Kiisu Buraun's  Instablog

Inflation is not constant... not exactly breaking news, I know.

However, if I am trying to project future inflation so I can decide if my retirement funds are growing quickly enough, its handy to know what historical inflation has been.

In a previous post (http://seekingalpha.com/instablog/134376-kiisu-buraun/852671-would-a-dogs-of-the-dow-retirement-portfolio-survived-the-last-12-years) I looked at historical inflation through the eyes of a new retiree in the year 2000. In the post, I looked back 10, 20, 30, 40 and 50 years to get an estimated inflation rate and used that rate to increase withdrawals from a retirement portfolio.

However, it is now mid 2012, not 2000 and I thought it might be interesting to see what has happend to our money.

InflationData (http://inflationdata.com/Inflation/Inflation_Calculators/Cumulative_Inflation_Calculator.aspx) provided the cumulative inflation data, and Investopedia (www.investopedia.com/calculator/CAGR.aspx) provided the CAGR calculator.

CAIR (Compound Annual Inflation Rate) is merely CAGR applied to inflation.

Examples help me understand. And I find the following examples enlightening:

For every $100 of buying power I had at the end of:

• 2008, I would now need $107.35.
• 2001, I would now need $127.71.
• 1961, I would now need $752.24.
• 1914, I would now need $2,234.38.

Thus, if we ignore taxes and my retirement projections are "golden" with a 3% inflation rate and future inflation mimics the recent sub 3% rate, all is well.

However, if in the future the CAIR creeps up and I don't adjust my projections accordingly, I can easily deceive myself with a rosy projection that does not meet reality.

And that could be "interesting."

The Question

Back in the late nineties I read a number of financial articles and books as a prelude to picking companies for my IRA. It was then I stumbled across something called the "Dogs of the Dow" or DoD.

I even tried the DoD method for a while before moving on to other things. But in retrospect I've wondered, how good a method was DoD; how well would it have survived, to twist a Southern phrase, "The Recent Unpleasantness;" and if I had retired in 2000 with a portfolio managed according to the DoD method, would the portfolio have survived that aforementioned "Recent Unpleasantness"?

For those unfamiliar with the DoD, I've summarized the method as:

I've purloined my DoD historical data from the informative website, http://www.dogsofthedow.com.

A First Look

I split the analysis into two scenarios. Both start with $10,000 cash in an IRA on 1 January 2000. And both end on 31 December 2011.

• Scenario A: the portfolio is liquidated at the end of the year and the entire cash balance is invested at the beginning of the following year.
• Scenario B: the portfolio is liquidated at the end of the year, cash is pulled from the proceeds and the remainder is invested at the beginning of the following year.

With Scenario B we withdraw $400 from the portfolio at the end of the first year before investing the balance on the first trading day of the new year. In the following years, we increase the withdrawals each year by 4%.

For simplicity I've made a few simplifying assumptions:

• The portfolio is equally balanced when bought. For example, in the first year $1000 of each stock is bought, which means on 3 January I would have bought 42.6621 shares of (what was then) Philip Morris.
• Transaction costs are zero. In other words, I've found the ultimate low cost broker, one that does not charge a commission.
• Annual performance is not taxed. I assumed the portfolio is held in either in a tax deferred account (i.e., IRA) with taxes paid on withdrawal, or in a tax-exempt account (i.e., ROTH IRA) with no tax imposed on withdrawal. Of course, this also assumes all the other legal requirements are met for penalty free withdrawals.

A Results

For scenario A, the computation seems simple and straightforward, multiply the invested amount by the DoD average annual performance. For example, the 2000 DoD performance is:

Table 1. Year 2000 DoD performance summarized from http://www.dogsofthedow.com/dogs2000p.htm.

Which gives an average rate of 2.65% for the year. Thus an investment of $10,000 would increase to $10,265.00

However, the DoD website contains the following caution... Note 1: 2000 % change figures do not include for dividends, commissions, or taxes. Similar notes exist for the other historical DoD results.

We've already assumed no commissions or taxes. But will ignoring dividends be a result altering mistake?

Table 2. Year 2000 DoD dividend performance.

(Notes: Historical data from Yahoo! Finance. EK historical data available as EKDKQ. GM historical data was available until the end of June 2012 as LTMQQ. SBC is currently listed as T because SBC later bought the original AT&T and adopted its name and symbol.)

$10,000 invested in the Dogs of the DOW on 3 January 2000 results in dividends of $255.08 or a 2.55% dividend return... nearly the same amount as the increase due to stock price increase.

If we adjust the posted results for dividends, the average annual performance significantly changes... for the better.

Table 3. Annual average DoD performance raw and corrected with dividend returns.

Chart 1. Annual average DoD performance raw and corrected with dividend returns.

At the end of twelve years we have the following results assuming we make a one time initial investment of $10,000.

Table 4. Result of $10,000 invested at the beginning of 2000.

