Understanding Returns

The conventional way to express the return on security (and investments in general) is in percentage terms. This is because it does not 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 changes each year. When the length of the investment is one year, the total and annual returns are equivalent.

Total Returns

The total percentage return is based on the final value (V_f), the initial value (V_i), and all dividend payments or additional incomes (D). 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.

\(\text{Return }=\dfrac{V_f - V_i+D}{V_i}\)

This type of return is 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 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):

\(CAGR=(\dfrac{V_f}{V_i})^{\dfrac{1}{t}}-1\)

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). The IRR is the discount rate at which the net present value (NPV) equals 0.