# Golf Options: An exersize in derivatives

In this article, I’ll try to explain derivatives using the price of a season pass to a golf course, the price of a gallon of milk, and from the perspective of a corn farmer.

Red Rocks Golf Club, in Rapid City, SD, sells season golf passes for \$1,450 per adult, plus an additional charge of \$525 for a single seat cart pass. An 18 hole round of golf at Red Rocks costs \$59, excluding tax, with an additional \$21 for a cart. Red Rocks is betting that patrons will golf 24.58 times over the course of the year, (1450/59). They’re also betting that you’ll use the cart 25 times over the year (525/21). By this measure, the cart pass is overvalued. The cart pass should be valued by the same metric as the golf pass; a club member should refuse to pay anything over \$516.18 (plus tax) for the cart pass.

How is this a derivative?

The golf course is selling you the option to golf. Whether you use that option enough times, i.e. golf enough rounds, is completely up to you. I would venture to guess that the price of a golf pass at Red Rocks has outpaced inflation. Why? Perhaps people are golfing more. If the golf course sells the pass, and the golfer gets 40 rounds in throughout the year, Red Rocks loses money on the investment, but the golfer gains. The intrinsic value of the golf pass can be expressed as such:

IV(golf pass) = Price of Pass – (# of Rounds* Price Per Round)

Note: Price of Pass and Price per Round are both constant and known; the only variable is how many rounds of golf the golfer plays.

Black Friday:

The BF price implies the commercially saavy golfer will only play 19.66 rounds of golf. The BF price on a cart pass (\$472.50) implies the golfer will use the pass 22.5 times. Personally, I don’t know many people who like to go to the golf course just for a drive. Why the discrepancy?

I would be curious to see how the rates have changed over time. I wonder if the number of rounds implied has changed over time or if the price is arbitrary. This is the type of problem for an actuary. Under a perfect price discriminatory environment and with perfect information, the club could sell to each patron at a price consistent with their past behavior. A retiree who lives near the golf course and golfs 80 rounds a year is exploiting the system, while someone who can only golf 15 times a year is getting hustled. Looking at a patron’s past should determine their rate, just like insurance.

“Golf is too hard,” some say. And rates of participation are showing it. Red Rock installed a defensive strategy into their rates. College students and millennials get a discount on their passes as a direct result. Supply and demand states that if demand drops so do prices. So instead of keeping a single sticker price on their passes and lowering it to compensate for the drop in participation rates, Red Rock split their pass into several age tenors after identifying who wasn’t buying passes. This is all guess work, but I’m sure this pricing scheme wasn’t conjured out of thin air. (Guardian)

Seniors also get a discount, as they are probably some of Red Rock’s most devout customers. They’re also less likely to tear up the course by duffing their tee shots and taking a ton of mulligans.

Financial options are similar, but instead of number of rounds being variable, it is the underlying spot price’s volatility. Options written on an underlying asset derive their value from the volatility of that asset’s price, for example, the price of a barrel of oil. Oil is a commodity that is highly traded and the price of oil is hotly debated. Big moves in the price of oil are much more likely that a big move in the price of milk; therefore, options on oil are more expensive than options on milk. The price of an option is called premium.

A call option is the right to buy the underlying asset at a certain price. For example, my view is that milk is undervalued, at \$2 bucks a gallon. One option would be to buy 10 gallons of milk and hold onto them until the price rises. However, I’d have to store the milk, keep it cold, and also make sure it doesn’t go bad before I sell it. All these things cost money, and diminish my profits. By buying a call option on milk, I can eliminate these costs. I’m betting that the price of milk will rise. I buy a call on milk at a strike price of \$2. This means I’ve just bought the right to buy milk at \$2, sometime in the future. To buy this right, I will pay the seller premium. If the price of milk goes to \$2.50 like I planned, I’ll exercise the option, buy milk at \$2 then sell it at \$2.50. My profit is:

If the option goes unexercised, meaning the price of milk moves in the opposite direction, say to \$1.50, then my option expires worthless and I’m only out premium. I don’t have an obligation to buy the milk at \$2.00, just the option. Profit in this example would be:

Similarly, a put option is the right to sell the underlying asset at a certain price. Buying a put option is a bearish view on the underlying asset. If you believe the price will fall, you want to lock in a sell price for your asset. As a farmer of corn, you notice everyone’s crops seem to be doing particularly well, and this harvest is set for a record year. A rise in supply causes the price of the asset to fall. You believe this will directly affect your profits for the year. In order to protect against this, you buy an option to sell your corn at a certain price, thus capping your downside. If the harvest is weak, and the price of corn rises the option expires and you’re only out the premium. If the harvest is strong, as you expected, you have the right to exercise the option and sell your crop at a higher price than the rest of the market.

