Archive for October, 2008

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]

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