Thursday, June 3, 2010
Well, luckily, baseball people are fanatic datahogs, meaning that public sites like Baseball Reference have stacks of data for everything we could possibly want.
First things first, the number of perfect games during a single season doesn't tell us all that much, because the number of games per season has changed over time. In 1964, when Jim Bunning threw a perfect game against the Mets, a total of 1620 games were played over the course of the season. When Cy Young threw his perfect game in 1904, a total of 1220 games were played. In 1880, which saw two perfect games, a mere 332 games were played*.
So, obviously, what is important in determining the odds of a perfect game in a season is the total number of chances for the event to occur. Since 1876, there have been a total of 188,921 baseball games played (as of 6.2.2010 at around 11pm at night) with 20 perfect games divided up between them, giving us an 0.0106% chance that on any single game, 27 hitters will not make it to a base as a result of hits, walks, or errors (though for Kip Wells, that number is probably smaller). Or, roughly, one for every 9,447 games. Alternately, we can look at the number of perfect games per total games played per season. Currently, we are at .002551 perfect games/total games played (hereafter PG/TG) in 2010. Since 1876, the average PG/TG is .000134. The standard deviation of the PG/TG ratio is .0005887.
This means that the current number of perfect games is about a 4 standard deviation event (assuming, of course, that perfect games are an evenly distributed random occurrence). Cy Young's perfect game was a 1 standard deviation event. And 1880, when both Lee Richmond and Monte Ward pitched perfect games? Well, that year was 10 standard deviations away from the expected.
As a side note, for just plain old no hitters, there have been a total of 258, or a 0.1366% per game. The No Hitter/Total Games average is .0016969, with a standard deviation of 0.002268, meaning that this year's three no hitters fall just under one standard deviation of the expected.
update: Roger Lowenstein ruminates with far greater skill than I on outliers in financial markets and baseball.
* I compiled these stats by adding up the number of wins for each team in each league (National, American, and the short lived Federal League).
Tuesday, May 25, 2010
- Stats: Data and Models (2nd Edition) by Richard D. De Veaux, Paul F. Velleman, and David E. Bock.
- The remainder of the chapters from Corporate Finance by Michael C. Ehrhardt.
- A Monetary History of the United States, 1867-1960 by Milton Friedman and Anna Jacobson Schwartz.
- Can "IT" Happen Again? : Essays on Instability and Finance by Hyman P. Minsky.
- Monstrous Regiment by Terry Pratchett
- and, of course, my pile of unread New Yorkers
Friday, May 21, 2010
EQUITIES just aren't what they used to be. It was once gospel that equities out-perform low-risk bonds. But if you invested in the stock market around 1999 the balance of your portfolio probably suggests otherwise. During the post-war era equity returns have been positive. Enough so that the equity-risk premium, the return equities generate in excess of the risk-free rate (which is normally short-term Treasuries), is often assumed to be between 5% to 8%.
Now, Aleph Blog and others are probably much more suited to discuss the finer points of the Equity Risk Premium, other than to say David Merkel usually uses longer term bonds in order to decide whether there is a risk premium for debt versus equity in general. A.S. here refers to the risk free rate, generally 3 month treasuries.
The first thing that strikes me is this theoretical person who dumped a boatload of money into the stock market in 1999, held it for 11 years, and is thus our layman's proof of the lack of an equity risk premium. Theoretical set and forget investors like this are wonderful rhetorical points, but would have most likely sold out in 2003 and not jumped back into the market until, say 2006. The classic "buy high/sell low" investor. But individual investor irrationality and inexperience doesn't prove or disprove the equity risk premium. Additionally, the problem with this type of data point, like Felix's advice and belief in zero equity risk premium, is that the way it is said begs interpretation from the lay person to stay away from equities entirely. Equities are risky, there is no equity risk premium, and oh look if I had just kept my money in cash I would be doing so much better than I would be doing now. Investing in hindsight is a wonderful way to lose sleep and otherwise confuse your strategies for the future planning.
Moreover, is A.S. taking into account just the price level of the index, or also including dividends? A $10,000 investment in the S&P 500 would have, with dividends reinvested, yielded $11,656 by April 1st 2010. A similar investment in T-bills would have grown to $13,674.
So, if we are going to assume an investor, why does A.S. assume a fully invested, maximum risk taking investor, taking no dividends? Well, convenience, surely. I spent most of the morning looking for monthly returns for the Lehman Aggregate Bond Index fruitlessly, and while Robert Shiller and Kenneth French keeps their data nicely updated, William Sharpe does not.
So, putting aside the likelihood that "real" investors are more likely to be bad trend followers, get nervous and try to market time, and otherwise engage in a whole host of poor investing decisions, what does a "real" investors portfolio look like?
First, lets assume that this investor is investing on a regular basis, through something like a 401k. Thus, a newly minted grad in 1999 (which A.S. may have been, who knows with the Economist's anonymous blogger policy) gets their first job in Jan 1 1990, and puts aside $1000 per month into their company sponsored Defined Contribution Plan. Next, let us also assume that this investor does not invest entirely in stocks, but also elects to invest some money in bonds (I used VBMFX as a proxy for the bond market, see above for the dearth of monthly LABI returns online). What do the different portfolios look like for an investor who is "in the market" versus one who puts their money into the three month t-bill each month?
From January 1, 1999, an investor who invested regularly on the first of month, every month, invested 100% in equities (represented here by the S&P 500), would have invested, over time, $136,000 and on April 1, 2010 have $155,864.79. This is a simple return of 14.61%, and a yearly geometric return of 1.37%.
