interestingly while 90 pct of historical data displays clear or slight negative auto

correlation pattern those 10 pct are distinctively positevely autocorrelated. sounds like a regime change occurs from time to time that flips the a-corrs .

Dimitry Murzinov, to be true I didn't scrutinized for deep insights, I just sample (with replacement) from historical returns. Of course it is just a very first approximation but still better than nothing :)

Dimitry Murzinov, I updated my essay and put the chart of ACFs of returns. There is virtually no (statistically significant) autorrelations.

(Wanted to put a pingback to this dicussion on my website, however, it is a closed group so most of the readers would not be able to open this link).

That is why it is virtually impossible to calculate truly optimal portfolios. Statistical properties do change with time.

Taiwo Ross, exactly! And this is what I am saying. However, even a simplified statistical modeling provide some insights. So I don't tell to an investor "here is you optimal portfolio", I tell him "Vanguard told you this is optimal for you, look how it MAY evolve and decide yourself whether this "optimum" is suitable for you".

Vasily, your chart says a lot more than just being a simple simulation. I see it as the picture of any portfolio simulation.

The discussion would center around the slope of the green line, the expected outcome. And it is not pretty. Green is a nice color, it is what it represent that is not so hot. Over the 10-year period presented, that is less than 2% CAGR. And if you are lucky, in the top 2% performer group of 2, you could reach 4% CAGR, again, if you are lucky.

But, that does not change the general information that your chart conveys. It is the general structure of any future portfolio that everyone faces. You could take the stocks in the S&P100 and obtain a similar picture which would say the same thing as in your chart. The thing that would change would be the slope of the green line (higher), the variance (higher) and the vertical scale.

Thanks.

Guy R. Fleury Yes, 2% or even 4% CAGR is quite a misery, probably that's why Vanguard avoids showing possible outcomes (since such a performance is more suitable for somewhat called a Rearguard :)).

On the other hand 2% is better than nothing ... and in my opinion a diversified ETF portfolio is likely the best option for a lazy(!) retail investor.

Vasily, may I make some suggestions.

The premise: use the same data sample, the same program that generated your chart. We know that even if you ran that program again and again, it would produce about the same chart as you already provided. It would just scramble the lines. There would be no real change in the green line except for minor variations due to the randomised re-sampling.

The new test: add a linear time function: f(t) = at, to each stock with a=%/250. Making for example: a=7%/250. This would raise your green line to about the market's secular average. Run the program 1,000 times, even if your fund sample is small. Then, study the output.

What you will get is what a future portfolio may look like. You won't know which line did what, but you will clearly see the green line. What you will have done is raise the average green line: the average market return. This would give your ETF performance estimate, and opportunity cost, compared to your previous chart.

How do I learn about this? I have different metrics for each portfolio and they have performed amazingly well. I would like many aspects automated. Been tracking performance since 2013.

Guy, nice idea but I think will bring too much communication overheads :)

Visitors statistics on letYourMoneyGrow.com shows that an average visitor spends less than 2 minutes to read a post (and I think it is a global trend: we are overloaded with information). So I try to keep everything as simple as possible.

For the qualified readers like members of this group "sample with replacements" says everything, it is a common and frequently used approach.

For the "mere mortals" I still can explain it with one sentence: "we randomly select historical daily returns and based on them we construct a future scenario".

But to communicate your idea I need more words and I doubt that people will read it.

Anyway, if you want to do this analysis and have time for it, I would readily send you the historical data I use (actually, you can get them from Yahoo.Finance but I have already done the preprocessing job).

Vasily, no, it won't be necessary, I've done those tests years ago, and already know the answers. In a way, I was just delegating, and giving you the opportunity to put your point of view on the table since we all have to face a chart like the one you showed, It's only that we all would like our “green line” to have a higher slope, something in the range of more than one order of magnitude, or better.

Good reading to start understanding robot advisory's methodology. I'm still a bit skeptic about asset allocation mechanism during eventually long period dominated by dislocations .