In twelve years from January 2000 to December 2011 the "raw" DoD portfolio experienced 7 up years and 5 down years with a net loss of $126 and a CAGR of -0.11%. If we account for dividends, the portfolio experienced 8 up years and 4 down years with a gain of $7,418.85 for a CAGR of 4.73%.

To quote Paul Harvey, "we now know the rest of the story"... dividends significantly improve the results published on the Dogs of the DOW website.

B Results

For scenario B, we need to compute the annual withdrawals. We start with 4% of the initial investment and increase the withdrawal by 4% each year. Why?

While 4% is arbitrary, it is a commonly used withdrawal rate. Why increase the withdrawal rate by 4%? Inflation.

For example I used the cumulative inflation calculator at inflationdata.com (inflationdata.com/Inflation/Inflation_Ca...) and the CAGR calculator at investopedia (http://www.investopedia.com/calculator/CAGR.aspx) to discover the following:

Table 5. Historical inflation table. $100 in 1991 would have to grow to $129.27 by 2000 to have the same purchasing power.

Based on recent history, increasing the withdrawal rate by 4% per year to account for inflation seems reasonable.

Table 6. Withdrawing 4% of initial investment at the end of the first year, increased by 4% each year.

When we make the annual withdraws the computations become a bit more complex, but the results are decidedly different.

Table 7. DoD with annual withdrawals.

Chart 2. DoD performance raw and corrected. Withdrawing 4% of initial investment at the end of the first year, increased by 4% each year

In the twelve years from January 2000 to December 2011 the "raw" DoD portfolio with annual withdrawals experienced two up years and ten down years with a net loss of $6,546.28... if we don't include the twelve withdrawals which total $6,010.32. If we do include the withdrawals we are still down $535.96.

If we include dividends in the DoD portfolio and make the annual withdrawals, the portfolio experienced 8 up years and 4 down years and gained $998.58... if we don't include the twelve withdrawals of $6,010.32. If we do include the withdrawals we are up $7,008.90.

I know of no one in the U.S. who would have retired in 2000 on $10,000, but the numbers are easily scaled. For example, multiply the numbers by 100 and an initial portfolio of $1,000,000 grows over twelve years to a value of $1,099,858. The initial cash 4% withdrawal at the end of 2000 grows from $40,000 to $61,578 at the end of 2011. The total amount withdrawn sums to $601,032.

The Answer

The results published on the Dogs of the DOW website don't include dividends. However, as shown above, Doggy dividends are absolutely critical.

If dividends are (unrealistically) ignored, this historical DoD portfolio fails with a CAGR of -0.11%. Annual 4% cash withdrawals (increased by 4% each year) crash the portfolio and generate a CAGR of -8.48%.

But actual DoD performance which includes dividends, paints a better and more realistic picture. For the period from 2000 to 2011 dividends exceeded required annual withdrawals for five years and contributed a significant fraction of the withdrawals in the remaining years.

A DoD portfolio created at the beginning of 2000 would have survived and grown nearly 75% for a CAGR of 4.73%.

Furthermore, even with the "Recent Unpleasantness" this DoD portfolio with annual withdrawals grew nearly $1000... even though we extracted 4% of the initial investment at the end of 2000 and thereafter grew the annual withdrawals by 4% each year. Over the 12 years we withdrew more than $,6000 even so, the portfolio grew with a CAGR of 0.80%.

So, yes a DoD portfolio established at the beginning of 2000 would have survived and grown... even if I had extracted 4% of the initial investment at the end of 2000 and thereafter grew my annual withdrawals by 4% each year.

But that raises another question, is there a better method? I'll examine that question in a future article.

When is the Average Annual Dividend Growth Rate (AADGR) the same as the Dividend Growth Rate (DGR) for the entire time period?
In other words, when is:

        AVERAGE(divt_n/divt_n-1-1;
             divt_n-1/divt_n-2-1;
             …;
             divt₀₊₁/divt₀-1) =
        (divt_n/divt₀)^(1/(t_n-t₀))-1

Where divt_m is the dividend payment for time period m.

Answer:

        AVERAGE(a; b; c; d; …; z)

is a shorthand notation for:

        (a + b + c + d + … + z)
        / (number_of_terms)

But if the individual terms, a, b, c, …, z  are all equal, then:

        (a + b + c + d + … + z)
        / (number_of_terms) =
        (a + a + a + a + … + a)
        / (number_of_terms)

And

        (a + a + a + a + … + a)
        / (number_of_terms) = a

Thus,

        divt_n/divt_n-1-1 =
        divt_n-1/divt_n-2-1 =
        … =
        divt₀₊₁/divt₀-1 =
        (divt_n/divt₀)^(1/(t_n-t₀))-1

Or for any sequential dividend payments, divt_m and divt_m-1

        divt_m/divt_m-1-1 =
        (divt_n/divt₀) ^(1/(t_n-t₀)) -1

Summary: If the AADGR is composed of a series of exactly equal annual DGRs, then the AADGR for the time period is the same as any individual annual DGR which is also the same as the DGR for the entire time period.