A portfolio’s Sustainable Withdrawal Rate (SWR) is the maximum amount a client can withdraw throughout retirement with an acceptable risk of depletion. It’s usually expressed in terms of a percentage, such as the famous 4% rule.

This rule suggests that if the client starts withdrawing the dollar amount equal to 4% of assets at the beginning of retirement, and then indexes these withdrawals to CPI throughout, she would have income for 30 years at a reasonable risk.

**Read: How to structure drawdown portfolios**

Different sources publish different SWRs, depending on inputs used. Here are some of the factors affecting SWR:

- Asset mix: Does the analysis use an arbitrary asset mix or is it optimized for the withdrawal rate?
- Equity index: Which equity index has been used? There are significant differences between the Canadian and U.S. markets. Generally, Canadian equities perform better during inflationary times.
- Total return versus index return: Using the total historical return will paint an overly optimistic picture, because the current average dividend yield is half what it was pre-1990s.
- Man-made simulators versus actual historical data: Simulators have deficiencies in modelling market behavior. They use smoothened data, which suffers from “loss of memory” of correlations and black swan events. On the other hand, actual historical data (aftcasting) preserves the sequence of returns, as well as all correlations between stocks, bonds, interest and inflation rates, resulting in a more reliable SWR.
- Portfolio costs: These can be an important part of SWR calculation (see my course “Determinants of Growth in Distribution Portfolios” on cecorner.ca). The higher the portfolio costs, the lower the SWR.
- Underperformance: Most fund managers and investors underperform the index over the long term, either because of behavioral risk factors or fund size and dynamics. This needs to be addressed in the SWR analysis.

There’s another important factor. We already know SWR is based on a reasonable risk of running out of money. This raises questions: What’s reasonable risk? Is a 0% probability of depletion too stringent? What about 50% probability of depletion?

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The answer depends on what your clients need the money for. To determine this, we categorize each expense item in one of three groups as follows.

### 01 Essential

Expenses that are necessary for survival under normal circumstance. Our risk criterion is that the occasional loss of purchasing power must not be larger than 10% at any age. This implies the probability of portfolio depletion must be zero. We don’t want to plan for our client going on a continuous dog-food diet, but we accept occasional belt-tightening.

### 02 Discretionary

Expenses the client is flexible with—the opposite of essential expenses. Donation expenses are an example. The client can accept a 50% probability of occurrence: if she doesn’t have the money, she just won’t donate. This category of expenses affords a much larger SWR. Here our risk criterion is that median outcome must last until death (i.e., 50% probability of depletion).

### 03 Basic

These are expenses for things the client wants, but they’re not critical for survival. For example, she may love going south each winter, but when push comes to shove financially, she can do without. While it’s a non-essential expense, it’s more important than a discretionary expense. Here, our risk criterion is that the probability of portfolio depletion should not exceed 10%. That means there’s a 10% chance the retiree might have to forego this type of expense.

Once we allocate each expense to one of these groups, we’ll have three piles of retirement expenses, each with its own degree of acceptable risk. This risk level is lowest for essential expenses, a little higher for basic expenses and a lot higher for discretionary expenses (see Figure 1, this page). This is the basis of the purpose-driven SWR.

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As for longevity risk, we want 90% certainty the client dies before the portfolio is depleted. We use 95 as the age of death for male clients and 97 for females or couples. For simplicity’s sake, we’ll use 96.

## Methodology

In most retirement plans, forecasts are based on using average growth rates and inflation. They follow the law of averages. In contrast, we use Murphy’s Law (anything that can go wrong, will go wrong) to ensure extreme events are covered.

We also use actual market history, which we call “aftcasting” (as opposed to forecasting). We don’t use Monte Carlo simulators.

Aftcasting displays the outcome of all historical asset values of all portfolios on the same chart. It provides the success and failure statistics with exact historical accuracy because it includes actual historical equity performance, inflation and interest rates, as well as actual historical sequencing/correlation of these data sets.

Our inputs are as follows:

- Equity benchmark and performance: S&P/TSX, index only, starting in 1919 (earliest available TSX data) until the end of 2013, plus an average dividend yield of 2.5%, less average total costs of 2%.
- Fixed income performance: A conventional bond ladder portfolio, held until maturity, with no capital gains or losses. Net yield after costs is 6-month CD plus 0.5%.
- Asset mix: Optimized for each sustainable withdrawal rate, rebalanced annually when the target mix deviates by more than 3%.
- Withdrawal amount: Indexed to historical CPI for each year.

Probabilities we discuss (such as probability of depletion, failure, success) are based on historical market extremes.

## Testing the 4% rule

Let’s see how the aftcast of the 4% rule holds up against our risk criteria. Example: Bob, 65, has $500,000 in his portfolio with an asset mix of 50% equities, 50% fixed income. Starting now, he needs $20,000 annually (4% of the initial portfolio asset value), indexed to CPI until age 96.

Our focus is on lifelong income. For that, we look to the income carpet (see Figure 2, this page). The horizontal scale shows starting years between 1919 and 2000. The vertical scale indicates the client’s age. Each pixel on the carpet shows income received for that particular starting year and age as a percentage of total real income required. Green is good, red is bad.

Historically, in the worst case, the portfolio ran out of money at age 87. By age 96, the probability of depletion was 12%. Let’s see how this risk compares to our guidelines:

### 01 Essential expenses

The maximum allowable loss of purchasing power is 10% at any age. That means we don’t mind seeing a few yellow pixels here and there, but no red (or reddish) pixels are allowed. Therefore, the 4% rule violates our test of reasonable risk for essential expenses.

### 02 Discretionary expenses

The maximum allowable probability of depletion is 50%. Therefore, the 4% rule can be comfortably used for discretionary expenses.

### 03 Basic expenses

The maximum allowable probability of depletion is 10%. Here, we have a 12% probability of depletion. So, the 4% rule also violates our test of reasonable risk for basic expenses, albeit by a small margin.

For an analysis of how to help Bob and to take the rest of this course, please go to cecorner.ca. It has been submitted to IIROC, FPSC and The Institute for accreditation.