Gold (NYSEARCA:GLD) has had a very impressive performance this year so far, after 3 years of poor performance.

*Source: Seeking Alpha*

25.8% YTD performance and a 21.6% one year return look very enticing to investors, but should investors chase this performance?

Yes, if they believe that past returns, over the last 10 years, and the correlations of returns will hold going forward.

There is a simple quantitative test to assess if a new asset class should be added to a portfolio using its Sharpe ratio and correlation to the existing portfolio. The equation is:

Sharpe (new asset) > Sharpe (Port.) * Correlation(new asset, Port.)

"â€¦ for the investor to gain by adding the asset class, that asset class's Sharpe ratio must exceed the product of the existing portfolio's Sharpe ratio and the correlation of the asset class's return with the current portfolio's return. â€¦ an asset class should be added if its risk premium per unit of risk is greater than the risk premium per unit of risk for the existing port- folio, adjusted for the new asset's correlation with the existing portfolio."

(Institute p. 202)

Source: Institute, CFA.

CFA Institute Level III 2014 Volume 3 Capital Market Expectations, Market Valuation, and Asset Allocation. John Wiley & Sons P&T, 2013-07-12. VitalBook file.

I should note that these Sharpe ratios are based upon expectations. I can imagine investors have different expectations for returns, but it is very difficult to forecast correlations over the long term, and one is typically left with historical analysis.

With those caveats let's look at the data.

The easiest way I found to conduct this analysis is to use the free web program from portfolio visualizer. The purpose of this program is to actually perform testing of market timing models; however, it provides performance data for the asset class selected. This includes the asset's Sharpe ratio and Correlation to the US Market (SP-500 or SPY if using an ETF).

One simply selects GLD for the tick and then SP-500 Total Return for the benchmark; we do not care what "timing" model is used. We only care about the performance metrics of the "Buy and Hold Portfolio" ticker which we entered and the Sharpe ratio of the "benchmark".

When one does this the following results are produced.

*Source: Portfolio Visualizer*

One can see that GLD and the SP-500 had the same Sharpe of .48 over this time frame (Jan 2006 - Jun 2006).

"Big Deal, I got the same risk adjusted returns just by investing in the SP-500. I don't need gold in my portfolio" a naive investor might say.

This investor forgot to think about the correlation effect on the portfolio. Over this time period GLD had very lowly correlation to the SP-500, only .05.

Going back to our equation, we can plug in the figures:

.48 > .48 * .05 which reduces to

.48 > .024

This is true, so we then know that historically adding GLD to a stock portfolio would have produced better risk adjusted returns.

One might say, "That is only because of this year's great performance!"

Fine. We can have the backtest stop in 2015, after GLD had 3 years of negative returns. These are the results.

*Source: Portfolio Visualizer*

I am not sure why, but the software now includes comparisons to not only the SP-500, but also the bond market and a "balanced portfolio" (which I assume is 50% GLD and 50% SP-500).

This "balanced portfolio" showed the highest Sharpe ratio over the testing period. It was not just 2016's performance.

We can even test it against a 60/40 stock and bond fund, Vanguard's mutual fund (MUTF:VBINX).

*Source: Portfolio Visualizer*

We again find that the "balanced" GLD and SP-500 portfolio had both higher Sharpe and Sortino performance metrics. The Vanguard 60/40 portfolio had a correlation of almost 1, at .99, while GLD was only .07. I think it would be a safe guess to think that GLD could possibly help a tradition 60/40 stock and bond portfolio.

Let us assume that statistically the correlation of VBINX is equal to 1, which is not hard since it was .99

Then plug into the formula:

.39 > .60 * .07

.39 > .042

Having gold would have helped the traditional 60/40 portfolio. This is also seen in the performance metrics of the new "balanced" portfolio (50% GLD and 50% VBINX I assume).

I therefore encourage long term investors to consider an allocation to gold in their portfolio. This investment thesis is meant for long term investors, and not short term traders or speculators. As always past performance may not be indicative of future results.

If an investor does their due diligence and comes to a conclusion that over the long term gold will have positive returns, which will have a low correlation to the SP-500, then gold, or GLD, should be in their portfolio. If you are scared about the recent run up in gold, then simply try the old stock routine of dollar cost averaging.

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

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I own physical gold and have positions in gold mining stocks