more on Weight Loss

Okay, so I'm trying to lose weight. I've written 'bout that before: click! There's this formula for the calories required to maintain your current weight. You consume more than this number and your weight goes North. You consume less than this number and your weight goes South. I figure it's worth providing some mathematical hand-waving to see what reduction in my daily calorie intake would lose, say, 10 pounds. I did that here Aaah, if'n I could only believe what it says. A simpler (and less appealing) calculation goes like so: ⊗ A pound of body fat is worth 3500 calories. ⊗ Ten pounds of body fat is worth 35000 calories. ⊗ At 100 calories per day, it'd take 350 days. That's close to a year. Fat chance!

 

Weight stuff (again)

I've become fascinated by the mathematical gesticulations associated with metabolic rates and weight loss. I've been playing with the Harris-Benedict equation Then I watched a TV special on fractals and, lo and behold, there's yet another magic equation ... Kleiber's law connecting the Energy expended to maintain a certain body Mass: E = k M3/4   where k is some constant The interesting thing about this one? It (supposedly) applies to everything from roaches to rhinos. If by Energy we mean calories ingested, then when we apply the magic law to Homo Sapiens, it suggests that a reduction in caloric intake is associated with a weight loss like so: See the blue dot? It says that a 10% reduction in caloric intake should (eventually) result in a 13% reduction in mass weight. . I've memorized the numerical values involved with the chart and, at every opportunity, mumble in crowded elevators: "Eat 10% less, weigh 13% less ..." I might point out that Kleiber's law is NOT universally accepted. Some suggest a 2/3 law instead, like: E = k M2/3 That's like saying that Energy requirements depend upon surface Area whereas Mass depends upon body Volume. That is (dimensionally speaking): E = C1 Length2   and   M = C2 Length3 ... so E = k M2/3 Anyway, using 2/3 gives the gray graph.

DOW stuff

Okay, January was a lousy month for the DOW: down 4.9%. It was also lousy for the S&P: down 5.2%. The Nasdaq? Down 7.0%. But the value of the DOW is proportional to the sum of the stock prices. Which of the 30 DOW stocks has the highest price? IBM at $122. The lowest price? AA at $12.73. So IBM has about ten times the weight in calculating the value of the DOW. Okay, so what about the S&P? Its value is proportional to the market caps. What if the DOW were calculated like the S&P? Which of the DOW30 has the largest mkt cap? XOM at $306B. The smallest mkt cap? AA at $12.4B So, if the DOW were calculated like the S&P (proportional to mkt caps), XOM would have about 25 times the weight!! And how did these guys perform, in January 2010? Click on the pretty picture to enlarge. Ain't it nice that AA has a small weight. P.S. AA stands for Alcoholics Anonymous Alcoa. ------------------------------------ To have your portfolio mimic the DOW, you'd buy one share of each of the 30 DOW stocks. Suppose you invested equal dollar amounts (rather than equal share amounts)? You'd invest $1 in each DOW stock. How would you have fared, in Jan, 2010? Just like the DOW or S&P: about -5%. ------------------------------------ Want to see the current weights, for DOW stocks? by MktCap and by Price and performance assuming $100K were invested with equal amounts in each stock ------------------------------------ Will February be better? 'course, they is variations from the average from bestest to worstest, eh? (Click on the chart.)

 

Weight Loss

Having stuck to that weight loss ritual and finding no change for the past week or two, we're trying something new: We got us a fancy scale and it measures (among other things) Body Fat and since I know nothing about how one measures that stuff, I figured it was time to larn: http://www.gummy-stuff.org/weight-loss.htm

 

Indexes

To calculate the DOW Index, you add all the prices. It's described as a "Price-Weighted Index". Similarly, the S&P is described as a "Market-Cap Weighted Index" ... presumably because its calculation requires you to add all the Mkt Caps. I've always felt that describing these Indexes as "Weighted" was misleading. Perhaps that's because I was thinking "Weighted Averages". Perhaps that's the result of creeping senility. Anyway, now I'm happy. I see that the Gains are weighted averages - even if the Indexes aren't. Besides my confusion over the use of the adjective "weighted", I've always been annoyed at the use of a Sum of Prices to generate an Index. I imagine Berkshire-Hathaway as being a component of a 31-stock DOW. It's weight would be obscene. It'd generate 99% of the value of the Index. On the other hand, as the component of a 31-stock "Mkt-Cap Weighted" DOW, it's weight would be respectable.

 

Weight Loss

I've been on this weight loss kick. I have no idea why nibbling works ... tho' it sho nuff works for me. Now I discover that rats normally nibble. However, if'n they're fed just three meals a day ... they get fat ! Click!

