Do you think a vote to Leave the EU on 23 June would have no detrimental effect on Lloyds Banking Group (LSE: LLOY) and the rest of our banking sector? Looking at the Lloyds share price, it appears the investing institutions would disagree with you.

Since the Brexit camp’s following has grown over the past few weeks, Lloyds shares have fallen by 12% to 64.8p,  taking them down 29% over the past year. And that’s a year in which the bank’s fundamentals have been improving with the shares now on a forward P/E as low as 8, and dividend yields of 6.5% and 7.6% forecast for this year and next.

The Bank of England has also weighed in, only this week saying that the EU referendum is the “largest immediate risk” faced by the world’s financial markets. The BoE has plans in place to support banks in the event of a leave vote, which highlights the reality of the risk.

On the other hand, should we get a remain vote, now could turn out to be the best time ever to buy Lloyds shares.

Single market

In another sector, consumer giant Unilever (LSE: ULVR) has warned that it would be harmed if Britain leaves the EU, saying that having access to “a single European market of 500 million consumers” has greatly helped its performance over the past 25 years.

In a letter to employees, Unilever’s chief executives and chairman wrote that “Unilever in the UK […] would be negatively impacted if the UK were to leave the European Union“.

And Unilever shares? After a strong start to the year, since 19 April we’ve seen a 7.4% price fall, to 3,084p. Unilever shares have traditionally commanded a relatively high P/E, but that’s largely dependent on its low risk and predictable markets. EU uncertainty is surely going to dent that confidence, and trusting the leave campaign’s claims that the UK’s European trade wouldn’t be affected if we quit the EU could be a very risky line to take for your investment security.

Aerospace troubles

Rolls-Royce (LSE: RR) is another great British company that’s said it expects to suffer if we leave. While the CBI was opining that Brexit would “put British businesses out in the cold“, Rolls-Royce bosses were writing to their employees to tell them it would “limit any company’s ability to plan and budget for the future”.

Chief executive Warren East told the Today programme that leaving the EU would provide a boost to US aerospace engine manufacturers at the expense of Rolls-Royce’s international competitiveness, adding that “uncertainty created by Brexit puts a lot of [the company’s investment decisions] on hold“.

After having been hit by a series of profit warnings, Rolls-Royce shares had been staging a bit of a recovery, but since early March we’ve seen a 15% drop to 617.5p, with a significant chunk of that coming on the back of the apparent rise in leave support.

Whatever other issues there are behind the EU referendum, looking at these three major companies in three vital sectors clearly suggests an exit won’t be good for your share portfolio.

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