mukramesh wrote:
I don't see why average returns would be useful for projecting forward.
I lost many hours of my life reading about this last night that I'll never get back. It's boring and confusing. Let me see if I can summarize so you don't suffer the same fate.
Let's look at an extreme example of playing roulette and always betting on black. You have a 50% chance of doubling your money and a 50% chance of losing everything with every spin (for the gamblers looking at me funny, let's ignore the zeros for now). That's about as volatile as you can get. Now let's say you spin twice. There's a 25% chance you have quadrupled your money, and a 75% chance you lost everything. Plan to do it ten times in a row, and there's a 0.1% chance you will increase your original bet by 1024x but I can pretty much guarantee that won't happen. Because of that small chance of a big gain, the average return for trying the same methodology repeatedly is not zero even if you will almost assuredly never achieve it.
Now let's say someone has an insane run and you watch them do it. Looking at their end wheelbarrow of chips and counting the spins, you calculate that their CAGR is 100%. Pretty great! But that's for something that already happened and ignores the low odds of that exact pattern repeating.
When trying to decide whether putting it all on black is a good retirement strategy for yourself and 10k of your closest friends, the average return is technically more accurate for projecting future average balances than a single (potentially anomalous) CAGR. However, it is still deceptive in that it does not convey your personal odds of achieving that average. Depending on how diverse your data set is, a long term CAGR can be a decent estimate for median return looking forward, and for conservative planning I personally prefer it to average returns if you insist on using one number. Watch the wheel spin 30 times after the lucky winner is long since gone (scooped up by suspicious casino personnel, probably), you would have figured that the CAGR/median for the future is most likely zero and stayed far away.
If that's all exhausting and confusing, I totally understand. Basically, predicting the future is hard and both average returns and CAGRs are imperfect for returns projections as neither tell the whole story. A math-free alternative is to ignore both numbers and play with the Hurricane calculator at PortfolioCharts (or Firecalc if you only care about broad stocks and bonds but want more history). It will help you see the full range of account balances using annual contributions or withdrawals and real-life historic returns that cover all kinds of economic conditions. Look at the max and min for your timeframe, and realize that the returns in the future will likely be somewhere in between.