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Saturday, May 26, 2007

The Banker and the Counterfeiter

Imagine a criminal was counterfeiting money. However, instead of spending the money himself, he loans the money to someone else. He prints $100,000 and lends it to someone for a year, charging 6% interest. A year later, he collects $106,000. By coincidence, among the $106,000 is the same $100,000 he lent out a year ago. The counterfeiter burns the $100,000 he printed and keeps the $6,000. The police conduct an investigation. The counterfeiter says "The $100,000 I printed is gone. Since I destroyed the $100,000 I printed, I didn't really commit a crime. By the way, here's a $5,000 bribe so you ignore my crime." The police don't investigate further.

Did the counterfeiter commit a crime?

Imagine a banker receives a request for a $100,000 loan. He borrows $100,000 from the Federal Reserve at 5% interest, and issues the loan at 6% interest. The Federal Reserve printed the $100,000 it lent the bank. Actually, the Federal Reserve doesn't need to print physical currency; it just creates a credit and debit in the books. A year later, the banker collects $106,000, repays the Federal Reserve $105,000 and keeps $1,000 as his own profit.

What the banker and Federal Reserve did was perfectly legal. Is it morally any different from what the counterfeiter did?

Usually, the banker doesn't borrow from the Federal Reserve and just loans out money already on deposit. In that case, the banker keeps the full $6000, but he did have to pay interest to whoever deposited the money.

There's another significant point to be made here. The $5,000 that the Federal Reserve collected in interest is NOT realized by the government as income. I don't know where that money goes. If the government didn't outsource its money making authority to the Federal Reserve, a private corporation, this interest income would be enough to pay off the national debt and substantially reduce taxes.

The banker effectively printed new money when he made the fractional reserve loan. As above, the profit made due to printing new money went to the banker, and not to the government. Fractional reserve banking is a form of legalized counterfeiting.

Monday, May 21, 2007

The Discounted Cashflow Paradox (aka The St. Petersburg Paradox)

The "Discounted Cashflow" model is the generally considered to be the most conservative valuation method for pricing stocks and investments. It's the model that Warren Buffett uses. Warren Buffett even mentioned this paradox at one of his annual shareholder meetings. The idea is that money in the future is worth less than money in the present. The value of a business is the value of all its future profits, discounted to the present. The paradox is that, under very reasonable assumptions, the Discounted Cashflow pricing model gives an infinite stock price.

I tried using the Discounted Cashflow model myself to price things, and came up with ridiculous results. Only recently, I figured out what was going on.

This is not to be confused with what I call the St. Petersburg Math Paradox. This is the following game: You flip a fair coin until a tails shows up, at which point the game ends. For each head, you receive a payment of $1*2^n, where n is the number of consecutive heads already seen. For an outcome of T (p=1/2), you receive $0. For an outcome of HT (p=1/4), you receive $1. For HHT (p=1/8), you receive $1+$2=$3. For HHHT (p=1/16), $1+$2+$4=$7. For HHHHT (p=1/32), $1+$2+$4+$8=$15. If you take the weighted infinite sum, you get that this game has an infinite value. Obviously, no game has an infinite value. If you were playing this game against a real opponent, at some point your opponent would be unable to pay off a sufficiently large string of heads. The value of this game, if someone ever actually offered it to you, would be finite, with the value based on how much money your opponent had.

The St. Petersburg Math Paradox is completely unrelated to the St. Petersburg Financial Paradox, which I describe and explain below. The St. Petersburg Financial Paradox has a perfectly rational explanation.

The idea of the Discounted Cashflow pricing model is that all future income is discounted to the present. The rate used for discounting is typically the long-term bond rate or the risk-free interest rate. That's the return you could get without any effort or risk by buying government bonds. I will use a fixed value of 5% here, to keep things simple. (Technically, the interest rate should vary based on the timeframe. However, the yield curve is pretty flat right now, so a flat 5% interest rate is a reasonable assumption.)

