# Prime Harvesting: Sleep Well At Night (1 of 3)

*[You can now read the **second** and **third** parts.]*

A while back I took a deeper look at the bond levels in Prime Harvesting and came away with some reservations about the strategy.

The problem, I decided, is that just looking at bond levels leaves a lot to be desired when judging risk. As an extreme example: if you’re 100 years old with $10 million in the bank and only need $50,000 a year to maintain your lifestyle…you probably don’t care much if your portfolio is 100% stocks or not.

“It seems like it needs some mixture of your age (i.e. how long the portfolio needs to last) as well as the current withdrawal rate (i.e. how much you’re actually taking out),” I told myself.

I was slowly working on some hackneyed, crappy metric to try to capture those nuances.

Thankfully I didn’t waste too much time on that before I stumbled across Moshe Milevsky’s “A Gentle Introduction to the Calculus of Sustainable Income” which uses Real Math to derive a simple formula for exactly this.

The formula has four variables:

- The portfolio’s expected rate of return. You can calculate this from historical data as a reasonable approximation.
- The portfolio’s volatility (standard deviation). You can also calculate this from historical data as a reasonable approximation.
- The life expectancy of the retiree. You can get this from any number of life tables.
- The spending rate as a percentage of the portfolio. Easy. We already know this!

In practice it looks like this:

>>> expected_return_mean = 0.052

>>> expected_return_standard_deviation = .1182

>>> life_expectancy = 22.30

>>> withdrawal_rate = 0.04

>>>

>>> probability_of_ruin(expected_return_mean,

... expected_return_standard_deviation,

... life_expectancy,

... withdrawal_rate)

0.097782639821254749

That’s pretty simple. Milevsky is a bad ass. All his papers are interesting to read, even if the math sometimes goes over my university-was-a-long-time-ago head.

Milevsky’s formula *actually* calculates the “risk of ruin” — the chances of a portfolio running out of money before the retiree dies. But I want to use it for a slightly different purpose: as a measure of whether the retiree can “sleep well at night” given their current portfolio, current age, and current withdrawal rate.

That means we should be less sensitive to the exact expected rate of return, exact volatility, and exact life expectancy.

What we want to do is, every year, calculate the “sleep well at night” (SWAN) level given the current state of the world for a retiree. Then we can chart it over time. This is the SWAN level for a 1966 retiree using a constant 4% withdrawal scheme with Annual Rebalancing:

That is what we would expect. There’s a big spike a few years in. In 1969 bonds returned -1.4%, stocks returned -8.55%, and inflation was 6.18%. The retiree calms down because the next three years see bonds return 9.74%, stocks return 12.3%, and inflation is only 3.99%. After that, though, it is a slow slide towards failure with anxiety continually mounting.

Now we have a tool to see whether the reduced bond levels in a Prime Harvesting portfolio are worth worrying about or not.

### Prime Harvesting: Better Income?

Fundamentally we want to try to answer whether Prime Harvesting has better risk-adjusted income relative to an Annual Rebalanced portfolio.

Before we dive into the “risk” part, let’s take a step back and see whether the “return” part looks true.

In his book, McClung compares the harvesting strategies by looking at their performance using “constant dollar” withdrawals and comparing the Maximum Safe Withdrawal Rate over a 30-year period. On bogleheads.org (in a long-running thread on the book) a number of people have raised concerns about that approach. The objection is, “Everyone knows that using a constant-dollar withdrawal method is dumb and unrealistic; a variable withdrawal strategy is the way to go. If you use a variable withdrawal strategy, I bet most of Prime Harvesting’s apparent benefit goes away.”

siamond makes this case with some charts that appear to show no real difference between Prime Harvesting and Annual Rebalancing. (It doesn’t matter which line is which, the point is that most of the time they are indistinguishable for a 1955-retiree.)

In Part 2, I’ll take a look at the income side of Prime Harvesting, see if I can replicate siamond’s results, and hopefully draw some pretty charts while I’m at it. In Part 3, we’ll circle back to the risk part of the question and hopefully try to come to some kind of answer about whether the low bond levels in Prime Harvesting are something that should keep us awake at night.