The fallacy of investing the equity from your home.

Maybe some of you out there have seen this scenario play out.

Ill-informed financial advisors married up with unscrupulous mortgage originators attempt to drum up business with the following value proposition: Cash the equity out of your home and invest the proceeds. Over the long-run, the S&P 500 has returned over 10%. If you borrow at a rate below this, you will be ahead of the game. Smart, huh?

The cardinal rule of investing is that there can be no return without accepting some level of risk. US Treasury securities are deemed to be the least risky of any asset class. Yields on these securities are therefore lower than other asset classes (stocks, corporate bonds, real estate, etc.). The stock market is certainly not without risk. Wealth can just as easily be destroyed as it is created as a result of fluctuations in stock prices. Many investors in technology stocks in the late nineties have yet to recoup their initial investment.

How can one make a better informed decision when presented with this value proposition? It is a straightforward calculation to measure return. How then should risk be measured? Fortunately, there is a set of tools that can help. The primary measure of an investment's return relative to its riskiness is known as the Sharpe ratio. The ratio measures the return per unit of total risk.

The definition of the Sharpe Ratio is:

S(x) = ( r_x - R_f ) / StdDev(x)

where

x the investment under consideration

r_x is the average annual historical rate of return of x

R_f is the rate of return of a "risk-free" security (US Treasury securities)

StdDev(x) is the range of possible return outcomes of x. Known in statistics a the standard deviation of r_x

Take for example, a scenario with the following characteristics:

x is a stock portfolio with an historical return of 10% and standard deviation of 6%

the risk-free security yields 4%

The Sharpe ratio for such a scenario is:

S = (10%-4%)/6%

S = 1.00

Now suppose instead of this strategy, one wanted to find the same measurement for simply prepaying a portion of one's mortgage.

x is the rate of interest for the mortgage. Assume x =6.5%

StdDev(x) = .01% (technically there is no risk, however the denominator cannot be zero)

The Sharpe ratio for this new scenario is:

S = (6.5%-4%)/.01%

S = 624

Clearly the proposal to retire the mortgage debt produces a superior return/risk tradeoff. Please note that an after-tax borrowing cost will produce a different outcome.

Therefore the un-glamorous financial counsel of "Borrow as little as you need and pay it off as soon as you can." proves to be the most sound.

With the current turmoil in the credit and stock markets, this will probably not be so frequently proposed, but if you do hear of it being proposed to your friend or client, now you may be able to offer them some better advice.