For the same period, an investor who invested regularly on the first of month, every month, invested 100% in 3 month treasuries, would have invested, over time, $136,000 and on April 1, 2010 have $155,301. This is a simple return of 14.19%, and a yearly geometric return of 2.81%.
Geometric returns doesn't take into account the amount invested during the time period. If we look at the Dollar Weighted Returns (using IRR), we see the that the Market portfolio yields 2.51% versus a 2.45%.
If we add bonds into the portfolio, the returns of the portfolio during the period increase even more (3.98% dollar weighted average for the time period for a 60/40 stock/bond portfolio).
All of this is to say that the academic question of the risk premium may or may not be related to the way that portfolios are (or should) be constructed in real life, and that even cherry picking the sample size of recent data can mask the differences in the way that returns are quoted. Obviously how well each investor slept with each portfolio is different, but that is a different post.
Alternately, past performance is no guarantee of future returns.
But seriously, if anybody has monthly bond index returns going back as far as Shiller's data, please email me.
Following other people's Google Readers also popped up when Chris Blattman recommended to follow Rajeev Ramachandran.
I have added these three people to my reader, and am amazingly happy with the results. Each acts as a curator for a different area of interest, and I reap the rewards (which I suppose makes this project second order curation, as we get more and more recursive).
So, the question becomes: Who do you follow on your reader? Who else should I follow?
Friday, May 14, 2010
Ben Bernanke on happiness.
Pimco's El-Erian's most recent outlook.
Why Did Rating Agencies Do Such a Bad Job Rating Subprime Securities? SSRN.
How do you talk yourself into something?
Tuesday, May 11, 2010
T***: Also, they adopted the Sanders (modified) amendment, but rejected a more fulsome audit of the Fed
It is really just despair. I think this expresses it well: https://self-evident.org/?p=820
T***: The Sanders audit is limited to info on who they gave money to in the last 3 years
The rejected Vitter amendment is a full audit, including minutes
Me: I mean, it isn't rational, insofar as I have no evidence for this, but I just feel that data points will be used as cudgels, either against the central bank or against specific banks, while leaving the bigger picture/necessary adjustments unaccounted for.
T***: That is a f****** stupid article
Me: I mean, the Goldman senate hearings were a laugh
Look, I like Barney Frank as much as the next guy
But he is more the exception, imho
T***: Seriously, absolutely pig ignorant about how hearings work
No, seriously, that is f****** retarded
Those questions were literally all written by public interest groups
And the audience sure as f*** wasn't Wall Street analysts
They were all political questions made for a political point
A political point which purposefully missed the fundamental purpose of the financial system.
T***: Using them to gauge the knowledge of the market among senators (and really, about Senate staff because who gives a f*** what senators know?) is retarded
The writer of this is far more ignorant about how Congress works than the average senator is of the market
It is garbage
Me: I mean, I suppose it is silly for me to expect that a hearing should actually be an attempt to inform and clarify, let alone that the tone and tenor of the hearing will influence the crafting of legislation
That is absolutely ridiculous to expect
Me: so you are saying that I should ignore the hearings? and that anyone involved has no input on the financial regulation in the pipe, and that the knowledge level that their questions implied in no way represents the knowledge level of the people actually crafting the regulation of the financial sector?
T***: Pretty much! You should basically treat them with the importance that you would treat a company’s press release regarding upcoming litigation
It is all posturing
And again, the questions don't come from the members about 90% of the time
They come from lobbyists
We do that all the time
Writing questions for hearings
T***: The analog between CEOs and Senators and their relevant expertise relative to their respective staffs is apt, except that Senators have more accountability, more diverse backgrounds and a higher level of personal achievement. Considering how s***** senators are, collectively and individually, that is the harshest f***ing burn of CEOs I can muster.
On further contemplation, I want to clarify my previous statements.
I worked with mid to high net worth individuals for most of my professional life before school, creating financial plans to provide for retirement, college education, and other goals. Determining the appropriate exposure to stocks is probably the most important thing that we did as advisers. Some clients are younger, less risk averse, or have higher income; some clients are older, more risk averse, and have less income flexibility. These metrics, amongst others, are the critical things to evaluate the risk tolerance, and thus the proper allocation of stocks.
Maybe this is a moment of delayed Upton Sinclair*, but risk tolerance shouldn't change because the market is volatile, and so an individuals portfolio shouldn't change because the volatility of the market has quickly changed (as it is wont to do). An individual's risk tolerance is in relation to the volatility of the market in general, not the volatility of the market on a daily basis. If an adviser has done his or her job right, they understand their client's psychology and will be conservative with their estimation of a client's risk tolerance when the market is bullish, and aggressive with their estimation of a client's risk tolerance when the market is bearish. Indeed, this is what we attempted to accomplish with our practice in 2006 to 2007, where the standard analysis suggested a 80/20% stock/bond portfolio, we moved clients to 65/35 stock/bond portfolios.
The implication of Felix's advice is that daily volatility is a reason to shift the allocation of a portfolio. If you've done your job right, the volatility that a client is exposed to is the volatility that they can stand. This means in low volatility time periods, they want to take more risk; in high volatility time periods, they run for the exits. A client should be unhappy with you in bull markets, but happy in bear markets.
Your investment allocation strategy shouldn't magnify the behavioral irrationalities of a retail investor.
* "It is difficult to get a man to understand something, when his salary depends upon his not understanding it!"