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Introduction

With the continued upswing in the price of gold many investors are once again either wondering if they should buy, sell, or hold the metal in their investment portfolios. This article will examine the contributions made by the gold asset class to an investment portfolio allocated according to Modern Portfolio Theory (MPT).

Used by many fund managers and investment professionals, MPT allocates asset classes according to a desired average rate of return while simultaneously minimizing portfolio risk. Risk can be looked at as fluctuations in portfolio returns; in MPT, risk is measured by a statistical term called the standard deviation.

Because of the broad scope, this discussion is broken up into two parts. In the first part, we'll compare allocations, returns, and risk in portfolios where gold is included to those portfolios where it isn't. This comparison will tell us to what extent gold is meaningful as an asset class in a diversified portfolio with a long investment horizon.

In part two, we'll revisit an article written a couple of years ago to see what effect the recent rally in gold has had on long term returns. We'll examine it using traditional MPT assumptions and compare the results to those obtained by adding the extra dimension of optimized market timing to see how we can actually decrease risk while increasing returns.

The politics of gold

Our MPT portfolio includes the nine traditional asset classes (see tables below). Monthly total return data from all of these asset classes were only readily available after 1928 which is when we'd like to begin our analysis. We could start later, but in statistics, the more data one has, the more reliable the results.

One problem with this approach is that the price of gold was politically controlled for much of the time between 1928 and the present. In 1933, Americans were prohibited from owning non-jewelry gold and in 1961 they were even barred from holding gold in foreign countries.

Further, the price of gold was fixed in 1934 at $35 per ounce. That changed in 1968 when a two-tiered pricing system separated official transactions at the fixed price while providing for a free market at fluctuating prices. In 1975, Americans were once again allowed to officially own gold as an investment class.

MPT analyses require that data from all asset classes be available for the entire time period with the earliest date being designated as the starting point. Some might argue that 1975 should be the start date since the price of gold was artificially fixed before that. On the other hand, the political nature of gold pricing is a significant reality that should be considered in any analysis. As mentioned above, the performance of the other asset classes is better evaluated using as much data as possible. So, starting the analysis in 1928 has the advantage of including a much larger database from which to predict the performance of asset classes going forward from the present time. [An analysis of portfolios with and without gold using 1975 as the starting date can be found in the July 7 and July 8 articles written in 2009.]

The rise of gold

The figure below shows that one dollar invested in gold in January of 1928 would be worth just over $74 today. [A note on pricing: Gold prices used here are the London Price Fix, the most commonly used benchmark since 1919.]

(Click to enlarge)

As you can see, much of the activity has occurred since 1968 when the two-tiered market came into being. The first significant runup in the price preceded the lifting of the legal ownership ban and the second spike accompanied a period of high inflation in the US. Recently, gold has seen a resurgence as confidence in other financial assets has waned.

Current portfolio returns with and without gold

What does this all mean for your portfolio? Should you own gold, and if so, how much? The answers to these questions depend on your risk/return objectives.

Table 1 below shows the current MPT risk/return allocations among the nine traditional asset classes (excluding gold). The average annual compounded rate of returns currently achievable by the MPT model are listed in the first column. The second column shows the risk (standard deviation) which naturally increases along with the required return. Subsequent columns show the probability of portfolio loss in any one year and the Sharpe Ratio which is a measure of return versus risk with higher numbers being more desirable. This table and the next one were derived from the SMC Analyzer portfolio optimization software.

(Click to enlarge)

[To use this table, decide which return in Column 1 is right for you, according to your own appetite for risk and your investment horizon. Then, form your portfolio according to the allocations shown in that row. Note that all of these asset classes having corresponding mutual funds and/or etfs that mimic the underlying asset class; for example, the SPY - the S&P 500 ETF - could be used as a proxy for large company stocks.]

Now let's see what effect adding gold as an asset class does to the above allocations. The right-most column in Table 2 below shows the gold allocations as calculated by MPT.

(Click to enlarge)

As you can see, MPT allocates gold into only the most conservative portfolios, and then only at modest percentages. Furthermore, the addition of gold provides virtually no risk reduction in those portfolios. This somewhat counterintuitive result supports the conclusion of economist Thomas Sowell who in his book, "Basic Economics: A Citizens Guide to the Economy,' noted that over time stocks and bonds have produced greater returns than gold.

A comparison of historical returns

The above chart shows that a portfolio constructed for a 6% return has the largest allocation of gold. Using this return objective, let's compare how a portfolio with gold would have compared with a comparable one without gold. Running the MPT analysis from 1928 to the present, we see from the figure below that while both portfolios actually exceeded their targeted return, the no gold portfolio did so with lower risk (6.8% vs 7.3%).

(Click to enlarge)

Conclusion

There is no doubt that over the past few years gold has indeed been a spectacular investment but the data show that growth is sporadic. MPT portfolios are not about producing extraordinary returns in the short term; rather, they are designed to achieve a defined objective return at minimum risk over the long haul.

If you're a die-hard gold bug who believes that the yellow metal has more room to run, then by all means go out and get yourself some. The moral of the story: Just don't overdo it.

In a follow up article we'll look at the effects of gold on a portfolio that uses an optimized market timing approach to MPT to see if we can achieve greater returns at lower risk.

Note: Pat Glenn contributed research and analysis to this article.

Source: The Effect of Gold on a Diversified Portfolio