
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:
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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 yearÂ The formula would produce 1100/1000  1 which equals 1.10  1 which equals .10 (10%).
Â
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.
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Real return  This is also known as inflationadjusted 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.
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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.
Â  Riskadjusted 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 riskfree rate of return (typically the current rate of shortterm 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:
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A client buys a DEF 10% bond at 105. The bond matures in 10 years. What is the current yield?
 10.17%
 9.52%
 9.69%
 9.13%
IntroductionThe 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).

Professionals
Measuring Portfolio Returns
NASAA Series 65: Section 16 Measuring Portfolio Returns. In this section different types of risk measures discussed and some sample questions. 
Professionals
Rates of Return  Internal Rate of Return
FINRA/NASAA Series 65  Rates of Return  Internal Rate of Return. In this section Internal rate of return, real return, riskadjusted return, beta and total return. 
Professionals
Introduction
FINRA/NASAA Series 66: Section 2 Measuring Portfolio Returns. This section discusses different return measures: return on investment, holding period, annualized, risk free and total returns. 
Fundamental Analysis
Explaining Expected Return
The expected return is a tool used to determine whether or not an investment has a positive or negative average net outcome. 
Required Return, Discount Rate and IRR: Concepts & Examples
Required return is a minimum level of rate of return that investors would agree to accept for a particular investment as compensation for delaying consumption and taking risk. This is also called ... 
Term
What's a Real Rate of Return?
A real rate of return is an annual percentage investment return thatâ€™s adjusted for inflation, taxes or other factors. 
Professionals
Bond Yields
FINRA/NASAA Series 66: Section 2 Bond Yields. This section discusses different bond yields: yield to maturity, yield to call, current yield, real interest rate 
Professionals
How To Measure Returns On The Series 65 Exam
An investor who is evaluating the performance of a portfolio manager must take into consideration the impact that any contributions or withdrawals made by the investor will have on the overall ... 
Professionals
Other Terms
FINRA/NASAA Series 66: Section 2 Other Terms. This section discusses measures of portfolio return: risk premium, expected return and benchmark portfolios. 
Fundamental Analysis
Calculating the Internal Rate of Return Using Excel
The internal rate of return on investments is explained and illustrated in different investment scenarios.

InflationAdjusted Return
A measure of return that accounts for the return period's inflation ... 
MoneyWeighted Rate Of Return
A measure of the rate of return for an asset or portfolio of ... 
Mean Return
1. In securities analysis, it is the expected value, or mean, ... 
Estimated LongTerm Return
A unit investment trust's estimated return over the life of the ... 
Target Return
A pricing model that prices a business based on what an investor ... 
Average Return
The simple mathematical average of a series of returns generated ...

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