Archive for the ‘Markets’ Category

Understanding Ponzi Schemes

Saturday, December 20th, 2008

Charles Ponzi (actually Carlo Ponzi, from Lugo, Italy, in the province of Ravenna) was living in Boston in 1918 and looking for a way to make money.  Then he discovered an apparent arbitrage possibility.  He could buy an international postal reply coupon (an IRC) in Italy that allowed him to buy a US stamp for less than the price of the stamp in the US. (See Ponzi’s Scheme: The True Story of a Financial Legend for a good biography.)

The mechanics of the transaction were (1) to send money to Italy; (2) convert the money to Italian lire, a currency that had depreciated after the end of World War I; (3) purchase IRCs in Italy; (4) ship the IRCs to the US; (5) use the IRCs to obtain postage stamps; (6) sell the stamps for cash. According to this account by the author of the biography noted above,  sending $1 to Italy would generate $3.30 worth of stamps in Boston. Ponzi offered his friends the opportunity to earn a 50% return in 45 days.

By February 1920, Ponzi took in $5,000 and Ponzi quickly grew famous.  By July millions of dollars were coming in to Ponzi every week; a careful financial analyst noted that if Ponzi was actually doing what he said (buying IRCs) he would own roughly 5000 times the number of IRCs in circulation.  By November 1920 Ponzi had pleaded guilty to mail fraud and he spent much of the next 15 years in prison.

Ponzi’s secret was the continuing arrival of new investors.  It is not obvious that he ever actually bought an IRC, but if he attracted enough investors, he could pay off the initial investors.   Some people were foolish enough to leave their money with Ponzi (allowing him to “reinvest” their funds); others actually mortgaged thier homes in order to invest money with Ponzi.  Of course when Ponzi’s scheme was finally ended, there was not enough to pay off those who had given Ponzi their money, as he had sent some to earlier investors or spent it on an extravagant lifestyle.

As a footnote, IRCs are still available today.  If you want someone to write back to you, you can enclose an IRC in your letter and they can use the IRC to obtain an international airmail stamp. See here for current US rules on IRCs and here for recent news of Italian IRCs.   The Italian post office does not heavily promote IRCs, but according to the article cited, an IRC costs 1.29 Euros.  Unfortunately for current day arbitrageurs, a US international airmail stamp costs $0.94 today, and an IRC would cost over $1.70.  But if the Euro dropped sharply, to around $.70, and if the price of the Italian IRC remained the same, then it would once again be possible for someone to buy an IRC and get the stamp and then sell the stamp.

To earn the return that the author cited above calculated, the Euro would have to drop to around $.22/Euro.  Starting with $1, you would get 4.5 Euro , buy 3.5 IRCs (at E1.29/IRC) and get three and a half 94 cent stamps worth $3.30.  But the Euro is well above $.22 (around $1.39 as I write today) so this transaction is not profitable.

But to make real money the Italian Posta would have to sell thousands of IRC and you would have to find someone to buy thousands of US international airmail stamps.

Current day Ponzi schemes have used other methods but the principal is similar.  Bernard Madoff apparently promised steady returns (10% with very little risk); instead of buying IRCs he allowed his clients to believe that he had special market expertise, possibly related to his large and apparently legitimate market making business.


Price Anomalies at Intrade

Monday, November 3rd, 2008

I wrote an article for Intrade showing that candidates with similar polling data have different Intrade prices, available here.

Intrade Prices and the Bradley Effect

Wednesday, October 29th, 2008

I wrote an article about the “Bradley Effect” and Intrade prices, available here.  I found that Intrade traders do not seem to believe that the black candidate (in this case, Sen. Obama) will get a smaller percentage of the vote on Election Day than he is getting in the polls.

Understanding Volatility (the Vix)

Thursday, October 23rd, 2008

Stock prices go up and down every day; volatility is an attempt to measure how much prices vary.  In this article I explain the VIX, a specific measure of market volatility.  But first I will briefly review a little statistical theory (defining volatility) and then I address the specifics of the VIX (readers who understand the concecpt of standard deviation can skip the next two paragraphs).

Very brief review of statistics:  Statisticians view data such as the change in stock prices as random numbers being generated by a statistical process such as an urn filled with balls with different stock returns (-7%, +9% and so on).  A statistician can summarize a distribution with two measures, the mean, or average change in stock prices and the standard deviation, which measures the spread of the data from the mean.