 

the DOW dump

On May 6, the DOW dumped almost 1000 points. That's about 10% of its value. That's quite remarkable, eh? So I've been reading that: [1] Somebody typed B (Billion) instead of M (Million). [2] Computers were "in charge" and goofed. [3] Software measured investor sentiment and reacted.       ... and MSNBC was showing video of Greek riots! [4] When traders started selling, there were few buyers.       ... and market orders kept going to low bidders. [5] Proctor&Gamble (PG) dragged down the DOW. [6] Cancelled trades weren't being recorded. [7] Circuit breakers on the NYSE kicked in.       ... so HUGE trading volumes went to other exchanges. [8] Was it manipulation by someone who made a fortune?       (That's from dilbert.) [9] Cyber terrorism. [10] Insert your own explanation. The DOW is proportional to the SUM of 30 stocks prices. How, then, did each DOW component react? What was their drop, from High to Low (on May 6)? They was like so: Figure 1 See? PG dropped the mostest! But does it constitute a large fraction of the Index? Here's the (current) weighting of the DOW 30. Figure 2 See? IBM (with the largest stock price) has the largest weight. And PG? A paltry 4.4%. If'n we take the 30 percentage drops (from Figure 1) and weight them (according to Figure 2), we'd get a 12% drop in the DOW (from High to Low). So ... what's my explanation for the DOW dump? GREMLINS Either that ... or mebbe:

 

Weight Loss Pills

Yesterday, Heidi & I started a weight loss program. After an exhausting exhaustive search, we decided upon Apidexin. It's got lots of sexy ingredients, it comes with a second collection of pills (DetoxuFree72) and it's all over in a month. First day? I'd gained two pounds !!

Losing weight ... maybe

Okay, so I've been taking Apidexin for ten days and look what's happening: Then I find that the reading on our ancient analog scale* depends upon where the scale is located.   AARGH!! So, this morning I buy a new, digital scale. They get pretty fancy, these digital scales. They can plot your weight over the past five days, measure body fat (heaven forbid), provide historical info for two people and check stock market prices ... just kidding. I bought the el cheapo model. Anyway, I'm looking forward to generating a new chart: * I notice that, on eBay, they refer to these scales as "retro".

 

Weighting

Recently, I talked about volume weighting stock prices, where prices associated with high volume were more significant. That was fun! Then Donald W. pointed out these weighting schemes for ETFs. ** That reminded me of the days when I dabbled in various schemes for calculating "weighted averages". Like evaluating a basket of stocks: Creating Indexes Equal-weighted Indexes Comparing Active & Passive performances Then there's weighting when it comes to looking at historical performances ... like weighted moving averages: Exponential Moving Average A host of other averages Mamma mia! That, too, was great fun! Mebbe, when people say: "The average was ..." we should respond: "Average? What average?"   ** Although it's not clear (at first), by "equal weighting" the author means equal dollar amounts invested in each, not equal shares. Here's an interesting fact: Had you bought 1 share in each of the 30 DOW stocks, one year ago, your gain would be 43%. That'd be equal-share-weight, eh? (The DOW Index has this weighting. More dollars are invested in stocks with higher prices.) Aah, but had you bought $1.00 in each of the 30 DOW stocks, one year ago, your gain would be 49%. That'd be equal-dollar-weight, eh? Before we get too excited about doing MUCH better, consider the previous year. Equal-share-weighting would have given us -37% whereas equal-dollar-weighting would have given us -36%. Here's a pretty picture (using the current 30 DOW stocks): For reasons I don't understand, the equal-shares weighting should be the same as the actual DOW. I reckon the DOW components have changed over the past year, eh? After all, GM was dumped ... and wasn't CISCO added?

 

Nibble all day

Once upon a time I went on a diet. Well, not exactly: I took magic pills to curb my appetite ... or burn fat ... or something (I guess)? Weight Loss more on Weight Loss Anyway, nothing worked very well, so I told Heidi that what I needed to do was "nibble all day". So I fixed a bowl of kidney beans, salt, pepper, garlic powder, oregano, olive oil and vinegar. That's like -- Italian dressing. The bowl sat quietly on the kitchen counter -- with a tablespoon stuck into the creation. Every time I got a little hungry, I'd have a spoonful. Next day the kidney beans were replaced by chick peas ... then corn and green beans with maybe pieces of celery or lettuce. By dinner, I was full -- but managed to finish off the last of the concoction. Did it do any good? It seems so. I never feel hungry and lost 10.9 pounds in 9 days. At that rate, in six months I'll be lighter than air, eh?

