How about this idea?   Borrow against your house and invest in the stock market.

You can borrow the money at, say, 7.5 percent. Even if your return is only equal to the long-term average return on common stocks, about 11 percent, you'll make money like clockwork.

Sound good?

Of course it does. It's the equivalent of free money.

There's only one problem.

The idea won't work that way, even though unknown thousands of investors are trying to do it right now. Some portion of the people borrowing to invest will end up with no investments but they will still have a mortgage payment.

The explanation for this takes some close attention. In a perfectly regular world, you'd borrow at 7.5 percent for 30 years and have monthly payments of $6.99 or $83.88 a year for every thousand dollars borrowed. With an 11 percent return on your investment, you'd be earning $110 a year per thousand dollars on your common stocks. That's more than enough to pay the mortgage obligation. Do that every year and at the end of 30 years your mortgage will be paid off and you'll have a slightly appreciated stock account.

Right?

No. Wrong.

The problem is a thing called "variance drag"--- the fact that stocks don't provide smooth, predictable returns. Instead, they provide wildly uneven returns, rising sharply some years (the years we like to remember) and sinking in others (the years we like to forget).

While variance drag isn't a real problem if you are accumulating money, it's a major problem if you expect to make a regular withdrawal from your investment fund. Just as a retiree can endanger his investment nest egg if he makes excessive withdrawals, a commitment to a regular mortgage payment can deplete a portfolio.

You can get some idea of the odds by examining the work of three professors at Trinity University, Phillip L. Cooley, Carl M. Hubbard, and Daniel T. Walz. In 1997 the three set out to examine how different withdrawal rates affected portfolios with different asset compositions. They found that an all-stock portfolio with a withdrawal rate of 8 to 9 percent--- the amount you would need to make payments on a 30 year mortgage at 7 to 8 percent interest--- had a survival probability of 78 percent to 68 percent for a 30 year period. (You can see the full tables on my website)

This means that 22 to 32 percent of the time, the portfolio would be exhausted before the mortgage was paid off.

If you shorten the mortgage period to 15 years, the odds get worse, not better. Why? The higher payment for a short-term mortgage would require a higher annual withdrawal rate. In that case, the survival probability would be about 63 percent, leaving about 37 percent of all investors with no portfolio to pay the mortgage.

This isn't entirely bad news.

Even though it is less than the sure thing it appears to be, odds are that you will "win" about two-thirds of the time.

And that raises another question: If borrowing to invest works much of the time, is making extra payments on a mortgage a bad idea?

No.

In this case we only compare the possible returns on each dollar. If your mortgage costs 7 or 8 percent, every extra dollar saves you future interest. If the interest is tax deductible, your effective return is 5 to 5.6 percent (assuming a 28 percent tax bracket). Either way, those are pretty good "returns" in dollar savings for a sure-thing investment.

Returns that high would be difficult to duplicate in today's retail investment market. Most Treasury obligations, for instance, are now yielding less than 6 percent before tax, 4.3 percent after tax. Only when the pre-tax yield is about 8 percent will anything in the fixed income world become competitive with making pre-payments on your own mortgage.