Simulating hypothetical future investment returns can be important for investors trying to make decisions regarding the riskiness of various investing strategies. The trouble is that it is difficult to do right, and I rarely see it done right. Here are some of the trouble spots:
1) You need to get the correlations right across assets. Equity returns need to move largely but not totally together, and the same for credit spreads and equity volatility.
2) You need to model bonds from a yield standpoint and turn the yield changes into price changes. That keeps the markets realistic, avoiding series of price changes which would imply that yields would go too high or below zero. Yield curves also need ways of getting too steep or too inverted.
3) You need to add in some momentum and weak mean reversion for asset prices. Streaks happen more frequently than pure randomness. Also, over the long haul returns are somewhat predictable, which brings up:
4) Valuations. The mean reversion component of the models needs to reflect valuations, such that risky assets rarely get “stupid cheap” or stratospheric.
5) Crises need to be modeled, with differing correlations during crisis and non-crisis times.
6) Risky asset markets need to rise much more frequently than they fall, and the rises should be slower than the falls.
7) Foreign currencies, if modeled, have to be consistent with each other, and consistent with the interest rate modeling.
Anyway, those are some of the ideas that realistic simulation models need to follow, and sadly, few if any follow them all.