Saturday, May 1, 2010

On Investment Singularities

The Gordon Dividend Discount Model establishes the price, P, of a stock based on dividends, D, at a required rate of return, r, that grow at rate g in perpetuity as P = D/(r-g). This has a singularity at r = g. While this may occur asymptotically or temporarily, it can never do so forever and always in a finite universe. There is always a finite number of people to bid for it, amount of money to buy it, or borrow against it. At most it would be potentially infinite with a trade off between those so wealthy they have no other outlet for their money and those for whom it is so much that the alternatives are as pleasant or even more so in case of boredom, and the impermanence of life and division between heirs or absence of them.

Consider too if our estimate of r-g were off by 1% or if when we wished to liquidate our investment it were off by 1% or if it drifted away by 1% over time. P would drop all the way from infinite to 100 D, so even if we thought we were getting a bargain, it could easily end up not being one. Our best estimate may be that of the next best alternative. Who would ever want to sell such an investment? Wouldn't the income flow ever be enough? If we were immortal, if our tastes never changed, if our investment never changed, perhaps not, but those are not that likely.

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