# A Simple Formula For The Fair Price Of Gold

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Includes: GLD
by: Difu Wu

Gold, which has no earnings, no book value, no cash flow and pays no dividends, can be difficult to value directly. Stocks, by comparison, are much easier to value. If we can link the valuation of stocks to gold, we have an indirect method for the valuation of gold. Fortunately, this link is provided by the historic Dow/gold ratio, as shown in Chart 1 below. Chart 1. 200 years of Dow/gold ratio, with trendline and 75% confidence interval in green. Chart from sharelynx.com. The trendline has a definite upward slope, which means that stocks have become increasingly valuable compared to gold over the past 200 years. This is not surprising, since gold is a stable nonproductive commodity, while companies have the ability to innovate and find ways to grow earnings along with human progress. This chart is a semilog plot, so equation for the trendline is given by log (F(x)) = mx + b. The Dow/gold ratio trendline sits at about 1 in 1860, and at about 20 in 2010, with a slope m = (log20-log1)/(2010-1860) = 0.00867. Plugging in F(x) = 20, x = 2010, and m = 0.00867, we get b = -16.12567. A formula for the fair value of the Dow/gold ratio can therefore be given by Eq 1 below:

Fair Dow/gold ratio = 10^ (0.00867*Current Year - 16.12567) Eq. 1

I propose a simple formula for the valuation of gold:

Fair Gold Price = (Fair Dow Price) / (Fair Dow/gold ratio) Eq. 2

The fair price for the Dow can be determined by a number of valuation techniques. One the most common and simplest method is via the price/earnings (P/E) ratio. Chart 2 below shows that the Dow's P/E has averaged about 15 since 1929. Chart 2. Normalized P/E of the Dow since 1929. Note that normalized P/E is calculated using earnings averaged from five years prior to five years after. Chart from observationsandnotes.blogspot.com. Although the Dow's P/E has shown marked variability through the years since 1929, it has averaged about 15, and we have little evidence to suggest that the fair P/E for the Dow in the future should be significantly lower or higher than its historic average. Therefore, we can estimate the fair value for the Dow as follows:

Fair Dow Price = Current Dow Price * (15/(Current P/E)) Eq. 3

Combining Eq. 1-3, we have:

Fair Gold Price = (Current Dow Price * (15/(Current P/E))) / (10^ (0.00867*Current Year - 16.12567)) Eq. 4

For example, say the current Dow price is 12,217 (on Dec 30, 2011), the current P/E is 15, and the current year is 2011. Plugging all these in gives us a fair gold price = \$599. Please note that my proposed valuation method for gold is imprecise, since both Dow/gold ratio and P/E show significant variability. Therefore, I further propose that the fair gold price should be estimated as a range, from half the estimated fair gold price calcuated, to twice the estimate. So given the estimate of \$599, we would estimate the fair gold price range as \$299 - \$1198. The current gold price is \$1564 (on Dec 30, 2011), which is clearly overvalued.

Bottom Line: 1. If the current gold price is below half the fair gold price as calculated by Eq. 4: gold is undervalued -- Buy. 2. If the current gold price is above twice the fair gold price as calculated by Eq. 4: gold is overvalued -- Sell. 3. If the current gold price is between half to twice the fair gold price as calculated by Eq. 4: gold is probably fairly valued -- Hold.

Buy gold if other assets such as stocks and bonds are overvalued. Sell gold if other assets such as stocks and bonds are undervalued and use the proceeds to buy the better valued assets. If stocks are fairly priced, I would favor buying stocks when gold is also fairly valued, because the long term trend for the Dow/gold ratio is up.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.