What does it mean when we say that a stock has a duration of 100 years?

It is both interesting and exotic to note that equities also have duration, i.e. they have interest rate sensitivity. In fact equities have a very high duration (hence if duration is the measure of the first order risks then stocks are very risky instruments). And this sensitivity to interest rate is expressed via the dividend yield of a stock (stock index). Interest rate volatility can significantly impact the price and value of equities if equilibrium is not maintained by the dividend yield.

The risk of a stock, if measured through its duration, is impacted most by the dividend yield. Quantitatively, the duration of a stock can be expressed as:

__Proof of the above__ :

We will take the dividend growth model to value (price) a stock. If is the initial dividend (say, as of today) that a stock pays, is the growth rate of that dividend and is the rate of return (that investors expect from the stock) then the price of the stock is given by:

The short term interest rates in an economy will directly and linearly affect and therefore to capture the variation of the stock price with respect to the interest rate we can write:

Thus the duration, the interest rate sensitivity, of the stock will be given by:

*End of the Proof *

The above makes perfect intuitive sense. Why do investors invest in stocks? To make money on their investment by participating in the profits of the company (let's for the moment forget of high growth tech and dot com stocks which pay no dividend but are still sometimes valued very dearly). So, higher the dividend yield (dividend as a ratio of the price of the stock) the better is the investment in that stock and hence lower the risk and vice versa. If the dividend yield of a stock is low (or zero!!) then the stock is more risky because either the company is not making money to pay profit to shareholders or the money that it is making is being sucked into the operations (invested back in) of the company and which may or may not yield a future profit (for the investor).

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