I hope this helped expand you’re knowledge of derivatives. Thanks for reading.

– tommander-in-chief

Sauces:

# Yahoo and Google: Democratic Responsibilities of Corporations

Overview:

China is renowned for keeping its citizens in the dark. They censor their television shows and ads. Now time travel, homosexuality, and luxurious lifestyle programs are banned from Chinese television (Time.com). They sensor Internet chat rooms to deter the conversations from issues like politics “towards [issues] such as which celebrities make the best role models.” The government even goes so far as to set up fake websites designed at luring in “would-be dissidents” for their “apprehension” (Dann and Haddow, p. 220).

The first question that needs answering is as follows: is the free flow of information a human right? Back before the Internet, how much access to information we had depended on both our monetary wealth and status in society. If we truly want a liquid society, where serfs can become kings, free flow of information should be of the utmost importance. Information is power.

By definition, markets cannot be efficient if information becomes scarce or censored. Those in power can use information to further sway those under their control; even in a democracy, controlling the information can make the electorate vote in a way that seems in their best interest but really they’re being influenced by the censored distribution of information. Without the freedom to distribute information, a democracy by name cannot be a democracy in practice.

The censorship in China is done by government entities to exert “paternalistic influence” over the population politically. Chinese economic freedom has evolved massively since the days of strict Communist rule (Dann and Haddow, p. 220). This economic freedom has allowed companies like Yahoo and Google to establish a presence in the formerly closed state. In order to do business within the Communist nation, however, foreign companies must comply with Chinese law. When law conflicts with a firm’s moral compass, which should have precedence?

Google complies with Chinese law and omits certain things from search results inquired within China. Before the establishment of Google.cn, every search inquiry had to pass through the “’the Great Firewall of China’” (Dann and Haddow, p. 221). This caused searches to take longer, thus less use of Google’s platform. Google set up a search database within China that already had politically undesirable items removed. This made the search engine faster and more accessible for many.

Hypothetically assume Google refuses service within China. Tech firms that are willing to swallow their moral obligation to society in favor of profit will step in and fill the void. A Chinese competitor, Baidu, soared from “2.5% market share in 2003 to 43% in 2005” (Dann and Haddow, p. 225). Google won’t solve anything by refusing service, except perhaps to exacerbate the problem. The search database will shrink, allowing less free flow of information.

Dann and Haddow argue Google produced a list of blocked items on its own, without “receiving direct orders from Beijing” (p. 226). By Dann and Haddow’s calculation, Google censored information without being directly ordered. Google was losing market share, and thus needed to revise their strategy. Dann and Haddow call this process an “outsource of censorship” by the Chinese government (p.226).

Yahoo!:

Yahoo!, an internet search engine and news site, allows its content to be censored in China as well. In Dann and Haddow’s research paper Yahoo is cited for aiding in the arrest of a citizen who “was sentenced to eight years in prison for posting comments that criticized government ofﬁcials of corruption” (p. 229). Yahoo, like Google, asserted it had little to no choice in the matter, as it had to play by the rules in order to play the game.

Should Yahoo have sacrificed its Chinese branch in order to maintain its values? When does morality trump profitability in the business world? The answer can be easy when answering for the self, but harder when those affected have no skin in the game. American investors in Yahoo wish to see the company grow more profitable, period. Perhaps by sacrificing their Chinese branches, they can improve public image and gain market share… but perhaps not.

