**From Intrinsic Value**

**Background**

peteyperson has presented us with the concept of

**intrinsic**value. Instead of working directly with prices as they happen to be, he would convert them back to more realistic values. He would scale according to P/E10 or something else that was suitable. He would manage his account on that basis, its

**intrinsic**value.

I do not yet have anything to work with directly in terms of intrinsic value. But I can design a reliable withdrawal strategy based upon high valuations. I have been able to determine the primary mechanism for failure in such cases. The usefulness of my strategy (as originally defined) declines as I move toward lower valuations.

It has occurred to me that I can scale a portfolio from normal valuations to high valuations and then design from there. What I have not been able to do well has been the opposite kind of scaling: that is, modifying the design process to work with normal valuations.

**The Starting Point**

What I can do well is design a dividend strategy when valuations are high. The basic idea is to live off of the dividends and touch principal very lightly, if at all. If the dividend amount is steady and grows enough to match inflation, then the initial dividend yield is just under the safe withdrawal rate. If you restrict yourself to withdrawing one percent of capital or less in any single year, you can tolerate a fair amount of price variation with reasonable safety.

The key is to have a steady income stream from dividends and to sell very few shares of stocks. You must make a downward adjustment if the dividend amount drops abruptly in the first two or three years. Otherwise, you just take care not to sell too many shares when prices are unusually low.

At lower valuations this process does not work nearly as well. It is much too conservative. Stock prices are likely to rise. With rising prices, you only have to sell a few shares to raise your income. You can do so safely. You do not have to worry about selling heavily at low prices.

**Scaling From Intrinsic Value**

Conceptually, we divide your portfolio into two separate parts. We treat the dividend income the same as before. As long as the dividend amount is steady or rising, everything is fine. If dividends drop abruptly, of course, we have to adjust to the lower rates. It is easy to calculate the dividend amount. It is the dividend yield times the initial balance. That initial dividend yield is the first component in our withdrawal strategy.

We treat the price component in an amazingly simple manner. We estimate what price would support the dividend income stream if prices were to remain stable, similar to what happens at high valuations. For my first scale factor, I estimated this alternative price by scaling it to a P/E10 equal to 24, which was the second highest value of P/E10 before the bubble. The scaled, alternative price equals the product of (24 / [the actual P/E10] )*(the actual price). It turns out that I should have scaled it a little bit higher. I will talk about that some more, later.

I just treat prices and dividends as if they were independent. They aren't, of course. It just seems to work out reasonably well.

I calculate the withdrawal rate from selling stocks at higher prices as if the price rose steadily from its actual price to its alternative, scaled, higher price thirty years later. (I assumed a portfolio lifespan of thirty years.) The ratio of the final price to the initial price is (1 + the annualized price increase)^30 for 30 years. The formula to use with a calculator is, as follows:

The withdrawal rate from selling stocks = -1 + antilog ( [1/30]* [log (24 / [the actual P/E10] ). If the lifespan were 40 years, the [1/30] term would be replace with [1/40] and so forth.

It turns out that you can still sell some stocks safely without dipping too deeply into capital even at a P/E10 of 24. Something around 30 or 36 seems to fit the data a little bit better. In terms of the calculations, the net effect is to add a factor of {the thirtieth root of (30/24) or the thirtieth root of (36/24)} into the formula. Those roots are 1.0074 and 1.0136. The net effect is to add 0.74% or 1.36% to the calculated values. That is, a year's actual safe withdrawal rate is just a little bit higher than calculated initially.

I have included three tables ordered by valuations, from the lowest P/E10 level to the highest, from start years 1921-1980. I list the start year, the P/E10 level for January of that year, the dividend yield for January of that year, the estimate (using the dividend yield and scaling to a P/E10 level of 24) and that year's safe withdrawal rate assuming an 80% stock allocation. (I used FIRECalc. I selected 20% commercial paper. I used CPI for my inflation adjustment. I set expenses at 0.20%. I used a 30-year portfolio lifespan. My calculations were scaled according to an initial balance of $1000. Other inputs were left at their default settings.)

I have placed asterisks with those years followed by an abrupt dividend decrease. Those years behaved differently from others.

The estimate should be best at the highest valuations and it is. The appropriate adjustment for determining a year's safe withdrawal rate is to add about 1.0% to the estimate. That works very well at high valuations and reasonably well at lower valuations. The scatter decreases as P/E10 increases. That is as it should be.

**Bubble Valuations**

Do not use this formula blindly to extrapolate into bubble valuations. As long as stocks provide a steady income stream, you do not have to sell any shares. That is, the price adjustment should always be positive or zero, never negative. Scaling to a P/E10 of 43.7 in January 2000, would give a negative adjustment even if you never sold any shares. That is inappropriate. The correct adjustment becomes the dividend yield (1.17%) + the 1.0% that is used in general. The year 2000's safe withdrawal rate was 2.2%.

That having been said, it may have been optimistic. The real dividend amount in January 2000 was $16.50666 (from Professor Shiller's database) and it

**decreased**to $15.022168 in June 2002, which was the last entry with a real dividend amount. That is a 9.88% drop in the dividend amount. (It had dropped as low as $14.623011 in June 2001.) The June 2002 real dividend amount is 1.05% of the January 2000 real price (index value). Thus, where our original calculation was for a 2.2% safe withdrawal rate in January 2000, it might have to be adjusted downward to 2.05% (in a calculation update resulting from subsequent events).

**Conclusions**

This simplistic scaling worked much better than I had expected. It extends our dividend design strategy down into the ranges of normal and even low valuations. However, it still works best at higher valuations.

Have fun.

John R.