The last time I had checked, the Big Six and Big Eight bets had all but disappeared from modern craps tables on the Las Vegas strip. The reason is because no one was betting them. The Big Six and Big Eight bets paid even money (1:1) for a payout, but there was another bet, called "Place Six" or "Place Eight" which paid better odds (7:6) and hit at the exact same time that the Big Six and Big Eight bets did. Because of this, bettors learned that it was smarter to use the place bets rather than the large, Big Six or Big Eight bets on the corners. (To try these out for yourself, you can find a nice craps flash game, no real money used, here.)
The Big Six and Big Eight bets violated a fundamental rule of financial mathematics:
Portfolios with equivalent payouts will have the same price at all points in time.
The concept is simple enough - portfolios of investments that provide the exact amount of reward, in exchange for the exact amount of risk, will sell for the same value. If not, the market will buy the more advantageous one and sell the less advantageous other one until the prices come to equilibrium. Note that once again, this is economic argument and not mathematical proof. However, once mathematicians accept this argument, they get their (very powerful) equals sign back and begin to work their magic.
It's very difficult to frame this article in the context of Second Life finances because many of the tools used to bring this principle into practice don't exist there. Short selling, options, futures, etc. all don't exist in Second Life (yet - I'm still holding out hope), and so these strategies likely will not work there. Instead, then, venture with me into First Life and the world of financial derivatives. First, some quick definitions (with links for better explanations):
Long Buy - This is the stock transaction we're all used to: buying a stock and selling it at a later date.
Short Sell - This is selling a stock you do not own with the promise to pay it back later. You are liable for any dividends, splits, etc. that the stock undergoes while you are shorting it.
Calls - This is an option which gives the holder the right, but not the obligation, to purchase a specified security by a specific time at a specific price, all of which are spelled out in the details of the call contract.
Put - The opposite of a call, this is an option which gives the holder the right, but not the obligation, to sell a specified security by a specific time at a specific price, all of which are spelled out in the details of the put contract.
In the put and call articles of those Wikipedia links above, the authors have provided a graph on which the vertical axis shows the payout (or profit with the dashed line) and the horizontal axis shows the underlying security's price. If you sell the call or put instead of buying it, you simply invert those lines over the horizontal axis to get your new payoff/profit graph. These are shown below the first graphs.
The payoff graph for a long buy is an upward-sloping line (with slope 1). For each unit the underlying security (the stock) goes up, you get another unit of payoff and profit. As I mentioned above, if you happen to short the stock, then the line slopes down (slope = -1) and for each unit the stock goes up, you lose another unit of payoff and profit.
There is also some consideration to be given to interest in this matter. Options take place in the future, and so you have to compensate the investor for giving up their money for a period of time. This is usually done at the risk-free rate.
Out of all these graphs and rates, you can push, pull, bend, and tweak various portfolios to have the exact same payouts, even though on the face they look very different. Some of these portfolios will make even the most seasoned investor's head spin, but because of financial mathematical principles, the price can be easily calculated.
A good example of this is the put-call parity formula. This formula tells how the price of a put, call, the underlying stock, and the interest rate all depend on each other. Given any three of those, you can solve for the fourth.
Let's get an example here. At the time of this writing, the price of 3M Corporation (NYSE:MMM) was $85.93. A January 2009 call for $90 is selling for $8.42, and a January 2009 put at $90 is selling for $9.40. Using the put-call parity formula, we can calculate what the interest rate must be in order for these prices to be in line. From the article (with symbols properly translated):
Call Price + (Strike Price)/(1+i) = Put Price + Asset Price
8.42 + 95/(1 + i) = 9.40 + 85.93
i = 9.3%
8.42 + 95/(1 + i) = 9.40 + 85.93
i = 9.3%
Investors in the 3M Corporation believe that they must receive exactly 9.3% interest between now and January 16, 2009 (8.28% annually) in order to make these prices work. Note, however, that the put-call parity formula assumes no transactions costs. Your 9.3% rate of return would be offset by these transactions costs. Still, if you happen to be looking for a decent rate of return (and don't mind making your broker sweat in order to get it), this is something to consider.
Questions? Comments? To me, this is one of the most fascinating concepts in financial mathematics, because it allows you to construct new portfolios, new investments, new ways of moving money around and still have a good idea of what the price should be. It also allows for you to more easily see arbitrage opportunities, and exploit them if they happen to exist.
I have no idea what the next Lesson in FM topic will be. Suggestions, anyone? It doesn't have to be overly complex - if a reader would like me to take a stab at explaining a concept, I'll do my best. Just leave your thoughts in a comment here, and it'll find its way back to me.
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