# Life Cycle Of Retirement Portfolios, Part 1

by: Roger F. Goodrich

This is Part 1 of 3 on the general subject of merging withdrawal methods for retirement portfolios.

It seems incongruous to consider the construction of a retirement portfolio without simultaneously taking into account its intended usage. There are 3 major retirement portfolio distribution schemes: a fixed initial percentage withdrawal increased by future annual inflation rates; a 1/T and fixed percent withdrawal that never depletes the portfolio; a bucket approach whereby assets are assigned to buckets which are depleted in sequence. There are advantages and disadvantages, which have been expressed in the media, for all 3 schemes. It may be that a combination would more fully optimize what is needed.

Consider the concepts 'Demand equals Supply' and 'Total Return equals Return from Principal plus Return from Dividends/Interest (D&I)'. These can be expressed by the equation

Eq. #1 Payout = P*Z/T + D&I where P is Portfolio Value, T is time (years) to go, Z is a constant or variable that modulates principal withdrawals

The term P/T can be derived from the amortization equation where the interest rate (market return from principal) is zero. Dividing by P

Eq. #2 Payout rate = Z/T + Yield

If Z = 1, we have the 1/T approach. If Z varies linearly from some number to zero at the end of the time period, we have the fixed percentage approach; i.e., Z = 1 at T = 40, Z/T = 2.5%; Z = 0.5 at T = 20, Z/T = 2.5%.

If the portfolio is divided into segments (bonds; dividend growth stocks; high yield stocks, core stocks, etc.) and a separate calculation of Eq #1 is used for each segment, as appropriate, we have the bucket approach. For example, in a dividend growth segment, let Z = 0 for the first half of the time period, then linearly increase to unity (1) at the end. No stocks are sold in the first half so dividends can increase, a combination of hefty dividends and deferred capital gains in the second half provide an abundant distribution to compensate for inflation.

Here's the drill: 1) separate like-minded portfolio assets into segments; 2) determine suitable withdrawal strategies tailored to each segment by choosing Z values for the entire time period to exploit favorable asset characteristics peculiar to that segment ; 3) ensure these segment withdrawal schemes are mutually compatible; 4) calculate yearly values of Z/T to provide a predetermined template for share sales for the entire time period; 5) in up-market years, set aside 1.5-2% of total payout for smoothing yearly payout and/or funding one-off expenses; 6) during the distribution phase re-balancing is not permitted; equal value exchanges between segments is allowed; 7) sell marginal assets early on, saving the best until last; 8) at mid term, adjust Z values as needed based on conditions at that time; 9) in the final years, re-assess conditions and adjust Z/T values to access residual shares if needed.

If we can determine an acceptable initial payout, increase that by an assumed average inflation rate over the time period and use those yearly distributions as payout goals, then we can gauge during distribution years how we are doing compared with the goal and take corrective action as necessary.

The approach described here is a 'management of shares' exercise. If Z = 1, an equal number of equivalent shares are sold each year. If K is smaller during early distribution years and is unity (1) at the end of the time period, deferred shares sold in later years at a higher market value also provides inflation protection.

The challenge is to construct a portfolio with the necessary elements and fundamental values along with specification of appropriate segment values of Z over time to accomplish these goals. Assets are purchased during the accumulation phase with this plan in mind. The process is divided into manageable segments so each part can be optimized, then assembled into a final portfolio to achieve the intended goal. With control via yearly values of Z, a determination can be made if the portfolio is to be totally depleted (Z = 1 at the end of the time period) or not. With this approach the portfolio is never inadvertently depleted because you are selling assets at a predetermined rate. Yearly payouts will vary to some extent due to market conditions (shares sold are worth more or less), but with a design where most of payouts are from D&I, this concern is diluted. Portfolio construction and distribution is under our control, results consistent with the merit of both. By selling under-performing shares or higher risk first in the stream, the portfolio should improve over time. Just make sure you unwind your portfolio before it falls apart.

Instead of reducing the value of T by one (1) each year, a improvement in distribution can be achieved by using the Life Expectancy Table found in IRA Publication 590, IRAs. It is available at irs.gov website, Publ. 590, Appendix C, Uniform Lifetime Table, page 102. To extend the table back from 70 years to 60 years, add 0.9 to each year going back. Thus at age 60, instead of T being 40, it is 36.4; which means early distributions are slightly larger. By the same token, at age 99, instead of T being 1, it is 6.7. This improves payout flow in later years (by not dividing by very small numbers), provides flexibility for one-time emergency withdrawals, leaves something on the table in case you live longer. It should be used for all portfolio segments (buckets) that span the entire time period. Segments that phase out early should use the normal time period method.

Before going further, let's set the stage by using some numbers to get a feel for what we are talking about. Assume an initial portfolio value of \$400,000 and a 40 year time period. The 4% rule would have us taking \$16,000 the first year. Let's increase that to \$24,000 as a goal. Assume a 3.6% inflation rate - this is about the yearly historic average, but it also divides nicely into 72. From this we can easily calculate how much we will need in future years to keep pace with inflation. Using the Rule of 72 and 3.6% inflation, the amount needed doubles every 20 years (72/3.6), to \$48,000 at mid-point and \$96,000 at 40 years. This is what we need our portfolio to generate just to keep a constant standard of living.