Yahoo can also assert that it was the responsibility of the individual involved to protect himself (or herself). If the individual hadn’t dissented against the government, there would be no wrongdoing and the individual would still be free today. Yahoo is merely providing the platform for conversation; they didn’t guide or start the discussion. Had Yahoo been actively endorsing the actions of the individual, they would be liable by Chinese law. Is it Yahoo’s responsibility to protect the users of its platform? If a controversial note was posted on a firm’s notice board, should the person who installed the corkboard be faulted or the individual who posted the note?

This turns the discussion to one of free speech rather than free flow of information. “It is the ability to exchange information that is valuable, not necessarily the worth of the information itself” (Dann and Haddow, p. 222). They argue it is the installer of the corkboard (from my example above) who is responsible for preserving the integrity of the information posted. Free flow of information is imperative to a democratic society. Uninhibited, unbiased news and information needs to be present in a truly free society.

Conclusion:

Google and Yahoo’s responsibly to Chinese citizens can be argued from both points of view. On one hand, Yahoo and Google must follow the rules to play the game. If they want to utilize and operate in one of the fastest growing economies in the world, they need to follow Chinese law.

On the other hand, they are actively participating in inhibiting the democratic process. The United States’ military has fought against the spread of Communism in several wars and hundreds of thousands had died to spread democratic ideals. Meanwhile, Google and Yahoo are assisting in the process of politically influencing entire generations of Chinese citizens.

-tommander-in-chief

Sources:

1. Dann, G.E. and Haddow, N., Journal of Business Ethics (2008). Retrieved: Sept. 2016
2. http://time.com/4247432/china-tv-television-media-censorship/

# Who’s got the power?

When interest rates go up, and they will, the 50% increase across the board will topple markets, namely bond markets.

Today’s interest rates are unprecedented. The lowest possible bound for an interest rate USED to be 0%. In finance terms, we call it the ZLB or the zero lower bound. Today bond yields in Germany and Denmark (among others) are NEGATIVE! What does this mean for me, the common investor?

Examples of Interest Rates  in History, for relativity:

I’ll admit, I’m not finished with the 700+ page novel written by Sidney Homer first published in 1963. The preface is packed with insightful information such as:

1.) In ancient India, the going rate of interest on livestock was 100%. Then: You can borrow my cow for one year, if after the year is over you’ll pay be back with two cows. Today: I’ll let you use my house for a year, but after that, I’m gunna need that house back, plus a whole extra house.

2.) In early 20th century Indo-China, loans on rice were given at a rate of 50% annually commonly.

3.) In British Columbia, a phenomenon called “potlatch” was first documented. The Kwakiutl, an Candaian Indian tribe, used thin white blankets currency, roughly valued at \$0.50 per item. The citizens of this tribe would give the blankets as ‘forced loans’ to one another, with the expectation of receiving what they gave plus interest. “Wealthy Indians vied with each other to see who could give away the most blankets, all with the understanding that even more would be given back—usually double.” – (p. 23, Homer) Kind of wonky huh? They gave because they were greedy.

4.) In Northern Siberia, domesticated reindeer, horses, and sheep were used to collateralize loans. They exchanged the animals like currency, usually charged at an annual rate of 100%.

All in all, lending is not new, but this new environment of negative interest rates is new. You have never  had to PAY someone so they can use your money, that just seems backwards. Remember quantitative easing (QE*)? The Europeans are doing the exact same thing. However, the European Central Bank (ECB) are buying up these negative interest charging bonds because the ECB is attempting to inject liquidity into markets. The ECB is allowing banks to use their cash and they’re paying the banks interest… hmm…

The goal of QE* is to inject liquidity into markets to avoid disastrous outcomes. The program is designed to allow debt to be more readily available for the average consumer. Lowering interest rates and loading up commercial banks with cash will help settle investors’ concerns surrounding a global financial meltdown without a doubt. This being said, if times are bad (economically), the average consumer will become risk averse, and will stay as far from debt as possible until things get better. When consumers get a pay raise or a new job, they might think about taking out a loan to build a new deck or get a new car. Demand drives supply and the policy makers who control interest rates and QE can only control supply. No matter how hard they try to get us to take out debt, we just won’t do it unless market conditions are appropriate. The final result of QE in the United States was a massive increase in the amount of cash that banks hold in reserves.

