Starting to look a little closer at my normal return assumptions

I've been using in my code a convenient fiction for returns by using the R normal distribution function.  How many times have I heard from other that returns aren't normal. Of course not. I know that but "they" are not trying to code while my kids want dinner. I use it because it is easy and I don't have to think too much.  I thought I'd take a closer look with respect to my recent ruin risk estimates.  This is not scientific or rigorous this is just another one of those "what does it look like" things.


Since I don't allocate myself to 100% US large cap equities I often use blended assumptions for returns that are netted of inflation and fees and such. For example in recent runs in past posts I've used an assumption of 4% return and 10% vol (based on an assumption of blended nominal returns of 8% and 10% vol). That's a convenient fiction too in the absence of more sophisticated simulation but it serves the goal of speed -- sometimes with answers that can be good enough.  Let's take a look.

Here are three cases:

• base = R normal 8% return, 10% vol 
• A = a 50/50 continuously rebalanced mix of S&P and 10 Treasury total return using data I lifted from the Stern school, and
• B = Vanguard's VSMGX 60/40 fund  

Here are the baseline data:

case	what shape?		mean	sd
base	normal		0.0800	0.1000
A	Stern 50/50		0.0832	0.1055
B	VSMGX		0.0808	0.1138

This is not exactly head to head serious analysis but will get me to the "what it looks like" thing with choices that feel like they are close in spirit.  If I ding the returns for inflation and fees and punch out a density graph based on some sampling, they look like this when charted on top of each other. Some non-normal stuff going on in there, mostly because I don't have a ton of real data, but not a lot of big differences. A little fat tail going on but small (remember this is annual data and blended risk). Looking at 100% equities would be a little different I suppose. Also, using monthly data rather than annual would rock the boat.

Now, if I run the joint probability approximation for lifetime risk of ruin that I have done in past posts and I use each one of these three distributions separately to create an estimate of risk with a 4% spend assumption, this is the data and outcome in terms of lifetime ruin risk:

case	what shape?		mean	sd	ruin est
base	normal		0.0400	0.100	0.12719
A	Stern 50/50		0.0432	0.106	0.11567
B	VSMGX		0.0408	0.114	0.16382

The visual in terms of life and portfolio longevity probabilities would look like this (did I mention this is for a 60 year old? Sorry for the change-up in colors):

The differences, I gather, are not strictly from the "shape" (but they might be, I can't really tell with this level of rigourlessness, if that's a word) but more from the variations in the return and vol in general.  Also, this might be obvious but notice the independence of the longevity probability part of this.

If the question is phrased as "is a normal return assumption ok enough for quick and dirty non-critical gut checks?" then I think I'm ok for now.  At least I know I can play around with this in the future if I need to look at other shapes which is something that Prof. Milevsky pointed out to me when we looked at this approach of mine.  Marlena Lee, in a 2013 paper "Stress Testing Monte Carlo Assumptions" (this kinda both is and isn't MC sim) concludes that normal is probably ok a lot of the time and the actual levels for return or vol will dwarf the impact of distribution shapes.  I have not said anything yet about any kind of dynamic correlation or volatility.