
any |
63 |
-26% |
-2% |
-41% |
Although gold’s average year-over-year returns as listed in table 1 correspond reasonably well with what is shown in figure 1, the big deviations from the average to the upside and the downside should be considered as well when using the table to predict the year-over-year returns.
The year-over-year change of the RFFR influences the gold price
Assuming that one year from now the RFFR will not have changed markedly from its current value, about -4%, can we simply use figure 1 or table 1 and forecast that gold will be 40-50% higher than its current price?
The answer is no, because the change of the RFFR over one year also influences the return, as we can see in table 2.
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Table 2
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year-over-year
change RFFR
ΔRFFR
+ and - 0.5%
|
Real Fed
Funds Rate
%
|
number of
occurrences
days |
year-over-year change of Gold price |
average
gain/loss
$ |
average
of all
occurrences
|
maximum
of all
occurrences |
minimum
of all
occurrences |
-6% |
any |
84 |
107.07 |
26% |
102% |
-4% |
-5% |
any |
237 |
112.53 |
39% |
144% |
-14% |
-4% |
any |
286 |
92.71 |
34% |
132% |
-35% |
-3% |
any |
780 |
112.17 |
19% |
123% |
-34% |
-2% |
any |
1156 |
51.50 |
13% |
116% |
-36% |
-1% |
any |
2071 |
25.14 |
9% |
278% |
-34% |
0% |
any |
2473 |
19.40 |
9% |
210% |
-37% |
1% |
any |
1989 |
21.23 |
14% |
110% |
-25% |
2% |
any |
1546 |
14.71 |
9% |
133% |
-36% |
3% |
any |
422 |
31.57 |
17% |
163% |
-36% |
4% |
any |
211 |
-22.36 |
-10% |
49% |
-41% |
5% |
any |
82 |
111.68 |
18% |
61% |
-33% |
6% |
any |
30 |
-10.01 |
-2% |
18% |
-36% |
7% |
any |
25 |
-218.52 |
-32% |
-21% |
-41% |
8% |
any |
3 |
-205.97 |
-32% |
-31% |
-34% |
It is evident from this table that gold’s year-over-year return has decreased as the year-over-year change of the RFFR increased.
What will be the gold price one year from now?
First, let’s examine the scenario I described above – no change in the RFFR over the next year. My analysis of the data found no previous record when the current RFFR and the RFFR a year later were both -4%, as shown in table 3 below. The best result would be from table 2 which indicates an average 9% increase in the gold price for a 0% change of the RFFR.
Scenario 1: no change from now, RFFR = -4%, ΔRFFR = 0%
(ΔRFFR is the year-on-year change of the RFFR)
Table 3 |
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year-over-year
change RFFR
ΔRFFR
+ and - 0.5%
|
Real Fed
Funds Rate
-4%
+0.5% & -0.5%
|
number of
occurrences
days |
year-over-year change of Gold price |
average
gain/loss |
average
of all
occurrences
|
maximum
of all
occurrences |
minimum
of all
occurrences |
-6% |
-4.5 to -3.5 |
11 |
81.25 |
39% |
102% |
6% |
-5% |
-4.5 to -3.5 |
39 |
41.28 |
38% |
83% |
2% |
-4% |
-4.5 to -3.5 |
19 |
232.53 |
87% |
117% |
5% |
-3% |
-4.5 to -3.5 |
80 |
404.43 |
49% |
123% |
18% |
-2% |
-4.5 to -3.5 |
9 |
522.56 |
44% |
49% |
32% |
-1% |
-4.5 to -3.5 |
0 |
- |
- |
- |
- |
0% |
-4.5 to -3.5 |
0 |
- |
- |
- |
- |
Now let’s consider what would happen if the RFFR rises. The inflation rate could drop over the next year to about 2%, and the federal funds rate should remain at 0% as announced by the Federal Reserve Chairman. Then the RFFR would be about -2% and its year-over-year change would be +2%. For this scenario we can use table 4 for an indication of the gold price change. One can then expect the gold price in one year from now to be about 25% lower than the present price; not 17% higher as implied by table 1 and figure 1.
