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The real dividend yield on a stock index is the same as the nominal yield. No inflation adjustment is appropriate.
There has been some confusion on this issue, perhaps stemming from the convention of stating the dividend rate in terms of dollars/year, regardless of the time frame under consideration. This does not, however, mean that that number of dollars has been or will be paid over the course of a full year. Just as a speedometer reading in your car of 40 miles per hour does not mean you have driven a distance of 40 miles over the past hour. It is an instantaneous rate. It is the distance you would travel if you maintained the same speed over a full hour.
Likewise, the term "indicated dividend" is used to denote the current rate of dividend payment. It does not denote a full years' dividend, but rather expresses the current rate in annualized form. It is the dividend you would be paid if you maintained the same rate over a full year.
It can be demonstrated mathematically that the real yield on a stock index is identical to the nominal yield. There are any number of ways of doing this; see, for example, this discussion at Morningstar (http://socialize.morningstar.com/New...81/152981.aspx):
This may be illustrated with actual data. Robert Shiller, professor of economics at Yale University and author of the book Irrational Exuberance, has put together a long term series of the S&P 500 price, earnings, and yield data that can be accessed at http://www.econ.yale.edu/~shiller/data.htm. The following is a sample of data from his series:
S&P 500
Note that Shiller includes both a nominal & real price and a nominal & real dividend. We can therefore calculate both a nominal and real yield directly from Shiller’s data. Below we add two more columns for this purpose:
The first is the "Nominal Yield" - the "Dividend" divided by the "Price";
The second is the "Real Yield" - "Real Dividend" divided by the "Real Price":
S&P 500
Of course, as expected from the formula above showing cancelation of the inflation term, in each case the "Real Yield" equals the "Nominal Yield". Interested readers can download Shiller's data and try it themselves.
Another route involves calculating a total return, both nominal and inflation adjusted. One can apply an inflation adjustment to a total return, and also apply an inflation adjustment to the price return and dividend return individually. But if one does so, the total inflation adjusted return does not equal the combination of the inflation adjusted price and inflation adjusted dividend returns!
The contradictory result betrays a flaw in the premises: in this case, the premise that one adjusts the dividend return for inflation.
In order to get mutually consistent results, one must adjust only the price return and total return, not the dividend yield. Only if one applies the inflation adjustment to the price return and omits an inflation adjustment to the dividend return, does the resulting combination give the same result as applying the inflation adjustment to the total return.
This can be illustrated with numbers as well:
Suppose you start with $1000 in a stock index that over the course of one year has no net price change and yields a 5% dividend. Over the same year, there is 5% inflation. One year later you have $1050, which after the 5% inflation has the same purchasing power as the $1000 you started with. Your real total return is 0%.
But if you first break that total return down into price and yield components, apply the 5% inflation adjustment to both of them, then recombine them to get total return, you get -5% plus 0% equals -5%. Specifically, the $1000 price stayed the same, so you back out 5% inflation to get -5%. The dividend return was 5%, so you back out 5% to get 0%. Then add them to get a real total return of -5%. This is incorrect - we just saw in the last paragraph that the real total return was 0%.
Since the inflation adjustment to the price is correct, the source of the error must be in the adjustment to the dividend. It's double-counted inflation.
Consequently, if you want to find real total return by adjusting the price and yield separately, you must adjust only the price, not the yield.
There has been some confusion on this issue, perhaps stemming from the convention of stating the dividend rate in terms of dollars/year, regardless of the time frame under consideration. This does not, however, mean that that number of dollars has been or will be paid over the course of a full year. Just as a speedometer reading in your car of 40 miles per hour does not mean you have driven a distance of 40 miles over the past hour. It is an instantaneous rate. It is the distance you would travel if you maintained the same speed over a full hour.
Likewise, the term "indicated dividend" is used to denote the current rate of dividend payment. It does not denote a full years' dividend, but rather expresses the current rate in annualized form. It is the dividend you would be paid if you maintained the same rate over a full year.
It can be demonstrated mathematically that the real yield on a stock index is identical to the nominal yield. There are any number of ways of doing this; see, for example, this discussion at Morningstar (http://socialize.morningstar.com/New...81/152981.aspx):
I think you are correct dividend yield, also earnings yield, are real rates like TIPS real rate.
