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# On Distribution Formulas

Before I get started this evening, I would like to offer an apology to those that read my recent piece, Simple Retirement Calculator.  I didn’t define all of the terms in the piece, and so here are the definitions:

• DB plan — defined benefit plan, a pension plan that offers a certain benefit, and the cost of funding that benefit varies.
• DC plan — defined contribution plan, a pension plan that allows for a certain level of contributions, and the benefit achievable varies.
• 100% J&S — 100% Joint & Survivor.  In an annuity, its payment is the same regardless of who dies first.  The one surviving does not see any reduction in payments.  In 50% J&S, the one surviving get only half the payment after the first spouse dies, which allows for a higher initial benefit than 100% J&S.
• CR — cash refund.  Some people getting an annuity hate, really hate the idea that the insurance company might make money off of them if they die early.  The cash refund option says that heirs receive the difference between the premium paid and benefits paid.  The cost of this option is a slightly lower benefit.
• Indexed — the annuity benefit rises with inflation, usually the CPI.

Now the table in the article tried to show how much of a person’s salary would be replaced at retirement, given a certain level of saving.  Another way of viewing it would be how many years of income would the accumulated value of savings be relative to their final salary at age 70.  That’s the “Accum Years Ending Pay.”  It’s surprising how few years of ending pay a person accumulates unless they save a lot.

That’s all.  Other questions, forward them my way, but please, ask, don’t demand…

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Now there was one more item from my piece Simple Retirement Calculator, the line that read 4% — i.e., pay out 4% of the lump sum annually, an assumption that has fairly broad acceptance for managing a lump sum without annuitizing it.  I myself came to endorse the 4% rule in 2001, after doing a series of analyses using what I thought was a good risk, inflation, and asset allocation model, concluding that the average person had 95% odds of not going bankrupt if they took just 4% of the initial sum invested, adjusted for inflation annually, as a distribution.

The data through 2000 did not allow for a “lost decade” like the one we have recently experienced.  During such a time, marginal returns on capital became very low.  GDP growth slowed, and yields on Treasuries fell.

Going back to Ben Graham, who when bullish never let his asset allocation go above 75% stocks (risky assets), and 25% bonds, and when bearish never let his asset allocation go below 25% stocks (risky assets), and 75% bonds, in the same sense, I use this to offer a new distribution rule for those that don’t annuitize and have to manage a lump sum:

As a percentage of your assets, spend no more than the 10-year Treasury yield annually, plus:

• 0% if the situation is bearish (risk assets are highly priced)
• 1% if the situation is neutral
• 2% if the situation is bullish (risk assets have depressed prices)

As for determining risk posture, I would use things like the Q-ratio, Shiller’s CAPE, and the difference between Moody’s Baa and Aaa spreads to be my guide.  At present, by those measures it would leave me halfway between neutral and bearish in the intermediate-term, and so I would be look to distribute only 2.5%/year from endowments as income.

Chintzy?  Today yes, but it respects the idea that depressionary conditions may persist longer than we might otherwise expect.  It also adjusts as inflation rises, to the degree that it gets reflected in Treasury yields, which may be held down by the Fed.  In such a case of the Fed constraining longer Treasury yields, gold prices and the prices of other materials may rise dramatically, because there is no penalty for holding commodities in real terms.

This views the asset markets through the eyes of a conservative but clever bond investor, who realizes that future equity returns are highly correlated with Baa-rated bond yields, and future bond returns are highly correlated with Treasury yields.

But, think of what this formula would have done in the early ’80s, when endowments were constrained, and they took little as income.  This formula would have anticipated the future, and allowed endowments to spend more aggressively, anticipating the recovery.

So let Treasury yields, the Q-ratio, Shiller’s CAPE, and the difference between Moody’s Baa and Aaa spreads be your guide in distribution formulas.  Better to distribute less now, than find yourself or your institution impoverished later.

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