LONDON -- Are you an investor in Aviva (AV 0.34%) (AVVIY 0.50%) or RSA Group (RSA)? How are you feeling now? Shaken? Exasperated? Let down?

I share your concerns. As a shareholder in both these companies, it has been a torrid few weeks. When you are hit by such bad news, the stock market can seem a very lonely place. You feel that everything that could go wrong, has gone wrong. You feel as if you paid out your bet on a "sure thing," only for it to fall at the first hurdle. And you know that the companies are now prey to shorters who could pounce at any sign of a slip.

If the whole premise of investing in a company is the dividend yield, a reduction in that yield surely negates that premise.

A dilemma for investors, and for companies
So, if the dividends of the highest-yielding companies are likely to be reduced, should we avoid seeking out and investing in the highest-yielding companies altogether? I call this "the dividend dilemma."

And, alongside this is a second dilemma: Should companies make every effort to sustain high dividends, even if this is costly to the company? After all, wouldn't any company want to avoid the recent share price falls of Aviva and RSA, and the resultant embarrassment and shareholder ire?

My answer to these questions is simple: First and last, we need to assess the fundamentals. There is no point in maintaining a high dividend yield if it is unsustainable. You should never check the dividend yield to the exclusion of everything else. Instead, you need to assess the broad range of fundamentals, from price-to-earnings (P/E) ratio and net debt to price-to-book value.

Take a contrarian view
Take Aviva: The company is on a forward P/E ratio of 6.9, the debt-to-equity ratio is 26%, and it is trading below book value. Despite all the current tumult, that is still as cheap as chips. What's more, with a new chief executive in place, these days, you almost expect some "kitchen sinking" in his first set of results. Good contrarians have already figured out that this is the time to buy Aviva, not sell.

Next, take RSA: This is on a forward P/E ratio of 10 -- not so stunningly cheap, but the company has better growth prospects. Again, this remains a good investment. For both companies, the reduced dividends are still substantial, they are now more sustainable, and they are still significantly higher than the FTSE 100 average. Thinking long term, the dividend reduction is actually to the benefit of the company and its shareholders.

It is easy to lose patience with these companies. But if shareholders are thinking of selling out and washing their hands of these businesses, my view is that these companies will come back strongly from this. My message to these shareholders is simple and it is clear, and is perhaps the most important lesson I have ever learnt in investing: Just. Hold. Your. Nerve.

I think both Aviva and RSA are shares that can take pride of place in a dividend investor's portfolio. We at the Fool are always on the look-out for high-yield shares, and we think we have found the ideal share for your portfolio. Read our free report on "The Motley Fool's Top Income Stock for 2013,"