Financial Economics Rate-of-Return and Present Value
Two Equivalent Conditions
The traditional theory of present value puts forward two
equivalent conditions for asset-market equilibrium:
Rate of Return The expected rate of return on an asset equals
the market interest rate;
Present Value The asset price equals the present value of
expected future payments.
We explain these two conditions and show that they are
equivalent—either condition implies the other.
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Financial Economics Rate-of-Return and Present Value
Market Interest Rate
The rate-of-return condition says just that all assets share a
common expected rate of return. The “market interest rate”
refers to the expected rate of return common to all assets.
We assume that the market interest rate R>0 is constant.
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Financial Economics Rate-of-Return and Present Value
Notation
Consider an asset with payment $tat time t. For a stock, the
payment would be the dividend. For a bond, the payment
would be interest or principal.
Let P
tdenote the asset price at time t.
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Financial Economics Rate-of-Return and Present Value
Expected Rate of Return
Definition 1 (Return) The return is the profit divided by the
amount invested.
Definition 2 (Expected Rate of Return) The expected rate of
return is the expected return divided by the length of the time
period.
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Financial Economics Rate-of-Return and Present Value
Disequilibrium
If the expected rate of return were greater than the market
interest rate, the security would be seen as a “good buy.”
Investors would like to buy the security; those holding the
security would not want to sell it. Demand would exceed
supply. The reverse inequality would lead to excess supply.
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Financial Economics Rate-of-Return and Present Value
Present Value
Definition 3 (Present Value) The present value of a payment
to be received in the future is the dollars attainable now by
borrowing against the future payment.
Definition 4 (Discount Factor) The present value is the future
payment multiplied by the discount factor.
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