For the S&P 500, the average annual price change since 1928 is around 12% per year and the standard deviation is around 20%.  Statistical theory tells us that roughly 2/3 of the time the price change will be within one standard deviations of the mean (or between -8% and +32%) and 95% of the time the price change will be within two standard deviations (or between -28% and +52%).

The VIX is called the market’s expectation of volatility over the next 30 days; the VIX is 100 times the standard deviation, so a VIX of 15 means that the market expects the standard deviation of the change in the S&P 500 should be 15%.

The details of the calculation of the VIX are beyond the scope of this site (see here), but the general idea is that volatility is an important determinant of the price of options to buy and sell the S&P 500, and by observing the prices of options one can infer the market’s estimate of volatility.

Options are the right to buy (or sell) something at a specific price in the future; for example, an S&P 500 1000 November call option allows the person who owns the option to buy the S&P 500 index at a price of 1000 in November.  As I write, the S&P 500 is trading around 910; it does not take much complicated mathematics to see that the volatility of the S&P 500 will affect the value of the option.  If the S&P 500 is unlikely to rise more than 10 or 20 points, then there is little chance the price will be over 1000 and the option will most likely expire worthless, and the price will be very low; if the S&P 500 is very volatile, then there is a chance that the index  will be, say, 1100, and the option to buy the index at 1000 will have significant value.

In general, if the market expects the S&P 500 to be volatile then the VIX will be high.  Below is a chart of the VIX from the CBOE (CBOE VIX charts are available here).  You can see that the VIX was mostly between 10 and 30, with occasional spikes to around 40 during periods of great turmoil.

Below you can see a chart of the VIX during 2008. During the financial crisis of the last few weeks the VIX reached levels of 60 or higher, as markets became more volatile than they had been in the past 20 years. Stock prices have been incredibly volatile in recent weeks, with markets swinging several percent every few hours.

One way to know how long the market expects the high VIX to last is to look at the price of VIX futures, that is what the market expects the VIX to be in future months.  As I write (October 23, 2008), the price of the VIX is 65.65, but the price of the November VIX is 47.81, the December VIX is 39.05 and the January VIX is 37.02.  This means that the market expects the VIX to drop sharply in coming months but it expects that the VIX will still remain well above the average level of the 1990s for several months.  Prices of VIX futures (delayed 15 minutes) are available here.

Understanding the TED Spread

Thursday, October 16th, 2008

The TED spread (see here for recent quotes) is the difference between the three-month Treasury Bill interest rate and the three-month LIBOR interest rate, that is, the TED spread measures the degree of riskiness of the bank lending market.  Increases or decreases in this spread are viewed by market participants as indicating the degree of problems in the banking system.  In this article we will briefly discuss the name (TED) of this measure, exactly what it measures (and how this has changed in recent years), questions about whether it measures exactly what it is supposed to measure and how it has performed during the recent crisis.

The name TED Spread comes from an earlier version that calculated the difference between the three month Treasury futures contract and the three month Eurodollars contract (hence the spread between T and ED).

The basic idea is that lending money to the US Treasury is essentially risk-free.  While there are various technical restrictions in place, the US Treasury can more or less pay off any US dollar obligation with cash.  The value of the cash you receive may be uncertain (due to inflation) but the Treasury has never failed to pay off its obligations and is unlikely to fail in the future.

The Eurodollar interest rate (or the current LIBOR—for quotes see here) represents the rate at which banks lend to one another.  Due to some regulations (reserve requirements) imposed by US banking authorities on US banks, a large market for US Dollar deposits developed outside the US.  The Eurodollar market in London became the place where Dollars were traded and the London InterBank Offer Rate (LIBOR) became the benchmark price for Dollar deposits.  Today the BBA LIBOR rate is a key reference rate for many loans in the US and elsewhere, including many mortgages.

During normal market conditions banks lend to one another at rates slightly above Treasury Bill rates.  There is a modest amount of risk of lending money to a bank, since unlike the US Treasury, banks occasionally go out of business and are unable to repay their loans.  But during crises in financial markets, when banks are in great difficulty, the LIBOR rate rises relative to Treasury Bill rates (increasing the TED spread) to reflect the additional risk of lending to banks.

