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Most casual investors believe gold underperformed stocks in 2012. SPY went from $122.78 (dividend adjusted) on Dec. 30, 2011, to $142.41 on Dec. 31, 2012, a return of 15.99% (dividends included). GLD moved from $151.99 to $162.02 over the same time period to return 6.60% (data from Yahoo Finance).

Trivially, 15.99% > 6.60% and this leads too many investors to proclaim that gold has underperformed stocks. However, this initial investigation is superficial. Remember, the name of this website is "Seeking Alpha." Alpha refers to Jensen's alpha, which is explained in an article here. The article offers the following formula:

Click to enlarge images.

Since the risk-free rate is currently zero, the formula reduces to the following:

Alpha = Return - [Beta(GLD,SPY) * Return]

I calculated the beta, using Excel, for the daily returns of GLD and SPY to be .3022 over 2012. Hence, plugging all of the inputs into the formula one gets the following:

Alpha = 6.60% - [.3022 * 15.99%]

Alpha = 6.60% - [ 4.83% ]

Alpha = 1.77%

Not great, but not bad for a supposedly barbarous relic!

Now, can this be improved? I noticed some interesting patterns occurring in a chart of GLD. If one had simply bought the open and sold the close every trading day in 2012, a trader could have made $13.53 -- trading just one share -- before trading costs. This would beat the advance over the whole year of $10.03, but after adding in $0.03 of trading costs per round-trip trade, then one would only be left with $6.03.

(I used $0.03 a share of trading costs because I can get a commission of $0.005 a share, and slippage is assumed to be not much at the open and close. A guess of $0.01 a share. Hence, $0.015 of slippage and commission at the open plus $0.015 of slippage and commission at the close is $0.03 a share.)

I then applied a mean reversion strategy to the basic buy open and sell close day trading rule. If today's close is greater than the close of the average close of the last 20 days (including today), then tomorrow, sell the open and buy the close. In other words, expect GLD to trade toward the 20-day simple moving average. If the close today is less than or equal to the 20-day average, then tomorrow follow the original rules of buying the open and selling the close. Again, this assumes over time GLD will trade toward its 20-day simple moving average.

I was greatly surprised by the results, since they not only beat buy and hold but blew it away. Before trading costs this strategy made $31.19 a share. After trading costs of $0.03 a share, the mean reversion strategy returned $24.26 a share, or 14.87% (totaling up the daily returns). That's over double the return of 2012, but this technique started trading on Jan. 31, 2012, when GLD closed at $169.31. An investor holding GLD until the end of 2012 then lost $7.29, or 4.31%, a share from this close. However, as discussed above, what are the risk-adjusted returns? That is, alpha?

To find out, I calculated the daily returns of GLD from Jan. 31, 2012, until the end of the year. I then computed the beta of GLD's returns to the mean reversion strategy's returns that counted trading costs. The beta result was -0.124. Therefore, plugging into the formula:

Alpha = 14.87% - [ -.124 *-4.31%]

Alpha = 14.87% - [ .54% ]

Alpha = 14.34%

A figure that every chief investment officer would love. Still, how does this compare to the standard benchmark -- that is, the SPY?

So I took the daily returns of SPY of the same time period the GLD mean reversion strategy ran: Jan. 31, 2012, to Dec. 31, 2012. Over this time frame SPY advanced 10.85% (including dividends). The beta of the GLD mean reversion strategy and SPY was -0.131. Again, plugging into the formula:

Alpha = 14.87% - [-.131 * 10.85%]

Alpha = 14.87% - [ - 1.42% ]

Alpha = 16.29%

That's the best result so far, and just by adding a simple mean reversion strategy. If slippage costs rose to $0.03 a share, at both the open and close, then with total costs it would be $0.07 a share. That results in the mean reversion strategy alpha falling to 8.63% and 10.58%.

Past performance is not necessarily indicative of future results. That said, in 2013, the mean reversion strategy has shown a profit of $2.54 a share after costs of $0.03 a share. All this while GLD moved up only $0.54 a share from $162.02 on Dec. 31, 2012, to $162.56 at the close on Jan. 15, 2013.

Investors and traders who do not expect a strongly trending market should look into incorporating mean reversion techniques. This research shows how it can be beneficial to a portfolio by using an instrument that does not advance or decline by double digits, in absolute terms, but double-digit absolute and risk-adjusted returns were achieved by using a tactical trading strategy. Here is a link on a working paper (PDF) to use mean reversion in the equity markets.

In the near future I will expand my analysis of GLD to the beginning of its trading and examine the results, so stay tuned.

Snapshots of my spreadsheets are shown below:

Here are the 2013 results until Jan. 15:

Disclaimer: Past performance is not necessarily indicative of future results. This article is meant for educational information only. Any trade or investment has risk and is the responsibility of the reader. The author makes no claims or guarantees of future profitability.

Source: Gold Mean Reversion For Alpha