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Introducing the Carb-Sharp Ratio

This post is a mash-up of finance and nutrition.

The finance piece: an adaptation of the Sharpe ratio to food selection and meal construction.

The nutrition piece: the importance of limiting “free carbs” in your diet.

Essential background reading is Dr. Fung’s book, The Obesity Code. Quick takeaway from Dr. Fung: fat is fine, protein is fine, but carbohydrates—more particularly, fiber free or low fiber carbs—are the most dangerous food out there.

Yo! Bloggerman—you ever hear of the Adkins diet?  Or Paleo? Where have you been?

Yes of course; but the point of this post is that carbohydrates are just food, no worse than any other kind of food, and fine to eat, but if and only if the carb-sharp ratio is favorable. Carbs ain’t bad; rather, foods, and especially meals, with a low carb-sharp ratio are to be minimized or avoided…if your primary goal is to lose weight.

The Sharpe ratio in finance: choice of investment

Briefly, the formula is: [% return on a risky asset minus % return on a risk-free asset] divided by the standard deviation of the risky asset.  So if stocks return 10%, and have a standard deviation of 20%, while Treasury bills pay 3%,* then the Sharpe ratio of a pure stock portfolio is [10 – 3] / 20, or 0.35.  In English: if you are going to take on risk, you should be compensated with an incremental return over Treasury bills; and that incremental return should be as high as possible, relative to that extra risk. In short: the Sharpe ratio calculates extra return per unit of risk. Higher ratios are better: these are investments that give more bang for the risk assumed.

The Sharpe ratio can be used comparatively. Say your alternative to stocks is to invest in junk bonds, with a return of 6% and a standard deviation of 12%.  Here the Sharpe ratio is [6 – 3] / 12, or 0.25.  Judged by the Sharpe ratio, junk bonds are an inferior investment compared to stocks.  The lower Sharpe ratio reveals that you are compensated less, per unit of risk.

*Yes I know that Treasury bills don’t yield 3% anymore; but it was a reasonable estimate back in the heyday of the Sharpe ratio.

The carb-sharp ratio in nutrition: choice of foods

Here is my analogue of the Sharpe ratio, termed the carb-sharp ratio for reasons that will become clear. It is calculated as [carb grams minus fiber grams] divided by fiber grams]. In English: how much risk do you take per unit of safety, when you eat this cracker / chip / bread / pasta / other carbohydrate-laden food?

The underlying concept will make more sense if you’ve read Dr. Fung, and understand and accept the following tenets:

  1. Fiber is safe. Actually, fiber is more than safe: it provides antidote, remedy, and absolution—forgiveness for carbohydrate sins.
  2. Carbs are potentially dangerous to the specific goal of weight loss. Fiber-free carbs are sugar, plain and simple, whatever the name that appears on the ingredient list. It may look like a cracker, or a serving of rice, or a gluten free pizza crust. But 40 grams of carbs, with no accompanying fiber, might as well be 10 teaspoons of white sugar swallowed straight.
    • Again, this will only make sense if you’ve followed Dr. Fung’s argument about sugar to insulin spike to insulin resistance to increased fat storage to long-term weight gain.

Now, with a few exceptions like table sugar, almost any food that contains carbs will have some fiber.  The purpose of the carb-sharp ratio is to quantify: how much curative, protective, forgiving fiber are you getting?  Or equivalently, how much incremental risk are you assuming, relative to the safe fiber you eat?

Since it is not possible to divide by zero, when computing the carb-sharp ratio for something like table sugar I will substitute 0.1 for 0.0, as the weight, in grams, of the fiber provided.  So for a teaspoon of sugar, about 4 grams, the carb sharp ratio would be [4 – 0.1] / 0.1, or 39.  But for two teaspoons, since fiber would still be zero, the carb sharp ratio would climb to 79 [8 – 0.1] / 0.1.

The carb sharp ratio in nutrition has the inverse interpretation of the Sharpe ratio in finance: when it comes to investments, more incremental return per unit of risk is good. When it comes to nutrition, less incremental danger per unit of antidote is the desired outcome. The carb sharp ratio is basically a matter of how much incremental carbohydrate risk you assume, relative to the amount of protective fiber you consume.

In terms of scale, in finance Sharpe ratios rarely move much above 0.5, so that ratios not much below 0.5 are considered good. In nutrition, carb-sharp ratios rarely fall below 1.0, except for vegetables or nuts, and rarely fall below 2.0 for any carb-rich food other than beans.  Hence for other foods and food combinations, anything on the order of 2.0 to 4.0 is “good,” while ratios either side of 5.0 are “acceptable, in moderation.” But when ratios start to climb toward 10, and beyond, then as far as your body’s insulin economy is concerned, you just had dessert. And if you are not careful, here in bountiful and carb-rich America, your every day will look like this: dessert for breakfast, dessert for lunch, dessert for snack, dessert for dinner, dessert, and then dessert for snack. You know where that path leads.

