Quantitative Methods - Rates of Return

Different measures can be used when discussing potential rates of return.

The internal rate of return used in time value of money calculations cannot be directly found by formula. It can be approximated by trial and error, but in the real world, it is simply found by inputting present value, future value, and the number of compounding periods into a financial calculator. Several measures of return can be selected for such a calculation:

  • Internal rate of return (IRR) - This interest rate makes the net present value of a series of cash flows equal to zero. The IRR can only be calculated by trial and error (or with a financial calculator) unless the investment has only a single cash flow, in which case the calculation is as follows:


Internal rate of return = Payoff / Investment - 1

An example of this would be an investment of $1,000 that would return $1,100 in one year  The formula would produce 1100/1000 - 1 which equals 1.10 - 1 which equals .10 (10%).

Look Out!
The fact that internal rate of return presumes that the net present value of the inflows and outflows equals zero seems counterintuitive. It may be helpful to think of the internal rate of return as the discount rate at which the expected returns equal the initial investment. However, on the exam, "net present value equals zero" will be the correct answer.


  • Real return - This is also known as inflation-adjusted return. By adjusting the stated (nominal) return of an investment to consider inflation, the investor has a more realistic assessment of return. Learn more about this in the Measuring Portfolio Returns section on Bond Yields.
  • Expected return- This is the average of the probability distribution of possible returns, calculated by taking the probability of each possible return outcome and multiplying it by the return outcome, then adding each of these together to get the expected return.
  • Risk-adjusted return - This calculation allows an investor to determine if the amount of return received is commensurate with the risk taken. It incorporates both beta and the risk-free rate of return (typically the current rate of short-term Treasury bills).

Look Out!
Look for questions on both the definition of total return and the inflation component of real return. Any answers that involve risk are incorrect.

Look Out!
Consider this sample question:


A client buys a DEF 10% bond at 105. The bond matures in 10 years. What is the current yield?

  1. 10.17%
  2. 9.52%
  3. 9.69%
  4. 9.13%

The correct answer is "b", since current yield is found by dividing the annual interest payment (in this case $100) by the current market price (in this case $1.050).

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