hmarkway wrote:So looking at #7980, with a 2004-2016 mean of 36.96 and a SD of 16.54, you get a mean/SD ratio of 2.2. Which means that at least 0.56 in 40 years should be negative, but at most (99% chance) 2.76 years out of 40 will be negative. Not terrible odds unless they are super negative years....
So if I decide that I'm more comfortable with a ratio of 2.8 where at least 0.104 years in 40 would be negative, but there's a 99% chance that not more than 0.74 years in 40 would be negative (and just over 1 year in 60). The strategy that "best" (= with the highest mean) fits 2.8 is 15560 with a mean of 35.74 and a SD of 12.27 with a ratio of 2.9.
Looking at the highest ratio on our chart, 3.4, the risk of a strategy with this ratio would boast a 99.9% chance that at most 0.256 years in 40 (or 0.64 in 100) would be negative. If you look at the current king of low risk, 15670, the ratio is off-the-charts at 4.44 (33.23/7.48), which would suggest that it will almost never be negative.
Of course we are dealing with a very small data set, so every year it will adjust, but I think it's safe to say, that unless I'm missing something, there are some really great options of different strategies that hold high means, but also provide warm fuzzies of low risk. Personally, I think I'm comfortable going for the highest mean with a ratio of > 2.8, which is 15560. Unless of course the mean margin of error matters more than I'm understanding, and in which case, 15242 with an SD of 6.96 or 15670 with an SD of 7.48 would probably be the way to go.
It may be more useful - and possibly less confusing - to use the Chance of Negative Return table to determine the relative risk of strategies having different Mean/SD ratios or σ0 - the multiple of standard deviations at which the result is zero.
In the previous example, Strategy A (mean of 30 and a SD of 10), σ
0 = 30/10 = 3.0. For strategy B (mean of 40 and a SD of 25), σ
0 = 40/25 = 1.6. Their respective chances of negative returns (at 0% confidence) are 0.135% and 5.48%. Therefore, B has a 5.48/0.135 = 40.6 times greater chance of having a negative year than A. At 95% confidence, the difference is 14.5 / 0.70 = 20.7 times greater.
hmarkway wrote:How is the margin of error in the mean proportional to the SD? I guess I'm still hung up on the margin of error chart. Double the error is okay if you have double the mean - because that puts the mean twice as far away from zero? "Okay" in terms of not likely to be negative? I'm sorry if I seem to be chasing my tail. I'm just really confused by that chart.
Take a look at
https://www.mathsisfun.com/data/confide ... erval.htmlX ± Z∙s /√(n)
Margin of Error is the part to the right of the ±.