# More on low yields

## Equity allocation, sequence of returns

In a world of low yields, you sometimes hear people wondering whether that means you need to allocate more to equities. In the paper I talked about last time they briefly cover this.

Unfortunately, increasing portfolio risk does not have a material impact. For example, the initial withdrawal rate for a 20% equity portfolio with a 90% probability of success for a 30-year retirement period is 2.7%. If the retiree increased the equity portion of the portfolio to 60% and lowered the probability of success to 80%, he or she could only raise the initial withdrawal rate to 3.2%. This would require 18.5% less savings, but would subject the retiree to considerably more market risk

They talk about it in terms of how much the withdrawal rate increases and how much you need to save.

Another way to look at it is to keep the withdrawal rate constant and see how increasing the equity allocation affects your chances of success.

This graph is based on a Boglehead Baseline Portfolio — no cash holdings and a lower cost than Blanchett et al. assumed. (See my last post for more on that.)

At 30% equities you have a 60% chance of success. At 50% equities you have a 70% chance of success. And things flatline at that point; everything above 50% equities has approximately the same success rate.

This echoes their point that making dramatic increases in your equity exposure doesn’t seem to help very much. You could triple your equities — going from 30% to 90% — and only see a 10% increase in your chances of success. Most people wouldn’t consider that a great tradeoff.

## Sequence of Returns

The whole reason I started down this path was that I was curious: what kinds of returns might a retiree actually see over 30 years in this low yield world that causes a 4% initial withdrawal rate to fail?

One of the difficulties of this kind of probability of success analysis is that it is difficult to come up with good metrics that capture all of the nuance. Earlier this year Milevsky wrote an article talking about this challenge.

Should a retiree be indifferent to all plans with an equal success or failure rate? All 10% shortfall probabilities are equal, but some are more equal than others. In less Orwellian but slightly more technical terms, different statistical distributions can share the same tail probability but have distinct risk and return profiles

Imagine a plan that has a 100% chance of failure. But “failure” means it was $1 short in the 30th year every time. Now imagine another plan that has a 1% chance of failure. But when ** it** fails, you run out of money 3 years into retirement. Suddenly just looking at probability of success feels like it isn’t telling you everything you want to know.

## Three scenarios from thousands

I took three of the Monte Carlo scenarios (chosen basically at random) from this Low Yield World to see what failure actually looked like.

For this retiree, the portfolio failed after 28 years. Most of us will be dead at that point in our retirement, so calling it a failure already begins to be somewhat questionable, but that criticism is common to all SWR research. Over the 30 year period, equities lost money 13 years, including 3 separate periods where equities lost money for at least three years in a row. (In all of US history there have only been 4 instances of back-to-back-to-back losses; the Great Depression; the 2000 bubble; 1912–1914; 1916–1918.) There are only 7 years when equities returned over 10%. The CAGR was a meager 0.31% over 30 years, which was driven by low equity returns that were pummelled by repeated losses.

Despite that grim outlook, the portfolio still lasted 28 years.

This time the portfolio was exhausted after 22 years. The first decade of retirement was brutal, with a 35% loss in the third year of retirement (which would make it the 4th worst year in market history). The CAGR of the first decade of retirement was -2.97%. Things pick up for the rest of retirement but there are still 14 losing years out of 30. (The Great Depression is only period of US history that saw a similar ratio of down years.)

The third scenario is pretty grim. Portfolio failure after only 12 years. The average life expectancy for a male at age 65 is 17 years, so you’re pretty certain to outlive this portfolio.

There are four years of losses to start off retirement: -21%, -7%, -15%, -23%. There are only 2 years of gains in the first decade of retirement. The CAGR of the first decade is a truly horrible -9.63%.

It is no surprise the portfolio ran out after that, though this feels like more a doomsday scenario rather than just a “low yield” scenario. Even the ten years around the Great Depression, 1929–1939, had a CAGR of only -1.16%. (Most people don’t realise that in the middle of the Great Depression the stock market returned 52% in 1933 and 1935.) So we’re talking about a scenario substantially worse than the Great Depression.

Am I able to draw any lessons from this limited sampling of failures? A lot of the failure seems to be driven by limited (sub 10%) equity returns when the market is up and frequent losses that keep knocking the portfolio down. Even under those trying circumstances, most portfolios last at least 20 years. (95% of Boglehead-style portfolios survive 20 years with the Low Yield model when taking 4% withdrawals.)

Do you think the next 30 years is going to look like one of those failure scenarios? I guess I’m too much of an optimist to buy into that. Even if returns are muted and yields are low…it is hard for me to believe that we will see such recurrent market losses. Maybe I just have too much faith in mean reversion and government intervention.

For what it is worth, the paper came out in 2013. Since then the market returns for the S&P 500 have been:

`2013: 33.35%`

2014: 12.43%

2015: 0.29%

2016: 14.61% (year to date, so still time to drop a lot!)

## P.S. Mortality-weighting

Finally, we know that using a fixed 30-year lifespan gives a misleadingly conservative picture. If we use mortality-weighting (i.e. you have to both run out of money **and** still be alive when it happens) then the chance of portfolio success for a low-cost 60/40 portfolio increases to 86%.