Since the UK voted to leave the EU, the FTSE 100 (INDEXFTSE: UKX) has been all over the place. This high degree of volatility looks set to remain the norm over the short run as investors gradually come to terms with what a post-EU UK economy will look like. And during this time the FTSE 100 may not make all that much ground as uncertainty will be high and investors may adopt a more risk-off attitude.

However, beyond the short term the FTSE 100 has huge potential. Realistically, it could reach 10,000 points by 2020. That’s because the world’s attention is unlikely to remain on Brexit over the medium-to-long term and investor sentiment will in any case be much more heavily influenced by the outlook for the US and Chinese economies. They’re the most important growth drivers for the world economy and due to the FTSE 100 being an international index made up of global companies, their performance will more heavily impact the FTSE 100 than the performance of the UK economy.

The US and China

Regarding US growth, it has recorded strong economic data in recent years. Jobs and GDP numbers are rising and now that the outlook for the EU is less stable than it was before the referendum, the Federal Reserve is more likely to maintain a dovish stance on interest rates. Lower interest rates for longer should boost the US economy and help FTSE 100 companies with exposure to the US to deliver improved financial performance.

Similarly, China has excellent long-term growth prospects. It’s successfully transitioning towards a consumer-focused economy and this presents tremendous opportunities for FTSE 100 consumer goods and financial services companies. The Chinese middle class is increasing both in number and in wealth. Although resources companies may not see demand for iron ore return to previous highs, other sectors could pick up the slack, deliver higher earnings and help to push the FTSE 100 to 10,000 points by 2020.

Clearly, a level of 10,000 points within three-and-a-half years may seem to be somewhat unlikely given that the FTSE 100 has traded no higher than 7,000 points in its history. However, it remains dirt cheap compared to other stock markets and therefore there’s scope for a major upward rerating. For example, the FTSE 100 has a price-to-earnings (P/E) ratio of around 13.5 versus a P/E ratio of 21.5 for the S&P 500. If the FTSE 100 was to trade on the same rating as its US cousin, it would mean a price level of over 10,000 points.

Weaker sterling benefit

One benefit of Brexit thus far for the FTSE 100 has been weaker sterling. This creates a positive translation effect for companies with international earnings and due to the majority of FTSE 100 earnings being generated outside of the UK, it could be argued that Brexit has been a good thing for the FTSE 100 thus far.

Furthermore, history tells us that the FTSE 100 has a rather good track record of shaking off doom and gloom to produce stunning returns. For example, following 1992’s Black Wednesday when the UK left the European Exchange Rate Mechanism (ERM), the FTSE 100 gained 47% in just 15 months. As such, 10,000 points by 2020 may not be all that challenging.

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Peter Stephens has no position in any shares mentioned. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.