Sequence of Returns Risk Dirk Cotton November 2014
What is Sequence of Returns (SOR) Risk? Most define SOR Risk as the probability that a retiree s portfolio will be prematurely depleted by a series of poor returns just before or just after retirement. It is actually a little more complicated than that.
The Basic Math Consider a 5-year series of stock market returns:
The Basic Math No matter how we order the returns, the terminal portfolio value remains $1.03 This is simply the commutative law from high school math: a x b = b x a As long as we are not buying or selling, the order of returns doesn t matter.
The Basic Math Algebraically, we could write the the terminal portfolio value with no spending or savings as: TPV = ( $100) ( 1.10) ( 1.02) ( 0.88) ( 1.08) ( 0.97) TPV = $103.44 We can order those terms any of the 720 possible orders and the TPV will always be $103. We can order the five market returns in 120 different ways
The Basic Math When we sell from this portfolio annually, however, the equation becomes quite different. Spending $12 at the beginning of every year, we get: TPV =0.97 (1.08 (0.88 (1.02 (1.1 ($100-12) - 12) - 12) - 12) - 12) = $44.47
The Basic Math
The Basic Math What is the best of the 120 sequences of returns? Sorted from best to worst.
The Basic Math What is the worst of the 120 sequences of returns? Sorted from worst to best.
SOR Risk and Accumulation We mostly discuss SOR Risk in the context of the post-retirement Spending phase. Is SOR Risk also present when we are saving for retirement? Yes, and we can see this by simply changing the sign of the spending amount in our example above. Let s change the plus $12 we spend to a minus $12 we save.
SOR Risk and Accumulation Algebraically, we simply change this: TPV =0.97 (1.08 (0.88 (1.02 (1.1 ($100 - $12) - $12) - $12) - $12) - $12) to this: TPV =0.97 (1.08 (0.88 (1.02 (1.1 ($100 + $12) + $12) + $12) + $12) + $12)
SOR Risk and Accumulation
Where does SOR Risk come from? It isn t there when we don t buy or sell, so it must appear when we do. It doesn t exist with Social Security benefits, pensions, bond ladders or other non-volatile sources of income we only see it with volatile portfolios. We don t see it with buy-and-hold stock portfolios, even though they are volatile. SOR Risk is the uncertainty of the prices of assets in a volatile portfolio when we will make future purchases or sales of those assets.
Vanguard Total Bond Fund vs. SPY
Interim prices don t matter when you don t buy or sell from a volatile portfolio. No buying or selling bonds
Frequency Spending $55 for 30 years beginning in 1970 with $1,000 portfolio Historical return sequence Worst Sequence -2,017 Best Sequence 2,474 Terminal Portfolio Value
Why are TPV s clustered around a mean?
Frequency Many ways to roll these cases One way to roll the worst case One way to roll the best case Terminal Portfolio Value
Why is SOR Risk so dangerous near retirement age? We ve seen that it stems from price volatility, but it is exacerbated... By the fact that we can t run a negative balance. By the time value of money. When we lose $1 early in retirement, we lose its compounded earnings for perhaps 30 years When we lose it late in retirement, we only lose a few years of its compounded earnings And...
Why is SOR Risk so bad a decade before and after retirement? Because around retirement age is when we are able to place our largest bets.
Why is SOR Risk so bad a decade before and after retirement? SOR Risk is dangerous in early retirement because our portfolio is large and losses are compounded for perhaps 30 years In Accumulation, it is less dangerous because the bets with long-term impact occur when the portfolio is small.
Asset allocation affects SOR Risk
Is a poor sequence of returns early in retirement necessary and sufficient to cause Early Portfolio Failure? Let s define Early Portfolio Failure risk as the probability of a retiree outliving his savings for reasons other than living a very long time. A poor sequence of returns is called a necessary condition for Early Portfolio Failure if you can t have Early Portfolio Failure without it. Overspending early in retirement could cause Early Portfolio Failure even with a good sequence of returns. A poor sequence of returns is not a necessary condition for Early Portfolio Failure.