You can calculate the TED spread yourself by using historical 3 month LIBOR rates from the BBA (available here) and 3 month Treasury Bill rates (available, among other places, here at Treasury Bills, secondary market, three month).  TED spreads in normal times are between zero and one percent, but during the recent financial market crisis (October 2008) have been over 4%.

But there are some questions about the way the BBA LIBOR is calculated.  The BBA essentially conducts a daily survey of banks (see here for some of the details) and there has been suspicion in the market that in the current difficult situation the survey may not be as meaningful as it has been previously (see, for example, here).  There is an “uncertainty principle” for much financial and economic data that means that the more attention that markets give to a particular number, the more likely the number does not measure what it was intended to measure.  In the case of the BBA LIBOR, market participants expect that the number measures the conditions in the interbank market.  But precisely at the time when there are problems in the interbank market (and the LIBOR is on the front page of newspapers and on “bugs” on financial TV channels), there are huge incentives for the banks that participate in the BBA survery to respond in a way that might help their short-run situtation and not reflect actual market conditions.

[My apologies to physicists, especially Werner Heisenberg, for using the phrase uncertainty principle in a way that probably makes no sense to them]

Understanding Political Futures Markets

Friday, August 22nd, 2008

At typical financial markets, traders make a market in financial instruments, such as corporate equity, government bonds and currencies.  But there are markets in many other items ranging from commdities (such as wheat and frozen pork bellies) to more conceptual items such as hurricanes or the number of jobs reported on the monthly Employment report.  Futures and options exchanges have rapidly expanded their product offerings in recent years (see here for a little history of the Chicago exchanges).

These markets have several roles; participants in the markets for these products can reduce their risk; a farmer can lock in a price for his crop at the start of the season or a manufacturing company can lock in a price for a particular commodity that it uses. But the futures price generated in these markets should be an accurate prediction of the price. Speculators should be willing to buy contracts when the futures price seems too low or sell contracts when the futures price seems too high, to profit from the expected price change; for example, suppose news comes about bad weather that will destroy a large part of the corn crop; speculators will start buying contracts until the price reflect the best expectation of the future price.  The logic is similar to the Delphi method (discussed here): a number of informed analysts will converge on the truth by pooling their information. In futures markets, the pooling is accomplished by allowing the analysts to trade and profit from their access to information or their ability to analyze it.

The University of Iowa became known for trading, among other things, presidential futures (see here for some history); on this market students trade “shares” of political candidates or parties. The market prices of the Iowa Election Market were fairly accurate forecasters of election results, even when compared to traditional polls (see here for some data). This prompted a great deal of interest in creating futures markets on many events, from sporting events to terrorist attacks (see here for an article about an unsuccessful proposal from the Pentagon).

Intrade is an Irish “incorporated service business” that allows the public to trade futures on many public events, ranging from the date of the capture of Osama bin Laden to the top marginal tax rate in the US in 2011.   These contracts are all of the “winner take all” variety; you can buy a contract on whether an event will occur and you receive $1 if you are correct and nothing if you are wrong. Below you can find the chart of the Obama and McCain contracts, that is contracts that will pay $1 if Obama or McCain is elected President.

INTRADE.COM Price for Obama to be elected President

INTRADE.COM Price for McCain to be elected President

At the time that I am writing (August 21), Obama shares are trading around $.60 and McCain shares around $.40. These prices imply that in aggregate, traders believe that Obama has a 60% chance of winning the election and McCain 40% (these two numbers should add up to a bit less than one if there is a small chance that someone else will win; if the of total prices were greater than $1, a trader could sell both contracts for, say, $1.05 and then pay off the winning contract $1 and keep the difference).

Both of these contracts have traded at much lower prices in the past, when other candidates (e.g., Hillary Clinton) were more likely to be elected President.  There are many other contracts traded and many ways to make use of them.  For example, there are contracts on how each state in the country will vote (recall that the US Presidential election is determined by the outcomes in the individual states, with the winner of each state election receiving the number of electors from that state; see here and here for more).  One site (see here) uses the Intrade prices from each state contract to predict the electoral college (see here for a lengthy pdf that describes the history of the electoral college and several criticisms).