 

Volume weighting

Once upon a time I got very excited about volume-weighted stock prices. Prices associated with high volumes should have a greater weight, right? I'd calculate the vol-wgt'd price like so: Pvol-wgt = Pclose * Volume / (Average Volume) Then I'd go through every conceivable Buy-Sell strategy (based upon closing prices) and substitute volume-weighted closing prices. For some reason, I lost interest in that ritual. Can you see why? ----------------------------------------------- What's remarkable (to me, at least) is that the violent behaviour of the vol-wgt'd price don't change things so much. For example, long, long ago (and far, far away) I played with a Buy/Sell ritual called ADX: the Average Directional Index. When I introduced volume-weighting (and called the result VDX), it don't hardly change the Buy/Sell signals. For example: (Without weighting it's ADX. With weighting it's VDX.) Indeed, only 3 of the 30 DOW stocks have their (current) signals changed.

 

Calories

It always amazed me that you can lose a pound or two ... overnight. If you were sleeping on a bathroom scale, you'd presumably see the indicator slowly drop by a pound or two. Where does it go? So I tried doing some weight-loss arithmetic, like so: ⊗ The body "uses" about 100 Calories per hour. ⊗ At 3500 Calories per pound of body fat, that's a pound every 35 hours. ⊗ Just living and breathing (without any caloric food intake), you'd lose (very roughly) a pound every 35 hours. ⊗ Then, while sleeping for 8 hours ... would you (could you) lose a pound or two??? Aah, but the body uses less than 100 Calories per hour while sleeping. It's more like 65 Calories/hour. So how does one lose a pound or two overnight? Okay, that 100 Cal/hr is approximate. It'll depend upon your BMR or Basal Metabolic Rate which will depend upon your biological configuration. To lose a pound in 8 hours ... wouldn't that require about 3500/8 = 437 Cal.hr? Impossible. While playing with the numbers, I discover that the calorie that I'm familiar with is NOT the Calorie noted on food products. Indeed, the calorie is defined as the heat energy required to raise the temperature of 1 gram of water by 1 degree centigrade. The Calorie will raise 1 kilogram by 1 degree. See? The Calorie is really a kilocalorie ... and the word is capitalized. Get it? 1 Calorie = 1 kilocalorie.

 

Central Limit Theorem

There's this remarkable theorem that goes something like this: Suppose we record the average daily temperature (measuring the temperature every hour, for 24 hours -- then averaging these 24 readings). Suppose, too, that we record these daily averages for a few years. Finally, we plot the frequency with which certain averages occur and get the green distribution shown here: The red curve is the world famous "Bell Curve". The fact that the frequency distribution looks like the Bell Curve is interesting, eh? What's even more interesting is the fact that if we plotted the average height of people we meet each day (or their average weight), we'd still get (very nearly) a Bell Curve. We might also repeat this ritual for the average of the number of kilowatts used by a city each hour or the average length of fish we catch each day (while fishing each day in Lake Ontario ... and catching lots of fish). These averages always look like the Bell Curve if there are lots of numbers involved in the average. (That is, we meet lots of people each day or catch lots of fish.) That's the Central Limit Theorem and (after a jillion years of ignoring it) I decided to explain it ... here.

 

gC2

I had forgotten that I did that that Stock Comparison a couple of years ago. However, now that I look at it again, I see that gSC is NOT what I want. gSC multiplies stock returns together. If their product is positive, the returns have the same sign ... and the two stocks move up or down together. gSC then adds all those products and fiddles scales the resulting number so it lies between -1 and +1. That means that LARGE returns have a greater product (hence a greater weight) than small returns. Is that what I want? NO! What I want is to be able to say things like: "Over the past 5 years, the weekly prices of Chevron (CVX) and Exxon-Mobil (XOM) have moved together -- 79% of the time." Now that calculation don't require no fancy fiddling scaling. We jest sorta count the number of times the returns have the same sign, eh? It's like -- a poor man's correlation. Then we get things like this: Am I happy? P.S. Did I mention that gC2 stands for Comparison #2. --------------------------------------------- If'n y'all want to play this game, here's the spreadsheet: http://www.gummy-stuff.org/Excel/gC2.xls I might also mention that, being old lazy efficient, I generate new spreadsheets by modifying old spreadsheets. Every time I do this, the size of the spreadsheet grows ... and grows. This one is obscene, at (almost) 6 MB! That used to bother me. It don't, no more. Once upon a time, somebuddy went through all my spreadsheets and created new ones -- reducing the size of each significantly. That was when there were a couple of dozen. Now there are over 500 of 'em !! --------------------------------------------- One thing that's interesting is persistence. Suppose you discover some neat relationship between a pair of stocks over the last 5 years. Will that relationship persist over the next year? Here are charts for 5-years and the subsequent year: --------------------------------------------- You decide.