The market turbulence of the past few days has thrown up some great bargains. For the astute long-term Foolish investor, these bargains come once a decade. Here are just five of some of the opportunities on offer.

Bright outlook

Aviva’s (LSE: AV) management was one of the first to come out and tell the market on Friday morning that the company doesn’t expect the EU referendum to have any significant impact on its day-to-day operations. Then, at the beginning of this week management moved to reassure the market further by announcing that despite the market turbulence, on Friday 24 June Aviva’s capital position remained close to the top of its working range of 150% to 180%. Aviva’s year-end 2015 capital surplus totalled £9.7bn, making it one of the strongest and most resilient balance sheets in the UK insurance sector.

Despite these assurances, shares in Aviva are still 15% below the level they traded at last Thursday. The shares currently trade at a forward P/E of 8.2 and support a dividend yield of 5.7%.

No impact in the long-term

International Consolidated Airlines (LSE: IAG) was one of the first companies to warn that the outcome of the referendum would hurt its business in the short-term. On June 24 the company issued a press release stating that it no longer expects to generate an absolute operating profit increase similar to 2015.

Nonetheless, while IAG’s near-term outlook is now cloudy, the company’s management remains optimistic for the long term. Low fuel prices and a rising demand for air travel will underpin the business’s long-term growth. What’s more, the group’s international exposure will protect it from any UK domestic Brexit shocks. With earnings per share of 90p, or €1.09, pencilled-in for this year, IAG’s shares look extremely cheap at current levels. 

As an international insurance, wealth management, and banking group, Old Mutual (LSE: OML) will see some impact from Brexit, but the company’s operations in South Africa and the US will offer some protection. Also, the group is in the process of selling key divisions to unlock value for investors. After recent declines, shares in the company trade at a forward P/E of 10 and support a dividend yield of 4%. The dividend payout is covered 2.5 times by earnings per share.

Housing shortage 

Shares in Taylor Wimpey (LSE: TW) lost a staggering 40% of their value in the two trading days after 23 June. However, while these declines may imply that the homebuilder is about to go out of business, Taylor’s day-to-day operations should remain mostly unaffected by Brexit.

Home prices may come under pressure during the next few months, but the fact remains that the UK is facing a severe housing shortage. And Taylor is in a prime position to capitalise on this. The shares currently trade at a forward P/E of 10.1 based on up-to-date City forecasts.

Demand for insurance 

Shares in Direct Line (LSE: DLG) have fallen by 10% since Friday morning, but consumers are unlikely to stop buying car, home, pet, travel, and life insurance due to the outcome of the referendum. Based on current City forecasts the company’s shares now trade at a forward P/E of 12.2 and are set to support a dividend yield of 7.2% this year.

The worst mistake you could make

The Brexit vote is a great opportunity to buy shares but mistakes could also be made. According to a study conducted by financial research firm DALBAR, the average investor realised an average annual return of only 3.7% a year over past three decades, underperforming the wider market by around 5.3% annually.

This underperformance can be traced back to several key mistakes that all investors make. To help you realise and understand the most common mis-steps, the Motley Fool has put together this new free report entitled The Worst Mistakes Investors Make.

The report is a collection of Foolish wisdom, which should help you avoid needlessly losing too many more profits. Click here to download your copy today.

Rupert Hargreaves 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.