Understanding Returns
This article will help you define and distinguish realized returns from unrealized returns. By the end of this section, you will be able to calculate an investment's dollar return and percentage return. You will also be able to describe how to use historical and average returns to predict future performance.
Percentage Returns
Percentage returns show how much the value of the investment has changed in proportion to the size of the initial investment.
LEARNING OBJECTIVE
-
Calculate an investment's percentage return using CAGR
KEY POINTS
- Total percentage returns divide the dollar returns by the initial value of the investment. This is also the return on investment (ROI).
- Annual returns show the percentage by which the value of the asset changes in each individual year.
- Average annual percentage returns can be calculated
by dividing ROI by the number of years, or by other methods such as the
compound annual growth rate (CAGR) or internal rate of return (IRR).
TERMS
- compound annual growth rate
CAGR. A method for finding the average annual return of an investment.
- return on investment
ROI. The dollar return of the investment divided by the initial value.
- internal rate of return
IRR. The rate of return on an investment which causes the net present value of all future cash flows to be zero.
The conventional way to express the return on a security (and investments in general) is in percentage terms. This is because it does not only matter how much money was earned on the investment, it matters how much was earned in proportion to the cost.
There are two types of percentage returns: total and annual. Total returns calculate how much the value of the investment has changed since it was first purchased, while annual returns calculate how much the value changed each year. When the length of time of the investment is one year, the total and annual returns are equivalent.
Total Returns
The total percentage return is based off of the final value (
), the initial value (
),
and all dividend payments or additional incomes (
). If the investment
is a security such as a stock, the final value is the sales price,
the initial value is the purchase price, and D is the sum of all
dividends received.
This type of return is also called the return on investment (ROI), where the numerator is the dollar return.
Annual Returns
In , the ROI is calculated for each individual year by dividing the dollar return by the initial value of $1,000. To find the return for the security overall, simply sum the dollar returns and divide by the initial value. The ROI can be annualized by dividing by the number of years between the purchase and sale of the security. This is the arithmetic mean of the return.
Cash Flow Return: The ROI is the percentage return, and is calculated by dividing the dollar return by the initial value of the investment ($1,000).
However, this does not fully take into consideration compounding. To do so, analysts use other formulas, like the compound annual growth rate (CAGR):
In this case, the only variable that differs from the previous formula is t, which is the number of years between the beginning and end of the investment. CAGR is a way of measuring the return per year. It is widely used because it allows for the easy comparison of the growth rates of multiple investments.
Another common method for finding the annual return is to calculate the internal rate of return (IRR). Recall that the IRR is the discount rate at which the net present value(NPV) equals 0.