OK it's not quite a GUT for equities, but a neat trick involving Munger, Buffet, Graham, Sharpe, Claude Shannon, Thorpe, Kelly, Chan, Mr. Market and Douglas Adams. Thus even if it isn't the GUT for Finance, this blog post is highly buzzword compliant.
Charlie Munger always says, "invert" which means look at the end or out come first. I think he is right. So lets look at the end goal first.
The goal of any trader, investor or asset allocator should be in the words of Warren Buffet, "to maximize terminal wealth", the long run in Keynesian terms. Maximizing terminal wealth is done be most efficiently allocating our risk or bets over time.
The brilliant Claude Shannon created information theory which lead to eventually to the Kelly formula used for optimal bet allocation and card counting. Ed Thorpe, card counter, hedge fund manager and mathematical bon vivant among others has made a lot of money using the Kelly formula to allocate risk in the hedge fund world. You can read about gamblers, mafioso, card counting and information theory in William Poundstone's truly entertaining read Fortune's Formula.
Recently Ernest Chan published Quantitative trading. For initiates to quant trading this book rules. The introduction to basic strategies is well done, clear and concise.
One section in the book ties the Sharpe ratio and the Kelly formula together giving the optimal leverage size for maximizing terminal wealth based on Sharpe ratio and thus the expected optimal annualized growth rate for any stable system. Please note implicit in the relationship is an assumed normal or guassian distribution of returns. As we all know Guass exits stage left when the real world of finance enters and one of those rascally characters like Levy or Mandelbrot enters. I met Mandelbrot while acting as Chief Analyst for Starlab, Europe's equivalent to the MIT media lab a few years ago, nice fellow. We researched Artificial intelligence, materials science, genetics, nano-tech, even time travel...no kidding.
Mr. Market at the end of the universe.
Mr. Market is Ben Graham's personified embodiment of the stock market, even though he is irrational sometimes, he should be working towards maximum terminal wealth so that he can eat at the Restaurant at the end of the universe with the late great Douglas Adams.
In order to do this Mr. Market needs to use optimal leverage in the equities market in order to maximize his terminal wealth and pay for dinner.
The thesis is that if Mr. Market is truly an optimal allocator of capital then the relationship for equities between the Kelly Formula and the equity market Sharpe ratio should approximate a leverage ratio of 1.00 for optimal growth. A 1.00 optimal leverage ratio shows Mr. Market is an efficient gambler and leaves nothing on the table. Given the standard equity assumptions below it looks like the old boy is pretty good at the tables.
Neat trick huh? Here is the spreadsheet. Download KellySharpeChan
Fortunately, this appears to be the case given the assumptions shown. Of course it isn't exact as the assumption all shift around, but it is close enough to interesting.
Thus information theory, Mr. Market and parts of Modern finance all seem to co-exist happily ever after until dinner time. From time to time the market gets a little ahead or behind itself, but in the long run optimal allocations for maximum terminal wealth are being made. Now the message is please stay away from leverage and assume that the co-variance matrix isn't stable. Efficient market theory individual is bogus, but in aggregate may be semi correct. Not Nobel Prize correct but okish. Scholes & Markowitz should still give back their prizes and Nobel winners like Dr. Amartya Sen should get more daylight as they ultimately help the human condition more.
Please feel free to weigh in with thoughts, critiques and considerations. The nice thing is that the equity premium puzzle gets resolved by using variance as a risk proxy.
Even if you don't like the thesis above, the tool is helpful in identifying leverage for a "Stable Asset Allocation System" regardless of horizon.
If anyone is looking for a global macro L/S PM with hints of quant talk to this guy, he returned +19.8% last year with +50% cash (no leverage) and a 1.0 Sharpe ratio, has worked in 6 countries and has a sense of humour. CV on request.
