I think the above two statements are very dangerous.
While its true a Monte Carlo simulator can be dangerous in the hands of an inexperienced operator, in that instead of historical data, you can adjust returns and standard deviations to fit your outlook, if done well, it can be very illuminating. For example, if you wanted to be ultra conservative in your modeling, you could use lower equity returns than the last (dominated by USA) century, and could increase standard deviation to make sure your portfolio could withstand periods worse than what we've historically witnessed.
As far as stocks and bonds being negatively correlated, the below link shows that sometimes that is the case, and sometimes not. One of the drivers of the Great Bull market of the 1980's was the decline in interest rates. Both bonds and stocks made excellent returns. My guess is that if we mirror the 1980s, and interest rates increase significantly from current levels, bringing bond prices down, equities will also suffer.
Correlation Between Stocks And Bonds - Business Insider
None of these tools do a good job of modeling what I think is one of the greatest risks we FIREs face, that of a short, or worse an extended, period of very high inflation.
Taken your 2nd point first, if you look at your chart it looks like about a dozen years were bonds had a high correlation about a dozen year out of the last 60,and had a negative correlation in even more years. Bernstein in his e-book book about correlation quotes .05% correlation between long bonds and stocks and .03% been T-bills stocks. That is close enough to 0 for me. As Bernstein points it is increasingly hard to find asset that are not correlated, small cap, large value, Europe, Emerging markets, and the S&P all have move more or less in lock step for the last decade making achieving diversification very difficult. So really only gold, bonds, and real estate provide diversified alternative assets which is why I think it is important that FIRECalc models bonds/fixed income better.
Like ERD I am willing to assume that I am not unlucky enough to be faced with inflation, market performance etc that are worse than the last hundred plus year. I also know that I am not nearly smart enough to make prediction of the long term returns of a bunch of asset classes.
So I find Monto Carlo simulators to be really dangerous forecasting tool, perhaps especially in the hand of experienced operators.
To pick on Dr. Pfau again, in his Monte Carlo simulator observed that US equity had better returns than the rest of the world so he lowered equity returns by at least 2%, which coupled with the Monto Carlo flaws, had him suggest withdrawal rate down in the 2.5% range and 30-40% equity position.
Another expert I think it was Speigel did a study that showed among English speaking/Commonwealth countries US equity performance is actually fairly average over the last 100 years of so.
In my opinion there are structural reason the US, Australia, Canada etc. stock market returns have been historically so much better. I also am sure that financial market over the last 30 odd years have become much more like the US rather than vice versa, so it seem logical that rest of the world equity returns will be more in line with the US than vice versa. But of course I could be dead wrong.
But the really dangerous thing about Monto Carlo simulators is they
assume that annual performance of the stock market is independent of the previous years, when clearly it is not. Plenty of people knew the stock market was really over valued in 1999. Why because the NASDAQ was up more than 400% in 5 years. Now I didn't know that 2000 would the year of the crash but I was very confident that we were far more likely to have bad bear market in the next couple of years than normal. Likewise plenty of folks on the board knew in 2009 that a bull market was far more likely than another bear market, why because the market was down almost 40% in 2008.
The reason I think Monto Carlo is dangerous is because the operator bad assumptions can lead to dumb behavior. For instead if the $1 million retiree had followed Dr Pfau advice and switched from a 60/40 to 30/70 AA based on his model in the last couple of year they are out more than $100,000 and perhaps just as importantly were spending at a level of only 2/3 what they could have.