Factor Analysis

This week I will attempt to write a multiple regression analysis to help me create a model for trading gold.

I downloaded 20 years of the generic (forward-rolling) spot gold price from Bloomberg. I also downloaded 20 years of the 10-year and 2-year treasury yield from the U.S Department of the Treasury (U.S. Department of the Treasury, 2020).

In addition, I downloaded 20 years of CPI inflation data from the Bureau of Labor Statistics (Consumer Price Index, n.d.). Considering the U.S. dollar is the currency of choice when dealing with precious metals, I downloaded, from Bloomberg, 20 years of the U.S. Dollar Index to indicate the general international value of the U.S. dollar compared to a basket of major world currencies.

I wanted to see if I could write a multiple regression equation to determine the appropriate value of gold by using the following variables:

• U.S. Dollar Index

• CPI Inflation Data

• 10-year treasury yields

• 2-year treasury yields

• The spread between 2 and 10-year treasury yields

I ran a stepwise linear regression exercise in SPSS and received the following results.

Source: SPSS

The first thing I noted was the correlations of the variables to the price of gold.

The U.S. dollar, CPI, and the 2 and 10-year yield all exhibited inverse correlations to the price of gold. The 10 minus 2-year (yield curve was a weak positive correlation).

Doing the stepwise calculation, SPSS decided to throw out two of the five variables (2-year yield and the yield curve).

Source: SPSS

The three variables that were included in this model were 10-year yield, U.S. Dollar Index, and CPI inflation data. Looking at the model summary, the combined variables are showing a correlation coefficient of .886 and a coefficient of determination of .785. The Durbin-Watson reading of .088 indicates the possibility of auto-correlation within the model. That is beyond my scope of knowledge but I figured I’d mention it. The F values in ANOVA all indicated p<.01.

Source: SPSS

These are the coefficients for the model. Using the third output I come up with a regression equation of:

G = 2720.157 - 210.880(t) - 12.339(d) + 38.232(i)

Where:

G = The projected value of gold

t = 10-year treasury yield

d = U.S. Dollar Index

i = CPI inflation data

I decided to go back and try to test the results. I plugged in the appropriate variables over the past 20 years and tracked the spread between the actual price of gold and my projected regression price. I then averaged the difference between the two and calculated the standard deviation.

I used specific rules to track the results. I decided to record the 3-month, 6-month, and 1-year price performance of gold when the spot price of gold was 2 standard deviations overvalued from my regression value. I conducted the same analysis when the spot price of gold was 2 standard deviations undervalued from my regression value. I also conducted the price performance of gold when it was within +/- 2 standard deviations of my regression value.

The results were fascinating.

Figure 1: Return results.

In each of the examples, the 3-month, 6-month, and 1-year results were greatly improved by using the regression value as an entry point for the purchase of gold. Over the 3-month time period, the average annualized return for gold, when undervalued by 2 standard deviations is 10.8% and is profitable 58.3% of the time. The average annualized price performance of gold when overvalued by 2 standard deviations is -3.8% and is profitable 33.3% of the time.

Over the 6-month time period, the average annualized return for gold, when undervalued by 2 standard deviations is 10.2% and is profitable 66.7% of the time. The average annualized price performance of gold when overvalued by 2 standard deviations is 0.2% and is profitable 44.4% of the time.

Over the 1-year time period, the average annualized return for gold, when undervalued by 2 standard deviations is 16.3% and is profitable 91.7% of the time. The average annualized price performance of gold when overvalued by 2 standard deviations is -4.9% and is profitable 11.1% of the time.

The charts below show the monotonic nature of the analysis by time period.

Figure 2: 3-Month Annualized Returns

Figure 3: 6-Month Annualized Returns

Figure 4: 1-Year Returns

So conceivably, I can go long gold when the spot price is 2 standard deviations undervalued from my regression valuation and go short gold when it is 2 standard deviations overvalued from my regression valuation and get returns that are equivalent to approximately 20% annualized, for a one-year holding period.

Joseph S. Kalinowski, CFA

Consumer Price Index (CPI) Databases. (n.d.). Retrieved August 11, 2020, from https://www.bls.gov/cpi/data.htm

U.S. Department of the Treasury. (2020, August 07). Retrieved August 11, 2020, from https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/TextView.aspx?data=yield