I. The Short Run Rate of Return on Equities (rr)

rr= gP + D/P

Where:

gP = The growth rate of equity prices

D = Dividends

P = The price of equities

Note that: P = P/E*E

Where: P/E = Price-earnings ratio

E = Earnings

Therefore: gP = gP/E + gE

Note that: D/P = (D/E)/ (P/E)

A realistic short run example:

gP/E = 1.5%

gE = 3.5%

D/E = 50%

P/E =25

rr = (gP/E +gE) + (D/E)/ (P/E)

7% = (1.5% + 3.5%) + 50% / 25

7% = 5% + 2%

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II. The Long Run Rate of Return on Equities (rrL)

In the long run equilibrium, the P/E ratio is assumed to be constant (gP/E = 0)

Since: gP = gP/E + gE

In long run equilibrium gP = gE

(The growth of prices equals the growth of earnings)

Therefore, the long run equilibrium rate of return on equities is:

rrL = gE + D/P

Note that : E = (E / Y) * Y

Where: (E /Y) = the share of GDP going to capital

Y = GDP

Thus: gE = g(E/Y) + gY

The long run rate of return on stocks can b e expressed as:

rrL = (g(E/Y) + gY) + (D/E) /(P/E)

It is likely that the E/Y ratio will be constant.

Therefore: (g(E/Y) = 0)

If so, the long run rate of return becomes simply:

rrL = gY + (D/E)/(P/E)

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An example based on the SS Trustees growth assumptions:

gY = 1.5%

D/E = 50%

P/E = 25

rrL = gY + (D/E)/(P/E)

rrL = 1.5% + 50% / 25

3.5% = 1.5% + 2%

 To get a long run rate of return of 7%, the P/E ratio would have to fall from 25 to 9. (An immediate 64% decline in stock prices).*

rrL = gY + (D/E)/(P/E)

rrL = 1.5% + 50% / 9

7% = 1.5% + 5.5%

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*An increase in the Dividend/ Earning ratio (D/E) would raise the rate of return temporarily; but this would slow the rate of investment and lower the growth rate of GDP (gY).