A Golden Portfolio (Part I)

Sources: LBMA, Nasdaq OMX Group

Many investors hold a portfolio containing only equities. Some 'balanced' portfolios will be a mixture of equities and bonds (often only conventional though with no index-linked bonds). But what is the effect of holding gold in your portfolio? The legendary investor Warren Buffet has famously disdained gold because of its lack of usefulness. But you don't have to go far on the Bank of England website to find a profusion of information on the subject. They boast of the 400,000 bars of gold in their vault. I make that around $240 billion at a current price of $1500/troy ounce. That's a lot of money just sitting there looking at you.

The chart above uses data taken from the US Federal Reserve database FRED. I've chosen to use the Nasdaq Composite because of the availability of data going back to the 1970s. This was a period of high inflation in which gold performed well but in subsequent decades it lagged. Still the chart clearly shows the superior performance of gold in many years. But more importantly for investors it shows very definite lack of correlation with equities (Nasdaq Composite). There are sharp peaks in each asset which are not present in the other. This suggests that there will be strong benefits to holding both in a portfolio.

Some Statistics

Firstly I'd like to investigate the statistical properties of the price series for gold and the Nasdaq. The result of some calculations are shown below.

The table lists some statistics for the returns of both the Nasdaq Composite and gold. The returns are just the daily change in the price of the asset expressed as a % of the previous day's price. So it's the normal % that you see on most financial websites. What is very striking about the table is the similarity between gold and the Nasdaq Composite. The mean returns are both nicely positive. The standard deviations are similar and equate to an annual volatility of around 20% that you'd expect for an equity index. The maximum and minimum % returns are also similar. Surprising here is that gold makes big declines as well as big advances. Financial journalists often pen stories about the price of gold jumping but almost never about it crashing. The maximum and minimum % price changes for gold both occurred in 1980 at a time of great geo-political instability following the Iranian hostage crisis.
The other figures in the table are for the skew and kurtosis which may be less common but nonetheless interesting. The skew describes whether the statistical distribution of the returns is symmetrical or not. The positive value for gold shows that it is skewed to the right - in other words positive returns and so the folklore about gold is correct. The gold price does jump up more than equities. The final figure is for the kurtosis. This is a measure of the long-tailedness of the returns distribution. The value of around 10 shows that for both gold and the Nasdaq Composite large price changes of either sign are far more frequent than you'd expect from a normal (Gaussian) distribution.

Another Perspective

If you're still sceptical of this striking statistical similarity between gold and an equity index I can present the data as a chart. After all a picture is often better than a table of numbers. Below you can see the distribution of the returns as histograms:

Distribution of returns histograms

Can you spot the difference? The spread of the distributions is about the same but if you look carefully you should be able to notice the positive skew of the gold distribution.

Correlation between returns

Technical note

The correlation between two price series is a statistical measure of their similarity. If one series tends to increase when the other increases and decrease when the other decreases they will be positively correlated. If, on the other hand increases in one series are associated with decreases in the other then they will be negatively correlated. The correlation ranges in value between +1 for perfectly correlated series and -1 for anti-correlated series. In my book "Quantitative Finance for Dummies" John Wiley 2016 you can read more about this in Chapter 9.

An interesting question is whether it is worth investing gold. There are differing views on this with Buffet being very negative. To an extent he is correct because gold comes with no dividend or coupon unlike equities or bond or plain simple interest from cash. Perhaps though soon it will become more popular as bond yields surprisingly become negative and so the lack of a coupon is an advantage! There are many 'gold bugs' who like the ability of the asset to outperform in times of stress such as the late 70s. And of course central banks have never tired of gold despite the economist Keynes regarding it as a 'barbarous relic'. Why central banks hold so much gold is an interesting question I may come back to.

My take on whether to hold gold or not is based on looking at the correlation between the price movements of gold and my representative equity index, the Nasdaq Composite. The chart at the top of this article clearly shows a long term tendency for the price of gold to rise. That's good. I don't feel qualified (or brave enough!) to comment on any shorter term moves. But will holding gold improve the performance of your portfolio as measured by, for example, drawdowns or the Sharpe ratio? The answer is almost certainly yes and you can tell this by looking at the correlations:

Correlation between returns of the Nasdaq Composite and gold

The chart shows for every year between 1971 and 2020 the correlation between the Nasdaq Composite and the gold price. The values fluctuate around zero. For anyone wanting to manage risk in a portfolio this is manna. Around 1980 you can see some big fluctuations in the correlation but they never get bigger in magnitude than 0.3. By comparison equities are often correlated at 0.9 between each other meaning that it is hard to diversify a portfolio consisting just of equities and reduce risk. Gold is a unique asset which can have a very beneficial effect on portfolio performance. I'll be investigating this in more detail in later posts.

Conclusion

On the Financial Times website I searched for 'gold' and came up with a list of many fascinating articles. As a Glaswegian it was interesting to read about the Cononish Glen  mine which is currently being developed. In another article Rana Foroofar says that 'You have to really believe the sky is falling in to hoard physical bars in a digital age'. Central banks clearly don't agree with her and neither do I. Of course investors can hold Exchange Traded Funds which have bullion backing but this amounts to the same thing. An opposing view, which I agree with, is an article by Paras Anand from Fidelity International 'Why Buffet is wrong to dismiss the benefits of gold'. Hopefully I've explained why in this post but I'll be returning to consider other aspects of this debate later in case I haven't.