# Volatility & Risk Part 2: Sequence of Returns Risk

Volatility poses two main risks to your financial success – a behavioral risk and a mathematical risk. How these risks affect us depends upon the journey and the destination.

The behavioral risk, that we will deviate from the plotted course, accompanies us throughout the journey. It causes our real-life human investor performance to lag what it would be if we were robots.

The sequence of returns risk is a mathematical risk that is caused by cashflow and magnified by volatility. It peaks as we approach and shortly after we’ve arrived at our destination.

## The impact of volatility is not symmetrical

If the price of a holding makes swings up and down of 10%, then the net effect is a slow erosion in value. This is because the percentage of the price movement applies to the amount of money that is there. For example, if you have a stock worth \$100 and there is a 10% drop, then it is now worth \$90. If that holding then goes back up by 10%, it is worth \$99. You’ve lost \$1. If this process repeats, then the value slowly erodes.

#### Average returns vs compounded annual growth rate

The simple average return for the above holding period is zero. However, the compounded annual growth rate (CAGR) is -1.6%/yr. This is why we look at CAGR when considering our portfolio performance rather than a simple average.

#### Fortunately, market swings are also not symmetrical.

Over time, there are generally larger percentage increases than decreases. However, the idea that a percentage price swing applies to the amount of money is important to understand the sequence of returns risk.

## Sequencing Risk or Sequence of Returns Risk

#### The sequence of returns doesn’t matter to a static portfolio.

Whether the good or bad returns come early or late in the investment period doesn’t really matter if the money was just sitting there. Let’s take two portfolios of \$100K that are static (no annual contributions or withdrawals). Both experience the same average annual return of 7%. However, the returns are not symmetrical (+10%, +20%, -10%) and they occur randomly. They have different “sequence of returns” or returns paths“. At the end of six years, there is no difference regardless of the sequence of returns. The CAGR is 7.1% for either portfolio.

#### The sequence of returns affects dynamic portfolios.

In contrast, when cash is being added or taken out of an account, then it does change the outcome. Money being added isn’t exposed to the returns that predate it and money that is taken out does not get the returns that follow. Hence, the sequence of returns before and after cashflows can make a difference in the outcome.

If there are bad returns when our invested capital is at its peak, then the impact is greater. A 20% drop for a \$100K portfolio is \$20K and for a \$1M portfolio, it is \$200K. When we need money, we need it in actual dollars and not a percentage of our account. So, the impact (in actual dollars) is much greater when our accounts have more money in them.

#### The risk from losses is greatest towards the end of the accumulation period.

This makes sense because that is the time when our invested capital will be the greatest. Let’s illustrate the math using another example. Two portfolios with the same sequence of returns used in the static portfolio model. The early riser has big gains early on and some losses at the end. The late bloomer has some losses early on, but a strong finish. Instead of a static portfolio, we will contribute \$25K/yr each year.

As you can see, even though these two portfolios had the same returns and same annual contributions, the one where the losses occured towards the end of the contribution phase did much worse than the one where the losses were experienced early on. The effect of a percentage loss or gain was largest when applied to the peak amount of money invested.

#### During the withdrawal period, the risk from a bad sequence of returns is highest at the beginning.

We would have our highest amount of invested capital at the beginning of drawdown (like the start of retirement). So, it makes sense that this would be the time when we are most vulnerable to losses. Let’s illustrate this with two portfolios worth \$500K that we draw \$25K/year from. In one, we make a clean escape from the workforce and have strong returns early on. In the other, we stumble into retirement with some losses early on.

As you can see, the portfolio with a favorable sequence of returns slowly grows despite the withdrawals at 2.2%/yr. Conversely, the one with losses early on never makes up for that and grows ~0.4%/yr. If inflation is in the 2%/yr range, then that portfolio is slowly losing its buying-power.

## Sequencing risk is greatest at our destination.

The destination is the point where you start to need the money that is in your portfolio. We can have many financial destinations for different goals, like paying for our kids’ education or buying a house. However, our biggest financial destination is likely to be paying for our retirement.

As we approach or are newly arrived at these destinations, our invested capital is at its largest. Therefore, so is our sequence of return risk.