Action implications

Now let’s look at specific food choices.  See below for caveats: briefly, I’m not a doctor and I have no professional qualifications in nutrition (or finance, for that matter). I made this stuff up as a tool to help me make choices at the supermarket shelf. It’s more particularly a tool for reading and making sense of nutrition labels, when trying to control carbohydrate risk.

Also, and very important, I have no dietary restrictions—I’m not a vegan, and I don’t even have high blood pressure.  I have no food-related medical issues at all. I just want to enjoy my meals while shrinking my belly back to where it was some years ago.

To this end, I found it easy enough to cut down on added sugar; you just get religious about reading the label. It was also not so hard to eschew obvious empty carbs, such as baked goods made from refined flour. Much harder, initially, was to determine what to substitute in their stead.

Here the problem is overwhelming choice. Lots of Americans attempt to diet; many try to reduce their consumption of certain nutrients, originally fat, now sugar; still others are vegetarian or vegan; and some suffer from gluten intolerance, etc. As a consequence, the shelves of Whole Foods, or any large urban grocery store on the coasts, groan with alternatives to the bread and pasta of my youth.

What should it be: rice flour in place of wheat?  Maybe quinoa? Is a corn tortilla the better bet over flour?  Must it be whole wheat pasta? Or—oh dear—pasta made from lentils?  Must the rule be no wheat at all? No grains at all? Does it have to be salad for breakfast, salad for lunch, and two salads for dinner? (No snacks in this second list—read Dr. Fung to see why.)

That recommendation would be problematic for me—I’ve never really liked salads. Rabbit food, as me and my bros used to say.

The carb-sharp ratio is designed to help the grain lover, the person who grew up on wheat flour goods (that would be me), to make an intelligent choice among these many alternatives to wheat cereal, wheat bread, and wheat pasta. From my standpoint, it would be a pity indeed to cut all ordinary grain foods from the diet, replacing them with yucchy, bland, off-tasting alternatives—that ended up providing pretty much the same amount of belly-expanding free carbs. I can give up wheat, and corn, and white rice—but only if the alternative is superior with respect to the goal of weight loss.  And, so long as the new regime doesn’t involve eating rabbit food for every meal!

First level comparisons

To anchor these comparisons, let’s first calculate the carb-sharp ratio for some common grain culprits, and compare these foods, on the numbers, to their virtuous replacements according to conventional recommendations. For the top set, we’ll do ordinary pasta, white bread, white rice, and white flour tortillas; for comparison, we’ll look at whole wheat pasta, whole wheat bread, brown rice, and (gluten free!) corn tortillas.

And for grins, we’ll put in a few foods to anchor the low end, just to show that there are some ordinary, familiar items with much, much lower carb-sharp ratios than, say, pasta. These will be black beans, avocados, peanut butter, and rolled oats.

Again, our bench mark for “awful” (i.e., “you have to do better than this”) is a teaspoon, or four grams, of sugar with a carb-sharp ratio of 39.0.

“White” products—the kind ordinary folk eat
Ordinary pasta White wheat flour White rice Flour tortilla
Carbohydrates* 74.7 72.5 80 23.6
Fiber 3.2 2.4 1.3 1.4
Carb-sharp ratio 22.3 29.2 60.5 15.9

 

“Whole grain” and “gluten-free” alternatives
Whole wheat pasta Whole wheat bread flour Brown rice Corn tortilla (corn meal)
Carbohydrates 73.4 72.6 77.2 10.7
Fiber 9.2 12.2 3.5 1.5
Carb-sharp ratio 7.0 4.9 21.1 6.1

 

A few comparison foods
Black beans Avocado Peanut butter Rolled oats
Carbohydrates 23.7 9 16.3 66.3
Fiber 8.7 6.7 8.9 10.6
Carb-sharp ratio 1.6 0.3 0.8 5.2

Sources: USDA nutrition database, immuneweb.org, web searches.  Numbers are per 100 grams.

The results for the top set of “white” products are about as bad as expected.  Carb-sharp ratios range between 16 and 60.  A slice of white bread has a carb sharp ratio not much lower than sugar—you assume a large amount of excess carbohydrate “risk” in each case.  And, however gluten-free it may be, white rice has a worse ratio than spaghetti. Nor is a wrap made from a flour tortilla, as a substitute for a sandwich made from white bread, going to do all that much to protect you.  Free carbs are free carbs, bread or rice, American cuisine or Hispanic cuisine or Asian cuisine.

