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Price return vs income yield

Price return is the finish minus the start, over the start. Income yield is cash received over the start. A $100 holding that ends at $105 and pays $3 returns 5 percent from price and 3 percent from income. Total return is 8 percent, the sum of the two slices.

 Price returnIncome yield
Formula(P1P0)/P0(P_1 - P_0) / P_0.D/P0D / P_0. Income added once.
Teaching sheetBegin $100, end $105. Price return 5 percent.Income $3 on that same $100 start. Income yield 3 percent. Holding-period return 8 percent.
When the price falls$50 to $40 is -20 percent from price.$2 of income is a 4 percent yield. The sum is -16 percent. The coupon did not cancel the fall.
When the price is flat$80 to $80 is 0 percent from price.$4 of income is a 5 percent yield. The holding-period return equals that 5 percent.
What it is silent onCash received in the window. The 5 percent is not the 8 percent sum.The two quotes. The 3 percent is not a capital gain.
One firmThe $100 holding. Do not paste this 5 percent onto a Gordon dividend yield.The same $100 holding. Do not paste this $3 onto a different firm's price.

Two slices of one window

Holding-period return is price change plus income, over the start. The two pieces have names.

Price return is the quotes:

P1P0P0\frac{P_1 - P_0}{P_0}

On a $100 start and a $105 finish that is 5 percent. Income yield is cash over the start:

DP0\frac{D}{P_0}

On $3 of income that is 3 percent. Add them and total return is 8 percent.

How price return works owns the 5 percent. How income yield works owns the 3 percent. How total return works owns the 8 percent. The total return calculator is that split.

The $3 is added once. It is not grown inside the window. The ending price stays $105.

A coupon is not a price rise

Start $50, end $40, income $2. Price return is -20 percent. Income yield is 4 percent. The sum is -16 percent. Quoting the 4 percent as if it were the holding's return is how a loss gets dressed as a coupon.

Start $80, end $80, income $4. Price return is 0 percent. The window equals the 5 percent income yield. Two holdings can print 5 percent for opposite reasons: the price moved and paid nothing, or the price sat still and paid $4.

Do not paste this $3 onto a Gordon share. Income yield against dividend yield is that other pair, on two firms. This pair is one window. This is educational material, not financial advice.

Worked examples

\$100 to \$105 with \$3 of income

A holding starts at $100, ends at $105, and pays $3 of income in the window. What is price return, and what is income yield?

  1. Price return: (105100)/100=0.05(105 - 100) / 100 = 0.05, which is 5 percent.
  2. Income yield: 3/100=0.033 / 100 = 0.03, which is 3 percent.
  3. Holding-period return: (105100+3)/100=0.08(105 - 100 + 3) / 100 = 0.08, which is 8 percent.

Price return is 5 percent. Income yield is 3 percent. Holding-period return is 8 percent. Begin $100, end $105, income $3.

\$50 to \$40 with \$2 of income

A holding starts at $50, ends at $40, and pays $2. What is each slice?

  1. Price return: (4050)/50=0.2(40 - 50) / 50 = -0.2, which is -20 percent.
  2. Income yield: 2/50=0.042 / 50 = 0.04, which is 4 percent.
  3. Holding-period return: (4050+2)/50=0.16(40 - 50 + 2) / 50 = -0.16, which is -16 percent.

Price return is -20 percent. Income yield is 4 percent. Holding-period return is -16 percent. The $2 of income did not cancel the fall from $50 to $40.

A flat \$80 price with \$4 of income

A holding starts at $80, ends at $80, and pays $4. What is each slice?

  1. Price return: (8080)/80=0(80 - 80) / 80 = 0, which is 0 percent.
  2. Income yield: 4/80=0.054 / 80 = 0.05, which is 5 percent.
  3. Holding-period return equals the income yield: 5 percent.

Price return is 0 percent. Income yield is 5 percent. Holding-period return is 5 percent. Begin $80, end $80, income $4.

Common questions

Is a 5 percent price return a 5 percent total return?

Only if income is zero. On the first sheet price return is 5 percent and total return is 8 percent, because income added 3 percent.

Does income cancel a price fall?

Only if it is at least as large as the fall. On the second sheet $2 of income against the fall from $50 to $40 leaves a -16 percent total return.

Is income yield a dividend yield?

No. Income yield is cash in this window over the start. Dividend yield is an annual dividend over price, on a different teaching sheet.

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.