Historically, stocks have improved their dividends by more than the bond yield rate, in the long-term. This has been true in every historic period of substantial size, so it's a very reasonable assumption. There are short-term fluctuations, but for now let's assume we're a long-term investor.

Let's price a stock that pays a dividend of $1 immediately and we expect will grow its dividend by 6% per year. This is a very conservative assumption, because most indices have had their dividend go up at a much higher rate historically.

I also will assume that the stock we invest in will never go bankrupt, that it will keep growing its dividend forever. If you like, consider this to be an investment in an index rather than a single stock. (For example, if every company in the S&P 500 goes bankrupt, you probably have bigger problems than the value of your investments.)

After 1 year, we receive a dividend of $1.06. To get $1.06 guaranteed a year from now, we would have needed to invest $1.06/1.05=$1.0095 at the risk-free rate a year ago. The present value of the $1.06 dividend is only $1.0095.

So, running our model for 1 year, we get a price of $1+$1.0095 or $2.0095.

Similarly, after 2 years, we get a dividend of $1.124, which discounts to $1.019. Our stock price is now $3.03.

Typically, these discounted cashflow models are run for something like 10 or 20 years. Running the model for 10 and 20 years gives a stock price of $11.53 and $23.13, respectively. A price of $23.13 sounds reasonable for an established company that pays a dividend of $1 now - that's a yield of just over 4%, comparable to companies like Verizon, AT&T, Bank of America, and Citigroup.

However, we're missing something. We're assigning a value of $0 to all payments later than 20 years from now. Surely an established, profitable company will still have some value then. We should be able to sell our shares for something, if we needed to. The person we sell our shares to 20 years from now is going to do his own discounted cashflow pricing, starting from the most recent dividend of $3.21.

A 40 year discounted cashflow calculation gives a price of $49.87. A 100 year simulation gives a price of $168.50.

Do you see the problem? We're summing an increasing geometric series. Under the assumption that the company never goes bankrupt and keeps increasing its dividend faster than our discount rate, we get an infinite stock price.

An economist would say that I'm doing it wrong. I really should be discounting at a rate that's higher than my expected dividend yield growth, such as 7%. Under those assumptions, it's a decreasing geometric series and a finite price.

But why should I discount at 7% instead of 5%? I can't find an investment that will give me a guaranteed 7%. I can only get a guaranteed 5%. A stock investment is "riskier" because its price may fluctuate, but when you take into account the increased expected return, the stock investment is actually less risky. Historically, stocks really have outperformed bonds in every significant time period. As long as the corporation never goes bankrupt, and doesn't get bought out for less than its value, your stock investment should eventually outperform the risk-free investment, no matter what price you paid.

Using the discounted cashflow model, I validly calculated that the correct price for any stock is infinite. If you know the company never goes bankrupt or gets bought out for too little, it will be a good investment provided you hold onto it for long enough, no matter what price you pay now.

Where's the mistake? I was bothered by this result for a long time before I figured out the answer.

The mistake is that a dollar is intrinsically worthless. The government will give me a 5% return if I invest in bonds, but the government prints new money at a rate of 6-10% per year! (or more!) That guarantees that if I keep my savings in bonds forever, it will be eventually be worthless, losing its value to inflation.

Even in the past, when the dollar was on a gold standard, the government from time to time devalued the dollar, decreasing the amount of gold each dollar represented. This happened often enough that anybody who owned bonds got cheated.

A stock is backed by something concrete, the productive value of a corporation. Even when the government prints new money, the stock will naturally rise in price to offset inflation. The corporation will see the prices of its supplies rise, but it will in turn increase the price it charges customers by the same amount. Even though corporate executives usually dilute your ownership by granting themselves shares and options, they don't do it at the same rate that the government prints new money. Plus, they usually try to repurchase enough shares to offset any grants they give themselves. Executive stock grants and share repurchases are a drag on a corporation's earnings, but this drag is already factored into the stock price when you buy. Unlike when the government prints new money, new share grants are clearly stated in the annual report. The actual amount of dollars in circulation is not published. (The Federal Reserve recently stopped publishing M3, because the values published would have been too embarrassing.)

