A thought on probability

I was at my in-laws yesterday and my father-in-law and I were watching some football. As the games were winding down, some channel surfing landed us on the movie, "Once Upon a Crime."

There's a scene where Marilyn Schwary (Cybill Shepherd) is playing roulette. She places her bet on 13 - and wins - on her first spin. On her next spin, she again places her entire bet (including her winnings from the previous spin) on 13.

My father-in-law asked, rhetorically, "what are the chances it will be 13 twice in a row?" I knew what he meant, but it got me thinking... The chances 13 would come up twice in a row is exactly the same as any other two numbers coming in sequence. The probability of that specific sequence occurring may be small, but low-probability events occur frequently.

What lowers the probability in this case is specification. To restate my father-in-law's question including the specification he probably intended, "what are the chances she will bet on 13 - and win - twice in a row?" That dramatically lowers the probability of the event occurring. In fact, if she were to bet on 13 and win 3-4 times in a row, everyone would start to be incredibly suspicious the game was rigged.

She wouldn't even have to bet on 13 each time. The specific sequence of numbers does not matter, since each sequence of 3-4 numbers has equal probability of occurring. What matters is that she correctly chooses the sequence of numbers ex ante.

Too Little, Too Late

According to a CNN Money article, the Fed is expected to propose rules to crack down on mortgage lending tomorrow. Some examples of the rules being considered are (emphasis mine):

• barring lenders from penalizing subprime borrowers - those with spotty credit or low incomes - who pay their loans off early.
• forcing lenders to make sure that borrowers, especially subprime borrowers, set aside money to pay for taxes and insurance.
• restricting loans that do not require proof of a borrower's income.
• examining lenders' failure, in some cases, to consider a borrower's ability to repay a home loan.
• improving financial disclosure so people better understand the terms and conditions of their mortgages and get this information when it is most useful.
• curtailing abuses in mortgage advertising.

All of these were obviously needed years ago, especially the point in bold. Probably most stated-income loans made in the past couple years should have never been originated. I say 'most' because these loans are legitimate for some borrowers, e.g. the self-employed.

It is beyond me why the Fed did not address this practice until now. How could they not know these loans were being mis-used, when it's their job to regulate the financial system?

Not only are these rules too little, too late - the market is currently addressing some of them. To ask a rhetorical question, how many lenders are currently originating sub-prime or stated-income loans?

While these rules are necessary, they will do nothing to help the current mortgage-induced liquidity crisis.

Source:
Fed to crack down on shady lenders
WASHINGTON (AP), 12/15/2007 12:08 PM ET

All in One Day

The following post is courtesy of Ryan, my good friend and fellow market-watcher. We regularly discuss the stock market. Below he provides his unique insights on today's (yesterday's) market action. So, without further ado...

I've been in banking for 7 years. I spent the first 4 years picking stocks for mutual funds, and worked on a trade desk the first 2 of those years. Those were really fun days in 2001 and 2002. Amongst other things, I witnessed the dot-com bubble burst, the first surprise rate cut by the Fed (a non-meeting 50bps cut), and Sept 11 - all from a unique perspective.

The last 3 years I've worked on the mortgage side, with the last year and half with Josh in capital markets. I have continued to follow the stock market the entire time. What is so amazing about today is that I can't remember a day quite like it. I remember many days when the market opened high, stayed high all day, and then gave back everything in the last hour... but that's nothing like today.

To put it into perspective (I'm going to use the Wilshire 5000 to represent the total market, though I'm sure you can pick any index and get a similar story):

Open: 14,923.64
9:15 AM: 15,256.52
3:15 PM: 14,820.01
3:45 PM: 14,999.82
Close: 14,994.54

The market deflated like a tire with a slow leak between 9:15 and 3:15. I can't remember such a slow, steady, uneventful decline after a strong opening during one trading day. It was really amazing to watch.

