Modeling human weight

As a former quant ( ex-GS, ex-BofA ), now working in the

space, I wonder about the uncanny similarities between these two completely disparate domains : weight-loss & option pricing.

Both have a robust model:
Price of a Euro call option is given by the Black-Scholes model, which results from solving a stochastic differential equation.

Human weight over time can be obtained using the Harris Benedict CICO model, which results from solving a differential equation.

Both the models are inaccurate:
Take the $90 call option on CLVS. If you plug into the Black Scholes model the values for the spot price $63.2, strike $90, duration 72 days, interest rate 0.525, historical volatility 56%, you get a price of only 69 cents. Yet, the option is trading in the market for almost twice that number, at $1.30 ! How come ?

Now take your own personal weight and plug into the Harris Benedict model above, you’ll seldom agree with those results!

Both the models can be tweaked:
When I brought up the call option market price discrepancy in the math-finance classroom, my Professor immediately said- fudge the input! Now, you can’t really fudge the spot price or the strike or the duration or the interest rate — those are ground truth realities. So you fudge the one thing you can - the volatility. Instead of using the historical volatility of 56%, you use “that number which gives you the right answer” !!! So that number happens to be 69%. We then dignify this made-up number “implied volatility” and say the market implies/believes the vol is 69 even though the true vol is 56. Implied Vol then leads to Vol Surfaces, Vol Smiles, lots of other technical fudge-factors.

Similarly, in the CICO model, you can fudge the “E” factor — the exercise rate, until you get the results you agree with. E varies from 1.2 for sedentary individuals to 2.0 for super-active athletes, so you have a lot of room to play.

Nobody’s using the model:
Working as a quant on option-trading desks, I found nobody actually using this model. Traders on the desk relied on heuristics, buying & selling based on technical indicators such as RSI & Bollinger Bands, or they might use a simple approximation, or rely on their own experience & intuition.

Similarly, no fitness instructor plugs his client’s weight & exercise factor into CICO models. They take a good look at you, measure some basic height/weight stats, then use simple rules of thumb on how much you must eat/exercise/sleep.

The Industry doesn’t care:
My wife is a physician. Most of her friends are doctors too. When I ask them about weight-loss, nutrition, difference between diets etc. the responses are highly unsatisfactory. Medical professionals care an order of magnitude more about treating the sick, compared to making healthy people healthier. Mostly the advice is along the lines of — eat smaller meals, walk more, watch your calories. You know, same old same old.

Most of my ex-colleagues are money-managers on Wall Street. When I ask them about option pricing models, that’s the last thing on their mind. The price of an option is not really driving their decision to buy or sell. They seem to rely much more on subjective market signals than objective math.

Laymen don’t know any better:
The guy on the street has no clue that body weight can be modeled, models can drive reliable forecasts, models can be used to tweak diet helping you to reach your desired weight goals much faster. They believe the human body is too complex. One VC I spoke to drew up a bleak portrait of subsidized farmers putting HFCS into every food on every shelf in every grocery store, leading to the 65% obesity epidemic we have on our hands! He believed weight-loss was mostly a matter of impulse-control. Don’t eat so much - that was the answer!

In the fitness community, you find pedantry and hair-splitting on whether low-carbs works best or low-fat, Paleo vs Keto vs WeightWatchers vs Nutrisystems vs South Beach vs the latest fad out there.

Similarly, laymen in finance get their advice from seminars & Gurus who claim to turn 5 digits into 7 digits within a year. I’ve yet to meet somebody who systematically makes 7 figures a year retail using math pricing models.

Juicing:
Everybody seems to know there is a hack, a faster way to get to the end point. They differ on what that is. In the fitness community, you see people popping caffeine pills & diuretics & laxatives to meet their desired goals. Some of this does work.

Similarly, everybody knows just buying plain stocks isn’t going to give them double-digit returns. To juice the portfolio, you see retail investors buying a few weekly call options on say Amazon right before the quarterly earnings. These things work too.

But none of this is consistent & steady. Women use some of these hacks & get into shape for bikini season, then a few weeks after the summer vacation they have gained back all they’ve lost & more.

An unscientific approach doesn’t lend itself to systematic analysis & execution. So inevitably those short-term gains, whether in finance or weight-loss, have a way of morphing into long-term sorrow.

And yet, there’s hope!
One might think scientific models have no way in hell of resolving any of this mess.
Trading is too subjective, driven on gut instincts. Markets change on the dime.
The human body is way too complex. There’s the endocrine system, there’s insulin, there’s enthalpy, we’re not just calorie burning machines, CICO is just bunk.
So then, let’s just close shop & go home!

In fact, new & improved models have been quietly making a comeback. Back when I worked at Goldman, we had 600 traders in 85 Broad. Today there’s just 2. Algorithmic trading & complex ML-enabled strats have taken over. NNs have learnt all those “subjective trader instincts” from training set encompassing historical data & labeled profitable/lossy trades of the past. I was speaking with some of my ex-colleagues who work over there, and in same cases the rules inferred weren’t particularly complex or outlandish. For all our human complexity, it turns out traders relied on simple heuristics like — if the market price was > 2x the Black-Scholes price & the security was sufficiently liquid with reasonable exit timeframe, then make a market. It was a bit more complex than that, with vol surfaces & smiles cluttering up the algo, but you get the idea.

Similarly, ML-enabled CICO has led to fairly predictive algos in the weight-loss domain. The original Harris-Benedict of 1918

gave way to a revised 1984 version -

which was further improved by Mifflin & St. Jeor in 1990 -

Instead of using hard-coded exercise rate numbers like below -

we at WeightGreat “learn” the precise exercise rate number using supervised learning on food-logs, exercise logs & sleep duration.

We open-source our ML models & code, even make anonymized food logs public. We’re building experimental ML dashboards that can run a variety of pluggable weight-loss models on the back-end. A predictive individual weight-loss model that evolves over time is the holy grail — we believe we’ll get there one day. The future is bright.