Is a poor sequence of returns a sufficient condition for Early Portfolio Failure? No, because portfolios often survive a poor sequence of returns early in retirement. What other conditions affect Early Portfolio Failure? Spending phase portfolios don t fail in accumulation phase, even with poor returns Periodic spending buy and hold portfolios aren t exposed to sequence risk Overspending a retiree spending 3% of portfolio value will survive more poor sequences of returns than one spending 5% Unfavorable equity allocation a retiree with a 50% equity allocation will survive more poor sequences than a retiree with a 90% equity allocation
A poor sequence of returns is neither necessary nor sufficient for Early Portfolio Failure. It is possible for your retirement portfolio to fail prematurely with what most would consider a good sequence of returns (i.e., is not necessary). It is possible for your retirement portfolio to survive with what most would consider a poor sequence of returns (i.e., is not sufficient).
Does SOR Risk go away after the first 10 years of retirement? No, but it diminishes with the expected remaining years in retirement.
From Milevsky, Robinson 2005
Do bonds have SOR Risk? Individual zero-coupon bonds held to maturity, as in a bond ladder, don t have SOR Risk because there is no uncertainty about their eventual value. Bond funds do have SOR Risk, because the price at which we will buy or sell shares in the future is subject to interest rate risk and unpredictable. However, sequence of returns risk is lower with bond funds than with stocks because the bonds are less volatile. In other words, their future prices aren t as uncertain. Lower duration bond funds have less SOR Risk than longer duration funds for the same reason.
Does SOR Risk show up anywhere else? Well, yes. If you are retired and have a mortgage you have foreclosure risk. If you plan to pay your mortgage by spending down a stock and bond portfolio, then you might run out of money due to a poor sequence of returns. If you run out of money and can t pay the mortgage, you might have your home foreclosed. So, you have exposed your home, already subject to foreclosure risk, to SOR Risk from your savings. One other place that comes to mind? If you play blackjack and lose a lot early, you will probably have a brief evening in the casino.
Does the market reward SOR Risk? No. Most investment risk has an upside higher returns. SOR Risk is not diversifiable and the market cannot compensate us for it.
Retirement Income Strategies and SOR Risk Pure annuity strategy has no SOR Risk. Pure SWR strategy has more than any other strategy constant dollar spending has the most; spending a percent of remaining portfolio balance has less. Floor-and-upside strategy degree of upside risk depends on the relative size of the upside (risky) portfolio. Time-segmentation (bucket) strategy can t protect you from a bad sequence of returns. Can Buckets Bail-Out a Poor Sequence of Investment Returns?, Moshe A. Milevsky, Ph.D. October 18, 2006
How can you mitigate SOR Risk? You can completely avoid it by funding retirement with Social Security benefits, TIPS bond ladders and life annuities. As the Sustainable Withdrawal Rates (SWR) studies show, you mitigate SOR Risk by spending less from your risky portfolio. However, doing so will lower your standard of living and increase the probability that you will leave a large unspent portfolio at the end of life that could have raised that standard of living. You mitigate SOR Risk by selling a percentage of your remaining portfolio balance each year, rather than a constant dollar amount based on a percentage of your initial portfolio value.
How can you mitigate SOR Risk? You can keep your risky portfolio s equity allocation between about 35% and 70%. You can mitigate SOR risk with a Floor-and-upside strategy that provides safe income to cover non-discretionary expenses and invests the rest in a risky portfolio of assets.
How many ways can 30 years of annual market returns in retirement be ordered? If we knew our future annual portfolio returns in advance, which of course we can t, there is still a huge range of possible outcomes depending on their order. We could know the best possible outcome (they arrive sorted largest to smallest) and the worst (sorted smallest to largest), but the range would be so gigantic as to be useless. There would be 30! possible orders of those returns and predicting the order is impossible.
How big is 30!? It s pretty big: 2.65 x 10 32 265,252,800,000,000,000,000,000,000,000,000
What is the probability that you will experience the worst sequence of returns for 30 years? 1/30! 0.0000000000000000000000000000000038 Same probability as the best sequence
But how big is 30!? 2.65 x 10 32 (30!) is a lot smaller than a googol. That s 1 x 10 100 or about 70!. Researchers at the University of Hawaii (where else?) estimate that there are 7.5 x 10 18 grains of sand (roughly 20!) on all the beaches on earth combined. 30! is 14 orders of magnitude greater. Scientists estimate that there are a septillion (1 x 10 24 ) stars in the observable universe (call it 24!). On a clear night we might see 2,500 of them. 30! is about 48 million times greater than 24!.
And that s why I use 5-year periods for my examples instead of 30-year periods.
Contact Information The Retirement Café http://theretirementcafe.blogspot.com/ E-mail Google+ Twitter JDCPlanning@gmail.com Dirk Cotton BeingSouthern