Valuations and Dividend-Based Strategies

Valuations affect Dividend-Based Strategies. Everyone is aware that prices affect yields. But they do more. They affect multiples. High valuations can cause the speculative return to become negative.

Dividend-Based Strategies

A retiree withdraws a fraction of his dividends and reinvests the rest. He reinvests what remains to replace stocks in companies that do poorly or fail. He hopes that his dividend amount will increase enough to match inflation or do even better.

History tells us that he is likely to succeed.

What is more: his income stream should last indefinitely, well into the foreseeable future.

The Dividend Discount Model

A person who is investing for the future will do well to take note of the Dividend Discount Model and what it has to say. It shows up in many forms. Perhaps, it is best to start with John Bogle’s formula and work backwards.

John Bogle divides the total return from stocks into two components: the investment return and the speculative return. You see various forms of the Dividend Discount Model for estimating the investment return.

The basic form of the Dividend Discount Model is: the investment return = the initial dividend yield + the dividend growth rate.

John Bogle prefers to use the earnings growth rate instead of the dividend growth rate. His formula for the investment return is: the investment return = the initial dividend yield + the earnings growth rate.

Mathematically, if the dividend payout ratio remains constant, the dividend growth rate and the earnings growth rate are identical. Dividend growth rates have been erratic. But the growth rate of smoothed earnings (i.e., the average of several years of earnings) has been highly predictable.

For our purposes, we simply note that your (percentage) investment return is proportional to the initial (percentage) dividend yield plus a (percentage) number that is (reasonably) predictable and steady. At least, this holds for an index that includes many companies such as the S&P500.

Hidden within the mathematics are assumptions about the availability of suitable reinvestments. The Dividend Discount Model is excellent in the intermediate-term. It fails in the short-term because there is a lot of year-to-year randomness in stock prices. It fails in the very long-term because of reversion to the mean. That is, prices are tied to earnings even if only loosely.

There are many other variants as well.

For more about the Dividend Discount Model, see Professor Peter Ponzo’s (Gummy’s) tutorial.
Gummy's Dividend Discount Model Tutorial

The Speculative Return

The other component is the speculative return. The amount that people will pay for an income stream varies with time. To the extent that price multiples increase, so does the total return. When price multiples decrease, the total return decreases.

There are many reasons for multiples to vary. Demographics is one. Baby Boomers are bidding up stock prices to finance their retirements. This will persist until 2018 (or so). Much more important are psychological perceptions. People have seen an extended period of rising stock prices. They expect it to continue. When cautioned about the disconnect between prices and earnings, they remember hearing such warnings a decade ago. Yet, prices continued to rise. Many are convinced that the bubble has finished popping in spite of what history tells us.

Total Returns versus Valuations with and without Dividend

I used my Deluxe Calculator Version 1.1A08, which is a modified version of the Retire Early Safe Withdrawal Calculator (version 1.61, dated November 7, 2002). I set the initial balance to $100000. I set the stock allocation to 100%. I set the withdrawal rate to 0.000%. I set expenses to 0.00%. I adjusted for inflation by using the CPI. I varied the dividend reinvestments.

Here are the regression equations of the real, annualized total return as y versus the percentage earnings yield 100E10/P (or 100%/[P/E10]) as x. I have based these on the years 1923-1972.

I have included withdrawals beyond the amount of the dividend itself. For example, a dividend reinvestment of –50% means that I removed the entire dividend and I withdrew an additional amount equal to 50% of the dividend.

At year 10:
1) With 100% of dividends reinvested, y = 1.5247x-4.5509. R-squared = 0.4135. Confidence limits: plus and minus 6% (eyeball estimates).
2) With NO dividends reinvested, y = 1.2692x-7.4542. R-squared = 0.2934. Confidence limits: plus and minus 7% (eyeball estimates).
3) With -50% of dividends reinvested, y = 1.1391x-8.9081. R-squared = 0.2292. Confidence limits: plus 8% and minus 7% (eyeball estimates).
4) With -100% of dividends reinvested, y = 1.0069x-10.363. R-squared = 0.1688. Confidence limits: plus 8% and minus 7% (eyeball estimates).
5) With -200% of dividends reinvested, y = 0.7343x-13.276. R-squared = 0.0738. Confidence limits: plus 10% and minus 7% (eyeball estimates).

At year 20:
1) With 100% of dividends reinvested, y = 1.0849x-1.4488. R-squared = 0.5096. Confidence limits: plus and minus 4% (eyeball estimates).
2) With NO dividends reinvested, y = 0.9537x-5.0299. R-squared = 0.4164. Confidence limits: plus and minus 4% (eyeball estimates).
3) With -50% of dividends reinvested, y = 0.8865x-6.8231. R-squared = 0.3467. Confidence limits: plus and minus 4% (eyeball estimates).
4) With -100% of dividends reinvested, y = 0.818x-8.6182. R-squared = 0.2726. Confidence limits: plus and minus 5% (eyeball estimates).
5) With -200% of dividends reinvested, y = 0.6758x-12.213. R-squared = 0.1435. Confidence limits: plus and minus 6% (eyeball estimates).

