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Expected returns

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asked Sep 9, 2018 in BUS 4027W - Actuarial Risk Management by anonymous

For chapter 22, page 6: 

They say the price of equity (with dividends paid in perpetuity) is equal to (dividend/dividend yield)

However, is the formula not:

D1/(i-g) where D1 is the dividends received in a year's time. 

They go on to say that:

1+i = (1+d)(1+g) 

I am not sure how they arrived at this equation ?

1 Answer

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answered Sep 10, 2018 by Rowan (4,010 points)


In the notes, they state that the price of an equity investment can be expressed as \(price = \frac{dividend}{dividend \space yield}\). This does not mean that it is the only formula for the price of an equity, just that it is the way they are looking at the price of equity in this section in order to make their point. The formula for the price of an equity which you give is also correct, and is simply another way to express the price of an equity.

As for the expression \(1+i = (1+d)(1+g) \), this is not related to equities in particular, but rather it is a comment on the fact that when an asset has both an income yield (d) and capital growth (g), the expected return should be written multiplicatively (as in the expression given), but sometimes to simplify matters an assumption of \(i = d + g\) is used instead.

commented Sep 16, 2018 by Mufaro (540 points)


Also, by definition: dividend yield = (dividend/price). They just rearranged this formula.

The price here could have been calculated using the perpetuity formula you've mentioned.