Tuesday, March 29, 2011

Why doesn't Black-Scholes model work in long period option pricing?

Buffett doesn't like derivatives and calls it as the financial weapon of mass destruction. Yet he wrote Billions of European Put Options of various stock indexes. The term is very long (10-20 years) and no collateral needs to be posted.

Apparently he thinks this is a good deal and he mentioned in his letter to share holders this is a way to show his belief that the Black-Scholes model doesn't work in long term option pricing. In this case, the price given by the formula is just too high.

There are a list of limitations and assumptions for deriving BSM. The number one is that the stock price follows Wiener process and it is log-normal distribution. In order to arrive at this conclusion, a big assumption here is that the price has same likelihood of going down and going up, no matter what the current price is. In another word, there is no such thing as "over-bought" or "over-sold". A large decline of the stock or index doesn't mean it will be more likely to rise later.

The primary source behind this assumption is again "efficient market assumption". If market is efficient, the current price is "always" justified, and of course, there is no such thing as "cheap" or "expensive" stock.

This may be true for many short term stock movement. But when we get to the stock index in 20 years term, it becomes more obvious that this assumption is not aligned with common sense. In history, we have observed that the price of stock or index eventually revert to their economic earning power, despite the possibility of long depressing period and bubble period (sometimes that period could last 5-10 years, but usually it doesn't last more than 2-3 years).

In a long time scale, it becomes obvious that the market is far from efficient, as we can find so many unbelievable and ridiculous bubbles in the history.

Put it in another way, we can invent a process called "economic arbitrage" (the term is to differentiate it from "trading arbitrage"). If a company's stock is very cheap comparing to its earning power, business people will find it compelling to buy the company's stock instead of investing on starting a new company in that industry. The other argument could be true, if the company's stock is too expensive, people could borrow money to sell short the stock or dump existing portfolio and use the cash proceed to fund a new company on their own.

Now the question is: if we have economic arbitrage, why could the stock price still go out of the reasonable range sometimes? The answer is simple, the market force that are willing to trade and focus on the short term is much bigger than the pure business force (after all, the ordinary Joes can't buy a company or start a new company). But eventually, business force (the weighing machine) will win, when the market force returns to their senses, or when the power of their mania is gradually worn off by the business force.

Saturday, March 5, 2011

Trader = speculator = gambler?

For long, I thought the traders are playing a zero-sum game and their only contribution is to provide liquidity to the market. Overall, they don't provide much value to our society and not surprisingly the general public view them as speculator and gambler too.

However, if we really study the market from the ancient world. At the very beginning, there is no currency. People exchange goods for goods. Of course, this is not convenient at all, since seller may have the goods, but couldn't find the buyer who want his goods AND also has the goods he wanted. The invention of currency creates an intermediary "common" goods that everyone needs.

Still, even with the currency, it is hard to find a buyer that needs the goods. Then it comes market that sets a fixed location for people to sell/buy stuff. Even with market, it is sometimes hard to find buyer/seller or enough buyer/seller for a certain goods. Then here it comes traders who don't need the goods themselves, but intent to act as intermediary to buy and sell to make a profit (catch the spread).

This trader's role needs to take risk on future prices and the risk of having to store the goods, along with the tied-up of capital. It also works on the price differences between markets at different location to balance the supply and demand between different regions or countries.

Overall, the trader's function is balance the supply and demand over "location" and "time", as well as providing more liquidity to facilitate the trades, and the competitions between traders also reduce the spread.

This function is quite important, but didn't get noticed for very long in China. Ancient China's noble class is not as clearly cut as western world, instead, Chinese Emperor has put people to 4 different classes: scholars, farmers, craftsmen and traders/businessmen. Scholars master the literature and knowledge of histories, it seems quite reasonable to put them to the top of the classes? But letting farmers sitting on the second class could be quite surprising to many other countries(even though it is just verbally so). This is because Emperors want to encourage farming and believes that is where the food and wealth comes from. Craftsmen also produce real goods, but that kind of goods are nice to have, but not have to have (like food). At last, the traders were considered as making profits from nowhere, since they didn't produce any real goods. These people were considered as making huge profits without actually doing the hard work. To discourage this kind of behavior, they were put to the bottom of the 4 classes.

Today, we have fully recognized the benefits of trades and think trades are equally important to our economy. However, the importance of trading in equity/derivative markets still haven't been fully recognized. In part, this is reasonable, the convenience of trading equity often makes people more short term oriented and more tempted on buying/selling for short term profit instead of long term investment. This fact is an unnecessary waste of resources and energies. Also, many people who want to profit from speculation ends up losing, a typical phenomenon of gambling.

Still, traders are not just speculators. Market makers and other liquidity traders make their profit primarily from providing liquidity to the market, not from speculation. And just because it is convenient and low cost to sell doesn't mean people should do so frequently with short term vision.

Tuesday, March 1, 2011

Is market efficient?

Warren Buffett said so many times that market is not efficient and the business school is providing misleading trainings in general.

On the surface, the market seems to be efficient since it is pretty hard to beat market for average people. But on the other hand, for traders and value investors, there are many people who can consistently beat the market for many years in a roll.

In my view, it is not a question of whether it is efficient or not. Instead, it is a question how efficient it is. Or in other words, how hard it is to beat the market consistently.

I believe for any normal person who study on the right track for 2-3 years and has enough patience, it is quite possible for him/her to beat the market consistently. In another word, market is far from the efficient level we were told in the textbooks.

Market is not so efficient for four reasons:
1. Human psychology. Many researches in Behavioral Finance shows that we as human being have behavior bias. We tend to neglect the bad part when we are focusing on profit potential (greedy), and neglect the good part when we are focusing on loss potential (fear). Also there is a tendency to be impatient (hope to get decent return in short term). Those who are patient and can control their emotions certainly have a big advantage.
The fact we have so many bubbles in history is not coincidence. It is a pattern keep repeating itself. The existence of these extreme conditions invalidate the assumptions that investment community always react rationally to public available information. It is very clear that experienced value investors were able to identify these bubbles and actually had a consensus among themselves. For example, many value investors sold all their positions and stand in sideline in year 1999. Despite repeated speeches from Buffett that the future return is not going to be good, nobody actually listen to him any more at that time.

2. Different Goal and time horizon. There are many investors competing on the stock market. But no all of them have the same time horizon. Most mutual fund managers have to explain their short term performance. For this reason, they may have trouble to pursue an opportunity that only gives good returns in long term, but will do poorly in short term, even though they do believe it is a good buy. In this case, the money manager's goal is to keep his job and keep getting the management fees, not for the best long term performance. Also, most people tend to be impatient and not tolerable to short term price fluctuations.

3. Different skills. Investors have different skill sets. Some are better on technical analysis, others are better on fundamental. Some only focus on current financial statements, others focus on people factor and long term growth as well. Those people who are on the right track and practiced their skills for many years certainly have an advantage.

4. If most people believe the market is efficient and don't exploit the weakness of the market, then the market will become more inefficient again.