### Effect of a terrible vs good sequence of returns on a simulated retirement portfolio.

Below are two simulated retirement portfolios with the same contributions and withdrawals. The investors save \$25K/year over a 30-year period and then draw an income of \$128K/year over a 30-year retirement. The annual returns are identical except for a 5-year window on either side of retirement.

The lucky investor gets good returns around their destination while the unlucky one has poor returns at the “time of arrival”. There is even a 30% bear market during that window. The unlucky investor experiences that the year that they retire and the lucky one gets hit 5 years later. The average annual returns during this “risk window” are the same (4.5%/yr) and for the overall period (6.8%/yr). The volatility as depicted by standard deviation is higher during the “risk window” at 16.9% than the overall time period (13.6%).

In the above model, the “danger period” was a couple of years on either side of the destination. If we were lucky, we end up with \$2M at the end of the period. If we were unlucky, then we run out of money before we die. The problem is that we don’t know whether we will get lucky or not in advance. Further, in real life, it is not an all or nothing “risk zone”. It is a continuum. How far in advance of or after arrival we want to attenuate our sequencing risk, if at all, is an individual decision.

## Sequence of returns and planning for your destination.

So, as demonstrated, how lucky we are with not only our investment returns but also the sequence of those returns can impact how big our portfolio gets when we arrive at our financial destination. The return path of those early years at our destination also impacts how well our financial capital survives. We cannot know or change how lucky we will be. However, we can plan more broadly to minimize the impact of luck on our success.

#### Sequence of returns risk only exists when there is cashflow.

We can affect how much cash flows into and out of our accounts. During the accumulation years, that means some combination of earning more and spending optimally. During the drawdown phase, we may not be able to earn more cash. There would be some baseline costs, but there may be some flexibility to adjust discretionary spending. For example, if in a bear market, perhaps putting off some “big spends” until it recovers.

##### Cash flow flexibility helps.

Spending wisely will look different to everyone, but may cost less money than you think. The decreased flexibility of extreme situations, like for those striving for leanFIRE, can make the sequence of returns particularly risky. Those who have achieved fatFIRE are in an obviously better position as long as they can stomach temporarily scaling back their financially-fatty lifestyle if they are unlucky.

#### The risk is highest when our portfolio is at its peak & it is magnified by volatility.

Knowing this, we can adjust the risk and volatility profile as we approach our destination to attenuate that risk.

Like all of investing, risk and reward are related. There are trade-offs between sequencing risk and other risks that we will explore in the next post. There are also many ways that we can plan for sequence of returns risk.

1. Lyndon says:

Another great post LD !. Something I am trying to wrestle with is the percentage of Bond allocation in a portfolio. Government Bonds to me represent a portfolio stabilizer as opposed to a long term wealth creator. In other words with low yields, taking into account taxation and inflation bonds represent ” dead money “. I feel the returns of bonds over the last 30 years look great because of the rates tumbling from high double digits to where we are today resulting in capital gains. We may be in a ” new normal of low rates for a long time “…only time will tell. The best predictor of a bond portfolio rate of return is the YTM which is below 2%. Assume a person has reached the ” destination ” and
1. Receives enough income from their investments by way of distributions/dividends to live on where they DO NOT need to access their capital, how does that change your sequence of returns discussion ?
2. There is a school of thought advocated by some investment counsellors catering to high net worth individuals, that one needs to have 3 years of living expenses in cash or equivalents to ride out a significant market correction so as to not access your capital at the worse possible time. This allocation would be as a substitute for a bond allocation in the portfolio. The rationale being equities create wealth in the long run. Your thoughts on this idea ??
Thanks as usual in advance,
Lyndon

1. Thanks Lyndon. I have exactly the same feeling about bonds and am oscillating about how much to hold. This is why I decided to break the stabilization piece into two parts. The effect of stabilization on behavioral risk is key to all of us. I think the mathematical risk is not necessarily important to all of us. If we have enough wealth that we won’t run out of money due to an unlucky path, then it is less important. For those with a long drawdown period, limited ability to scale back spending, or a borderline sufficient portfolio (like for leanFIRE) – it becomes very important.

