How price return works

Price return is what the quoted value did, with income left out:

$$\text{price return} = \frac{P_1 - P_0}{P_0}$$

On a $100 start and a $105 finish that is 5 percent. Income on this sheet is $3, a 3 percent income yield. The holding-period sum is 8 percent. Total return owns that 8 percent. How income yield works owns the 3 percent. This page owns the 5 percent.

The other walk is $P_1 / P_0 - 1$, which is the same 5 percent. $105 / 100 - 1 = 0.05$.

The total return calculator on this page splits the window into price change and income yield. The total return explorer holds the start still and lets you drag the finish. Price return against income yield is the two slices on one sheet.

Start $50, end $40, income $2. Price return is -20 percent. Income yield is 4 percent. The holding-period sum 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. This page owns the -20 percent. The cousin pages own the 4 percent and the -16 percent.

Start $80, end $80, income $4. Price return is 0 percent. Income yield is 5 percent. The holding-period sum is 5 percent.

When the price does not move, this page prints 0 percent and the window equals the income yield. That is a coupon period, not a claim that the holding cannot fall next time. Two holdings can print 5 percent for opposite reasons: the price moved and paid nothing, or the price sat still and paid $4. This page is only the first of those two stories.

It is not a capital gain in the tax sense. A capital gain is sale proceeds minus basis, realised when you sell. Price return is a quoted-value change over a window you name. The 5 percent on the first sheet can sit on a holding you never sold.

It is not a CAGR. CAGR is $\left(V_t / V_0\right)^{1/t} - 1$, an annualised return. Price return is one window, however long that window was. A 5 percent price return over six months is not 5 percent a year.

It is not income yield. Income is cash received. Price return is the two quotes. Adding them is how total return works.

A price return quoted without its dates is not a number anyone can use. The formula sees a start and a finish. It does not know whether that was a month, a year, or a decade.

The two quotes have to be the same object. Mixing an ex-dividend close with a cum-dividend open is how one holding looks like two. Income belongs in the income column, not pasted onto the finish.

It is not an annualiser, not a tax lot, and not a ranking of funds. The three sheets are $100 to $105 (5 percent price, 3 percent income, 8 percent total), $50 to $40 with $2 of income (-20 percent price), and a flat $80 price with $4 of income (0 percent price). This is educational material, not financial advice.