When not at work with students, I spend my time in my room either reading, calculating something using pen and paper, or using a computer. I read almost anything: from the pornographic to the profound, although my main interests are mathematics and physics. "When I get a little money I buy books; and if any is left I buy food and clothes." -Erasmus

## Monday, August 24, 2015

### Sinatra, or why older is sometimes better

When I was a lot younger, the only music I would hear in the house would be jazz standards. And so I grew up with Tony Bennett and Sinatra and Nat King Cole being played by the radio all day long. (Does anyone even listen to the radio anymore?) Of these singers, I got to appreciate Sinatra only when I was older.

Sinatra always put me off because I felt that the way he sang his songs (at least in the albums I did hear) felt shallow. I suppose the teenagers of his time might have found his rendition cute, but it never did hit me right. I It was only when I was about to enter university that I started to appreciate his music, and the catalyst was a live album: Sinatra 80th Live in Concert. I used to play it over and over again, and sing with it.

When I finally got internet access, I started searching for mp3's and videos of Sinatra's other albums, and it hit me: I still felt that his early albums were not as good. The clue that led me to understand why was found, of all places, while reading Mario Puzo's The Godfather. One of the characters, Johnny Fontaine, was modeled after Sinatra, and you could divide his career into two phases, before he lost his voice, and after he regained it. And I realized that in the same way there are two phases in Sinatra's work: when he was younger (which I disliked) and when he was older (which I loved). I'll link to two youtube videos so that you can sample how he does the same song, once as a youngster, and the other when he was much older. I think the older Sinatra wins.

Here's the younger Sinatra (1959)

and the older Sinatra (1982) below.

## Tuesday, June 16, 2015

### Less Than Meets The Eye

I saw this on my facebook timeline today:

and I would like to invite you to guess what's wrong with it.

If you look at the numbers, you should be immediately suspicious of the grams of protein to calorie ratios. The better measure of protein content is grams of protein to grams of food. Take broccoli for instance. One of the things we can expect is that broccoli, on a per gram basis, does not contain the same amount of calories per gram as meat. (This is the reason, by the way, why dieters love veggies. You can get the feeling of being full without taking in as many calories if you eat the same mass of veggies as meat.)

I did a search on the per gram protein content of broccoli, and one of the websites I hit was this. Go read it, as it is both informative and hilarious.

This case reminds me of other places where numbers can be used to mislead. I've recently acquired various books on the analysis of financial statements: Mulford and Comiskey's The Financial Numbers Game: Detecting Creative Accounting Practices, Schilit and Perler's Financial Shenanigans, and Fridson and Alvarez's Financial Statement Analysis: A Practitioner's Guide, so I suppose that in this instance, I was already primed to check the numbers. After finishing Kahneman's Thinking Fast, Thinking Slow and Thaler's Nudge, I've decided to entertain myself with financial statement analysis. I'm reading slowly through Fridson's book, and one of the insights that I've gained is to examine income statements in terms of percentages of sales. Unfortunately, after reading these books, one leaves with a less than charitable impression of corporate management.

## Monday, June 8, 2015

### Unfair wagers

I've been reading a few books with a decidedly behavioral economics theme. The two most recent ones were Dan Ariely's Predictably Irrational, and Belsky and Gilovich's Why Smart People Make Big Money Mistakes -- And How To Correct Them. I've had a lot of time for all this since I'm currently out of work, and waiting for a government funded writing project. I'm also seriously considering becoming self-employed, since I much prefer doing something self-directed. My main expected headache, though,  is how to deal with taxes if I do take that route.

From my recent reading, I encountered the following problem: Assume that you have a fair coin (equal likelihood for heads and tails), and you were asked if you were willing to make the following wager: USD 150 for you if it's heads, and USD100 for the house if it's tails. Would you be willing to take that wager?

A simple calculation shows that the expected payoff if you do take the wager is USD 25, which is obtained in the following way: Expected payoff $=(150)(0.5)+(-100)*(0.5)$ =USD 25. So if you were the rational man of classical economics, you should take the wager.

Unfortunately, there is something that's really wrong with the rational man. If your total net worth is USD 100, then if you were unlucky, then you may be faced with ruin at a single toss of the coin. That's certainly not a good outcome. And if you have a net worth, for example, USD 200, then the odds of getting both tails would be 0.25. Again, if you were unlucky, you could face ruin after two tosses with probability $\frac{1}{4}$.

The only realistic way that you could play this game is if you had a margin of safety, if the bets you make were small compared to your net worth. I'm not sure, for example, if the bank would be willing to extend credit while you take the losses while you undergo large number of bad runs. Given how hard it is to raise additional capital, even unfair wagers where you have the advantage may be a bad idea.

