April 7, 2007 Letters to the Editor

Updated: April 12, 2007.

Formalizing the Algorithm

I received this letter from ElLobo, a regular poster at the Income and Dividend Investing discussion board at Morningstar.

Formalizing your [Income Stream] algorithm is helpful:

Here is my crack at this:

Let V0 be the value of a portfolio at the beginning of the year. Let V1 be the value of that portfolio at the end of the year. The value at the end of the year FIRST includes the value at the beginning of the year plus any contributions to the portfolio minus any withdrawals to the portfolio. Thus,

V1 = V0 + C - W equation (1)

The value at the end of the year ALSO includes the total return TR achieved by the portfolio during the year. TR, in turn, is defined as the sum of the yield Y of the portfolio plus/minus any share price appreciation/depreciation (CG) experienced by the portfolio.

Therefore,

V1 = V0 + C - W +/- TR equation (2)

V1 = V0 + C - W + Y +/- CG equation (3)

where CG is positive if share prices appreciated (a gain) or negative (a loss) if share prices depreciated.

Assume the portfolio is comprised of different assets. The equation for V1 holds for each asset, and the value V1 of the portfolio is the sum of the values of each asset. Thus,

V1 = V1,1 + V1,2 + V1,3 + . . . . . +V1,n equation (4)

where n is the number individual assets held in the portfolio.

Likewise,

V0 = V0,1 + V0,2 + V0,3 + . . . . + V0,n equation (5)

Each individual asset has its own unique yield and capital gain term associated with it, so (3) can be expanded:

V1,1 + V1,2 + V1,3 + . . . . . +V1,n =
V0,1 + V0,2 + V0,3 + . . . . + V0,n + Y1 + Y2 + Y3 + . . .Yn +/- CG1 +/- CG2 +/- CG3 +/- . . . . +/- CGn + C – W equation (6)

Now, the value of each asset is equal to the number of shares held times the share price. That is,

V = N * P

Likewise, the yield for each asset is equal to the number of shares held times the dividend distribution per share. Thus:

Y = N * D

Finally, the capital gain/loss is equal to the share price at the end of the year minus the share price at the beginning of the year times the number of shares held at the beginning of the year. That difference will be negative if a drop in share price occurs, taking care of the sign change (+/-) in that term. Thus,

CG = (P1 - P0)*N0

Substituting these three definitions into (6) gives the following equation:

V1 = SUM(N1,n * P1,n) =
SUM(N0,n * P0,n) + SUM(Nn * Dn) + SUM(P1,n - P0,n)*N0,n + C - W equation (7)

This is a general equation that holds regardless of whether one is in the accumulation phase or a retirement withdrawal phase. If accumulating, C has a value, while W is zero. If retired, C is zero, while W has a value. However, since we are examining a retirement withdrawal strategy, assume no further contributions are being made to the portfolio, but withdrawals are being made each year.

It is useful to rearrange this equation to group the individual yield terms with the withdrawal term. Also, for simplicity, let’s also revert the summation terms back to their generalized terms, as if the portfolio consisted of a single asset. Doing this, (7) becomes:

(N1*P1) = (N0*P0) + (P1 - P0)*N0 + [(N0 * D) - W] equation (8)

(N1 * P1) = (P1 * N0) + (N0 * D) - W equation (9)

First note that all terms in these equations are in dollars. Next note that the yield term (N0*D) is always positive. Also, if that yield term is greater than the withdrawal term, the difference between the two is also positive. However, if the yield term is less than the withdrawal term, then the difference is negative. This is a simple statement of the boundary between a yield based withdrawal strategy (positive term) and a total return, or liquidation, strategy (negative term).

To see this, solve (9) for N1:

N1 = N0 + [N0*D - W]/P1) equation (10)

N0 * D is the total dollar amount of yield generated by the portfolio. W is the dollar amount withdrawn. If the (N0 *D - W) term is positive, than that amount of excess yield can be invested back into the portfolio. At a share price of P1, then [(N0 * D) - W]/P1 shares will be purchased, which, whenever added to the initial number of shares, N0, results in a larger number of shares N1. If the yield doesn’t cover the withdrawal, the [(N0 * D) - W] term is negative, and, at the same P1 share price, [(N0 * D) - W]/P1 shares will be sold, and N1 will be smaller than N0.

Liquidation occurs whenever N1 goes to zero.

Finally, if the (N0*D - W) term is zero, N1 will always be equal to N0!

Equation (10) is written, for simplicity, assuming only one asset in the portfolio. For a multiple asset portfolio, simply go back to the summation form of the equation.

Now notice that, for the case where the yield exactly covers the withdrawal, equation (10) is both a buy and hold strategy, where one doesn’t worry about the withdrawals, and one where share price fluctuations have absolutely no effect on the withdrawals, and are generally meaningless and inconsequential.

