LONDON -- Crazy days! Interest rates have been stuck at all-time lows for more than four years, and the first rate hike could be another four years away. This has led to some crazy anomalies.

You can now get a five-year fixed-rate mortgage charging just 2.74%, up to 60% loan-to-value (LTV), or a 10-year deal at 3.99%, up to 75% LTV (subject to status, as they say).

At the same time, you can earn a yield of 5% and 6% by investing in solid FTSE 100 favorites, plus the prospect of capital growth if QE-fuelled markets keep rising.

I wouldn't normally urge you to borrow to invest in shares, because gearing adds an extra layer of risk. But does it make sense today?

Borrow and buy
Do you expect your portfolio to deliver a total return of more than 4% a year over the next decade? I certainly do. If so, and if you've got enough spare equity in your home to access a best-buy home loan, then, maybe, just maybe, you should be in less of a hurry to pay down that mortgage.

If you're tempted, I would suggest taking out a long-term fixed-rate loan, preferably for 10 years, so your plans aren't scuppered by a sudden upward lurch in interest rates.

To add an extra layer of security, you could then invest into a fat FTSE high-yielder or three. Dividend income is taxable, so, if you're bold enough to follow this controversial course, use your ISA allowance.

I'll leave you to find out the cheapest way to borrow money, but here are three stocks you might consider investing in.

AstraZeneca (AZN 1.27%) (AZN 0.57%) currently yields a base-rate-busting 6.1%. Pharmaceutical stocks are supposed to be defensive, but it is some years since this one has appeared solid at the back. AstraZeneca scored an embarrassing own goal with its $15.6 billion acquisition of Medimmune in 2007, while sales and revenues have plunged lately, as lucrative drug patents expire, and the pipeline of new products remains blocked. New chief executive Pascal Soriot has just announced a major reorganization, axing 1,600 jobs, and investing in new research and development (R&D) centres in the U.S., U.K. and Sweden, in a bid to "put science at the heart of everything we do" and improve R&D productivity. The overhaul will last for three uncertain years.

These disappointments have knocked AstraZeneca's valuation, which trades on a mere seven times earnings, roughly half the FTSE 100 average. Given its forecast earnings per share (EPS) growth of -19% in 2013, and -3% in 2014, that lowly valuation looks richly deserved. But it does give the share price plenty of scope to recover, if Soriot gets his strategy right. Despite its recent troubles, AstraZeneca is up 7% over the past 12 months, giving a total return of 13%. AstraZeneca is also the biggest single holding in dividend dangerman Neil Woodford's Invesco-Perpetual High Income fund, at 8.53%, and he tends to get these things right in the longer term.

National Grid
National Grid (NG 1.33%) is a nuts-and-bolts business, or rather, a pipes-and-wires operation, responsible for running the U.K.'s network gas and electricity network. It currently yields 5.3% a year, nicely above the 3.99% you might get on a 10-year fixed rate. Its share price has sizzled lately, up 7% in the last month, as the market admired its January trading update's claim that it is "well positioned to deliver another year of good operating and financial performance." Long-term investors should also appreciate the Grid's strong balance sheet and progressive dividend policy.

National Grid is unlikely to deliver stonking share price growth, if past performance is any guide. Over the last five years, it grew just 17%. Recent share price growth makes it pretty fully valued, at 14.6 times earnings. Forecast EPS growth is a modest 2% and 4% over the next couple of years. It also carries net debt of £20 billion, due to the cost of investing in the network, and its share price is at the mercy of power regulator Ofgem. That's a worry, given that 60% of its profits come from its regulated business, and it has to appease two different regulatory frameworks. But we are not looking for a high-risk, high-return stock here, just one that can deliver more than 3.99% a year. If National Grid can't do that, who can?

Vodafone Group
Mobile telecommunications giant Vodafone (VOD -0.11%) (VOD 0.33%) has shrugged off Neil Woodford's recent thumbs-down to rise more than 12% over the past month, to 185 pence. Most investors view this stock as an income machine, rather than growth engine and, on that front, Vodafone still delivers. It currently yields 5.1% -- once again, much more than today's market-leading mortgages. Vodafone has plenty of positives, including recent 8.7% revenue growth from its joint venture with Verizon, strong data revenue growth, and market share gains in emerging lands such as India and Turkey, which have offset the slowdown in Europe. It is also working hard to drive down its costs.

There are negatives, as well, such as southern Europe, tax wrangles in India, and stiff competition. Woodford rang off because he was worried about future growth prospects, but forecast EPS growth of 8% to March 2014, and 6% to March 2015, look steady enough to me. Trading at 12.5 times earnings, you aren't paying over the odds for its prospects. Plus, its dividend policy is progressive. Personally, I'm holding. And I have a mortgage.

Risky rewards
Borrowing to invest adds an extra slice of danger, and most investors should play it safe. I would only do it after locking into a long-term home loan. If we do get the inflation everybody predicts, 3.99% could look dirt cheap in five or six years. You might even get a better return on cash. I wouldn't recommend you remortgage your home to invest in the stock market, but maybe you shouldn't be in such a hurry to pay down your equity, either.

Would you borrow money to invest in a fund that has turned 10,000 pounds into 193,000 pounds since launch in 1988? That's the amazing return you would have gotten from Neil Woodford's High Income fund. You can find out where he is investing now by reading in our special in-depth report, "8 Top Blue Chips Held by Britain's Super-Investor." This updated report is completely free, and shows where Invesco-Perpetual's dividend dazzler believes the best high-yield stocks are to be found. It won't cost you a penny, so download it now. link