A better way of consumption smoothing with Monte Carlo?!
The way I understand how Monte Carlo simulation currently works is the following:
- Within a simulation trajectory the engine calculates the smoothest consumption based on the assets of the then current year and applies the (random) return on assets and then advances to the next year, where it repeats this.
The problem with this approach is that the randomness inherent in Monte Carlo doesn't really make for much smoothness in consumption. Even selecting a "cautious" Spending Behavior doesn't really help, especially if you have a stock-heavy portfolio. So in my 5% percentile and the "Very low" trajectory I'm noticing that the consumption in the first year falls off in the 2nd year and even more in the 3rd year only to catch itself after 10 years or so.
I'm not sure, if this has even been suggested (if so I'd appreciate a pointer to that discussion), but this kind of simulation - while valid - answers a question that I don't have. My question would be a different one: Which what kind of smooth consumption would I get through x% of the simulated trajectories?
So I'd like to see a variant on the current Monte Carlo simulation, where in each trajectory the system is prescient and "knows" the return for all the years of that trajectory and calculates a smooth consumption for that trajectory based on that prescience.
Then you could rank the various consumptions and trajectories just like you do know, giving information about consumption in the 5th/25th etc percentile and trajectory. I feel that this information would be much more meaningful as it avoids too much consumption in the early years in light of uncertain asset returns.
Best Regards,
Bernhard
RSS
Granted that this is time consuming, but why not multiple basic module runs with varying rates of return, since that's essentially what you're asking for.
Granted you won't get random rates of return, but by introducing foreknowledge of the rates of return, you're basically just running then basic reports again and again.
Best,
Dick Munroe
Hi Dick,
Yes, you're right that this calculation is actually easier, since in each trajectory of the Monte Carlo simulation you only have to calculate the consumption once for all years in that trajectory.
Running multiple basic module runs are no substitute though precisely because you won't get random returns that way and - even if you did - I don't see it being feasible to manually create dozens or hundreds of models, run them and rank them.
Now even though that calculation is easier than the current one, I still believe that it is very useful, not so much the individual trajectory of course, but in aggregate it provides a smoother consumption than the current Monte Carlo approach.
Best Regards,
Bernhard
The problem is that by introducing "foreknowledge" of the rates of return, the rates of return are, by definition, no longer random, simply varying and due to the law of large numbers (I think that's the one, anyway) you'll should see a mean return, more or less. I'll have to defer to Larry on the theoretical details and may have my head wedged.
Best,
Dick
Hi Berhard,
With pre-knowledge of the path of returns, you have some paths with low returns early and high returns later and some with high returns early and low returns later and some with medium returns most of the time. The return, will, on average, be similar across all the paths, where the average is taken across all your future years. What would lead the consumption paths to differ is the timing of the returns. High returns early and low returns later would beat the opposite because of the ability to earn interest on interest. Also, low returns early means you are more likely to be borrowing constrained. So there would be some variations across such prescient lifetime consumption paths. But I don't get how such paths help you plan since you don't, in fact, go through life knowing what returns you will earn in the future. Call me at 617 834-2148 if you want to discuss. best, Larry