With just over a month to go until the EU referendum, it seems prudent to look at which stocks may help investors sleep soundly, regardless of whether Britain decides to stay or go.  Today, I’ll be focusing on two companies that appear to offer more stability than most, despite operating in very different industries.

Keep the lights on (and dividends coming in)

Cautious investors could do worse than park a portion of their cash with National Grid (LSE:NG). One of the attractions of this utilities company is its relatively low beta. Simply put, this means that the share price of the FTSE100 giant will be less volatile than other stocks in the market and the index as a whole. If Britain does decide to leave the EU next month, this £37bn cap could still fare a lot better than most, giving properly diversified investors time to reassess their portfolios.

Of course, National Grid also catches the eye due to its stonking yield. In a period that’s already seen dividend cuts from a number of ‘safe’ companies, National Grid is offering its loyal investors 43.7p a share in dividends, covered 1.4 times by earnings. Analysts predict that this will increase to 44.8p per share in 2017, giving a yield of just below 4.5%. Given the reassuringly high probability that we’ll all need gas and electricity beyond 23 June, investors may struggle to find a more dependable company at the current time. Indeed, this view doesn’t seem to have escaped the market in recent weeks. The share price has now risen to a new high of 1,008p.

Nothing more certain?

Companies such as funeral services provider Dignity (LSE:DTY) may not be every investor’s cup of tea but, like National Grid, they arguably offer more security than most due to the nature of their business. As such, this is another excellent choice for those wishing to dodge volatile shares in the short term.

The Sutton Coldfield-based firm, which controls just over 12% of the funeral market, issued a first quarter trading update on Monday. Despite a dip in revenue levels compared to the same 13-week period last year (due to an abnormally high number of deaths in 2015), the board’s expectation for the full year was unchanged. Positively, it remains committed to growing earnings by 10% per year for the foreseeable future. Make no mistake, Dignity is on a mission to take advantage of a highly fragmented industry. The only slight drawback is its relatively modest yield. At a forecast 0.98%, this isn’t a stock to make income investors salivate. That said, the yield is forecast to rise by 6.5% in 2017, covered well over 4 times by earnings. This, coupled with the occasional special dividend and high growth potential, makes the company a very appealing investment opportunity.

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Paul Summers owns shares of National Grid and Dignity.  The Motley Fool has recommended shares in National Grid.  We fools don't all hold the same opinions, but we do believe that considering a diverse range of insights makes us better investors.