At year 30:
1) With 100% of dividends reinvested, y = 0.4159x+3.764. R-squared = 0.3018. Confidence limits: plus and minus 2% (eyeball estimates).
2) With NO dividends reinvested, y = 0.2902x+0.3906. R-squared = 0.2252. Confidence limits: plus and minus 2% (eyeball estimates).
3) With -50% of dividends reinvested, y = 0.2263x-1.3014. R-squared = 0.1387. Confidence limits: plus and minus 2% (eyeball estimates).
4) With -100% of dividends reinvested, y = 0.1615x-2.9971. R-squared = 0.0602. Confidence limits: plus and minus 3% (eyeball estimates).
5) With -200% of dividends reinvested, y = 0.0288x-6.4009. R-squared = 0.001. Confidence limits: plus and minus 4% (eyeball estimates).

Lessons at year 10

Even if you reinvest all of your dividends, you can lose money at year 10. This happened in 1965-1973. There was also a very small loss in 1937. The biggest earnings yield with a loss was 5.35% in 1973 (with P/E10 = 18.7).

The Calculated Rate was always positive in the years 1923-1972. The total return is equally likely (50%-50%) to be above or below the Calculated Rate.

When I removed all of the dividends, there was always the possibility of a loss. Surprisingly, there was even a loss in 1932 with P/E10 = 9.3 (and an earnings yield of 10.75%). The Calculated Rate was zero when the percentage earning yield 100E10/P was 5.9 and P/E10 = 17.0.

The slope of the Calculated Rate was always positive, regardless of how much I withdrew. At year 10, the odds of getting a positive return (instead of sustaining a loss) improve as the percentage earnings yield increases (and as prices decrease).

Lessons at year 20

If you reinvest all of your dividends, you are likely to recover any losses and make money by year 20. Applying the equation, the lower confidence limit, which is 4% less than the Calculated Rate, equals zero when the earnings yield equals 5.0% and P/E10 = 20. There were no years with losses at year 20 in the actual record.

When I removed all of the dividends, there was always the possibility of a loss. The Calculated Rate is zero when the earnings yield is 5.3% and P/E10 = 19.0. There was even a loss in 1927 when the earnings yield was 7.58% and P/E10 = 13.2.

The slope of the Calculated Rate was always positive, regardless of how much I withdrew. At year 20, the odds of getting a positive return (instead of sustaining a loss) improve as the percentage earnings yield increases (and as prices decrease).

Lessons at year 30

If you reinvest all of your dividends, you are virtually certain to make money by year 30. Applying the equation: the lower confidence limit, which is 2% less than the Calculated Rate, never falls to zero. The lowest gain at year 30 starting in 1923-1972 was 4.01% in 1965.

When I removed all of the dividends, there were no instances in the actual 1923-1972 record of a loss at year 30. The Calculated Rate never falls to zero. The lower confidence limit, which is 2% less than the Calculated Rate, equal zero when the earnings yield is 5.4% and P/E10 = 18.0.

The slope of the Calculated Rate gradually fell as I withdrew more and more. It was very close to zero when I removed the dividend and withdrew an additional amount equal to twice the dividend. At year 30, the odds of getting a positive return (instead of sustaining a loss) improve as the percentage earnings yield increases (and as prices decrease) unless you withdraw heavily.

The Speculative Adjustment

Notice that the slope of the Calculated Rate is high at 10 and 20 years. The slope at year 10 is 1.5247 if you reinvest all dividends and 1.2692 if you remove all dividends. The slope at year 20 is 1.0849 if you reinvest all dividends and 0.9537 if you remove all dividends.

Every 1.0% increase in earnings yield improves your total return by 1.0% to 1.5% annually over the next two decades.

The odds of making a gain are better than 50%-50% at year 10 when P/E10 is 17 or less even if you withdraw all dividends. You need to reinvest some of your dividends when valuations are higher. The odds are 50%-50% at year 20 when P/E10 = 19 (or less).

What this Means

The earnings yield is currently in the range of 3.5%.

If P/E10 falls to 20 at the top of the bubble region, dividend-based strategies will deliver a (ten to twenty year) speculative return of 1.5% to 2.3% bigger than they do today.

Add in the effect of the price decrease on dividend yields: it multiplies them by 1.4.

Assuming that you are withdrawing all dividends and that your dividends are 2%, the total boost is 0.8% (to 2.8%) from dividend yields plus another 2% from capital gains. Both are in addition to inflation. If you are starting with a dividend yield of 3%, which is typical of a conservative dividend-based strategy in today’s market, the boost is 1.2% (to 4.2%) from dividend yields plus the other 2% from capital gains.

The change in the speculative return caused by price changes is larger than the change in the investment return caused by higher dividend yields.

Have fun.

John Walter Russell
September 9, 2005