Scenario 2: RFFR = -2%, ΔRFFR = +2%
Table 4 |
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year-over-year
change RFFR
ΔRFFR
+ and - 0.5%
|
Real Fed
Funds Rate
-2%
+0.5% & -0.5%
|
number of
occurrences
days |
year-over-year change of Gold price |
average
gain/loss
$ |
average
of all
occurrences
|
maximum
of all
occurrences |
minimum
of all
occurrences |
-6% |
-2.5 to -1.5 |
0 |
- |
- |
- |
- |
-5% |
-2.5 to -1.5 |
37 |
229.39 |
37% |
55% |
28% |
-4% |
-2.5 to -1.5 |
60 |
126.52 |
36% |
70% |
0% |
-3% |
-2.5 to -1.5 |
79 |
213.30 |
24% |
36% |
-7% |
-2% |
-2.5 to -1.5 |
124 |
141.92 |
24% |
105% |
-14% |
-1% |
-2.5 to -1.5 |
97 |
76.27 |
20% |
103% |
-11% |
0% |
-2.5 to -1.5 |
87 |
103.76 |
6% |
32% |
-26% |
1% |
-2.5 to -1.5 |
17 |
155.42 |
6% |
28% |
-25% |
2% |
-2.5 to -1.5 |
14 |
-46.48 |
-25% |
-21% |
-28% |
3% |
-2.5 to -1.5 |
27 |
-46.87 |
-26% |
-19% |
-29% |
4% |
-2.5 to -1.5 |
21 |
-43.97 |
-26% |
-24% |
-28% |
5% |
-2.5 to -1.5 |
0 |
- |
- |
- |
- |
But, lastly, what if inflation increases over the next 12 months by 1%? With the federal fund rate remaining at 0%, the RFFR would be about -5% and the year-over-year change of it would be -1%. My analysis of the data found no previous record of such an occurrence, as shown in table 5 below. The best we can do is to go to table 2, which shows an average increase of 9% for a year-over-year change of -1% for the RFFR. Figure 1 and table 1 show an increase of 38% and 14%, respectively, for a RFFR of -5%. All values are positive, and gold should gain under this scenario.
Scenario 3: RFFR = -5%, ΔRFFR = -1%
Table 5 |
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year-over-year
change RFFR
ΔRFFR
+ and - 0.5%
|
Real Fed
Funds Rate
-5%
+0.5% & -0.5%
|
number of
occurrences
days |
year-over-year change of Gold price |
average
gain/loss
$ |
average
of all
occurrences |
maximum
of all
occurrences |
minimum
of all
occurrences |
-6% |
-5.5 to -4.5 |
33 |
24.85 |
20% |
49% |
-4% |
-5% |
-5.5 to -4.5 |
64 |
130.07 |
49% |
144% |
-5% |
-4% |
-5.5 to -4.5 |
24 |
235.62 |
86% |
132% |
0% |
-3% |
-5.5 to -4.5 |
0 |
- |
- |
- |
- |
-2% |
-5.5 to -4.5 |
0 |
- |
- |
- |
- |
-1% |
-5.5 to -4.5 |
0 |
- |
- |
- |
- |
0% |
-5.5 to -4.5 |
0 |
- |
- |
- |
- |
Conclusion
Gold’s year-over-year return is dependent on both the RFFR and the RFFR’s year-over-year change.
One must monitor the federal funds rate and the inflation rate in order to predict the direction of gold prices. If, from its current level, the RFFR trends upwards, and the year-over-year change in the RFFR is greater than +1%, then one can expect the price of gold to decline. If the trend is downwards or zero, however, then the gold price should continue to advance.
Georg Vrba is a professional engineer who has been a consulting engineer for many years. In his opinion, mathematical models provide better guidance to market direction cthan financial “experts.” He has developed financial models for the stock market, the bond market and the yield curve, all published in Advisor Perspectives.
Read more articles by Georg Vrba, P.E.
