In a previous article, we examined Sustainable Withdrawal Rate (SWR), which is the maximum amount clients can withdraw in retirement with an acceptable risk of depletion. The analysis involved categorizing expenses as either essential, basic or discretionary; defining the acceptable risk of depletion for each expense type (10% for essential and basic, 50% for discretionary); and developing a base case to calculate SWR for various ages.
A key takeaway of that analysis was that the famous 4% rule won’t prevent many retirees from running out of money.
Impact of alpha
Alpha is a measure of how a portfolio performs relative to its benchmark index. All else being equal, positive alpha means your equities are performing better than the index; negative means they’re performing worse. How does alpha impact SWR? Here are the numbers:
Table 1: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses (Optimum Equity/Fixed Income) 

Worse: Alpha = 2% 
Base Case: Alpha = 0% 
Better: Alpha = 2% 

60  2.80% (50/50)  3.03% (55/45)  3.59% (55/45) 
65  3.07% (50/50)  3.31% (55/45)  3.85% (55/45) 
70  3.46% (50/50)  3.68% (55/45)  4.20% (55/45) 
75  4.07% (40/60)  4.29% (55/45)  4.83% (60/40) 
Table 2: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses (Optimum Equity/Fixed Income) 

Worse: Alpha = 2% 
Base Case: Alpha = 0% 
Better: Alpha = 2% 

60  3.35% (60/40)  3.67% (60/40)  4.34% (60/40) 
65  3.69% (60/40)  4.01% (60/40)  4.64% (60/40) 
70  4.22% (60/40)  4.51% (60/40)  5.13% (60/40) 
75  5.05% (40/60)  5.31% (60/40)  5.89% (60/40) 
Table 3: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses (Optimum Equity/Fixed Income) 

Worse: Alpha = 2% 
Base Case: Alpha = 0% 
Better: Alpha = 2% 

60  4.13% (40/60)  4.48% (70/30)  5.50% (70/30) 
65  4.68% (45/55)  5.13% (70/30)  6.08% (70/30) 
70  5.43% (50/50)  5.93% (65/35)  6.78% (70/30) 
75  6.73% (55/45)  7.07% (55/45)  7.92% (70/30) 
Alpha has a significant impact on the SWR for all three expense categories. The higher the alpha, the larger the SWR.
Impact of beta
Beta measures the volatility of your equities relative to their benchmark index. But what if your equities perform the same as the benchmark but with lower volatility (beta less than one), or higher volatility (beta larger than one)? Here are SWRs for each situation:
Table 4: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses (Optimum Equity/Fixed Income) 

Lower Volatility: Beta = 0.8 
Base Case: Beta = 1 
Higher Volatility: Beta = 1.2 

60  2.95% (65/35)  3.03% (55/45)  3.12% (45/55) 
65  3.22% (65/35)  3.31% (55/45)  3.36% (45/55) 
70  3.62% (65/35)  3.68% (55/45)  3.73% (45/55) 
75  4.23% (65/35)  4.29% (55/45)  4.33% (50/50) 
Table 5: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses (Optimum Equity/Fixed Income) 

Lower Volatility: Beta = 0.8 
Base Case: Beta = 1 
Higher Volatility: Beta = 1.2 

60  3.36% (60/40)  3.67% (60/40)  3.94% (55/45) 
65  3.71% (60/40)  4.01% (60/40)  4.24% (55/45) 
70  4.28% (60/40)  4.51% (60/40)  4.79% (60/40) 
75  5.17% (50/50)  5.31% (60/40)  5.48% (50/50) 
Table 6: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses (Optimum Equity/Fixed Income) 