More disconcerting are the results for whole grains and for wheat alternatives; compare the middle section to the top section. On the one hand, in every case, there is measurable improvement, with the largest gain coming from substituting whole wheat for white wheat.  Whole grains do make a difference.  The carb-sharp ratios for the whole grains fall in every case, sometimes substantially—mostly because the pitifully small fiber totals for refined products, in their whole grain versions, double or triple.

But on the other hand, in terms of my rule of thumb that carb-sharp ratios should be well under 10, and preferably below 5, even the whole grain versions in the middle section mostly fall short.

Next, take a look at the bottom section: here at last we see some svelte carb-sharp ratios! Heading up the list is a serving of avocado, with a carb-sharp ratio of less than 1.0. Rolled oats score way better than any of the “white” grains in the top table, and better than most of the whole grains; but they don’t come close to an avocado or to peanuts, and oats are no more than on par with whole wheat.

Takeaway #1: Healthier grains are still going to get in the way of weight loss, and contribute to long term weight gain. Not because they are grains, and not because they are carbs, but because they still provide too many free carbs, unanchored by fiber. Put another way: eating healthy does not mean you will lose weight as well.

To drive home the point, here is the same sort of table, now with entries for, dare I say, some newer and more fashionable whole grains and legumes, different from anything that I ate in my youth.

Quinoa Amaranth flour Red lentils Garbanzo beans
Carbohydrates 30 20 30 63
Fiber 3 3 15 12.2
Carb-sharp ratio 9.0 5.66 1.0 4.16

Sources: Quinoa, Red lentils from nutrition labels on Trader Joe’s products; Amaranth flour from nutrition label on Bob’s Red Mill product; Garbanzo beans (chickpeas) from web search (per 100 grams).

Uh oh. Quinoa may be a super food, and in fact it is a seed, not a grain.  Nonetheless, quinoa still supplies all too many fiber-free carbs, with a carb-sharp ratio rather worse than whole wheat. Amaranth flour isn’t too bad, but it isn’t any better than whole wheat or oats.

Conversely, red lentils have an outstanding carb-sharp ratio, better than some common vegetables. Then again, just because something is a legume doesn’t guarantee a super low carb-sharp ratio; chickpeas aren’t much better by this metric than whole wheat.

It’s a fact: whole grains are better for you and probably have all the health benefits commonly attributed to them.  But this blog post is not about healthy eating; it’s about not gaining weight while still eating tasty stuff that’s not unhealthy. Weight loss is not the same goal as health.

If you are concerned about your weight, you have to avoid or minimize grains, seeds, and any other carb source with carb-sharp ratios of 20, 30, 40, or 60. The effect of these foods is little different from spooning straight sugar into your mouth. There are plenty of other foods out there with far lower carb-sharp ratios.

Now a cautionary note. The carb-sharp ratio doesn’t care whether something is a grain, a legume, or a super food. It’s strictly a numerical analysis, blind to the individual food, and blind to all other nutrients. That’s its virtue but also its flaw.  Quinoa may indeed be a superfood over all, and much better for the body than corn or wheat; but it isn’t going to assist much in weight loss—which is all the carb-sharp ratio cares about.

The idea, courtesy of Dr. Fung, is that from a healthy nutrition standpoint a rich American (redundant, in the dietary context) is going to get all the protein he or she needs, and doesn’t have to worry about the fat he or she consumes, as long as what is eaten is food and not a chemical slurry.  With respect to these two nutrients, no dietary changes are required for health—fat doesn’t have to be avoided, and protein doesn’t have to be sought out. Just eat the abundant food we have here, focusing on minimally processed products.

But that same ordinary American, without a deliberate and sustained alteration in their diet, is going to get way too many fiber-free carbs, and will gain weight, year after year, decade after decades—slowly, but inexorably.

Hence, when you decide to alter your diet, and bring your carb-sharp ratio way down, you have to be cautious. You can’t use simple heuristics like “legumes good, wheat bad.”  You have to read the label, especially if what you are considering is a food preparation that didn’t exist 100 years ago.

Case in point: I have in my pantry some red lentil pasta, from when I first started this new dietary kick; and a bag of toasted garbanzo beans from Beanitos. Yes I will lose that wheat belly!

Then I took a closer look at the nutritional labels.  Here is what I found:

Red lentil pasta (Trader Joe’s) Beanitos toasted chickpea snack
Carbohydrates 32 18
Fiber 3 2
Carb-sharp ratio 9.66 8.0

 

Whoa! In both cases, the carb-sharp ratio has deteriorated sharply with respect to the unprocessed lentils and chickpeas tabled above, rising to values well above what we see in whole wheat or oats. What happened?  Presumably, some aspect of how the lentils and chickpeas were processed has removed fiber. The package no longer contains “whole food,” and the official USDA values no longer apply.

Caveat emptor!

It’s the meal, not the food

In finance, the Sharpe ratio can be applied to portfolios, even mutual funds, as well as to individual assets and asset categories.

