A riff on time...

I know I'm more oblivious than most so I am probably the last reader of finance to have come to this kind of epiphany. For several decades I was under the illusion that the "amount" or the number of things is what matters, which it does of course in some essential way, but really it all seems, in the end, to be a little bit more about time. I mean, yes, in grad school we learned all about managerial accounting and present value analysis and yield curves and stuff like that but any discussion of continuous-time finance or geometric returns or other time effects was more absent than not. MBA is not really where one learns that stuff of course -- or it didn't used to be in the 80s -- but it seems a little odd now in retrospect that I missed it. 

Volatility, spending and horizon wealth

There is nothing necessarily new or systematically thorough or dispositive here. Just curious about something I think I might have already covered years ago.  The idea is to take $1, grow it at 4% with volatility of N[20%, 15%, 10%, 5%] and a spend rate of 4% over 30 years; 10,000 iterations. This is standard MC sim territory. No epiphanies or conclusions out of this. Just wanted to see what these distributions (using R standard density function) looked like when overlaid. Ignore the interpretation of negative wealth for now.  

X is wealth outcome at horizon = 30

Y is density inferred from the simulation. Might have been better to have done a P mass/hist but the lines are easier to see

• black = 20% vol
• blue = 15%
• red = 10%
• green = 5%

Would I pick up a million dollar bill in the street?

I'm one of those oblivious and penurious cheapskate cranks that wants to live more or less forever and spend only portfolio income and then die with way too much unconsidered legacy that will go to the ungrateful and the unaware.  You know, an ex South FL girlfriend once even called me a parsimonious tightwad and killjoy. Ok, she didn't really say that exactly and "parsimonious" was not in her stunted vocabulary anyway. (Heh, Sorry X)  Also, it turned out she was only miffed because I wasn't pointing a flow of nest egg units towards her (this being So FL and all) but rather towards present-me, future-me and my kids -- what I call my razor's edge path. Another "heh" (sorry again X, my kids and razor's edge trumped your self interest!)

How much faith do I have in the forthcoming equity risk premium for planning purposes?

To ask the title question is to probably have an opinion in hand which I do. I've read a lot of finance over the years. The academic papers and the advanced practitioner papers that focus on markets and instruments and factors -- as opposed to those that deal with retirement, consumption and decumulation -- will casually mention the equity risk premium as if it is a Newtonian force or a guarantee. Take risk, must get paid. Heh. I mean, yes there is something to it and certainly in productive and relatively unfettered economies, capital used for growth gets compensated one way or another or at least it has historically been comped in the US. And yes, there is of course risk that is usually measured in standard deviations. But the wise will also consider shocks, chaos and fat tails. But in addition to all that there are also macroeconomic and policy forces along with crud that someone once referred to as "opulence, corruption, extravagance and waste" that might force one to eventually bend a knee in abject submission, forces that could make one doubt the whole enterprise of planning using historical data for conjuring forthcoming return expectations over our human planning horizons.

Visualizing the impact of spend choice

As in the last post, nothing really new to me or the literature here. 

This is how it works at RH: if I go back to old code I wrote -- even if it is well commented -- long ago, I often have no idea what I did then and I usually can't make it work well without a bunch of work and we here at RH are a little lazy. So when I have new code I will sometimes pile on: "hmmm, I wonder what x would look like as long as I have this code up?" That was certainly the case with the last post where a reader, reasonably, asked "what am I missing, this is simple?" yep, just goofin around. 

Geometric mean, simulation, short horizons and portfolio choice

I don't think this post is all that innovative. We see this kind of stuff in thousands of papers because this is basically just simulation but without the spending and fancy parameters one ususally sees. I just wanted to see how some stuff works here. 

In this post I'll look at 2 strategies -- 1) high return, high vol & 2) lower return lower vol -- to see what it all looks like. We know that we can use deterministic N-period geometric return formulas to estimate the N-per geo mean, something typically and probably incorrectly evaluated at infinity, for evaluating portfolios -- especially for the possibility of a "crossover point" where one strategy should dominate another. We also know that we can also construct a geometric efficient frontier in order to try to limit the portfolio choice interval to the one from risk free to the Kelly optimal (growth optimal) portfolio given believable inputs. Even Markowitz says that. But that latter method again often evaluates at infinity. What is missing is shorter horizons. Hence the post.