Lower Volatility: Beta = 0.8 
Base Case: Beta = 1 
Higher Volatility: Beta = 1.2 

60  4.01% (70/30)  4.48% (70/30)  4.98% (65/35) 
65  4.71% (70/30)  5.13% (70/30)  5.56% (70/30) 
70  5.52% (60/40)  5.93% (65/35)  6.40% (70/30) 
75  6.62% (60/40)  7.07% (55/45)  7.47% (65/35) 
Beta has a minor impact on the SWR for essential expenses, some impact on basic expenses, and a large impact on discretionary expenses.
The general belief in the financial industry is that lower volatility is better for portfolios. Our aftcast shows the exact opposite: Reduced volatility reduces the SWR. That means if you withdrew the same amount from a portfolio with an index return (beta equals one) and then somehow managed to reduce its beta while keeping its alpha exactly the same, you would end up with a shorter portfolio life.
If you want the same portfolio longevity with lower beta, you must increase alpha. If that weren’t so, cash in the bank would yield a longer portfolio life (or a higher SWR) than a portfolio with an optimal asset mix. And we all know it doesn’t.
Keep in mind that during the distribution stage, it is not the volatility of returns that reduces the portfolio’s longevity but the sequence of returns and inflation. (For more on this, see the course Determinants of Growth in Distribution Portfolios.)
Impact of asymmetric beta
After 2008, some fund manufacturers introduced products they billed as having lower volatility with a downside limit, making fluctuations asymmetrical. While these strategies may look attractive in theory, it’s still unclear how they’ll perform during future black swan events.
We’ll look at two scenarios:
 The equity portion has a beta of 0.6 (60% volatility of the index), and it’s designed not to lose more than 10%.
 The equity portion of the portfolio has a beta of 0.7 and it’s designed not to lose more than 15%.
With these loss limits on the equity portion, the portfolio’s overall loss will likely be lower. Here are the SWRs:
Table 7: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses (Optimum Equity/Fixed Income) 

Beta = 0.6 Max. Equity Loss=10% 
Beta = 0.7 Max. Equity Loss=15% 
Base Case: Beta = 1 

60  2.92% (65/35)  2.96% (70/30)  3.03% (55/45) 
65  3.25% (65/35)  3.26% (70/30)  3.31% (55/45) 
70  3.67% (65/35)  3.67% (70/30)  3.68% (55/45) 
75  4.39% (70/30)  4.30% (70/30)  4.29% (55/45) 
Table 8: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses (Optimum Equity/Fixed Income) 

Beta = 0.6 Max. Equity Loss=10% 
Beta = 0.7 Max. Equity Loss=15% 
Base Case: Beta = 1 

60  3.17% (60/40)  3.29% (60/40)  3.67% (60/40) 
65  3.55% (60/40)  3.67% (60/40)  4.01% (60/40) 
70  4.14% (60/40)  4.23% (60/40)  4.51% (60/40) 
75  4.98% (60/40)  5.09% (60/40)  5.31% (60/40) 
Table 9: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses (Optimum Equity/Fixed Income) 

Beta = 0.6 Max. Equity Loss=10% 
Beta = 0.7 Max. Equity Loss=15% 
Base Case: Beta = 1 

60  3.93% (70/30)  4.05% (70/30)  4.48% (70/30) 
65  4.44% (65/35)  4.60% (70/30)  5.13% (70/30) 
70  5.17% (55/45)  5.35% (60/40)  5.93% (65/35) 
75  6.46% (35/65)  6.44% (60/40)  7.07% (55/45) 
With asymmetric beta, we observe a lower SWR than in the base case. The cost of maintaining a lower beta exceeds the benefits of limiting losses. (This conclusion needs to be revisited after the next black swan event using data from the actual experience.)
Impact of rebalancing
Some investors rebalance annually if the asset mix deviates from its target even by one dollar. Others leave the mix alone unless the deviation exceeds a specific threshold, such as 3% or 5%. How do different rebalancing thresholds impact the SWR?
In High Expectations & False Dreams: One Hundred Years of Stock Market History Applied to Retirement Planning (2001), I show that rebalancing once every four years can increase portfolio life. You’ll get best results when you follow the wellknown Presidential Cycle—rebalancing only at the end of the U.S. presidential election year.
Below are details on the sustainable withdrawal rates for rebalancing threshold and frequency.
Table 10: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
Annual Rebalancing Threshold = 0% 
Base Case: Annual Rebalancing Threshold = 3% 
Annual Rebalancing Threshold = 5% 
Rebalance Every Four Years 

60  3.04%  3.03% (55/45)  3.06%  3.21% 
65  3.33%  3.31% (55/45)  3.33%  3.48% 
70  3.70%  3.68% (55/45)  3.72%  3.85% 
75  4.29%  4.29% (55/45)  4.32%  4.49% 
Table 11: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
Annual Rebalancing Threshold = 0% 
Base Case: Annual Rebalancing Threshold = 3% 
Annual Rebalancing Threshold = 5% 
Rebalance Every Four Years 