That's the answer to the Discounted Cashflow Paradox. A dollar is inherently worthless. In the long run, you can't trust the government to not dilute its value via inflation. The bond rate is insufficient compensation for inflation.

A stock doesn't have infinite value. A dollar has zero value and there's a division by zero error when you run the Discounted Cashflow model for a sufficiently long investment horizon. A dollar has temporary value, because there are only a finite number of dollars in circulation right now, and people haven't caught onto the scam yet. The government has the right to print as many dollars as it desires, and it exercises this right as much as it can. The moral is that there's no point holding dollars, or bonds that pay dollars in the future. You'd better convert your dollars to a tangible asset as soon as possible. Only keep as much cash as you need to cover your short-term cashflow needs.

The Discounted Cashflow model can still be used to price stocks. Provided you use the same time horizon, and assume the same long-term trend growth rate, you get a valid comparison. The Discounted Cashflow model will tell you which investments are most efficient for you to purchase with your soon-to-be-worthless dollars.

So there's your answer. If you ever though economics was just so much nonsense, now you know why. Economics is nonsense because the fundamental unit of value, the dollar, has a value of zero. All of economics is just one big division by zero error.

Saturday, May 12, 2007

Distributed Costs and Concentrated Benefits

The main problem in the current political and economic system in the USA is that it fails to solve the "Distributed Costs and Concentrated Benefits" problem. This is any situation where the cost is spread out over millions of people, but the beneficiaries are just a few corporations or individuals. Since each individual loses only a few dollars at a time, there's no incentive for them to protest or organize an alternative.

In a properly functioning media, "Distributed Costs and Concentrated Benefits" situations would be exposed and reported. In a properly functioning government, the government would intervene to disrupt such a situation when it arises. Over 100 years ago, that was what government did sometimes, such as when it broke up the oil and railroad monopolies. Nowadays, all it takes is some campaign contributions or bribes and the government will look the other way, or even directly create a "Distributed Costs and Concentrated Benefits" situation. Some people estimate that the rate of return for political campaign contributions is 1000%-10,000% or more. The average person is unaware or is only losing a few dollars to each of them, so they don't protest. However, when you add them all up, it's a lot of money. The few people who do notice and protest have trouble communicating the problem to others.

A lot of the stuff that I'm going to be writing about is specific examples of the "Distributed Costs and Concentrated Benefits" problem. I think that each of these specific things are symptoms and not the underlying problem.

Here's a list of the "Distributed Costs and Concentrated Benefits" problems I can think of:

- One example is any industry that is a monopoly (just one provider) or oligopoly (several providers who collude to fix prices).

- A big problem is the concentration of control of the media in the hands of a few individuals. This is what allows all the other "Distributed Costs and Concentrated Benefits" situations to go unreported and unresolved. The average person thinks that if something really bad was going on, the newspapers and television would report it, but that's just not true anymore. News is mostly about entertainment and product placement. There really isn't any serious investigative journalism in mainstream media anymore.

- Who gets elected is also controlled by the media. It's hard for a candidate to win an election without all the free publicity in the form of "news". Every story about Clinton, Obama, Guliani, or McCain is free advertising for them. When they are touted as front-runners they become front-runners. For example, a lot of people on the internet are saying they like Ron Paul and he performed well in the debates, but he hasn't been mentioned at all elsewhere. The media doesn't say "we don't like Ron Paul", which would merely draw attention to him. The easiest way to censor him is not mentioning him at all. Their argument is "we can afford to not mention Ron Paul because he has no chance of winning", but that becomes a self-fulfilling argument.