I have also been thinking about your second point about having some cash or GICs as a buffer. I think that it is more psychological or a form of mental accounting because it is basically the same as having a fixed income or cash allocation. That doesn’t mean it is bad. From a behavioural risk standpoint, I emotionally would be better able to whether a downturn knowing in a very straightforward way that I have enough money to live in the near term. In the long-term it may cut into my returns mathematically. However, my emotional beast doesn’t understand long-term or math – it lives in the now and is simple. I plan to hit some more of the math around the pros/cons of trying to attenuate sequencing risk with asset allocation in the next post.
-LD

1. Grant says:

LD, Larry Swedroe looked at this and found it to be suboptimal, although helpful from a behavioural point of view. Having a cash cushion is essentially a form of bucket strategy. By spending from the cash bucket during a crash, you are not rebalancing (buying stocks when they are down), so miss out on getting stocks on the cheap so impairing long term returns. So better just to stick with a fixed allocation stocks/bonds portfolio and rebalance and spend from it during the withdrawal phase.

1. Thanks Grant. That is actually how I feel too. Separating a “cash reserve” or temporary bonds ladder is mental accounting. It can be psychologically soothing (which is important for many people to execute), but is mathematically/logically flawed. I think the right behaviourally-driven asset allocation is the way to go. If a sequencing disaster, then income and spending are the other (probably better) levers to pull. Those who are skimming the edges of viability with no income/spend lever are at risk.
-LD

2. camille goure says:

Hey great visual demonstrations of retirement portfolio risk. Love your blogs and explanations.
What are your thoughts on borrowing \$\$ if your the unlucky investor and allowing your portfolio to recover before beginning drawing down? Otherwise I’m thinking the unlucky investor will have to postpone their retirement a few years.

1. Thanks Camille. It is an excellent question that will require some posts to flesh out. A few points. There is an argument to “diversify” against temporal risk (ie an unlucky sequence of returns) by making your invested capital more steady over the investing lifetime. That basically means using leverage when young (to magnify the lack of cash) and then not when older. Of course, the problem with any leverage is that it magnifies the emotions of fear and greed that drive bad investor behavior. Especially when you have little financial wiggle room (like when young) or at a major life-change point like retirement. If retirement is going to be tight, then planning to attenuate sequencing risk leading up to it may be helpful. However, that also comes at a potential cost. I think this is a great use of a professional financial planner a few years before planning retirement.
-LD

3. Anant Murthy says:

Hi LD.

I’m young (~50) and close to retirement, so sequence of return risk, clearly explained as always by looniedoctor, is a major concern for me, especially now with coronavirus market instability.

As LD says, during accumulation phase, work (earn) a lot, spend little, save a lot, and have enough bonds for behavioral risk and perhaps return optimization. It’s too late for me.

At drawdown (more or less now), I propose to “clamp” expenses. For a high income professional, that clamp could be very high, say \$200K. Then, as Lyndon says, set aside >3x that in low risk holdings, which for me is HBB (corporation to stabilize annual dividend draw down), bond fund (TFSA) and ZAG (RRSP) to be drawn down in that order.

That frees me from further concern about equity-bond asset allocation and for that matter from overly detailed asset location decisions – except for the way I view the TFSA, I pretty much use LD’s portfolio optimizer.

I’d like feedback from experts like you as it’s not too late to correct course!

icudoc

1. Hey ICU Doc. I’d say my financial expertise is a work in progress 🙂 I think having enough discretionary spending built into retirement planning that you can roll with the punches is very important. I would experiment with clamping expenses before retiring to see how palatable it is. My uncle FIRE’d in his early forties and they “practiced living poor” as the referred to it for year in advance. They discovered what they could handle (less restaurants, making clothes and other items for themselves) and what they could not (powdered milk). For the high-income crowd it is definitely relative!
-LD

4. Love the analysis LD.

SORR is something to consider/fear as you approach your retirement date. There are things you can do that can minimize its impact such as having a few years of living expenses in cash so you don’t have to touch the portfolio in a down market. Of course that means you have cash drag on your portfolio doing so but it may be worth it for peace of mind.

Last year I started de-risking my portfolio as I am approaching the window of danger for retirement. Of course the market went on to have one of the best years ever and I didn’t quite capture all of it but in the long run its safer to still have done it