A Golden Portfolio (Part II)

Bust of Empress Domitia (reverse) Domitian's son on a gold coin 82-83AD

With kind permission from The British Museum

This post is a continuation of an earlier post on the 23rd January in which I compared gold bullion with equities (Nasdaq Composite) as an investment. The results there showed that the statistics of the gold price were, surprisingly, very similar to those for the Nasdaq Composite. But the gold price has an almost zero correlation with equity prices. In this post I'm going to show that this makes gold a very valuable holding alongside equities in a diversified portfolio.

As the picture above indicates gold has been used as a currency and store of value for millennia. Rome issued gold coins with art work that wouldn't be too out of place in mints today such as the Royal Canadian Mint which still issues coins for investment purposes. Modern finance has made it easier to invest in gold though, using instruments such as Exchange Traded Funds (ETF) which track the bullion price. ETFs are issued by major investment managers such as BlackRock and Vanguard. For both retail and professional investors there is no reason not to hold gold.

Who holds Gold?

What's not to like about gold? Well, many 'diversified' portfolios set up by established investment managers do not feature gold. There is a modern uneasiness about gold. Maybe Keynes's 'barbaric relic' comment has something to do with it. But that comment was about the gold standard and not about gold itself. For a historical perspective on the gold standard in the US this Congressional Research Service report is very helpful. It was only in 1973 that the US dollar could no longer be redeemed for gold. But that didn't mean the end of gold in the financial system. The bar chart below shows the values given in billions of US dollars of the gold reserves of some major economies. The numbers look large but to put them into perspective several tech stocks such as Amazon have a value (market capitalisation) in excess of $1000billion (=$trillion) Outstanding treasury notes amount to a debt of almost $10trillion. But nonetheless the prevalence and magnitude of government holdings of gold says something about its value even today. UK Treasury holdings of gold are low by international standards following the sale of substantial amounts between 1999 and 2002. The reason for this was probably to prepare for the introduction of the euro by purchasing some of the new currency. The price of gold had been in decline for over a decade (see my previous post for a chart) and this may also have played a role. But subsequent history was cruel with the price rising sharply in the following decade. With Gordon Brown as the Chancellor of the Exchequer (Finance Minister) at the time financial traders unkindly called this significant low in the gold price during these sales as the 'brown bottom'...

Data source: TradingEconomics.com

If you're wondering just how much these gold reserves are physically I calculate that the US holds around 8,133 tonnes of gold which, given the density of the metal, is not such a big pile.

Correlations Again

To make the disconnection between equity prices and the gold price clear I've shown a chart below of the rolling correlation between the gold price and the Nasdaq Composite for the past 50 years.

Data source: St Louis Fed FRED database

The long term average is clearly zero although there have been short periods such as in the early 80s when there seems to be a short period of positive correlation. Government bonds also show low correlation with equity indices although historically they have often shown a positive correlation and so cannot be considered as diversifying. So if gold has little or no connection to the equity market what does drive the gold price?

Gold's dynamics

In the popular imagination the gold price is moved upward by wars and disasters. It's a hedge against unwanted events. Perhaps that is why holding it seems distasteful. But in fact it's part of the reason that makes gold a good form of insurance in an investment portfolio. It's better than insurance though because in the long run the gold price grows and can protect against inflation as it did in the 70s. Portfolio insurance such as options cost money (there's a premium to pay) and often expire valueless. This disaster insurance story only explains part of the price dynamics for gold. The histogram for the price returns of gold in my first post (23rd January) show that there are as many sharp declines in the price of gold as there are sharp rises. This is puzzling given that almost all media stories I've read about gold are when it rises.

Real Rates

Another key factor that drives the price of gold is the real interest rate. That's the nominal interest rate less the rate of inflation. When the real interest rate is high the price of gold tends to be decline and when it's low it tends to rise. You can see this in the chart below.

Influence of real yields on the gold price.

Data source: St Louis Fed FRED database

To a great extent the curves mirror each other especially in the past year. The data I've used for the real yields originate from the market for US Treasury Inflation Protected Securities or TIPS. This dynamics of the gold price is presumably related to its lack of yield. When the real yield is high good returns can be achieved using government bonds and so there is less point to holding gold. However with a low real yield gold is still attractive as a hedge against inflation and so its price often rises.

This connection between the real interest rate and the price of gold may be more significant than at first glance. Professor Jonathan Haskel from Imperial College in London UK has argued that the rise in importance of intangible assets such as software and patents has reduced the real rate of interest. The arguments are subtle but stem from the fact that intangible assets cannot be used as collateral for a loan. You can read more about this at Bank of England Speeches. Perhaps this is part of the explanation for the systematic rise in the price of gold since the dot.com boom of 2000.

Building a Portfolio with Gold

If gold is good for your portfolio then how much of it should you hold? I'm going to try and answer this with a simple example using only the Nasdaq Composite to represent equities and the gold bullion price in $US. This is clearly a simplification over a realistic portfolio for long term savings but perhaps not to much. The Nasdaq Composite is a very broad diversified index, perhaps more so than many portfolios used for long term investing. My experiment here is to see how much benefit there is to holding gold as well as the Nasdaq composite. I expect the conclusions to hold true for other major equity indices such as the FTSE 100. I shall assess the portfolios holding gold and the Nasdaq Composite using the Sharpe ratio which is the mean return of the portfolio divided by the standard deviation of the returns. The Sharpe ratio is commonly used to measure the performance of investment funds as it establishes a balance between risk and return. Lower volatility portfolios will have higher Sharpe ratios given the same mean return. The chart below is a picture of my findings:

The curve shows the effect on risk(σ) and return of varying the fraction of gold in a portfolio .

The efficient frontier is shown as a thick black line. These are the portfolios with the highest return for a given level of risk (σ). I'm measuring risk here using the standard deviation of the portfolio returns, indicated by σ, and commonly called the volatility. The curve plots the possible portfolios that can be built using gold and the Nasdaq Composite starting from 100% gold in the lower right and ending with 100% Nasdaq Composite in the upper right. The efficient frontier consists of portfolios in which the majority is held in equities, in this case the Nasdaq Composite. The optimum portfolio in terms of the Sharpe ratio turns out to be with 40% gold and 60% Nasdaq Composite. In the table below I compare this optimum portfolio with gold and the Nasdaq Composite. The numbers are for a portfolio valued at US$100 in 1971 and running until 2020.

Performance of Portfolio of Gold (40%) and Nasdaq Composite (60%)

The table shows that the optimum portfolio has a Sharpe ratio slightly higher than the Nasdaq Composite but with a reduced and significantly shorter maximum drawdown. Nice.