[aquaswim47]

So Wall St. Golfer, are you suggesting that by having SSO or DDM that you're risk neutral; in other words, you don't get any marginal return for the additional risk taken on? If that's the case, he should invest in SPY or DIA. Or is it, that you get additional return due to the additional risk but on a risk/return basis, it's neutral?

Good points. I welcome your feedback.

If you bought DIA, and deposited 50% in a margin account, you could invest in 200% of DIA. Assume that DIA has a normal rate of return of 11%, an 8% margin rate, and a 12% standard deviation; it would imply that you would have a 14% average ROR (11% x 2 - 8%) and a standard deviation of 24%. The fluctuations in value would be double of the DIA investment; the investor deems a marginal return of 3% to be worth taking on double risk for the index. That means that DIA in a cash account would lose 1% if the index was one standard deviation below the mean, 13% if it was 2 standard deviations below the mean, and 25% if it was 3 standard deviations below the mean. Likewise, if it was 1 standard deviation above the mean, you would earn 23%, 2 standard deviations, 35%, and 3 standard deviations, 47% above the mean in a cash account. In a margin account, one standard deviation below the mean would be a staggering 10% loss, 2 standard deviations would be 34% (and a margin call would probably occur), and 3 standard deviations would be a 58% loss. Likewise, if you were one standard deviation above the mean, you would earn 38%, 2 standard deviations would earn 62%, and 3 standard deviations would earn 86% (2 X 47% - 8% margin interest rate). The problem with buying DIA on margin would be if you had a margin call, you would lock in your 60% loss and thus would have to see a 150% increase in the value of your new investment just to break even.

In a recession, one standard deviation might be a flat year (as the investor incurs only a 1% loss). Two standard deviations might be like what happened during the 2000-2002 era. Between three and four standard deviations would be like the 1987 crash, and the Great Depression was five standard deviations below the mean for an average of four years (late 1929 to early 1933) since the Dow plummeted approximately 90% (an average rate of decline per year of 49% which is 5 standard deviations from the mean).

One standard deviation, either positive or negative has about a 31% chance of occuring, 2 standard deviations has about a 6% chance of occuring, and three standard deviations has about a .3% chance of occuring (very rare). These are all assumptions.