The graph below shows the level of reserves banks have on their balance sheet from 1984 to 2008. In 1999, banks jacked up their reserves because of Y2K scares; if the whole system imploded at the turn of the century, they wanted to have enough cash on hand to prevent a catastrophic collapse of our financial system. Notice how the level was just shy of \$70 billion.

This graph below shows what has happened to reserves since the beginning of quantitative easing. In 1999, (from above) the level of reserves his \$70 billion, here \$70 billion isn’t even on the scale. This is where all the bailout money went, onto the balance sheets of big banks.

Holding reserves used to be an implicit tax for banks, because the more cash they held, the more return they were missing out on (opportunity cost, for you econ buffs). The banks could have put the currency to work in stocks or bonds to achieve a higher return. However, the less cash a bank has on hand, the more risky the institution is. The Fed instituted a return on cash of 50 basis points (0.5%) in order to incentivize holding cash reserves (both required* and excess). The banks can hold all of it in cash and make a half a percent annually or they can buy negative yielding bonds. It’s a positive, riskless yield. Why wouldn’t banks take advantage?

*Note: by law, the required reserve ratio in the US is 10% for big banks.

QE works as a mechanism to prevent economic collapse, but demand drives supply; thus, you cannot force people to buy things they don’t want (except maybe in Communist Russia where they don’t actually tell you what you’re taking until you’re disqualified for the Olympics) QE cannot create prosperity because no matter how available you make debt, it is the preferences of the consumers that ultimately drives demand for loanable funds.

The Federal Reserve of the United States holds way, way more power than Donald Trump and Hilary Clinton, yet when they make a statement in the press, it usually doesn’t even make the front page. The Fed has the power to control interest rates. They also have the power to create money, as in printing currency (yup, money growing on trees). They control what you pay on your mortgage and they control how much interest your money makes (in markets and in savings accounts). This affects how soon you will be able to retire, how much your house is worth, how much your pension has in cash (i.e. how much risk your pension can take), how much your kid’s college fund will make… you name it, the Fed controls it. The best part is, you didn’t get to elect these officials. The US government deemed it too risky to put big financial decisions in the hands of under-informed citizens (*cough* Brexit *cough*).

– tommander-in-chief.

Note: For more on pensions taking on too much risk check out this economist article, http://tinyurl.com/hg4rbjl

Sources:

Side note on bond prices –

Bond prices are inversely related to bond yields. That is, when the rate on a bond rises, it’s price will drop. Because today’s rates are so low, the effect that a rise in interest rates will have will be massive. For a little relativity, interest rates (the fed funds rate) in 1999 was around 5%. A 50% increase in this rate would raise the rate to 7.5%, which is a massive jump. Now, we are debating a 25 basis point* increase in rates, which brings them from 25-50 bps to 50-75 bps. This may seem trivial, but that represents the same 50% increase in the fed funds rate!

*Note: a basis point is a ten thousandth of a percent; 1 basis point = 0.01%

# Bud Light sucks…

Fun fact: This is what happens when you Google, “what is American beer?”

“Light beer, which was introduced on a large scale by Miller Brewing Company in the early 1970s, is a beer made with reduced alcohol and carbohydrate content, and has grown to eclipse many of the original pale lager brands in sales. Bud Light, brewed by Anheuser-Busch InBev, is the top-selling beer in the United States.” -wikipedia