Another general consideration is the initial split between income producing assets and capital gains (by selling principal). The traditional 60/40 split between stocks and bonds is there for a reason. Initially, more payout is needed from the D&I part of Eq. #1. Otherwise you are selling shares at lower market value which, once sold, are gone and cannot contribute to future capital gain or dividend growth/bond interest.

A further tie-in between Eq. #2 and traditional distribution approaches can be gleaned from data published by William Bengen, the father of the 4% Rule, in his book "Conserving Client Portfolios During Retirement" (Pg 104). He provides a data set of remaining years vs. withdrawal rate ((T/WR)): 35/4.3%, 31/4.4%, 27/4.5%, 24/4.7%, 21/5.0%, 18/5.4%, 16/5.7%, 12/7.2%, 8/10.3%, 4/15.8%. Inputting these values in a spreadsheet and graphing them as 2 variables (x-y plot) reveal they can be described by a hyperbolic relationship of the form y = a/x + b. Solving for 'a' and 'b' using 5 data pairs yield values of a & b averaging 0.52/0.027. This equation is the same form as Eq. #2, with Z=0.52 and yield = 0.027 (2.7%). These are reasonable values given his safe return goal and portfolio of 40% large cap, 20% small cap, 40% intermediate gov. bonds. Bengen mentioned in his book that he used (as yields) 1.8% for large-cap , 0% for small-cap and 5.4% for bonds in his calculations. Using this info, the equivalent yield is 2.9%, close to the 2.7% determined above.

A simple two-bucket (segment) approach could be the traditional 60/40 stock/bond split with Z = 0.55 throughout, collecting D&I as issued. After 40 years, using the Uniform Lifetime numbers for T, there are 23.6% of shares remaining.

Since every portfolio should have at least one segment dedicated to dg, it is useful to determine an initial value of Z using metrics from applicable segments to help bind the whole process together. If we were to graph two of the important equations, we can show how salient portfolio parameters and desired payouts inter-relate. Let G be the initial payout goal mentioned earlier. This would increase exponentially at the inflation rate, INFL. The bulk of actual payout comes from D&I (at least initially), this increasing (assume exponentially) at a portfolio weighted average dividend growth, DG. With normal conditions of a) D&I less than G and b) DG more than Infl, the two curves will intersect at a point in time where values of the two equations are equal. Here we have a 'free' variable, that point in time. It was determined empirically (meaning a little trial and error) that 3 years is a good choice. From all this, we can determine the value of G, being

Eq. #3 G = D&I [(1+DG)/(1+Infl)]^3

Furthermore, G and D&I are related via Eq. #1 in that their difference is P*Z/T. Solving for Z,

Eq. #4 Initial Z = (G - D&I)*T/P where P is the initial value of segments involved in Initial Z.

Final values of Z can be found as a function of dg by the relationship Final Z = a - b*dg, where Final Z is zero for dg equal to and greater than dg0, and Final Z is unity (1) for dg equal to and less than dg1. For the range between dg0 and dg1, a = dg0/(dg0 - dg1) and b = 1/(dg0 - dg1). This allows taking advantage of high dg by selling fewer shares and selling more shares when dg is lower in order to generate a comparable payout.

The next step is to construct a table depicting distribution calculations to be made each year during the time period. For each segment, determine values of T and Z for each year. The product Z/T multiplied by year-end segment values is the amount of principal to be sold in that segment. Incremental yearly values for Z can be obtained from the formula: (final Z - start Z) / (T-1), where T is the number of years between the final and start years (including those years).

Another important issue is consistency of dividend growth. Some insight can be gleaned, at least in solid dg stocks, by analyzing data found on David Fish's U.S. Dividend Champions spreadsheet. He has a group of columns showing dg increases year-to-year for all stocks listed. I used the EOY 2011 spreadsheet with the following results:

11.30 6.50 5.97 8.75 11.40 10.90 11.50 11.50 The first line shows averages from '2000vs1999' to '2007vs2006'.

11.70 6.12 5.59 7.85 ? The second line shows averages from '2008vs2007' to '2011vs2010'.

There is amazing similarity in these average dg numbers going through two major market crashes; dot-com (top line) and financial crisis (bottom line). There is about a 50% drop in dg (note - still an increase in dividends) and it takes 4 years to recover, assuming the 2012vs2011 data (?) verifies this. Average yield for his population of stocks was 2.94%; an excellent place to start cherry picking. I have analyzed other data, mostly my own portfolio, and found similar results with other asset classes.

Even the S&P500 has dg: 5.3% average from 1970-2009; just a step ahead of inflation, which clocked in at 4.5%. Corresponding values for the last 20 years of this range are 3.5% vs. 2.6%. Declines in dividends (negative dg) was experienced in the years 1971, 1986, 2000, 2001, 2009.

This withdrawal scheme invites innovative approaches. For example, a high beta-no dividend segment could have shares sold only during major up-markets. Monies gained would be used in lieu of shares sold in dg and or high yield segments, saving those shares to accumulate D&I.

Part 2 will cover one application of this process. Part 3 will host a distribution simulation.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.