60  3.67%  3.67% (60/40)  3.68%  3.84% 
65  3.98%  4.01% (60/40)  4.01%  4.22% 
70  4.50%  4.51% (60/40)  4.52%  4.70% 
75  5.33%  5.31% (60/40)  5.31%  5.52% 
Table 12: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
Annual Rebalancing Threshold = 0% 
Base Case: Annual Rebalancing Threshold = 3% 
Annual Rebalancing Threshold = 5% 
Rebalance Every Four Years 

60  4.50%  4.48% (70/30)  4.48%  4.64% 
65  5.13%  5.13% (70/30)  5.12%  5.46% 
70  5.91%  5.93% (65/35)  5.92%  6.06% 
75  7.05%  7.07% (55/45)  7.05%  7.18% 
Increasing rebalancing frequency from annually to once every four years provides a slightly larger SWR in all expense categories. That’s because, in multiyear down markets, rebalancing compounds permanent losses. Rebalancing every four years helps you avoid this. On the flipside, in an up market, it allows you to compound gains more effectively. It is also important to note that the automatic monthly or quarterly rebalancing options some funds offer can harm portfolio longevity.
If rebalancing annually, variations of the threshold between 0% and 5% have no perceivable impact on SWR. If you want to reduce costs related to frequent rebalancing (capital gains taxes, trading costs, your time), use a 5% threshold.
Impact of not rebalancing
In this scenario, we start with the optimal asset allocation. Withdrawals are initially from the fixedincome portion of the portfolio, until it depletes. After that, withdrawals are from the equity portion. The portfolio is never rebalanced. Here are the sustainable withdrawal rates:
Table 13: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
No Rebalancing  Base Case  
60  3.41%  3.03% (55/45) 
65  3.68%  3.31% (55/45) 
70  4.04%  3.68% (55/45) 
75  4.58%  4.29% (55/45) 
Table 14: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
No Rebalancing  Base Case  
60  3.54%  3.67% (60/40) 
65  3.89%  4.01% (60/40) 
70  4.39%  4.51% (60/40) 
75  5.06%  5.31% (60/40) 
Table 15: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
No Rebalancing  Base Case  
60  4.56%  4.48% (70/30) 
65  5.03%  5.13% (70/30) 
70  5.65%  5.93% (65/35) 
75  6.96%  7.07% (55/45) 
Figure 1: Typical average asset mix for the No Rebalancing Strategy, starting with 50/50 asset mix, 3% initial withdrawal rate
Not rebalancing during retirement increases the SWR for essential expenses only, which means early black swan events are managed better. There’s little or no improvement for basic and essential expenses.
Agebased asset allocation
With agebased asset allocation, the equity portion’s reduced each year. The popular formula is:
Equity % = 100 – Age
At ages 60, 65, 70 and 75, the equity allocation is 40%, 35%, 30% and 25%, respectively. Sustainable withdrawal rates are:
Table 16: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
AgeBased  Base Case  
60  2.55%  3.03% (55/45) 
65  2.90%  3.31% (55/45) 
70  3.27%  3.68% (55/45) 
75  3.91%  4.29% (55/45) 
Table 17: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
AgeBased  Base Case  
60  2.91%  3.67% (60/40) 
65  3.37%  4.01% (60/40) 
70  3.89%  4.51% (60/40) 
75  4.56%  5.31% (60/40) 
Table 18: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
AgeBased  Base Case  
60  4.30%  4.48% (70/30) 
65  4.79%  5.13% (70/30) 
70  5.55%  5.93% (65/35) 
75  6.70%  7.07% (55/45) 
Accelerated agebased asset allocation
This provides a more aggressive portfolio than the standard agebased asset allocation just described. The formula is:
Equity % = (100(Age × Age)/100)
So, at ages 60, 65, 70 and 75, the equity allocation is 64%, 58%, 51% and 44%, respectively. The following figures show the average asset mix for both types of agebased asset allocation strategies:
Figure 2: Typical average asset mix for the AgeBased Asset Allocation Strategy
Figure 3: Typical average asset mix for the Accelerated AgeBased Asset Allocation Strategy
Here are the sustainable withdrawal rates:
Table 19: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
Accelerated AgeBased  Base Case  
60  2.57%  3.03% (55/45) 
65  2.98%  3.31% (55/45) 
70  3.35%  3.68% (55/45) 
75  3.92%  4.29% (55/45) 