Bud. Light. Sucks. There. I’ve had my say.
Before I get started, I want to clarify that this article is on the stocks of Boston Brewing Co. (SAM), Anheuser-Busch (BUD), and Molson Coors  (TAP) stocks, not an opinion article on Bud Light, but now we all know where I stand.
The idea is that similar stocks will follow similar patterns in the stock market. You wouldn’t think that a construction company and a biotech firm  would move together. That is, you wouldn’t expect the two to be positively correlated. But you would expect stocks like Pepsi and Coke to move together, as any new information affecting one would probably affect the other, right?
WRONG. The correlation coefficient between Coke (COKE) and Pepsi (PEP) is 0.2014, which means only one in 5 days do Coke and Pepsi stocks move together in step… hmm.. ok maybe it’s just Coke and Pepsi acting weird. Here are the correlation coefficients for BUD, SAM, and TAP:
Only roughly one in three days do SAM and BUD move exactly together (the same with SAM and TAP). TAP and BUD only move exactly together every other day.  They move mostly as we expected (direction), but they certainly don’t always move exactly together (magnitude).
Diversification means don’t put all your eggs in one basket. It means you need to branch out, own stocks in many sectors. It implies that stocks in similar arenas move together.
“But wait, didn’t we just find out that stocks in similar areas of the market don’t move in step? Is my finance advisor feeding me bullshit?”
Home Depot and Lowe’s are practically interchangeable, unless you have a penchant for orange or blue. The correlation between their returns is 0.8486. What affects one, directly translates to the other on eight of ten days.
In this article, I indirectly tested diversification. All jokes aside, diversification states that stocks in similar industries will move together on average. This idea is not trash, as none of the example groups of stocks returned a negative correlation coefficient, which would imply that they moved oppositely more often than together. You can still correctly assume that, on average, stocks in similar industries will move in similar directions.
Rest assured, diversification still works. It just doesn’t work as well as you thought it might… or at least I did.
– tommander-in-chief
Further, I’ll test to see if there is a profitable strategy to put in place regarding the three stocks. I’ll see if there are any two stocks whose outcomes will predict the third’s return.

# Sick of the RNC

Sick of the RNC yet? Enough of the political mumbo jumbo. Here’s some stuff you might already know, but haven’t seen the data.

The last row of the following table shows GDP per Capita growth of Sweden, UK, Germany, Greece, Spain, and Italy relative to the United States.

Over the time period, German production per head grew 16.54% faster than in the United States . Since 2005, Germans “gained” on the United States in terms of wealth. Countries in duress, such as Spain, Italy, and Greece lost in terms of wealth over the time period relative to the US. Americans became wealthier than the UK, Greece, Spain, and Italy over the 10 year time period. Americans lost wealth relative to Sweden and Germany.

The above graph shows per capita growth of the economies of Sweden, the UK, Germany, Spain, Italy,  and Greece relative to the United States.

Savings and Unemployment rates:

Theoretically, we would expect savings rates to rise as unemployment falls, and vice versa. As economies go through booms, people will spend more but also save more. As economies recess, people will lose jobs and spend less, but savings is spent. Dueling effects:

1. Wealth Effect – As unemployment rises, wealth falls. As wealth falls, savings rates increase. This effect results in unemployment and savings rates to move together.
2. Income (cyclical) Effect – Consumption rises and falls with the business cycle. In other words, as unemployment rises, incomes fall. As income falls and more people are in between jobs, savings must be spent. This effect results in unemployment and savings rates to move inversely.

Correlation between Savings Rates and Unemployment:

From the correlations between Savings Rates and unemployment, we can infer about the was a country behaves in times of boom and bust. (break it down into time periods). The marginal propensity to save (mps) is an economics term used to describe what percentage of each paycheck we save. From the above data, we can safely assume that Americans will save more when the economy is in recession relative to others, whereas the savings rate in Sweden is relatively impervious to fluctuations in unemployment. Italy actually has a positive correlation coefficient between Unemployment and Savings rates! This means as unemployment goes up savings rates go up! The dominating effect here is the wealth effect. People will spend much less when they don’t have a job. The dominating effect in the US economy is the cyclical effect.

Perhaps this is a result of work force participant optimism. Perhaps the fear of getting another job in the near future after being let go is small in the United States. This could also be the result of cultural differences between Italy and the US, such as employee turnover rate. However, turnover rate in Italy is higher.

Italy’s job turnover rate has been declining over the last ten years (http://tinyurl.com/zefsqc2). This metric is computed by dividing the number of employees who left jobs by the total number of employees still working. In the United States, the figure for May of 2016 was 3.4%, or 11.8% annually. In Italy, the figure was 23.9% in 2004 and 17.3% in 2014. This higher turnover rate means Italians are leaving jobs at a higher frequency, both by choice and otherwise. The rate in the United States has largely remained unchanged since 2002, hovering around 12% annually.

Perhaps it is cultural differences. Maybe Italians are more prone to save when they don’t have a job because they have a firmer family structure than the average American. They are taken care of at home, and aren’t forced to spend on groceries and rent. Again, this is all guesswork.

