How do math and statistics play a role in economic speculation and hedging?

[alech4466]

My question/topic of discussion is, "Economic Speculation and Hedging". For many people this is just a mysterious thing that big bad Wall Street bankers do, and I want to find out about it.

How does the calculus and the other maths apply to speculation and hedging? I understand that math is required in order to speculate and hedge, but I do not understand how it is applied. How do you determine whether or not a stock is a good bet or not? On the other hand, how do you determine if you should hedge a bet? Can you give an example of the process used.

I understand that most people here are mathematicians and physicists, but I'm fairly confident in my assumption that at least a few people know how the math is applied

 

[micromass]

Moved to social sciences.

 

[alech4466]

Okay, didn't see that section when looking to post this.

 

[John Creighto]

Look up Value at Risk,
http://www.investopedia.com/articles/04/092904.asp#axzz26BYUdVf0
http://en.wikipedia.org/wiki/Value_at_risk
http://en.wikipedia.org/wiki/Financial_risk#Liquidity_risk

In order to hedge you have to have a risk model. Value at risk quantifies the type of risk which a company tries to achieve. Var basically quantities the maximum loss a company is expected to see in a given time frame:

“For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day in 20.”

I believe there are regulatory requirements for banks where over a given time frame (say a year) a bank must have a probity of at least (say 99%) of not exceeding a level of loss (enough loss to effect their capital adequacy).

Now various types of assets have certain statistical properties such as correlation to the market, anti-correlation to the market, susceptibility to tail events. If we could know the statistical properties of various types of assets we might be able to quantify risk. If we can quantify risk we can choose our assets to keep some risk metric (such as VAR) below a certain threshold.

Bank regulators asses the ability of each banks, risk models ability to measure the expected/maximum losses. They de-rate their assets to compensate for past errors in risk predictions. The problem with this is that banks change their risk models over a much shorter period of time then major market events. The consequence is that the risk models always appear better then they actually are. This allows banks to over value the worth of their risk weighted capital. This props up the value of their stock and the amount of money they are allowed to borrow.

 

[Alesak]

When Genius Failed: The Rise and Fall of Long-Term Capital Management.

Get this book, it's gripping story about pioneers in this field.

They used Black-Scholes model(which is based on heat equation) to model prices of certain assets(mainly government bonds) and when, say, price of 2 bonds with different maturity dates were too different, they made bet that the prices would converge. But the profits from this were very very tiny per $, so to get any reasonable profits they had to use huge leverage ratio - borrow huge amounts of stuff from banks that are vital for non-financial economy - and on one magical day the bet did not work, so they were not able to repay the stuff to the real, non-investment, banks.

As for how the math is applied - look e.g. for econophysics books on amazon. Basicaly anything short of string theory was probably tried on economics.

 

[Tosh5457]

How does the calculus and the other maths apply to speculation and hedging? I understand that math is required in order to speculate and hedge, but I do not understand how it is applied. How do you determine whether or not a stock is a good bet or not? On the other hand, how do you determine if you should hedge a bet? Can you give an example of the process used.

Mathematics is certainly not required to speculate, and for hedging it depends on how complex that hedging will be. For an example of using statistics in this field, you can check out the book Analysis of Financial Time Series (Econometrics).