Needless to say, speculators in political futures markets are not perfect.  During the 2004 election, exit poll data (that is the results of surveys of people who voted on election day) revealed that John Kerry was doing much better than expected.  The political futures markets reacted sharply and the price of the Kerry contracts rallied, before the actual data showed that George Bush would win the election (see here for a nice write-up).

Understanding Stock Market Indexes (and Index Trading)

Wednesday, August 6th, 2008

Thousands of individual stocks trade every day on various stock markets around the world. There are a number of stock indexes that track the movements of stock markets.

The simplest stock indexes (for example, the Dow Jones Industrial Average (DJIA) in the US) are price-weighted indexes. To calculate the value of the index you add up the price of the 30 individual stocks. But over time, the stocks in the index have changed and some of the companies have split their shares; to correct for these changes there is a divisor, so the sum of the prices of the shares in the DJIA is divided by approximately 0.123 (see here for calculation). This means that a $1 change in the price of a stock in the index results in a roughly 1/.123 or 8.1 point change in the index.

One problem with price-weighted indexes is that a company’s influence in the index depends on the per share price and not the value of the company. In the Dow Jones Industrial Average, Merck, with a share price (as I write) around $35, has a larger weight in the index than General Electric which trades around $30, despite GE’s much larger market capitalization (GE has many more shares outstanding; the total value of the GE shares is around $300 Billion compared to Merck’s roughly $75 Billion).

There is a second class of indexes called value-weighted indexes that assign a value in the index proportional to the size of the company. The Standard and Poors 500 is such an index; recently (December 2007) Exxon, the largest company in the index had a weight of almost 4%, General Electric had a weight of almost 3% and Microsoft around 2.5%; the other 497 companies combined have a weight of only 91% of the index.

Some investors find it useful to own indexes. Individual investors who wish to diversify their portfolios can buy all the firms in an index; this allows individuals to reduce the risk of their holdings (the variability of a group of stocks tends be smaller than the variability of individual stocks). Using index funds individuals can invest in the broad US stock market (say, the Wilshire 5000 index which includes most traded US stocks) or a specific sector (say, the iShares S&P North American Technology Sector Index Fund which tracks US traded technology companies).

Institutional investors can use index funds to hedge their portfolios; hedge funds often use these funds to reduce the correlation between the return on their funds and other indexes.

Investors can purchase these indexes in various ways. You can try to buy all the stocks, but unless you are a very large investor it is costly to acquire different amounts of 500 companies. More realistically, you can buy either mutual funds or ETFs.

A mutual fund that tracks the S&P 500 may not buy all 500 companies either, as the improvement in tracking the index from owning small amounts of the smallest companies is minimal. The important distinction between a mutual fund and an ETF for an investor is that mutual funds have only one price per day, set shortly after the end of the trading day, while ETFs are traded throughout the day. A mutual fund investor who buys the fund acquires the shares at that price and can sell it only at the end of the day price at a later date. These funds are designed for medium to long term investors, and not for traders who wish to buy and sell at different times during the day. The basis for evaluating such funds is how their return compares to that of the index, which tends to improve with the size of the fund (bigger funds, lower fixed costs, better tracking of the index).

An ETF (exchange traded fund) is a portfolio of stocks that is designed to track an index (see here for the SPY ETF designed to track the S&P 500) that is traded on an exchange. So you can buy the ETF at 11am and sell it at 2pm if you want. For many small investors it is more convenient to hold mutual funds (for example funds will allow you to invest smaller amounts every month) but some investors find the flexibility of ETFs more important.

There are also futures traded on the S&P 500. Like any future these contracts are traded at a futures exchange (in Chicago at the CME) and not on the stock exchange (see here for more information). The futures contract is equivalent to trading the portfolio of stocks for delivery at a future date. In other words, in any month, you can arrange to buy or sell the index in the next month or some month after that. There is a fairly close relation between the price of the future and the index (price of future equals price of index times (1 + appropriate interest rate)). Futures require much smaller initial investments than stocks, and trade after stocks have stopped trading (S&P index futures trade more or less continually from Sunday night US time until Friday afternoon). So one can follow the market even when the stock exchanges are closed by watching the price of the futures markets, although the relation between the end of the day cash and futures price must be carefully examined (see here for a discussion of how “fair value” is calculated, and how to examine the difference between the price change from the closing price relative to fair value).