Likewise, in nutrition, what counts is not the chemical breakdown of individual named foods, but the overall profile of the meal. I have to remind myself, and maybe you should remember too: We are not machines that process chemicals, but human beings who dine.

The carb-sharp ratio of a meal is computed by summing the carbs of each component to get a new numerator and summing the fiber grams to get a new denominator (don’t forget to subtract the new fiber denominator from the new carb numerator). Here are two examples: white rice plus black beans, and an open-faced sandwich consisting of white bread spread with peanut butter.

White rice with black beans(100 grams each) White bread spread with peanut butter (100 grams each flour, peanuts)
Carbohydrates 80 + 23.7 = 103.7 72.5 + 16.3 = 88.8
Fiber 1.3 + 8.7 = 10.0 2.4 + 8.9 = 11.3
Carb-sharp ratio 9.4 6.8
Comparison carb-sharp ratio: whole grain analogue (brown rice / whole wheat), no beans or peanut butter 21.1 4.9

 

Kinda shocking, huh? The white grain, paired with an appropriate companion, either has better carb-sharp ratio than its whole grain analogue eaten in isolation (rice), or one that is no longer dramatically worse (wheat).  The ratios would be better still if the whole grain analogue was substituted; but even white grain, paired with a more fibrous food, quickly improves its carb-sharp ratio to a level that is measurably less than that of white sugar.

Conversely, if you substituted the whole grain (slices of whole wheat bread, for example) but unfortunately, also added another ingredient with a bad carb-sharp ratio (making it a peanut butter and jelly sandwich, say), you could end up not much better off than if you ate plain white bread with peanut butter only.  Here’s the math:

Whole wheat bread (100 grams flour) Peanut butter (100 grams peanuts) Strawberry jelly (45 grams or 3 tbsp) white bread & peanut butter
Carbohydrates 72.6 16.3 40.5
Fiber 12.2 8.9 0
Carb-sharp ratio = 5.13 = 6.8

 

Takeaway #2: it’s not choice of grain that matters most, but what you pair (and don’t pair) with the grain. And / or, whether you eat (much) grain at all.

It occurs to me that now I know why wheat gets such a bad rap among writers in the alternative nutrition, New Health spheres. Two reasons, specific to some degree to modern America:

  1. Wheat is the grain most likely to be eaten in isolation from any fibrous accompaniment in its refined flour version (e.g., pancakes, sandwiches, crackers, pasta)
  2. Wheat is the grain most likely to be eaten with a sugary accompaniment: syrup, honey, sugar.

Few in America will eat a bowl of rice by itself; it will be accompanied by a stir-fry of vegetables with great carb-sharp ratios in themselves, constraining the overall carb-sharp ratio of the meal. But there are all kinds of opportunities to eat wheat straight or with sugar, from pancakes to rolls and bagels and muffins to cookies, crackers and pasta (tomato sauce won’t bring to pasta the same benefits that vegetables bring to rice; tomato is a fruit).

Concluding note

I hope to follow this post with others; but I’ve described the carb-sharp ratio sufficiently, and given I hope enough pertinent examples, that you can apply it to food selection yourself.

Here are a few more takeaways

  1. You don’t have to obsess about whether the nutritional label says “0 grams of sugar.” These grams show up in the carbohydrate total, and will drive up the carb-sharp ratio if they are excessive.  In the case of most grain products—bread, for example—there are dozens of grams of non-sugar, non-fiber carbohydrates that act in the body exactly as does white sugar taken straight.  Why obsess about the one or two grams of sugar labelled as sugar, as in the honey that might be added to bread, when you are eating dozens of grams of carbohydrates-equivalent-to-sugar-but-not-labelled-as-such?
  2. You can’t ever drink your sugar. Orange juice, fresh-squeezed or no, isn’t that much better than drinking coca cola for breakfast—again, from the very specific standpoint of weight-control. Same for a Native, organic, yada yada, fruit juice made from “Look! this many whole strawberries and bananas.”  Read the label—in any fruit drink, you are drinking oodles of the worst kind of sugar.  If you would not expect to lose weight while consuming high fructose corn syrup, you should not expect to lose weight while drinking any kind of fructose-rich fruit juice.  Zero it out.

Last, I’ll leave you with this final carb-sharp ratio, for some 88% dark chocolate I’ve taken to eating with my after-lunch coffee, in place of the fruit bars or cookies that were driving up my weight.

88% Chocolate

x o x o x brand

Carbohydrates 10
Fiber 4
Carb-sharp ratio 1.5

 

That’s for the recommended serving, which is twice what I allow myself. Sure it has added sugar (4g for the serving, 2 for my consumption), but it’s got more fiber than 100 grams of any of the “white” foods listed above.  And, way, way fewer total carbs.  A worthy addition to my diet!

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