Below, Corrections displays the distribution of (log) market equity (price times shares outstanding) of the NYSE, NASDAQ, and AMEX in 2012 (click to enlarge). As always, log means natural log. Note that the graph would be essentially unreadable if it were transformed into levels: the skew in market equity is very large.

The large cap nature of the NYSE is evident: the breakpoint denoting the NYSE's 20th percentile is around the NASDAQ's 60th, and AMEX's 80th percentile.

## Tuesday, June 25, 2013

## Monday, June 24, 2013

### Benefits of Diversification

Below, Corrections displays the benefits of diversification. Returns from the the 1990-1991 stock period, we display the simulated standard deviation from a randomly-chosen portfolio of a given number of stocks and holding it for a year (click to enlarge).
Obviously, choosing a random number of stocks gives the same

*expected*return. But choosing more stocks reduces the expected noise around that return. Choosing only one stock will yield a more noisy process than another. As more stocks are included, the standard deviation of portfolio returns converges down to the market's standard deviation of returns (around 18% for annual returns).### Size-Based Portfolios

Below, Corrections mimics the "size" part of Fama-French (1992), replicating 99.7% of the return variation in Kenneth French's size-based portfolio results in Kenneth French's website using raw CRSP data.

Imagine, each year, after markets close on the last day of June, you form a portfolio based on market equity (market cap). Take the NYSE and find the size decile breakpoints (smallest 10%, smallest 20%, and so on). Then, apply those breakpoints to the NYSE, NASDAQ, and AMEX, form an equally-weighted portfolio of all stocks in that size category.

We can form those portfolios at the end of each June and then look at the average returns (price appreciation as well as reinvested dividends included) from 1926-2012. The results of each strategy are depicted graphically below (click to enlarge).

Imagine, each year, after markets close on the last day of June, you form a portfolio based on market equity (market cap). Take the NYSE and find the size decile breakpoints (smallest 10%, smallest 20%, and so on). Then, apply those breakpoints to the NYSE, NASDAQ, and AMEX, form an equally-weighted portfolio of all stocks in that size category.

We can form those portfolios at the end of each June and then look at the average returns (price appreciation as well as reinvested dividends included) from 1926-2012. The results of each strategy are depicted graphically below (click to enlarge).

As one can see, the lowest decile of stocks returns approximately 18%, while the rest return only 11%. We can also see this small-cap premia evolve over time if we look at the yearly returns of these portfolios, rather than taking the average over many years. While yearly returns are volatile, I compare the 10-year results of rebalancing on size each year (click to enlarge). Again, returns include dividends, producing an equally-weighted 14.5% average yearly return from the stock market rather than 12% from price appreciation alone. Further, the returns are 10-year returns and are net and in percent (e.g. 30 on a certain date means that rebalancing to a certain-sized portfolio for the 10 years leading that date would yield a 30% net return (you would possess 1.3*original assets). To be clear about dating, the last date of December 2002 represents the return of a strategy of holding the June 2002 portfolio from December 2002 to end of June 2003, and then reforming the portfolio for every year until liquidation in December 2012: yielding a return around 14% for the small-cap portfolio.

It is important to remember that this is in no way indicative of an "inefficient" market: if some stocks are more risky, they should have more rewards. If the smallest 10% of stocks are illiquid in times when liquidity matters, then they should have a higher average return, to compensate for their bad qualities.

## Saturday, June 15, 2013

### Options Price vs. Spot Price

Below, Corrections took the price, over nine months, of an option to buy a share of GE stock for $15. We graphed the price of the option plus $15 against the spot price (click to enlarge).

### GDP Per Capita as a Fraction of US GDP Per Capita over Time

Below, Corrections depicts the GDP per capita as a fraction of US GDP per capita for a series of OECD countries (click to enlarge). GDP per capita is in constant prices, PPP with 2005 as the basket reference year. We exclude Luxembourg and Norway, the two countries that have higher values than the U.S. in these terms. A few things stand out:

- Korea's growth in the last decade has been astounding. Far faster in per capita terms than China's.
- China is exceedingly poor.
- The Russian Federation is exceedingly poor.
- Ireland's "Celtic Tiger" growth is astounding, even taken with its catastrophic fall.

## Wednesday, June 12, 2013

### Proportion of Murders Committed by Age of Offender

If you ask anyone, you'll quickly learn that kids today commit far more murders than they used to. Kids and teenagers today are just more violent, more brutal, right?

As with every "the world is worse" stories one is told by anyone over twenty (who inevitably believe that the world is always worse), this one is incorrect. Below, Corrections plots the proportion of total murders by age (click to enlarge).

### One-Year Growth in Employment: Three Surveys

Below, Corrections plots employment growth data from the Quarterly Census of Employment and Wages, the Current Employment Statistics data, and the Current Population Survey. The QCEW and the CES are related but separate measures, while the CPS is completely independent: a survey of workers not of employers. The three measures match growth nicely (click to enlarge).

## Tuesday, June 11, 2013

## Monday, June 10, 2013

### FDA Approval Times

From the article "An exploratory study of FDA new drug review times, prescription drug user fee act, and R&D spending," Corrections depicts the time until FDA approval from submission (click to enlarge).

A hastening of the review process by about 3.6 years to 1 year represents an reduction by 71% of wait time: a dramatic technological improvement (or reduction of waste) accessible to the pharmaceutical industry, holding quality of drug constant.

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