It probably is normal, because the distribution of annual stock returns for the last 96 years is pretty close to normal. However, the distribution of many trials for an N-year random sequence of returns with annual contributions and compounding is NOT normal; as noted before it's log-normal (or chi-square). It's skewed to the left of the average (median is less than mean; not equal) and the very high balance outcomes are very low probability (fat tail to the right). This happens in part because of the time-value of money in a compounding investment (a huge crash early in the sequence is not at all the same impact as a the exact same value crash late in the sequence).I don't fully understand the distribution of monthly mutual fund/ETF VOO returns but let's assume that it is normal.
Your implied use of "something near the middle" assumes a normal distribution so mean = median, which won't happen for compounding investments over time. It will work for a single random draw of the return in any one year, with many trial for just a one year period (no compounding, no contribution). Also, you can't simply take the average of all your individual yearly returns (which would be normal and "near the middle") and then apply that to your initial balance, again because that's not how the time-value of money in a compounding investment with contributions works (a bad return late in the sequence is devastating, while early in the sequence it's much less impactful). You don't care about the average return of your underlying holding... you care about how much your particular investment grew.If so, then random draws from this should give me high/low/somewhere in the middle returns. Since I am doing this for 15 years (and part of, say 60% of, my portfolio beyond that), then extremes should cancel out and I should get returns near the middle.
Again, the simple answer (that likely doesn't answer why very well) is that your returns over 15 years involve contributions and compounding... you're not simply flipping a coin with a 50/50 outcome each time, but let's talk about a coin-toss betting game. Imagine you get incredibly lucky at the casino playing a gambling game where it's all or nothing on your accumulated winnings every coin toss, and your lucky streak is 15 heads in a row with an initial bet of $1.In my case, why do I have historical 15 year paths that have big range (I think it was between 5m and 40m, with an average of 12m). Why is the ending value not close to 12m? Also why is the upside (12 to 40m) higher than the downside 12m to 5m)?
Bet 1: $2 (you bet $1 and won $1)
Bet 2: $4 (you bet $2 and won $2)
Bet 3: $8
Bet 4: $16
...
Bet 15: $32,768
That's the extreme lucky case. Now take the average unlucky case... you lost the first bet (tails on the first toss), so the game's over and you have $0. So the range is incredibly extreme between $0 and $32,768, with only $1 "invested," but the likelihood of $0 is 50% (first coin toss), while the likelihood of $32,768 is about 0.0031% (1/(2^15)). Those are the two extremes, but there are many other "paths" (essentially lucky streaks that end at Bet 2 through Bet 14) and for this particular distribution they're all decreasing from 50% on Bet-1 down to 0.0031% on Bet-15 (a Poisson distribution for discrete binomial probabilities).
Pictures probably would help, but I don't have time to search for something applicable (or make something up in Excel). Read an engineering statistics book!
Statistics: Posted by bonesly — Thu May 30, 2024 1:23 am — Replies 148 — Views 10563