How total return works

Total return is the holding-period return: what the price did, plus what the holding paid, over what you started with:

$$\text{HPR} = \frac{P_1 - P_0 + D}{P_0}$$

On a $100 start, a $105 finish and $3 of income, the price change is $5 and the total gain is $8. Over $100 that is 8 percent: 5 percent from price and 3 percent from income.

The total return calculator on this page is that split. The total return explorer holds the start still and lets you drag the finish. How dividend yield works is the income piece when $D$ is a dividend and the period is a year. This page is the whole holding-period sum.

Total return against CAGR is one period against a root over $t$ years.

The 5 percent price slice has its own page. How price return works owns that 5 percent. This page owns the 8 percent sum.

Price return against income yield is the two slices on one sheet: 5 percent from the quotes, 3 percent from the cash, 8 percent when they sit together.

Start $50, end $40, income $2. Price change is -20 percent. Income yield is 4 percent. Total return is -16 percent.

The $2 of income is real. It does not make the fall from $50 to $40 go away. Quoting the 4 percent income yield as if it were the holding's return is how a loss gets dressed as a coupon. The first sheet's 8 percent added a 5 percent price rise to a 3 percent income yield. This sheet adds a 4 percent income yield to a 20 percent price fall. Income is added once, in the same window as the two prices. It is not a second year of coupon pasted onto a one-period loss.

Start $80, end $80, income $4. Price change is 0 percent. Income yield is 5 percent. Total return is 5 percent.

When the price does not move, total return equals the income yield. That is a coupon year, not a claim that the holding cannot fall next period. The 5 percent is the same rate as the first sheet's price change, reached here entirely from income. Two holdings can print 5 percent for opposite reasons: the price moved and paid nothing, or the price sat still and paid $4.

How dividend yield works is this income piece when $D$ is a dividend and the window is a year. This page is still the whole holding-period sum.

It is not a CAGR. CAGR is $\left(V_t / V_0\right)^{1/t} - 1$, an annualised return. Total return is one window, however long that window was. An 8 percent holding-period return over six months is not 8 percent a year.

It is not a money-weighted IRR. Deposits in the middle need dated cash flows. How money-weighted return works is that other rate.

It is not a real return. Inflation is not in this split. How real returns work takes the Fisher step.

A total return quoted without its dates is not a number anyone can use. The formula sees two values and one income line. It does not know whether that was a month, a year, or a decade.

Income has to be cash received in the window, not an indicated annual yield pasted onto a shorter stretch. Mixing an annual dividend with a three-month price change is how one holding looks like two.

It is not an annualiser, not an IRR, and not a ranking of funds. The three sheets are $100 to $105 with $3 of income (8 percent: 5 percent price, 3 percent income), $50 to $40 with $2 (-16 percent), and a flat $80 price with $4 of income (5 percent). Income is added once. This is educational material, not financial advice.