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January 24, 2006
More on reinvestment
Back in late November we discussed how reinvestment (along with limited liability) was a critical to make money in investment strategies where the principal value converges to zero value given enough time.
Yesterday afternoon I was at Bloomberg, attending a training class on options valuation techniques. Dr. Steven Heston was there as one of the two lecturers, and talked about no arbitrage models. You see, the way most options (stock options or otherwise) are priced is to figure out how to buy a combination of stocks and treasuries (this is slightly different for other option types) that behaves like the option (this is called the replicating portfolio) while the stocks and bonds stay about where they they are. Then, as they move, you re-balance that replicating portfolio so that it always locally behaves like the option. If you figure out what that strategy costs, you then know the price of the option. He asked a tantalizing question. How do we know that a given replicating portfolio is the unique (or at least cheapest) solution?
We don't, and as it turns out, we can't, at least under a variety of situations, such as:
1) There is a bubble in the asset prices, but its magnitude and duration are unknown
2) Put call/parity doesn't hold.
Consider a share of stock that costs $100. Let's say the call option with a strike price of $105 (the right to buy the stock for $105 regardless of actual stock price) costs $5. If you buy the option and invest the rest in government bonds, then it turns out that this should have exactly the same performance as buying the put at 105 (the right to sell at 105) while buying the stock with the remaining money. Take a look a the previous link, you'll see that this is an obvious and reasonable proposition, although one that happens to break down.
Unfortunately, both of these things are known to happen, primarily when there is an inability to short the underlying asset. Take for example real estate. it is very difficult to borrow real estate, sell it, wait for it to fall in price, then buy it back and return it to whom your borrowed it. Or consider the
shares of Palm stock when they were being spun-off from 3Com. The total value of the Palm shares was as large as the total value of 3Com shares, yet the 3com had real economic value. Sure enough, there were no shares available to short and put call parity broke down in the option market.
I'll link to the presentation when they send it to me and you can see a explanation of how a bubble in asset prices still allows the profitable and unique pricing of options, you just can't use ordinary no arbitrage methods.
Posted by OneEyedMan at January 24, 2006 9:04 AM
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