However, once the yield doesn’t balance the withdrawal, share prices simply determine the number of shares bought, or sold, over time. If buying shares (withdrawing less than the yield), again share prices are meaningless, in terms of risk. If selling shares, share price behavior is crucial. That is, long term rises in share prices push back the final liquidation date, falling share prices move it up closer.

Given all of the above, this algorithm can now be fined tuned to include the effect of dividend growth rates (affecting D) and inflation (affecting W, and possibly even D). Also, multi year analysis can be performed by now summing equation (10), which was derived for a one year time period, over 10, 20, 30, 40 years. I don’t know if going to the differential form of these equations (integrals versus sums) buys you anything, since the equation is simple enough.

Anyhow, JW [John Walter Russell], this is my crack at an algorithm. It seems to behave the way I thought it would (in terms of using yield as a basis for a withdrawal strategy).

With this as an algorithm for either type of withdrawal strategy, it’s clear how Monte Carlo analysis of share price behavior leads to probabilities of success. After all, once you need to sell shares each year, you will eventually liquidate. It’s just a question of the probability of doing so before, or after, you die.

HERE IS MY RESPONSE

Thank you, ElLobo.

ElLobo posts regularly at the Income and Dividend Investing discussion board at Morningstar. This letter grew out of Conversation #1853, “Best Growers.....” started by SCMariner. Refer to paragraph 24 “OK, folks, here's the skinny” where ElLobo presented his own Income Algorithm in detail.

In this letter, ElLobo broke out individual components of the income stream. Such formalism is helpful. It makes it easier to isolate the original cause that generates an effect.

Sheltering strategies: dividend payers

I received this letter from Arty.

"Until you have a substantial portfolio, you should be 100% in stocks or 100% out of stocks, depending upon valuations."

I'm involved on Rob Bennett's board and have appreciated your posts.

At present, I am now out of stocks and sheltering in money markets and soon CDs to await better allocation areas.

Objective

I want alternatives to being in CDs even though I can get decent yields on 3-year ones. Obviously, I want to do as well “as possible” in this sheltering period even though high returns from stocks will not be forthcoming. Here, protection of principal is #1 but surely there is more that can be done.

I see where you mention TIPS. Are these bought only at auction or are there Funds with low expenses that can be used (like Vanguard inflation protection)?

Dividend Payers

Mostly, I am interested in what sort of funds you can recommend as "examples" of good dividend payers in this time of high valuation. I've found none and don't know exactly “how” to find them. Are these found in a particular “category” (like, I'm more interested in the principles--how to find them on, say, Morningstar--than any specific recommendation?

For example, in the category of Conservative Allocation, I find: Permanent Portfolio (PRPFX).

Here, some of the holdings pay dividends (the precious metals do not). But overall, it does seem to have some protection in high valuation times. Don't know if I'm on the right path.

Anyway, I just want to understand better what you mean by these dividend payers and how to find them.

Thanks.

HERE IS MY RESPONSE

You are doing well. The benefit of preserving capital is much more important than small discrepancies in interest rates. The benefit of favorable valuations will be substantial.

Read Atul’s letter of January 24, 2007. It addresses many of your issues. Continue, reading Rob Bennett’s letter as well.

January 24, 2007 Letters to the Editor

For short term holdings in a taxable account, be sure to consider ibonds. You can withdraw at your convenience after one year. TIPS are better for longer term holdings inside a tax sheltered account. Bloomberg lets you know about the secondary market for TIPS. (There is no secondary market with ibonds.) I recommend against bond funds, including TIPS funds. They behave differently from the bonds (TIPS) themselves.

I Bonds
Treasury Direct TIPS
Bloomberg Interest Rates

I checked PRPFX at Marketwatch.com. Its expenses looked excessive to me. Lipper gives it high marks in Total Return and Tax Efficiency. Lipper uses equal weightings of a fund’s returns relative to its peers at 3, 5 and 10 years.

Marketwatch Web Site

I listed what I consider to be the most useful books in my response to Atul.

Let me add this: I consider high income vehicles (Master Limited Partnerships, REITS, tankers) different from traditional dividend stocks. They contain an unspecified amount of risk because of their limited history. We have a much longer history with traditional high dividend paying stocks.

Keep this distinction in mind when visiting the Morningstar discussion boards.

I prefer the more traditional dividend payers. But I think that adding higher income vehicles can be worthwhile.

The following articles will be helpful. I wrote them in 2005. They are a little bit outdated, but not much.

What Should You Do?
What Should You Do: Addendum?

Most of all, remember that you have time.

Letters to the Editor in 2007

Letters to the Editor in 2006

Letters to the Editor in 2005