Both are ratios of two nominal values so the inflation adjustment terms cancel
Dividend Yield = Nominal Dividend / Nominal Price
= infadj* Real Dividend / infadj * Real Price
= Real Divided / Real Price
where infadj = CPI(today)/CPI(base year)
So comparing dividend yield and P/E to nominal interest rates makes no sense.
Both are ratios of two nominal values so the inflation adjustment terms cancel
Dividend Yield = Nominal Dividend / Nominal Price
= infadj* Real Dividend / infadj * Real Price
= Real Divided / Real Price
where infadj = CPI(today)/CPI(base year)
So comparing dividend yield and P/E to nominal interest rates makes no sense.
S&P 500
| Date | Price | Dividend | CPI | Real Price | Real Dividend |
|---|---|---|---|---|---|
| 2000.01 | 1425.59 | 16.5733 | 168.8 | 1602.10 | 18.6254 |
| 2000.02 | 1388.87 | 16.6667 | 169.8 | 1551.64 | 18.6200 |
| 2000.03 | 1442.21 | 16.7600 | 171.2 | 1598.06 | 18.5711 |
| 2000.04 | 1461.36 | 16.7400 | 171.3 | 1618.33 | 18.5381 |
Note that Shiller includes both a nominal & real price and a nominal & real dividend. We can therefore calculate both a nominal and real yield directly from Shiller’s data. Below we add two more columns for this purpose:
The first is the "Nominal Yield" - the "Dividend" divided by the "Price";
The second is the "Real Yield" - "Real Dividend" divided by the "Real Price":
S&P 500
| Date | Price | Dividend | CPI | Real Price | Real Dividend | Nominal Yield | Real Yield |
|---|---|---|---|---|---|---|---|
| 2000.01 | 1425.59 | 16.5733 | 168.8 | 1602.10 | 18.6254 | 0.01163 | 0.01163 |
| 2000.02 | 1388.87 | 16.6667 | 169.8 | 1551.64 | 18.6200 | 0.01200 | 0.01200 |
| 2000.03 | 1442.21 | 16.7600 | 171.2 | 1598.06 | 18.5711 | 0.01162 | 0.01162 |
| 2000.04 | 1461.36 | 16.7400 | 171.3 | 1618.33 | 18.5381 | 0.01146 | 0.01146 |
Of course, as expected from the formula above showing cancelation of the inflation term, in each case the "Real Yield" equals the "Nominal Yield". Interested readers can download Shiller's data and try it themselves.
Another route involves calculating a total return, both nominal and inflation adjusted. One can apply an inflation adjustment to a total return, and also apply an inflation adjustment to the price return and dividend return individually. But if one does so, the total inflation adjusted return does not equal the combination of the inflation adjusted price and inflation adjusted dividend returns!
The contradictory result betrays a flaw in the premises: in this case, the premise that one adjusts the dividend return for inflation.
In order to get mutually consistent results, one must adjust only the price return and total return, not the dividend yield. Only if one applies the inflation adjustment to the price return and omits an inflation adjustment to the dividend return, does the resulting combination give the same result as applying the inflation adjustment to the total return.
This can be illustrated with numbers as well:
Suppose you start with $1000 in a stock index that over the course of one year has no net price change and yields a 5% dividend. Over the same year, there is 5% inflation. One year later you have $1050, which after the 5% inflation has the same purchasing power as the $1000 you started with. Your real total return is 0%.
But if you first break that total return down into price and yield components, apply the 5% inflation adjustment to both of them, then recombine them to get total return, you get -5% plus 0% equals -5%. Specifically, the $1000 price stayed the same, so you back out 5% inflation to get -5%. The dividend return was 5%, so you back out 5% to get 0%. Then add them to get a real total return of -5%. This is incorrect - we just saw in the last paragraph that the real total return was 0%.
Since the inflation adjustment to the price is correct, the source of the error must be in the adjustment to the dividend. It's double-counted inflation.
Consequently, if you want to find real total return by adjusting the price and yield separately, you must adjust only the price, not the yield.
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