Variability is not the same as risk

Here are three things that the market sometimes overlooks.

1. Variability is not the same as risk.
  Analysts use historical Beta to come up with a cost of equity for a company. Beta is determined by taking the stock's variance in relation to the market by some squares formula. Fun stuff. It's more elegant than it is useful in my opinion. First of all more than just correlation or variance is important, because correlation of correlation and variance of variance affects things, but these are not included in typical formulas, Re = Rf + B(Rm - Rf). Rf is the risk-free rate (U.S. t-bills although they're really not risk-free), Rm is the historical market return, B is the correlation between the stock's return and the overall market. But that's a side story.

The real issue here is that past variability does not predict future variability; in other words, variance is not the same as risk. Cost of equity is attempting to determine the uncertainty of a company's future income. The idea that the past correlation of the company's stock with the market is predictive of the company's future income. That is not true. Let's be practical and look at it with a couple of examples: Let's say a company had a news story come out that it was being investigated by the SEC. The stock price plummets. Then it comes out the next week that the story was bogus. The price rises. Now you have a company with higher Beta, and according to the market a higher discount rate. But the certainty of the company's future cash flow has not changed in the slightest. 

Now a real-world example: Rambus (RMBS) was hinging a lot of future profits on the outcome of a lawsuit against Micron. Using historical Beta, you might discount Rambus's future income projections at around 15-20%. But just looking at it practically, they should have been discounted based on the probability that Rambus would win the suit. Maybe a 30-50% discount rate. Rambus stock plummeted when some negative news about the suit came out, an analyst suspended coverage, etc. The same is true for USEC, Inc. (USU), dependent on a loan from the Department of Energy to create a nuclear power plant. Future income should have been discounted heavily (much higher than WACC based on the historical Beta) because of the higher risk of USU not receiving the loan guarantee.

Let's try to come up with a formula to determine what your discount rate should actually be:
Simple model:
A 50% return, coin flip scenario

Bet $1 today to win $2 tomorrow.
Winnings*P(Winning)/(1+Rf)
1/(1+Rf) is what you should pay for the bet. Not quite done. Now consider the impact of this bet on the rest of your finances. Since it's small, it won't matter. But let's say it's a billion dollar bet and you are a company. In the event that you win, your cost of debt and equity will decrease. But if you lose, your cost of debt and equity will rise, and it will rise more than it would decrease if you won. Because of diminishing returns. So we have to measure how the event of loss would change an individual's or company's discount rate in order to determine the true cost of equity in a project. In other words - ding ding ding - a cost of equity is not just project specific, it depends on both the investor and the project. That's why the historical Beta model doesn't work.
Winnings*P(Winning)/(1+Rf) - Assets*(increase in WACC)*P(losing) + Assets*(decrease in WACC)*P(winning)
or something like that

Now, let's say you've got the same scenario, but there is 5% risk that the person you are betting against will be insolvent.
$2*.5*.95

Actually I'm getting tired and this is complicated; we'll come back to this later.



2. Markets are not perfectly efficient.

Duh. But so many people believe they are. Some people are better at picking stocks than the market because they have more information. Others are able to interpret information better. Others interpret information worse. Just look at all these Chinese ADRs being exposed as scams. The short selling firms who gather the information, of course they are going to beat the market because they have more relevant information and they are able to act on it. Like Muddy Waters.

Markets are subject to bias - recency bias, bias against illiquidity, and many more. You've got to find the bias and exploit it. It's hard. Markets are mostly right. But there's room for improvement.


3. A company with a strong balance sheet should have higher P/E than a company with a ton of debt.

What is the formula? Something like
WACC = Re (E/V) + Rd (D/V) (1-T)

Who cares? It's wrong. It's wrong because analysts use Beta to find Re, but actually Re is influenced by the amount of debt a company takes out. If a company with a B = 1.5 and a clean balance sheet with assets of $1 billion tomorrow takes out a $1 billion loan, the cost of equity should go through the roof. But using the formula listed Beta and Re would not change.




What risks are investors trying to avoid when investing in a stock or bond?
1. On one end of the spectrum, the risk of default, or nonpayment
2. On the other end, the risk of inflation that renders returns valueless



Disclosure: I don't own any of these guys mentioned here. Won't take out any positions in the next 72 hours. Why do I have to say this here?