We woke on the morning of 24 June to see the FTSE 100 (INDEXFTSE: UKX) in turmoil as the world reacted to the result of the referendum. The index of top UK shares fell as low as 5,789 points during the day, for a loss of 8.7%.

We’re dooooomed…” Except we weren’t, and almost as soon as the FTSE slumped, it bounced back up again. Since market close on 27 June the index has regained 9.3% to 6,540 points — and now stands higher than it was on the eve of the result.

What are the lessons, and should we pile-in to the new buying frenzy? Well, the initial sell-off was overdone, as it always is when panic attacks. It’s well known that investors overreact to news, whether good or bad. Even though investors know they overreact, they still do it.

Stay cool

The key to success is to not join in the panic — and don’t, as a couple of people I know were contemplating, rush to sell your investments because you think the sky is falling. But now the market is bouncing back, don’t just assume all will be fine. Just as those who joined in the massive sell-off really knew nothing about how the long-term value of the UK’s top companies have changed, neither do those who have jumped back in and pushed the FTSE back up again.

What we do know is that things are more uncertain now. Economics experts are predicting slower GDP growth, with some of the bears suggesting we could see a new recession, and there certainly are some sectors facing much bigger risks now than before — banking springs to mind.

But at the same time, the falling pound will make our exports cheaper and provide a boost for our multinational companies, and the Bank of England has made it clear it will do whatever it thinks prudent to soften forthcoming economic blows. So the overall effect is… we just don’t know.

What should our strategy be? The first thing to do is re-examine the shares we hold and consider whether the companies still look sound and whether they still look cheap at today’s prices. An obvious one for me is Aviva, which was one of the first to state clearly that the vote to leave the EU “will have no significant operational impact“. Despite that, Aviva shares are down 10% to 402p on the sell-off in the insurance sector — and I’d be buying more if I had spare cash to invest right now.

Assess the changes

It’s worthwhile considering your sector weighting too, after a ‘flight to safety’ has pushed up the prices of shares like GlaxoSmithKline, Unilever and National Grid. The strategies of those who’ve done this seems entirely wrong to me. Including safer shares as part of your portfolio should be an ‘always’ strategy, not an ‘only when I panic’ one, and with the right long-term balance there should be no need to change along with short-term events.

Another thing to do is look at depressed sectors and decide whether companies like Barclays and Taylor Wimpey are oversold bargains and whether you might want to risk some money on them.

But to me, the bottom line is to avoid the short-term mistakes that so many are making (enriching nobody but the brokers taking their commissions). And rather than doing anything driven by emotions, it’s almost certainly better to do nothing at all.

What else should you avoid?

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Alan Oscroft owns shares of Aviva. The Motley Fool UK owns shares of and has recommended GlaxoSmithKline and Unilever. The Motley Fool UK has recommended Barclays. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.