What would the optimal portfolio allocation in gold have been according to Modern Portfolio Theory over several different periods of time? This article has a look at how an investor could have combined gold and equities to enhance risk-adjusted returns.
So asks Axel Merk in edited excerpts from his original article* entitled The Case for Gold: Optimal Portfolio Allocation.
[The following is presented by Lorimer Wilson, editor of www.munKNEE.com and has been edited, abridged and/or reformatted (some sub-titles and bold/italics emphases) for the sake of clarity and brevity to ensure a fast and easy read. This paragraph must be included in any article re-posting to avoid copyright infringement.]
Merk goes on to say in further edited excerpts:
Modern Portfolio Theory
…The Modern Portfolio Theory presents an Efficient Frontier [consisting of] an investment mix that maximizes expected returns for a given amount of expected risk. An Optimal Portfolio provides the highest risk-adjusted return; often defined by professional investors as the portfolio with the highest Sharpe ratio, a measure of return per unit of risk as measured by standard deviation of returns.
Figure 1 below shows a typical way of depicting the Efficient Frontier between stocks and bonds, indicating what the optimal portfolio with the highest Sharpe ratio would be; the particular allocation to stocks and bonds respectively that would yield the best risk-adjusted return. The theory is not without its critics, notably because hindsight is often a key ingredient as to how an Optimal Portfolio is constructed.
Time Horizons Studied
Our paper analyzes what an Optimal Portfolio containing gold and equities would have looked like over three different time horizons:
- Past 10 years (daily data from February, 2004 – February 28, 2014)
- Since August 1971 (monthly data from July 31, 1971 – February 28, 2014)
- Since 1934 (monthly data from December 31, 1933 – February 28, 2014)
While a 10-year horizon appears reasonably long, keep in mind that five years ago, we were right at the peak of the financial crisis; we wanted our time period to be long enough to include “normal” times as well as “crisis.”
For a longer historic comparison of over 30 years, we choose August 1971 as a reference point to gauge the long-term performance of gold; it was on August 15, 1971, that President Nixon ended the convertibility of the dollar to gold. While that is truly a long-term horizon, one could argue that the gold price was artificially depressed until then; and as a result, any return calculated since then might overstate the potential long-term rate of return for gold.
To address the above mentioned criticism, as a third variant, we went all the way back to the beginning of 1934: when the Gold Reserve Act changed the nominal price of gold from $20.67 per troy ounce to $35. By going back to 1934, we had to limit ourselves to a comparison between gold and stocks (using the S&P 500) to reduce data quality issues with bond indices if we wanted to include bonds. Also note:
- We include dividends in equity returns, and consider a “risk free” rate to find the Optimal Portfolio.
- The S&P 500 Index was only created in 1957, but a composite of the index is available that we believe is a good representation of the preceding years;
- Dividend information is not readily available for all years. As a result, we relied on research of others. Since 1934, the average dividend yield of the S&P 500 (INDEXSP:.INX) has been approximately 3.69%.
When studying the results of our analysis and the accompanying figures, please keep in mind:
- These are not investment recommendations;
- These models use perfect hindsight, i.e., suggesting what would have been the Optimal Portfolio given the returns and risks prevalent during the period;
- The Optimal Portfolios are chosen in the beginning of the period and never rebalanced. In a future analysis, we will discuss the impact of periodic rebalancing.
1. The 10-Year View
Figure 2 shows the Efficient Frontier between stocks and gold over a 10-year time horizon. We used the S&P 500 Index as a proxy for the stock market. Figure 3 summarizes the allocation to gold and stocks (S&P 500), respectively, that would yield the Optimal Portfolio for the same time frame.
These findings suggest that given a choice between investing in the S&P 500 and gold, an investor would have had the best risk-adjusted returns investing 68% in gold and 32% in the S&P 500. Allocating more to equities might have yielded higher returns, but the volatility of returns would have been substantially higher.
Does this mean an investor should have more than half of their investable assets in gold? No, among other reasons, because:
- We don’t know what returns gold and the S&P 500 will provide going forward;
- The investment universe is comprised of more than the S&P 500 and gold.
One possible conclusion is that adding any uncorrelated asset to the S&P 500 may improve an overall portfolio but the data also suggests that if one’s outlook for gold or the S&P 500 is different from what it has been in the past ten years, the “optimal portfolio” may look different.
2. A 43-Year View
For a longer time period, please see Figures 4 and 5.
In the 30+ Year View going back to August 1971, the optimal gold allocation drops from 68% to 29%. Mind you, this includes the run-up in 1980, as well as the subsequent 20-year bear market in gold that followed. It’s likely there aren’t many investors that piled up on gold and the S&P back in 1971, then never rebalanced their portfolio. Still, the takeaway should be that diversification with uncorrelated assets matter, as it is possible to substantially lower the volatility of a portfolio by adding an uncorrelated asset. That applies despite the fact that gold was more volatile than the S&P 500 since 1971 (different from the risk profile over the most recent 5 year period where gold was less volatile than the S&P 500).
3. An 80-Year View
Now, let’s go back 80 years: please look at Figures 6 and 7.
Allocating 41% to gold since 1934 would have, according to the theory, provided the “optimal” risk adjusted return: by sacrificing just a little in return, the overall volatility of the portfolio could have been substantially lowered.
A couple of caveats:
- There were restrictions on own gold ownership for U.S. persons from 1933 – 1974; the rules were amended over the years; effectively, starting in 1964, U.S. persons were able to at least invest in gold certificates.