Table 20: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
Accelerated AgeBased  Base Case  
60  3.47%  3.67% (60/40) 
65  3.67%  4.01% (60/40) 
70  4.12%  4.51% (60/40) 
75  5.02%  5.31% (60/40) 
Table 21: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
Accelerated AgeBased  Base Case  
60  4.40%  4.48% (70/30) 
65  5.07%  5.13% (70/30) 
70  5.73%  5.93% (65/35) 
75  6.83%  7.07% (55/45) 
Agebased asset allocation strategies provide a markedly lower SWR for all expense categories. There are two reasons:
 As time goes on, more assets are allocated to bonds. This reduces volatility. Reducing volatility while keeping the same alpha on the equity side reduces the SWR, as we saw earlier with the impact of beta.
 Unlike conventional bonds, equities provide some degree of inflation protection. With agebased asset allocation strategies, as time goes on, the portfolio has less equity, diminishing the ability to protect against inflation.
The glide path
Downward Glide Path: The client allocates 50% to equities during the first 10 years of retirement, 40% during the next 10 years, and 30% after that for the rest of his life.
Upward Glide Path: This is the opposite of the downward glide path. Proponents claim the impact of the sequence of returns is highest during the early years of retirement, hence the lower equity allocation during that period. The client allocates 30% to equities during the first 10 years of retirement, 40% during the next 10 years, and 50% after that for the rest of his life.
Figure 4: Typical average asset mix for the Downward Glide Path
Figure 5: Typical average asset mix for the Upward Glide Path
The sustainable withdrawal rates are:
Table 22: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
Downward Glide Path 
Upward Glide Path 
Base Case  
60  2.87%  2.98%  3.03% (55/45) 
65  3.14%  3.26%  3.31% (55/45) 
70  3.54%  3.65%  3.68% (55/45) 
75  4.17%  4.30%  4.29% (55/45) 
Table 23: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
Downward Glide Path 
Upward Glide Path 
Base Case  
60  3.44%  3.33%  3.67% (60/40) 
65  3.78%  3.69%  4.01% (60/40) 
70  4.34%  4.17%  4.51% (60/40) 
75  5.12%  4.96%  5.31% (60/40) 
Table 24: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
Downward Glide Path 
Upward Glide Path 
Base Case  
60  4.28%  4.33%  4.48% (70/30) 
65  5.03%  4.82%  5.13% (70/30) 
70  5.78%  5.46%  5.93% (65/35) 
75  6.97%  6.69%  7.07% (55/45) 
Glidepath strategies consistently produce a lower SWR compared to the base case.
Asset allocation based on the Presidential Cycle
Historically, markets experience belowaverage growth during the first and second years of a presidential term. The picture becomes brighter in the third and fourth years. Since 1900, the Dow Jones Industrial Average (DJIA) grew on average 6.6%, 1.1%, 11.5%, and 7.8% during the first, second, third and fourth years of a presidential term, respectively.
We anticipate better outcomes by harmonizing the asset mix with this cycle, just as we did with rebalancing. Using aftcasting, we calculate the optimal equity allocation for Canadian markets as 55%, 50%, 70% and 70% during the first, second, third and fourth years of the presidential term, respectively. Here are sustainable withdrawal rates:
Table 25: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
Presidential Cycle  Base Case  
60  3.05%  3.03% (55/45) 
65  3.32%  3.31% (55/45) 
70  3.67%  3.68% (55/45) 
75  4.31%  4.29% (55/45) 
Table 26: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
Presidential Cycle  Base Case  
60  3.57%  3.67% (60/40) 
65  3.88%  4.01% (60/40) 
70  4.47%  4.51% (60/40) 
75  5.22%  5.31% (60/40) 
Table 27: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
Presidential Cycle  Base Case  
60  4.43%  4.48% (70/30) 
65  5.03%  5.13% (70/30) 
70  5.88%  5.93% (65/35) 
75  7.01%  7.07% (55/45) 
The results are clearly not better than the base case. We saw earlier that rebalancing every four years based on the Presidential Cycle produced better results than the base case. Following this strategy reduced the negative effects of a potential multiyear bad sequence of returns, while keeping the asset mix reasonably steady.