Understanding Short Selling

Friday, July 25th, 2008

If you think that the value of a stock will rise, you can buy the stock and sell it later when the price is higher. If you think that the value of a stock will fall, the situation is a bit more complicated. One way to bet on a falling stock price is to sell short, that is to sell stock that you do not own, with the idea of buying it back when the price is lower. But selling something that you do not have creates a potential risk to the buyer, who receives a promise instead of the thing he wanted to buy. Clarification: I am not a lawyer and nothing in this article is intended to constitute legal advice; I am an economist attempting to analyze what happens in securities markets.

If you buy a stock from someone, the seller of the stock gets paid at settlement (a few days after the transaction is done). You pay cash and receive the shares of stock and there is no further risk to either party. But if you sell stock that you do not own the settlement transaction is problematic. You receive the cash but the buyer of the stock only receives a promise to receive shares from you in the future. If you have excellent credit this should not present much of a problem. The buyer of the stock will want occasional payments (the short seller must pay the buyer all dividends paid by the corporation) but otherwise should be satisfied having your promise to eventually deliver the stock. There would be an arrangement between the short seller and his stock broker, where the broker would guarantee the eventual delivery of the stock by requiring a substantial deposit from the short-seller.

But US regulators impose an additional complication, that the brokerage firm lend the shares to the short-seller, typically from the account of another investor at the same brokerage firm (see here for the SEC’s 2005 explanation of Regulation SHO governing short sales). The short seller must pay the brokerage firm interest for the loan of the shares, in addition to covering the dividend payments noted above. Under the SEC rule the brokerage firm delivers the shares at the time of settlement to the buyer; the only open transaction is typically inside the brokerage firm, between the seller of the shares and the account that lent the shares.

Even so, there are occasional “naked” short sales, where the seller does not deliver the stock at the time of settlement (”failure to deliver” in the language of the SEC). The SEC slyly notes that “[n]aked short selling is not necessarily a violation of the federal securities laws or the Commission’s rules”, a statement guaranteed to cause brokerage firms to regularly consult their legal staff. The SEC set up a list of “threshold securities”, that is companies that regularly experience delivery failures to ensure that there are no further problems with these shares (see here for the NYSE list of threshold securities and here for the NASDAQ list). Presumably brokerage firms are more careful when their customers try to sell short firms already on these lists.

The SEC’s stated purpose is to prevent abusive short sale practices, something that SEC Chairman Cox has termed “short and distort” (see here for a law firm’s discussion). This practice is the negative version of “pump and dump” (see here); the “pump and dump” scenario is an unscrupulous promoter will buy a large position in a small company and then spread rumors to try to drive the price of the stock up (my spam folder was full of these messages a few years ago; see here in the section E-mail spam), selling the shares once the price rose a bit. “Short and distort” would involve taking a large short position in a company and then spreading rumors to drive down the share price.

On July 15, 2008, the SEC released an emergency order (see pdf here or a subsequent explanation here) that more or less says that no naked short selling would be permitted for a number of large banks and investment banks (the so-called primary dealers, see here) and Fannie Mae and Freddie Mac.

Why GE stock fell so much on Friday April 11

Tuesday, June 24th, 2008

Last Friday (April 11), General Electric Corp (GE) announced that quarterly earnings were $0.43 per share, or about $4.3 billion. This would seem to be fairly good news; the number was down a bit from profits a year ago, when quarterly earnings were $0.44. Yet the \stock price dropped by almost 13%; largely in response to this news, the rest of the market dropped by 2% (see here for a typical newspaper story).

Why does a stock fall so sharply on what would seem to be not so bad news? The answer has to do with the market’s expectations for GE, and GE’s past aggressive use of a tactic known as “earnings management”. (Disclaimer: I am not an accountant and have never actually analyzed GE’s accounting statements. I own a bit of GE stock through investments in broad market indices. This essay, like all essays on this site is not to be construed as a recommendation to buy or sell any particular security but is intended to increase your understanding of markets to help you make better investment decisions.)

The market expected GE to earn around $0.51 per share, and GE had indicated that they expected to earn between $0.50 and $0.53 per share. From this perspective, the result of $0.43 was a big disappointment to the market, especially for GE, which rarely disappointed the market with earnings announcements.

