How income yield works

Income yield is the cash the holding paid, over what you started with:

$$\text{income yield} = \frac{D}{P_0}$$

On a $100 start and $3 of income that is 3 percent. The ending price on this sheet is $105. Price change is 5 percent. The holding-period sum is 8 percent. How total return works owns that 8 percent. This page owns the 3 percent.

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. Income yield against dividend yield is this one-period slice against annual cash over price, on two different firms.

The other slice is the quotes. How price return works owns the 5 percent on this sheet. This page owns the 3 percent.

The $3 is added once, as $D$. It is not compounded inside the window. The ending price is still $105. Grow the $3 at any rate and you have left this formula.

That is a one-period convention, not a claim about what a fund does with a dividend after the ex date. Total return as an index series often assumes reinvestment. This sheet does not. Name the convention before lining two numbers up.

How the CAGR formula works has no income column. If the cash is still in the account, it is already inside the ending value. There is no separate $D$ to add after a root.

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

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

When the price does not move, the window equals the income yield. That is a coupon period, not a claim that the holding cannot fall next time. The 5 percent here is this page's slice. It happens to equal the sum because the price term is zero.

Dividend yield is an annual dividend over the share price. Trailing uses the dividend just paid. Implied uses next year's. How dividend yield works is that fraction, on a Gordon teaching sheet this page does not take.

Income yield is cash received in this window over the beginning value. The window can be a month, a year, or a decade. The formula does not know the dates. Mixing an annual dividend yield with a three-month income yield is how one holding looks like two.

A yield quoted without naming the cash and the dates is not a number anyone can use. Coupon yield, dividend yield, and this income slice share a family name and do not share a sheet.

It is not an annualiser, not a reinvestment model, and not a dividend screen. The three sheets are $3 on a $100 start (3 percent), $2 on a $50 start (4 percent), and $4 on a flat $80 price (5 percent). This is educational material, not financial advice.