Autocorrelation occurs where past data can be used to predict the future. *snore*. If you’re still reading, think about it like this. If you know your friend, Alex, is always late, you will assume that he will arrive late every time. But if Alex is only late some of the time, you’re not sure when he will actually arrive on time, or when he will be late. We can observe what’s happening or use an ARCH test. Hang with me here.

Let’s say Alex is involved in an afterwork softball team, and they play on Tuesdays and Thursday. Games tend to run longer than scheduled. You notice that he only late on Tuesdays and Thursdays; you can start to predict his tardiness. So if your buddy wants to get beers on a Tuesday after softball, you can expect him to be late. You’re using past data to predict the future.

If I had used an ARCH model to predict when my buddy would be late, it would have told me that on average, my friend is late on Tuesdays and Thursdays more than any other days.

Maybe I missed my mark here, but the idea is not simple. If you need further clarification here’s the investopedia version: http://www.investopedia.com/terms/a/autocorrelation.asp

The goal of the ARCH test is to control for autocorrelation in variances, then see if there is any kind of pattern there. Control for the mean, then look for a pattern in the errors. If there’s a pattern in the variances, and we can predict when the next period of high variance will be. You’ll be predicting big booms and drops. Timing the market would be possible, and also arbitrage opportunities more easily identifiable (which is what hedge funds do).

**ARCH outline:**

First log returns to make your data symmetrical. To get rid of autocorrelation in the variances you use a “lagged time factor” of volatility. The ARCH and GARCH models control for a stationary mean in the variances. Like this, using σ for variances in returns:

σ_{t}²≡β_{0}+β_{1}σ_{t-1}²+ε_{t}

If you look at the equation above, you’ll see that we want a β_{1 }value of 1 in order to prove that past volatility is a predictor of volitility. If β_{1} doesn’t equal 1, that means all currently accepted limits of risk are bogus.

**Implications:**

Investors use these tests to forecast how volatile markets will be in the future. All current models of risk used at big banks all over the country assume volatility is random and normally distributed and that it can’t be predicted. Volatility rises and falls randomly, following a random path according to these models (Monte Carlo, Analytical).

Lehman blew up at the end of 2008 because it was using Monte Carlo simulations to predict how much the bank could lose on any given day. This model assumes normal behavior; i.e. normal returns, normal variance. In times of panic, the market’s behavior is far from random. The ability to predict when these times of high volatility will be remains allusive to companies and investors alike.

There are also some implications in proving how inefficient (unfair) options prices are. If you can prove that future options premiums are over- or underpriced, there’s an opportunity to make money.

My professor, Mr. Asensio, used the analogy of charging someone for “falling tree insurance”. The insurance company will give you a quote; say $2,000 dollars a year to cover your house if a tree falls on it. Say the average damage cost for a homeowner is $40,000 every time a tree falls into their home. The insurance company is expecting a tree to fall on your house once ever twenty years. If you pay $2,000 a year for 20 years and in the 20^{th} year a tree falls on your house, you broke even. You got out ($40,000) what you paid in ($2,000*20). (Assuming the exact cost to fix your house was $40,000).

**Futures:**

A futures contract is an agreement to purchase an asset at a set price at a future date. For example, if I’m going to sell you my car and you can’t pay me until next month, but I agree to sell you the car at the agreed price next month. We’ve just entered a futures contract.

Further, suppose your car was an expensive, one-of-a-kind Ferarri; custom-built for you. One of one. After you agree on a set price, news comes out that they’re building 500,000 more Ferarris just like yours. The price for your Ferarri is going to drop because it’s no longer the only one of its kind.

But who cares, I’ve already locked in the price and my buyer is still on the hook to pay me the full amount.

Again, using the Ferarri example, say before he buys, the buyer hears rumors that Ferarri was going to start producing the model of your Ferrari again. He expects the price to go down, but he still isn’t sure how much the price will fall, because Ferarri has yet to announce how many new cars they will produce. He wouldn’t buy the Ferarri at today’s price, he would negotiate for a lower price; guessing how far it will drop when Ferarri announces their increase in production. He is essentially forecasting the price drop when the news is announced.

For instance, the buyer assumes that there will be 500,000 more Ferraris made. He makes his views known in the negotiation process, but the seller disagrees. The seller thinks they’re only going to make 250,000 more. They hammer out a deal, each weighing their risks if the other party’s predictions are correct. They arrive to an estimate somewhere in the middle, say 375,000 and price the car accordingly, each happy they got a deal.

The buyer is happy because he is purchasing a Ferarri at less than market price. The seller is happy because he knows the price of the Ferarri could drop much lower than the agreed upon price.

The problem with this occurs when one party’s predictions are correct a higher percentage of the time, and the price on the futures contract doesn’t take that into account.

Bob from Big Bank of America is a seller of futures contracts. He understands markets very well, and is able to predict futures prices better than you (the buyer). You think you think your prediction is just as likely to be correct as his, so you hammer out a deal somewhere close to the middle of your two estimates. He is getting the better deal, because his estimate of the prices is always closer, but he can negotiate for a better deal.

Assume per gallon price of gas is $2.50 today. Bob says he will sell me gas for $2.25 a gallon, but I can’t have it until tomorrow. Bob expects the price to drop to $2.00 tomorrow. Playing the ignorant investor, I think buying gas for $2.25 a gallon is a steal. So I take his deal and tomorrow the price actually drops to $2.10 a gallon, I get caught with my pants down, because I’m stuck overpaying for gas today. Bob gets a great deal, because, although he was wrong about the drop, he still sold the gas at higher than market price.

The ARCH test tries to find when Big Bank Bob is hustling markets. They try to find where one party is better at predicting the price over the other. As an investor you want to put your money on the party that is usually right. You can make big money on these using levered bets. Risky? Yeah. Dangerous? Maybe. Potentially Lucrative? Absolutely.

I hope I increased your understanding of futures markets and how these things are calculated.

– Tommander-in-Chief

Disclaimer: If markets are efficient, you can’t make money here. If insurance companies are paying out exactly how much they charge for their products, they don’t make money. The insurance is appropriately priced, and neither party would engage in any type of transaction. But people buy insurance on everything from houses, to boats, to teeth. They think that by paying a small amount each month, they can avoid being slammed at by a big bill. Buyers of insurance certainly think they are getting a good deal. If insurance companies achieve a steady stream of cash flows and predictable payouts, they can generate profits by charging a tiny premium on your insurance over the predicted value. Essentially this tiny premium is a “peace-of-mind premium”; so you can sleep at night not worrying about if the tree in your front yard goes through your living room window you’ll be slapped with a big bill. All in all, insurance are arranged so both parties gain.