GE has long been accused of “earnings management”, that is arranging its business transactions in a way to produce continuously improving accounting results (see here for more on the topic). There are perfectly legal methods that a firm can use to ensure that earnings meet a particular target. For example, a firm whose income is a bit less than expected can delay some expenses until the start of the next quarter. If income is unexpectedly high in another quarter, the firm might realize some expenses earlier than necessary. Both these transactions will smooth out quarterly earnings.
As long as the amounts involved are relatively small, and the company is growing profitably, there is little cost associated with such transactions.

But once in a while a firm cannot meet the earnings target; perhaps all the news toward the end of the quarter was bad. In this case the company has to make a decision: should they make a heroic effort and still miss the market’s expectation by a small amount? Or should they admit as much negative news as possible, missing the expectation by a large amount, but setting the stage for positive developments in future quarters?

GE announced a number far below the market’s expectation and the market reacted strongly, because of GE’s history of meeting (or beating) the quarterly earnings expectations. But analysts more familiar with GE than I am will be able to decode the accounting statements and decide whether GE made all possible efforts and announced the best possible result (in which case the outlook for the future is very gloomy), made minimal efforts and announced the worst possible result (in which case the outlook for coming quarters should be fairly bright) or was somewhere in between.

The general lesson is that news does not have any particular significance outside the context of market expectations. Most people outside financial markets would have thought that earning $4.3 billion in three months represented a reasonable performance; only when you understand the specific history of GE’s alleged practices can you begin to understand why the market might react so strongly to such a number.

How do traders lose so much money?

Tuesday, June 24th, 2008

Every few years there is a story of a trader who loses huge amounts of money; most recently, Jerome Kerviel at Soc Gen, but there were many before him. The magnitude of these losses is a great mystery: how can one person lose Euro 5 billion? Didn’t someone realize that there was a problem when M. Kerviel lost his first billion? I believe that there is an answer to this question that lies at the heart of financial regulation.

Traders are similar to professional football players. The best football players will help their club earn championships and in turn will be paid huge salaries. There is tremendous competition to become a top player, and players will use every available technology (such as equipment and training) to become faster and more powerful. Referees are not so highly rewarded. While a top referee may make a good salary relative to other professions, the reward is nothing like that of a football player. Few spectators decide whether or not to attend a game on the basis of who will be the referee; while many will argue at great length about the quality of the decisions the referee made, referee errors are considered a part of the game, and clever players will exploit a referee’s shortcomings. Often one gets the sense that referees fail to accurately make decisions in part because they are not at the same talent level as the players on the field.

Traders, instead of scoring touchdowns on the field, take risky positions in order to make profits. They adopt complex trading strategies combining computer models and their own intuition. But banks place limits on the traders, to minimize the chance of a large loss. The risk managers can be seen as referees, enforcing the bank’s risk limits. Risk managers, like referees, are seen as a necessary burden. The risk manager is often viewed as a cost-center, bringing no added profit to the firm.

While we are likely never to know the full story of M. Kerviel (nor that of Mr. Leeson, the trader who lost so much money at Barings Bank), the outline is fairly clear. Kerviel knew the “back office” systems fairly well, having started his career in the part of the bank that accounts for traders’ activities. Kerviel was supposed to make small bets, but wanted to make larger bets to show his trading skills to his superiors. He used his knowledge of the bank’s accounting systems to conceal the size of his positions, allegedly avoiding the normal control procedures. Whatever the details, it is quite clear that Kerviel was a step faster than the referees, who were unwilling or unable to restrain his behavior until he had large losses, which were subsequently multiplied as the bank may have had to quickly sell off his positions at a greater loss.

There is no obvious solution to either the referee problem or the trader problem. Football leagues are willing to spend some money to improve the quality of referees, but only just enough to keep fans watching, and not enough to have perfectly refereed games. Every few years an important game will be decided by what appears to be an incorrect decision by a referee and some fans will pay less attention to that sport in the following years.

Banks need to allow creative traders to trade, otherwise they would lose these employees to other firms (note how many traders have already left traditional financial institutions for private equity and hedge funds). The risk is that every few years a financial institution will disappear, a risk that many institutions seem to think is worth taking.


Bad Behavior has blocked 628 access attempts in the last 7 days.

FireStats icon Powered by FireStats