Required versus Expected Rates of Return: The Role of Efficient Markets
We have defined two ex ante (before the fact) measures of interest rates. The required rate of return is used to calculate a fair present value of a financial security, while the expected rate of return is a discount rate used in conjunction with the current market price of a security. As long as financial markets are efficient (see below), the current market price of a security tends to equal its fair price present value. This is the case most of the time. However, when an event occurs that unexpectedly changes interest rates or a characteristic of a financial security (e.g., an unexpected dividend increase, an unexpected decrease in default risk), the current market price of a security can temporarily diverge from its fair present value. When investors determine a security is undervalued (i.e., its current market price is less than its fair present value), demand for the security increases, as does its price. Conversely, when investors determine a security is overvalued (i.e., its current market price is greater than its fair present value), they will sell the security, resulting in a price drop. The speed with which financial security prices adjust to unexpected news, so as to maintain equality with the fair present value of the security, is referred to as market efficiency
Realized Rate of Return
Required and expected rates of return are interest rate concepts pertaining to the returns expected or required just prior to the investment being made. Once made, however, the market participant is concerned with how well the financial security actually performs. The realized rate of return ( r ) on a financial security is the interest rate actually earned on an investment in a financial security. The realized rate of return is thus a historical interest rate of return it is an ex post (after the fact) measure of the interest rate on the security To calculate a realized rate of return ( r ), all cash flows actually paid or received are incorporated in time value of money equations to solve for the realized rate of return. By setting the price actually paid for the security ( P ) equal to the present value of the realized cash flows ( RCF 1 , RCF 2 , . . . , RCF n ), the realized rate of return is the discount rate that just equates the purchase price to the present value of the realized cash flows. That is:
Realized Rate of Return
Required and expected rates of return are interest rate concepts pertaining to the returns expected or required just prior to the investment being made. Once made, however, the market participant is concerned with how well the financial security actually performs. The realized rate of return ( r ) on a financial security is the interest rate actually earned on an investment in a financial security. The realized rate of return is thus a historical interest rate of return it is an ex post (after the fact) measure of the interest rate on the security To calculate a realized rate of return ( r ), all cash flows actually paid or received are incorporated in time value of money equations to solve for the realized rate of return. By setting the price actually paid for the security ( P ) equal to the present value of the realized cash flows ( RCF 1 , RCF 2 , . . . , RCF n ), the realized rate of return is the discount rate that just equates the purchase price to the present value of the realized cash flows. That is:
If the realized rate of return ( r ) is greater than the required rate of return ( r ), the market participant actually earned more than was needed to be compensated for the ex ante or expected risk of investing in the security. If the realized rate of return is less than the required rate of return, the market participant actually earned less than the interest raterequired to compensate for the risk involved
The valuation of a bond instrument employs time value of money concepts. The fair value of a bond reflects the present value of all cash flows promised or projected to be received on that bond discounted at the required rate of return ( r b ). Similarly, the expected rate of return, E(r b ) , is the interest rate that equates the current market price of the bond with the present value of all promised cash flows received over the life of the bond. Finally, a realized rate of return ( r b ) on a bond is the actual return earned on a bond investment that has already taken place. Promised cash flows on bonds come from two sources: (1) interest or coupon payments paid over the life of the bond and (2) a lump sum payment (face or par value) when a bond matures
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