‘Cat Food’ revisited – testing dynamic spending rules – Part 3

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In part 3 today, we’re going to discuss 1) adding a parameter to change the way we increase the spending rate as we get older and 2) reducing equity allocation as we get older. Finally, we’re going to do a brute-force search for the highest initial spending and best parameters for each level of shortfall risk (skip to conclusion).

Adjusting how fast spending rate increases with age

Suppose we are willing to accept the portfolio in bold and spending rate, which has never resulted in a decline greater than 24.7% below the initial spending amount. We use spending factor s=0.5, equity = 75%, smoothing factor = 2. We end up with a spending profile that looks like this:

Notice the ‘hump.’ In the average case, spending rises steadily, then drops. Ideally, we would like a flatter spending profile, preferring less variability in spending. If we could take the hump and spread part of it earlier, without increasing shortfall risk, it would increase the safe spending rate.

The spending rate at age 99 is s/life_expectancy=0.5/2.19 = 22.8%. Spending rates at advanced ages are too high, decimating the portfolio and causing the decline in spending. If we reduce them, maybe we don’t need to build as big a war chest in middle years to support such a high spending rate in late years.

There are several ways we could change the model to flatten the spending profile. The one we choose is to add a parameter we’ll call ‘life expectancy buffer’ to life expectancy, so we’ll spend at a rate of s/(life_expectancy+buffer). If the parameter is 2, then when our life expectancy is 3, instead of spending at a rate of s/3, we’ll spend at a rate of s/(3+2). If life expectancy buffer is 0 or low, the spending rate will rise relatively quickly as we age; if life expectancy buffer is large, the spending rate will change slowly as we age.

With a buffer of 2, we get a flatter spending profile later in life, without changing too much at the start of retirement.

Let’s compare efficient frontiers, with and without the buffer:

We find in all cases, the buffer gives us a higher level of initial spending for any level of shortfall risk. However, increasing the buffer does not always increase lifetime spending and sometimes worsens the tradeoff.

It’s a mixed picture. The buffer may in many cases allow us to spend safely at a higher initial rate, but doesn’t always improve lifetime spending. Sometimes it reduces portfolio growth and overall lifetime spending.

Third dynamic rule: Changing equity allocation over time.

Does it make sense to reduce the equity allocation as you get older? Let’s introduce a variable to gradually reduce the amount of equity. As long as your life expectancy is > 15 years, use the initial allocation. After that, we’ll reduce the equity percentage by stepdown percentage points per year.

What I thought would happen: stepping down equity over time would let you start with more equity, relying on smoothing to get you over early drawdowns and strong long-run real returns to catch up. Then with lower equity in later years you wouldn’t be exposed to big drawdowns late in life.

What actually happened: stepping down equities always worsens the risk/reward tradeoff.

Apparently my preconception was faulty, or this is the wrong model, stepping down too early and killing returns, or there’s a mistake somewhere (although I don’t think so). Watch this space for possible future elaboration or ninja-edit. I’ll consider this a first draft and move on.

Discarding the stepdown, we now have 4 parameters: spending factor s, starting equity, smoothing factor, and lifetime buffer. We have discussed how each one impacts the spending profile and shortfall risk. Let’s put it all together, try running a full range of reasonable values, and come up with the best efficient frontier over all values.