- The government dilutes the money supply via deficit spending and inflation. The cost is that any cash you have loses its value over time. Anyone sufficiently wealthy can buy assets that are protection against inflation, such as stocks, real estate, or precious metals. If you have a lot of money and are aware of the inflation problem, you can protect yourself. That's why the inflation problem goes unresolved; an aware wealthy person is protected. Poor people tend to hold mostly cash and have benefits such as pensions and social security that aren't properly adjusted for inflation. Inflation allows the government to confiscate the gains due to increasing efficiency in the economy. That's why the improving economy disproportionately benefits the wealthy; they have assets that are hedged against inflation plus they are able to get the government to give them lucrative perks and contracts.

- The corporate boards and insiders vote themselves and the CEOs huge pay packages and option grants. The costs are paid by the shareholders via excessive expenses and dilution of their shares, but it's typically only a few cents per share per year. The check on abuse by insiders exists only in theory and not in practice. Still, the executives can't be too greedy or they'll face shareholder lawsuits, but only the most egregious abuses get punished occasionally. Stocks still are a good investment in spite of these abuses. That's also one of the benefits of buying an entire company (i.e., taking it private) - by stopping the insiders from lining their pockets, the corporation is worth a lot more.

- The specialists on the NYSE collect a fraction of a penny off each transaction, due to their privileged market position. Those pennies add up, but the ordinary person just views it as a cost of trading. Also, brokers that have "payment for order flow" deals are guilty of this.

- War is another "Distributed Costs and Concentrated Benefits" situation. Military contracts are frequently given out on no-bid to people with political contacts.

- The drug industry promotes harmful drugs. The FDA is supposed to be watching, but it's a "Captured Regulator" that sides more closely with industry than with the people it's supposed to be protecting. There also is "tort reform" that limits the liability of drug companies when they're caught doing bad things (such as with Vioxx). Typically, even when a drug company is caught covering up harmful side-effects of a drug, their liability is limited and is usually less than 1 year of profits from that drug. A drug company considers its customers to be the doctors who prescribe the drugs and not the people who actually take the drugs. A drug company has no fiduciary responsibility for the safety of the people who actually use its product, because its liability is limited when its product is shown to be harmful.

- Another example is any industry that is unionized and has wages above the market rate. Doctors and lawyers have a very strong union. However, being a doctor isn't as lucrative as it used to be due to pressures from HMOs, but the doctor's union does a good job of controlling the supply of doctors by limiting the number of slots per year in medical schools. Lawyers also have a strong union; the average person has to spend $50k-$100k if they wind up involved in a lawsuit. The legal system is intentionally too complicated for someone to be able to represent themself. Legal language has evolved so it's incomprehensible compared to normal English, which is job security for lawyers. The longshoreman's union is another good example.

- Any tax break or subsidy for a specific industry is a "Distributed Costs and Concentrated Benefits" situation. For example, farm subsidies help a few people and come out of your taxes and show up as distortions in the price of food. Some websites say that farm subsidies cause unhealthy food to be cheaper than healthy food.

- The government sold/gave spectrum to cell phone companies for far less than the real market price of that spectrum.

- If the telecommunications companies succeed in stopping "network neutrality" that would be a huge "Distributed Costs and Concentrated Benefits" situation for them. Even though they've received huge public subsidies in the form of cheap spectrum and easements to lay their cables, they're still saying they need the extra profits they could get by ending "network neutrality". They have billions of dollars to spend lobbying and advertising. The supporters of network neutrality only have millions of dollars and will most likely lose.

- Any industry that pollutes is taking advantage of "Distributed Costs and Concentrated Benefits". It's hard to quantify the cost of pollution. Even when they get caught, damages tend to be less than the profits earned by polluting and the real cost of cleaning it up. Nowadays, the government really isn't interested in enforcing anti-pollution laws.

The average person winds up losing a HUGE amount of money each year to "Distributed Costs and Concentrated Benefits". It's only a few dollars to each of them, but there's a lot of them. It's hard to get outraged over someone stealing a few dollars from you, but you have to multiply it by the number of times it occurs. That's why it's such a serious problem.

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