## Friday, June 5, 2015

### Mandelbrot, Fat tails, and other things

I spent yesterday continuing my reading of Mandelbrot's book on the (Mis)behaviour of Markets. Although I 've read excerpts before (my thesis adviser has a copy somewhere in the theoretical physics group room), it was only yesterday that I obtained a copy, and was able to read it through.

One of the things that I keep coming back to is probability estimates, and quantifying risk. (This is one motivation for reading Mandelbrot, as he forces me to think again about these things.) Conventional finance has such measures (the volatility of stock prices of a stock, or index for example), but I'm not sure how reliable it is.

Part of the things we studied in the theory seminars I've attended is the study of random walks. There are a lot of flavors, apparently, and it all boils down to the probability distributions that you use for each step. Conventional finance calculations seem to rely on Gaussian distributions, and for these, experimental estimates of probability can be obtained by taking the mean and standard deviation. From these, the sophisticated machinery of confidence intervals and parametric tests emerge.

The world, however, is not so nice. If, for example, the underlying distribution for the steps in a random walk are Cauchy distributions (an example of a fat-tailed distribution), then the probabilities of very large steps are more likely than an experimental measurement of mean and variance will indicate. In finance, these large steps either produce great fortunes or ruin.

And yet, I keep procrastinating on the studies of probability and statistics that I need.

Still, I need to dust off those finance books and random walk books, so that I can start reading and rereading, as well as calculating. Some of the finance material has applications after all. But I'm not sure about rereading; sometime, it's more fun to read enough to understand the problem, and then work out the solution, than it is to read both.

I do have lots of questions to think about: what determines the risk premium for stocks over bonds? How do we measure the performance of an index fund relative to the index it's supposed to follow? (I want quantitative measures, and a suitable motivation for the definition of the measure.) How do we know if a fund consistently beats the index? (The problem is finding the right definition of "beat the index")

## Wednesday, June 3, 2015

### Gaming the P/E

One of my current projects (for entertainment purposes) is the calculation of the Price to Earnings ratio (P/E) of the PSEi index. My interest in it lies in its usefulness as a rule of thumb way of comparing returns on investment of stocks versus bonds.

There are various ways of calculating this quantity (and therefore various ways of misleading the people who use this ratio). The most primitive method is to look at the current stock price of a company and then divide it by the most recently reported earnings per share, a quantity that should show up in the financial statements of a corporation.

Another way of calculating this is to use analysts best estimates for the future earnings per share. This can be confusing, especially since some news services do not actually specify where the earnings per share value used comes from.

What are the disadvantages of these two methods? The first one is the tendency of management to inflate the earnings per share value reported, especially when management compensation comes from stock options. Meeting or beating analysts predictions is one way of encouraging the increase of the stock price. I've read of many such cases in the US; every time there's news of an earnings restatement, I wonder about the auditors and the management. The most famous example of earnings statement manipulation is Enron.

The second disadvantage lies in analysts being human. Precise figures are produced without error bars just looks like black magic. Any prediction about the future will contain uncertainty, and the error bars get larger as the length of time involved increases. Weather prediction, for example, gives only a week or so. Typhoon paths for example, contain error bars, and the error bars increase with time. I've read studies of analyst accuracy, and they don;t make a good showing.

One way of getting around the uncertainty of past year earning estimates is to take a time average, for example, over ten years (suitably indexed to take inflation to account), and then use this average earning per share to calculate P/E. The problem, of course, is how representative this average is of present or future earnings.

One case where this average seems to be useful is for the stock market as a whole. Shiller, in Irrational Exuberance, uses this ratio for the S and P index to check whether the market as a whole is overpriced. The claim is that "normal" levels would be at around 15, and numbers above this mean the market is overpriced.

I sometimes calculate the inverse of the P/E ratio as a way of comparing the return on investment on a stock to that of a bond. If you divide 100 by the P/E, then you have an estimate on the return on investment, assuming you just bought the stock at that price. 15 means a return of around 6.8 percent, slightly better than the current return on BBB bonds which is, as of writing, at around 4 percent per annum. This number of course is most meaningful if you take the perspective of the controlling shareholder, assuming you bought control at that price.

One should not read too much into the P/E ratio. There are other ratios that Graham and Dodd suggests as a way of measuring the health and return of a corporation, e.g. Total Earnings to Current Assets, etc. One ratio that I'm partial to (if only getting that information for free is so damned difficult) is the Price to Corporate Income Tax per share ratio, since it gives similar information as the P/E but this time, based on actual taxable income. Alas, like all financial ratios, it is also possible to game.