I've inherited about $250,000 that I want to invest in stocks and bonds. But I'm worried stocks may be overvalued and that rising interest rates will hurt bonds. Any suggestions for how I should invest this money, what stocks and bonds I should buy and over what time frame I should invest? --Mary, Connecticut

I can understand why you're skittish. A number of stock analysts feel that this bull market's age (more than seven years old now) combined with somewhat lofty stock price valuations make it vulnerable to a major setback. And given that bond yields are at or near all time lows, many investors see the bond market as a bubble ready to pop.

But guess what? There's always reason to worry that the markets might turn against you just as you're putting your money in. Take stocks. There have been many times during the spectacular run the market's had since its March 2009 low (up more than 200%) that people were convinced that stocks were in for a major setback.

Just recently Brexit, or Britain's vote to withdraw from the European Union, was supposed to lead to a stock plunge. And before that slowing growth in China, the downgrade of U.S. Treasury debt and Greece's debt problems created fears of a major selloff. Even when the market was at or near its bottom in the dark days of the financial crisis, people were more worried that stock prices would continue to fall than they were sure prices were on the verge of soaring.

Related: The problem with putting all your retirement savings in stocks

As for bonds, well, we've been hearing predictions of doom and gloom about them for at least six years. And I'm sure that one day interest rates will rise and bonds will take a hit. But neither I nor anyone else knows when that day will come or how far bonds prices will fall. Besides, while bonds certainly seem risky in that at their current low yields they're especially vulnerable to rising rates, viewed from another angle they may be a lot more valuable than many investors realize. That's because recent data shows that the correlation between stocks and Treasury bonds is at or near its lowest level in 145 years. What that means (without getting into a lot of boring technical stuff about correlation coefficients) is that bonds are more likely to provide at least a bit of a buffer when the stock market takes a dive.

All of which is to say that you can't base your investing on anxiety and gut feelings, or for that matter on investing pundits' prognostications du jour. If you want a reasonable shot at seeing your money grow over the long-term, you've got to come up with a strategy that can thrive in a variety of market conditions and provide decent upside potential while also offering some downside protection.

As a practical matter, that means settling on a broadly diversified mix of stocks and bonds that jibes with your tolerance for risk and is compatible with your financial goals. You can achieve that balance between risk and reward by going to this risk tolerance-asset allocation tool. Answer 11 questions designed to gauge what sort of loss you can tolerate before you bail out of stocks and determine how long you expect your money to remain invested, and you'll come away with a recommendation of what percentage of your portfolio you should invest in stocks and what percentage should go into bonds.

You'll also be able to see how that suggested portfolio and others more conservative and more aggressive have performed on average over many decades as well as in up and down markets. This should give you a decent idea of whether you want go with the recommended mix or shift more into stocks or more into bonds. (You'll also want to keep enough cash in an emergency reserve to pay roughly three months' worth of living expenses or, if you're retired, one to two years' worth of essential living expenses beyond what's covered by Social Security and any pensions.)

Related: The easiest way to invest your retirement savings

After you've settled on a stocks-bonds mix, you can now turn your attention to deciding which stocks and bonds to buy. The choice is simple: You can engage in the guessing game of trying to figure out which stocks, bonds or mutual funds are likely to outperform their peers. Or you can build a portfolio by investing in broad-based stock and bond index funds that give you exposure to wide swaths of the entire stock and bond markets in a single fund.

For example, you can get virtually the entire U.S. publicly traded stock market in one fund, a total U.S. stock market index fund. You can do the same for bonds with a total U.S. bond market index fund. If you want to add international securities to the mix (which I think is a good idea, but it's not as if you're doomed to failure if you skip them), you can add a total international stock and a total international bond index fund as well.

I can't guarantee that going with index funds will earn you the highest possible returns, but research shows that index funds tend to perform better than funds with managers that attempt to beat the market. You'll also shell out a lot less in fees by going with index funds, many of which charge less than 0.20% a year vs. 1% or more annually for many actively managed funds. Minimizing expenses is a good thing, as Morningstar's 2016 fee study shows that low-fee funds generally outperform their high-fee counterparts.

If you insist on trying to find funds you think might outperform the market -- or you just want to throw an actively managed fund or two into the mix beside your index funds -- you can look for candidates using criteria such as expenses, past performance and Morningstar's famed star rankings by going to this Morningstar Mutual Fund and ETF Screener.

Related: How to retire if you're going to live to 100

When it comes to how to get to the portfolio mix you've chosen, I know that most personal finance journalists and many advisers will say you should dollar-cost average, or move your inheritance money gradually into stocks and bonds, typically over the course of a year. So, for example, if you've decided to invest your $250,000 in a mix of 60% stocks and 40% bonds, each month you might move $12,500 into stocks and $8,333 into bonds, which, ignoring any investment gains or losses, would leave you with $150,000 in stocks and $100,000 in bonds after 12 months.

But when you think about it, this strategy doesn't make much sense. By dollar-cost averaging you just take longer to get to the stocks-bonds mix that you've decided is the right way to invest in the face of market uncertainty. For most of the year, you'll be investing more conservatively (that is, more in bonds and in cash, assuming you're now holding your $250,000 in cash at the moment) than you should be.

So if you really believe that your asset allocation, 60% stocks-40% bonds or whatever, is right for you, you should go to that allocation immediately. If you're emotionally or psychologically unable to do that, then at least get to your target stocks-bonds mix as quickly as you can, say, over a few months rather than over the course of a year.

Finally, once you've got your money divvied up between stocks and bonds the way you want, don't go fiddling with it or, worse yet, make dramatic changes because you think (or some putative market expert opines) that the market might tank or surge. Other than periodically rebalancing or perhaps shifting more to bonds as you get older, you should largely stick to your stocks-bonds allocation regardless of what's going on in the financial markets.

In other words, in the future as now, your best shot at investing success lies not in guesswork and intuition -- or chasing after trendy or gimmicky investments -- but in setting a reasonable strategy you'll feel comfortable following in good times and bad.