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Are the UK and the US stock markets correlated?

A lot of UK investors purchase US stocks as the strong market performance has not gone unnoticed. They are easily accessible via most brokers in the form of stock, ETFs and CFDs.

Some of these investments have long term horizon, therefore, it is important to find out if US assets would help diversify a buy and hold portfolio.

Study parameters

I will use the historical monthly performance of major market indices and bonds over the past 5 years. The period includes the corona virus pandemic which is important in order to determine how would these assets behave during a market crash.

We all know that diversification across markets and assets classes reduces the overall volatility of returns. However, during a market crash everything can become correlated.

This is a situation where assets with low correlation such as bonds, gold and stock all plummet simultaneously. Therefore, the correlation increases on the way down.

I will use three UK instruments for the study: FTSE 100, FTSE 250 and VGOV

The US will be represented by the following: S&P 500, Nasdaq 100, Dow Jones 30, Russell 2000, TLT and TLH

Results

I calculated the standard deviation of the returns of each asset, variance, beta, mean return per year and the coefficient of variation.

I used the S&P 500 as a benchmark for the beta calculation. Then I used the data to create a correlation matrix and efficient frontier graphs.

Standard deviation and beta

At this point I have no idea what the results will be as I wrote this part of the article prior to opening the spreadsheet just to make it more interesting.

So let’s have a look at the standard deviation and the beta first:

Standard DeviationBeta
FTSE 10012.43%0.53
FTSE 25015.31%0.80
VGOV7.47%-0.15
Dow Jones15.12%0.98
Nasdaq 10018.01%1.10
Russell 200020.04%1.21
TLT11.94%-0.30
TLH7.96%-0.24
S&P 50014.99%1.00

I was expecting the UK indices to have a higher beta, however, I think that this just means that the UK-US correlation will be lower than I anticipated.

Otherwise in both cases the small market capitalisation stocks (FTSE 250 & RUT) were a bit more volatile than their respective large market capitalisation counterparts which is to be expected. All the bonds move inversely to the stocks regardless of the market.

The most interesting part is that the standard deviation of the S&P 500 for the 5 year period is 14.99%. This supports the view that the square root of time is very close to the realised standard deviation as √250 trading days equals 15.8%.

Correlation

The correlation matrix below shows how each of the securities would move in comparison to one another. A value of 1 means that they move in the same direction all the time. Then -1 means that they move exclusively opposite of each other. Finally, 0 means that the two instruments are not correlated at all.

The results show that S&P 500, Dow Jones (DJI), Nasdaq 100 (NDX) and Russel 2000 (RUT) have a very high correlation. This means that if you have a portfolio consisting of these indices you are not diversified. The US bonds (TLT & TLH) are also highly correlated.

The correlation between UK and US stocks and the respective bonds is not near 1, however, the range of 0.51 – 0.81 is still considered a high correlation.

I will try to find out if this information can be used to maximise return while reducing risk in the next section.

Diversification

The purpose is to reach the efficient frontier, maximum return with minimal risk.

Based on the matrix above I decided to use the S&P 500 and FTSE 100 as they consist of the biggest companies. The bonds will be represented by VGOV and TLT.

Stocks

This is what you get from the indices:

The x axis represents the risk while the y axis represents the mean return per year. 0.61% return represents a portfolio consisting of 100% FTSE 100. Every step introduces 5% of the S&P 500 and removes 5% FTSE 100. Therefore, 1.21% is 95% FTSE 100 5% S&P 500. The next step, 1.82% is 90% and 10% and so on until the end where the portfolio is 100% S&P 500 at 12.74% return.

A theoretical portfolio of 100% FTSE 100 would have a mean return of 0.61% per year with a standard deviation of 12.43% while a 50:50 portfolio would have delivered 6.68% with a standard deviation of 12.41%. The overall result of the 50:50 split is a 10x increase of the return with the same risk! I think that’s pretty great.

Some may choose to invest in the US market alone to get the 12.74% mean return at a standard deviation of 14.99% is not that much higher than 12.43%. Others may choose to reduce risk further and try to achieve 4.25% return at the minimum available risk of 12.07%.

Whatever the choice, the takeaway is that the two indices are correlated and a 3.5% difference in the standard deviation is not that significant.

It is important to put these numbers into a context. I think that the recovery of the FTSE 100 from the corona virus is slower than the S&P 500 and that dragged the return down. The results will probably be different if the crash was excluded.

The graph clearly shows that even a small exposure to the US market would have reduced risk slightly while increasing return for the period of interest.

Bonds

The bonds situation is a little different:

The graph is exactly the same as the previous one. On the left we have 100% UK bonds, on the right 100% US bonds. Each step is a 5% interval, 100/0, 95/5, 90/10, etc.

There doesn’t seem to be any risk advantage in mixing the bonds unless an investor wants to fine tune risk vs return. The result is not surprising as the correlation between the two ETFs is quite high at 0.74, hence the graph is a straight line.

In the next section I will add FTSE 100 and S&P 500 to the bonds to see if that would improve the outcome.

Stocks and bonds

These two asset classes have a negative correlation so it will be interesting to see if this will improve a hypothetical portfolio.

UK market

The graph uses the same 5% increments as the previous ones. 0.61% return represents 100% FTSE100, 4.28% return represents 100% VGOV

That’s really something! A portfolio of 80% bonds and 20% FTSE 100 results in a return of 3.54% at a standard deviation 6.27%. This is a 5x increase of the return while reducing the risk by 50% compared to a portfolio of 100% FTSE 100!

Intuitively this shows that bonds outperformed stocks for the period. Only time will tell if this is a doing of the pandemic or a new trend.

US market

The graph uses the same 5% increments as the previous ones. 6.52% return represents 100% TLT, 12.74% return represents 100% S&P 500.

The US market maintains a more traditional relationship between stocks and bonds with a pronounced negative correlation (-0.38). The standard deviation of the products is 11.94% for TLT and 14.98% for the S&P 500.

However, a 50:50 portfolio has a standard deviation of 7.59%! This reduces the return to 9.63% which is close to the average of the 2 assets at reduced risk.

A portfolio of 80% S&P 500 and 20% bonds would return 11.50% while maintaining the risk (11.30%) similar to a 100% bond portfolio.

If the assets are highly correlated like the S&P 500 and the Dow Jones (0.97) we’d get something that looks more like a straight line as in the bonds graph above, only this time it is vertical.

This means that a portfolio split between the two is unlikely to deliver any improvement of returns or the risk profile. Here is the graph:

The graph uses the same 5% increments as the previous ones. 12.32% return represents 100% Dow Jones, 12.74% return represents 100% S&P 500.

Conclusion

Diversification is sometimes frowned upon due to a perception that it reduces returns. This is because it is meant to reduce risk which often reduces returns too. I have no objections against this as everyone should invest in a way which suits their goals.

However, the data presented in the article clearly indicates that diversification across markets and asset classes could have improved returns over the period examined.

A different period can yield different results, however, this one was chosen to reflect the current macroeconomic conditions as stock market returns vary from decade to decade.

The data also indicates that the benefits of diversification increase in the presence of a negative correlation between the assets. The approach presented here is suitable for long term buy and hold type of investments such as pensions.