- Until 1971, the price of gold was not free floating; the model, as a result, gives the appearance that gold was less risky (i.e., the dollar price less volatile) than it might have been in a free market. We are talking about hidden risks here not well captured when using historical standard deviation of returns, although the risk was ultimately more to the U.S. dollar that plunged relative to gold once the yellow metal was cut loose in 1971.
- The above chart shows that the Optimal Portfolio is not at the tip of the curve; to understand why, look back at Figure 1: to find the best risk-adjusted return, the portfolio with the highest sharpe ratio, it is in the context of a benchmark risk-free return. Since 1934, the average “risk free” rate over the past 80 years was 3.67%. It’s fair to question using the same average risk-free rate for all those years.
- By using December 31, 1933 as the starting point, we are putting gold at a competitive disadvantage, as the market had plunged relative to the heights seen before the 1929 stock market crash. At the end of 2013, a Wall Street Journal article referenced the long-term annual return of the S&P 500 as 5.5% since 1927. Alternatively, we observed almost double the amount at 10.55%. Aside from the 1929 crash (from which there was a partial recovery by the end of 1933), the difference is explained by the fact that the returns stated by the Wall Street Journal exclude the reinvestment of dividends.
Gold in a Balanced “60/40” Portfolio
With this context provided, let’s look again at the past 10 years, but this time, adding bonds into the mix. We assume a static 60/40 ratio of stocks to bonds, often referred to as a Balanced Portfolio, then add the “optimal” amount of gold to the mix – again using hindsight: take a look at Figures 8 and 9.
Unlike the first example that suggested a 68% allocation to gold when combined with stocks, a 42% allocation to gold added to a Balanced Portfolio would have yielded the Optimal Portfolio. Here, gold outperforms the balanced portfolio by a tad, yet one can lower the overall risk profile of a balanced portfolio by adding a gold component.
Clearly past returns are no proof of future results. Will the seemingly meteoric rise of stocks continue? Have we reached a peak in bonds?…[Might gold experience another] significant price decline like it did in 2013? Indeed, if one extrapolated from the recent negative returns of gold, the “optimal portfolio” may well suggest a 0% allocation to gold, assuming other asset classes yield positive returns.
What are the Other Alternatives?
Most investors don’t allocate 30%+ of their portfolios to gold; neither can we make such an investment recommendation, but…we should really be asking the opposite question: is it sensible for investors to have up to 70%, possibly more, of their portfolio in stocks? This exercise shows that adding investments with low correlation to stocks may improve a portfolio by enhancing its risk-adjusted return.
Aside from including international stocks and bonds, other candidates to consider for inclusion in an investment portfolio are:
- Real estate
- Commodities, including gold
- Currencies (directional), such as a managed basket of currencies
- Currencies (non-directional), such as an absolute return “long/short” strategy
- Managed futures
- Hedge funds
To find an Optimal Portfolio, it’s important to understand how the underlying securities in the portfolio interact with one another…as correlations across securities and asset classes are not stable….
Figure 10 shows a selection of other alternative investments and how they correlate to both equities and bonds.
Note that, in recent years, international equities have had a comparatively high correlation to the S&P 500. We have been arguing for some time that investors in international stocks may have primarily been receiving additional return through commensurately higher risk rather than improving the overall return/risk profile of their portfolios. As a result, we encourage investors to consider truer forms of diversification, noting that currency strategies may provide particularly low correlation to U.S. stocks and bonds. Gold is a well-known way to diversify out of the U.S. dollar, however there may be other opportunities worth exploring further.
The theory works best when we plug in “expected” returns….In practice, [however,] many investors use historical returns [and,] as you might imagine, these models heavily favors assets that had a good return during the given look-back period – so don’t think the result is unbiased simply because you let a computer generate results. Indeed, one of the biggest challenges in presenting Optimal Portfolios is that they are heavily influenced by the underlying assumptions. Someone can show you that a given investment would have made a fantastic addition to your portfolio, but you may want to look more closely whether the assumptions are realistic going forward.
Just as returns play a role, so does risk. In finance, a lot of investors employ standard deviation of returns as a measure of risk yet many investors are just fine with “upside risk,” but do have a problem with “downside risk” (there’s a measure for that, the Sortino Ratio). Maybe just as relevant, these models are not very good at capturing high risk, low probability events, also called market crashes. In other words, an optimization analysis that uses historical returns may understate risk if the time period used does not capture a market crash in that given asset. Furthermore, many measures of risk are relative to a benchmark “risk free” rate; but in today’s world, one might argue that there’s no such thing as a risk free investment in an environment with negative real interest rates placing one’s purchasing power is at risk no matter what one does.
Optimal Portfolio: Really?
The takeaway from this exercise may be to look at alternatives in general as a supplement to a traditional equity and bond portfolio. Investors may want to take a pro-active approach to learn how to add value to a portfolio, keeping an open mind about the risks and opportunities out there, especially after the run-up the stock market has had.
To invest profitably, it may be more about developing a robust investment process rather than plugging in make believe numbers into a model….
[Editor’s Note: The author’s views and conclusions in the above article are unaltered and no personal comments have been included to maintain the integrity of the original post. Furthermore, the views, conclusions and any recommendations offered in this article are not to be construed as an endorsement of such by the editor.]
*http://www.merkinvestments.com/downloads/2014-03-20-case-for-gold-optimal-portfolio-allocation.pdf (© 2014 Merk Investments LLC)
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