Tuesday, February 2, 2010

Share price as net present value

In theory, the price of a share should be the net present value of all the future cashflows. Simple enough, but the problem is we can't know what rate of interest to use (over the last thirty years or so, interest rates on gilts haven't even correlated with share prices), what the cashflows will be, and what the risk associated with those cashflows is.

The article I discovered this alternative approach through has an alternative approach, with quite a neat explanation for the volatility of stock markets, which far exceeds what one would expect for models based on discounted cash flows.

The simplest state-contingent security is a bet. Financial services provider Paddy Power is offering seven-to-four on John McCain becoming the next US president. If you hold £1 of this asset, you get £2.75 in states of the world in which McCain becomes president, and nothing in other states.

You can think of the All-Share in a similar way, except - we hope - that zero pay-offs are less likely.

For example, imagine two states. In one, the All-Share yields 5 per cent, as it often did until the early 1990s. This implies an index value of around 2300. Think of this as a world in which economic volatility keeps shares cheaper than we have been used to in recent years. In the other state, the index yields 3 per cent - giving a level of just under 3900. This could be what we would get if the 'nice' decade returns.

You can now imagine the index's current value as signalling that we have a 70 per cent chance of entering state one, and a 30 per cent chance of entering state two. That is: (0.7 x 2300) + (0.3 x 3900) = 2780, which is roughly where we are as I write.

Now, imagine that the probability of entering state one - our bad state - were to rise by just one percentage point. Then, the price of the All-Share would become: (0.71 x 2300) + (0.29 x 3900) = 2764. This is a drop of 0.7 per cent.

In other words, tiny, reasonable changes in the probability we attach to differing but plausible states of the world can produce quite large moves in the index.


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