Utilize your financial knowledge, give your answer or opinion to the input question or subject . Answer format is not limited.

Formula that predicts whether one is better off investing or paying down debt
The formula you are looking for is pretty complicated. It's given here: http://itl.nist.gov/div898/handbook/eda/section3/eda3661.htm You might prefer to let somebody else do the grunt work for you. This page will calculate the probability for you: http://stattrek.com/online-calculator/normal.aspx. In your case, you'd enter mean=.114, standard deviation=.132, and "standard score"= ... oh, you didn't say what you're paying on your debt. Let's say it's 6%, i.e. .06. Note that this page will give you the probability that the actual number will be less than or equal to the "standard score". Enter all that and click the magic button and the probability that the investment will produce less than 6% is ... .34124, or 34%. The handy rule of thumb is that the probability is about 68% that the actual number will be within 1 standard deviation of the mean, 95% that it will be within 2 standard deviations, and 99.7% that it will be within 3. Which isn't exactly what you want because you don't want "within" but "less than". But you could get that by just adding half the difference from 100% for each of the above, i.e. instead of 68-95-99.7 it would be 84-98-99.9. Oh, I missed that in a follow-up comment you say you are paying 4% on a mortgage which you are adjusting to 3% because of tax implications. Probability based on mean and SD you gave of getting less than 3% is 26%. I didn't read the article you cite. I assume the standard deviation given is for the rate of return for one year. If you stretch that over many years, the SD goes down, as many factors tend to even out. So while the probability that money in a given, say, mutual fund will grow by less than 3% in one year is fairly high -- the 25 - 35% we're talking here sounds plausible to me -- the probability that it will grow by an average of less than 3% over a period of 10 or 15 or 20 years is much less. Further Thought There is, of course, no provably-true formula for what makes a reasonable risk. Suppose I offered you an investment that had a 99% chance of showing a $5,000 profit and a 1% chance of a $495,000 loss. Would you take it? I wouldn't. Even though the chance of a loss is small, if it happened, I'd lose everything I have. Is it worth that risk for the modest potential profit? I'd say no. Of course to someone who has a billion dollars, this might be a very reasonable risk. If it fails, oh well, that could really cut in to what he can spend on lunch tomorrow.