The Expected Rate of Return on Equities

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

rrs = gP + D/P

Where: P = The price of equities

gP = The growth rate of equity prices

D = Dividends

 

Note that: P = P/E * E

Where: P/E = The price-earnings ratio

E = Earnings (Corporate Profits)

 

Therefore:        gP = gP/E + gE

Note that:       D/P = (D/E) / (P/E)

Where:     D/E = Dividend-earnings ratio

A realistic short run example:

gP/E =1.5%

gE = 3.5%

D/E = 50%

P/E = 25

rrs = (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

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

Therefore:        gE = gE/Y + gY

Thus the long run equilibrium rate of return on stocks can be expressed as:

rrL = (gE/Y + gY) + (D/E) / (P/E)

It is likely that in long run equilibrium, the E/Y ratio will also be constant (gP/E = 0). If so, the long run rate of return becomes simply:

rrL = gY + (D/E) / (P/E)

An example based on the SS Trustees growth assumptions:

 

gY = 1.5%

D/E = 50%

P/E = 25

rrL = gY + (D/E) / (P/E)

3.5% = 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)

7% = 1.5% + 50% / 9

7% = 1.5% + 5.5%

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