Side note: Here is the annualized employee turnover rate in the US broken down over each month. More people leave jobs in January and August than any other months in the year.

– tommander-in-chief

# Does Communism Cause Cancer?

Provocative subject, so let me clarify. How are smoking habits today associated with who we sided with in World War Two? Further, how are our smoking habits associated with the GDP of our respective countries?

Walking around San Francisco, you can’t go a block downtown without getting smoke blown into your face, and cigarettes are expensive. They’re addicting, sure, but what kind of income do you need to be making in order for this addiction to no longer be economically possible. At what point, economically, are citizens forced to give up tobacco in order to simply survive? Another way of asking this is what does the demand curve for tobacco look like?

An article on tobaccoatlas.org shows consumption of tobacco geographically, changes in consumption by region, and pie charts to depict consumption by country.

The countries that consume the least tobacco annually are:

 ·      Guinea ·      Solomon Islands ·      Kiribati ·      Uganda ·      Rwanda ·      Samoa ·      Democratic Republic of Congo ·      Ethiopia ·      Vanuatu ·      Guyana

The countries that consume the most tobacco per capita are:

 ·      Bosnia and Herzegovina ·      China ·      Luxemborg ·      Belgium ·      Slovenia ·      Russia ·      Macedonia ·      Lebanon ·      Belarus ·      Montenegro

For a little relativity, the average Montenegrin smokes 4,124.5 cigarettes per year, or 11.3 a day (or 15.5 a day if you only count trading days).

In the names above, do you see any particular pattern? Think economic, political, cultural similarities.

Granted, most of the low consumption countries were merely occupied by the Allies as they island hopped their way to Japan. Also, if you sum the GDP per capita of the bottom 20 countries, you get just barely over the GDP per capita of the USA.

If I expand my list to the top 20 tobacco consuming countries, just three were on the Allies side of WWII. That’s 85% of the top 20 tobacco consuming countries that fought for the Axis powers. Analyzing the bottom 20 tobacco consuming countries, 18 of the 20 were on the side of the Allied powers. That’s 90% of the bottom 20 countries that fought for the Allies! The cluster at the top right in the graph are the top 20 consuming countries, the cluster at the bottom left are the bottom 20 tobacco consuming countries.

Now the line of thinking goes, “how much does wealth impact my desire to smoke cigarettes? Tom just said, all the lowest tobacco consuming countries are tiny compared to the largest tobacco consuming economies; shouldn’t it be that the lower you income, the less likely it is you’ll smoke?”

I did an analysis across 181 countries across the globe using data from tobaccoatlas.org in order to see if GDP per Capita has explanatory power in determining annual consumption of cigarettes within each country. Side note: to control for the mean, I took the natural log of all data.

Testable Equation: (i represents each respective country)

Cigarettes Per Dayi = α + β(GDP Per Capitai)

If there is a direct, positive correlation between GDP per capita and Cigarettes smoked, we’ll see a beta value of one and an alpha value of zero. Running the regression across 181 countries returns the following:

 Alpha Interpret Beta Interpret 3.997 Large alpha; greater than zero .7335 Positive beta; less than one

Graphically:

The beta value less than one, but still positive implies that there is a strong correlation between GDP per capita and amount of cigarettes smoked. Intuitively, the more money you have, the more cigarettes you can buy. This means consumers see cigarettes as a “normal good” for all you econ buffs. Normal goods are usually things like Coke as opposed to generic brand. Meanwhile, we are continually fed ads depicting people whose lives have been ruined by cigarette smoke.

The large alpha value means that nicotine is still addictive; it means people will still smoke 54 (e^4) cigarettes a year even if their country’s GDP per capita is zero. Kinda funny, kinda not.

In conclusion, does communism cause cancer? Cigarettes cause cancer. Seventeen of the top 20 tobacco consuming countries were part of the Axis powers in WW2. I’ll let you decide for yourself.

– Tommander-in-Chief

p.s. Email me if you want the whole data set: tom.schleusener@gmail.com

External Articles:

# Predicting the Future…

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:

σt²≡β01σt-1²+εt

If you look at the equation above, you’ll see that we want a βvalue of 1 in order to prove that past volatility is a predictor of volitility. If β1 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 20th 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.