For those keeping count, the first 15 minutes returned 2.23%, or approx. 0.15% a minute. For the next 5 hours of trading, the market gradually worked its way to a -0.69% return on the day (the market's low point). The amazing thing is that anybody who bought the market at 9:15 AM had lost 2.86% in 5 hours (or -0.0095% a minute). So, they were giving away 1 minute of gains from the morning's rally every 15 minutes and 30 seconds that passed after that peak.

But the market wasn't done; then it rallied for another gain of 1.21% at the peak around 3:45 PM. That's a gain of of 0.04% a minute. The VIX showed this as the period with the greatest amount of volatility. The market finally closed with a gain 0.47% on the day.

To summarize: you have a gain of 2.23%, loss of 2.86%, gain of 1.21%... IN ONE DAY!!! If you told me these were market returns, I would tell you that was 3 separate days of activity. But nope, it happened in one day.

Today's market behavior underscores investors' ignorance of the depth and magnitude of the credit crunch. Five of the largest central banks were effectively forced to work together, and that's something to cheer about? Ironically, not long after the central banks' announcement, Wachovia and Bank Of America both issued additional warnings on their exposure. Its like the market was cheering "Yeah, they're going to get us out this mess," and then screaming "OH NO!!! THE MESS!!!".

As I write this, the Nikkei is down 1.51% (its lunch time over there right now). I guess they don't think much of the worlds' central banks' coordinated efforts either.

Non-Farm Payrolls: 12-07-2007

To quickly recapitulate the press release:

• The unemployment rate remained unchanged at 4.7%
• Employment increased 94,000 to 138,467
• Hourly earnings rose $0.08 to $17.63
  

Judging from the economic calendar on CNN Money (please advise if there's a better calendar) and the reaction of S&P 500 futures, the unemployment rate - which was expected to increase - and employment were better than expectations.

However, average hourly earnings came in quite a bit above expectations (0.46% MOM versus an expected 0.30%). That doesn't bode well for inflation expectations...

Will today's stronger-than-expected employment situation change market expectations of Tuesday's Fed action? I'll update with the information from the Cleveland Fed after the market closes.

UPDATE:
Estimates of a 50 bps reduction in the Fed Funds Rate declined using either December of January options. Expectations of a 25 bps cut now stand near 60% and 70% for December and January options, respectively (in each case the remainder represents the probability of a 50 bps cut).

The USD and EU Inflation

Jim Jubak wrote a great piece on the woes of the USD this past Tuesday. The article focuses on inflation in the European Union affecting the USD. The entire article is worth reading, but I highlight a very significant portion below.

I'll admit I don't know what the two banks will decide Thursday and Dec. 11. But I do know what will happen if the interest-rate gap between the two currencies shrinks further:

• The U.S. dollar will fall, and the euro will climb.

• The price of oil, which trades in U.S. dollars, will go up again, as oil producers adjust prices so that they at least break even on the dollar's decline.

• Gold prices will climb as investors seek an alternative to the U.S. dollar as well as safety from uncertainty about the global economy and a likely bump in U.S. inflation.

• U.S. equities will rally in the days after a Federal Reserve rate cut but then give much of the gains back as overseas investors pull money out of the U.S. financial markets in response to the dollar's weakness.

Today the ECB held their target rate at 4.0% instead of raising it, as Jim anticipated. The overnight interest rate spread between the US and EU remains 50 bps (instead of falling to 25 bps if the ECB had raised their rate). That may give the Fed a bit more breathing room to cut by 50 bps instead of 25.

As of today, the Fed Funds Futures market expects a 60% probability of a 25 bps cut and a 30% chance of a 50 bps reduction using January options (click for image). Using December options, the expectation is about 50% for both 25 and 50 bps reductions. You read that correctly, nearly a 100% expected probability of a rate cut.

Source:
The dollar's perfect storm worsens
Jim Jubak
Jubak's Journal, 12/4/2007 12:01 AM ET
http://articles.moneycentral.msn.com/Investing/JubaksJournal/TheDollarsPerfectStormWorsens.aspx