Here, we go one step further: We create significantly larger fluctuations in the asset mix throughout the presidential cycle. However, not all cycles form a bad sequence of returns. Changing the entire asset mix—as opposed to rebalancing it—leads to overkill. The strategy does not, therefore, produce better results than the base case.
Asset allocation based on P/E ratio
Because we’re interested in the entire market, we use the average P/E for the index. This gives us a measure of market exuberance or lethargy. If the P/E is low (e.g., below 10) it indicates an undervalued equity index with upside potential. If it’s high (e.g., over 20), it indicates an overvalued index.
After a secular bullish trend, an overvalued index corrects itself—often violently. This creates an adverse sequence of returns, which can drastically reduce portfolio life. By correlating the asset mix to market P/E, we’re trying to minimize this damage.
We optimize the asset mix as a function of P/E for maximum SWR and generate the following formula:
Equity % = 90 – (2.7 X P/E )
P/E ratio is only one of many factors that can influence future performance. Markets can be overvalued for several years before a significant correction takes place. We don’t recommend abandoning equities altogether just because of high P/Es. By the same token, we don’t recommend allocating excessively to equities simply because P/Es are low. We maintain a minimum 30% and maximum 70% equity allocation, regardless of the result of this formula. Here are examples of asset allocations for various P/E ratios:
Table 28: Asset Allocation in the Calendar Year Following the PE Ratio Observed  
Market Average P/E Ratio at the end of the year: 
Asset Mix during the following year: (Equity/Fixed Income) 
5  70 / 30 
10  63 / 37 
15  50 / 50 
20  36 / 64 
25  30 / 70 
30  30 / 70 
Here are sustainable withdrawal rates:
Table 29: Sustainable Withdrawal Rate for Essential Expenses  
Retirement Age: 
SWR for ESSENTIAL Expenses  
P/E Based  Base Case  
60  3.65%  3.03% (55/45) 
65  3.96%  3.31% (55/45) 
70  4.38%  3.68% (55/45) 
75  5.03%  4.29% (55/45) 
Table 30: Sustainable Withdrawal Rate for Basic Expenses  
Retirement Age: 
SWR for BASIC Expenses  
P/E Based  Base Case  
60  3.99%  3.67% (60/40) 
65  4.35%  4.01% (60/40) 
70  4.87%  4.51% (60/40) 
75  5.75%  5.31% (60/40) 
Table 31: Sustainable Withdrawal Rate for Discretionary Expenses  
Retirement Age: 
SWR for DISCRETIONARY Expenses  
P/E Based  Base Case  
60  4.62%  4.48% (70/30) 
65  5.12%  5.13% (70/30) 
70  5.75%  5.93% (65/35) 
75  6.82%  7.07% (55/45) 
P/Ebased asset allocation produces a significantly larger SWR for essential expenses. The improvement’s less pronounced for basic expenses. As for discretionary, there’s no significant difference.
P/Ebased asset allocation can make an important contribution in reducing the effect of “unlucky” outcomes. But, it has an insignificant effect for the median outcome over the long term.
Assumptions
We use the S&P/TSX index as the equity benchmark, plus an average dividend yield of 2.5%, less average total costs of 2%.
The fixedincome return is a historical 6month CD plus 0.5%, net of costs. This approximates a bond ladder with an average maturity of 5 to 7 years. Rebalancing occurs annually, if the target asset mix deviates by more than 3%.
Withdrawal amount is indexed to historical CPI rates annually.
This article is an excerpt from Part 1 of a twopart course, available on cecorner.ca, that takes the key lessons of our discussion of SWR (also available on cecorner.ca) and applies them to a variety of common retirement income strategies.
We discuss:
 Investment Performance: The impact of alpha and beta on SWR
 Asset Allocation: Agebased (regular and accelerated), glide path (up and down), presidential cycle, P/E ratio
Part 2 covers:
 Growth Harvesting and Asset Dedication
 Time Segmentation: Bucket strategies
 Withdrawal Strategies: Freeze Cost of Living Adjustment (COLA); limit withdrawals based on portfolio growth or value; pay cut
 Equity Benchmarks: Canada, USA, Britain, Japan, Australia