mercredi 4 avril 2018

Accumulation-Dynamic Decumulation


Accumulation –Dynamic Decumulation Strategy

Executive Summary

Accumulation-Dynamic Decumulation (ADD) Strategy is an elegant solution for managing withdrawals through retirement. It withdraws a percentage of the available fund. These removes the risk of ruin at the expense of having volatile withdrawal. ADD also uses:
  • A smoothing of the fund:  This reduces the retirement date risk and applies a simple filter for a rational estimate of the fund over the long run.
  • An increase cap on the withdrawal and accrued withdrawal: This provides a provision for adverse deviation and reduces the retirement date risk.
  • A reserve: This manages the negative volatility of the portfolio. It provides protection over 95% of withdrawals.

You can see below the cash flow path in nominal terms at various retirement dates using this strategy.

Features:
  • No risk of ruin
  • No sequence of returns risk over the fund’s value
  • Reduces the date of retirement risk
  • Reduces the volatility of withdrawals
  • Perpetual withdrawals, high bequest* 
  • No direct protection against inflation 
For Spreadsheet testing please use either DropBox or GoogleDrive links.
Please consult the Full Study if you want to explore some more the method.


*May use ADD in combination with Variable Percentage Withdrawal to leave low bequest

Introduction 


The key challenge for preparing for retirement is how to ensure enough money for retirement. The two main methods are buying an annuity or managing our withdrawals. Annuities are safe, illiquid and do not leave money to heirs. Annuities are insured by a third party and as such should be honored. The mortality risk is handled by grouping a large number of participants together and averaging out the mortality. They offer low liquidity as they can’t be sold after they are bought. In their simplest form, they offer no lump sum at death. Managing our withdrawals keeps liquidity and often leaves more than the full principal at death. However, it offers no safety. This post is focusing on the latter method.

The Accumulation Phase

Often we look at decumulation in silo of the accumulation phase. However, there are advantages in looking at them in combination. During the accumulation phase, we can have an early discussion if and how much we want to manage decumulation versus buying an annuity. Buying an annuity requires a great lump sum at a fixed target date. For that objective, a low equity asset allocation is best. However, if you want to manage your withdrawals only a small portion of the fund will be used each year. Even if the market value at retirement is volatile, a small portion of the fund is still available. This enables us to be more aggressive in our asset allocation, even through retirement because the volatility of the rate of return will be spread along each year of retirement.

The volatility of the market still exists. I believe that we can reduce our negative behavior by looking at the linear smoothed market value (SMV – see annex for more detail) instead of the current market value. If we look at SMV, it has the same volatility as the 5 years returns of the market value. It also allows for an automatic sanity check on how things stand. In an economic crisis, SMV is higher than market value. It reminds us that the future is likely to be brighter than the past. In today’s market, SMV is lower than the market value. It tells us that the future is likely bleaker than the past. By extension making our percentage withdrawal on the SMV instead of the market value reduces the volatility of the withdrawals.  It is not a silver bullet as it often only delays the gains & loss. At best, short loss gains are compensated by short term gains, but there’s no guarantee.

Another step that can be taken through the accumulation phase is to create a provision for adverse deviation. A number of ways exist to do this. This strategy explores the idea of capping the “accrued” withdrawal by 115% from last year “accrued” withdrawal. The accrued withdrawal is what you would be able to withdraw if you retired today. This cap has two effects: Calculating it makes you aware of what you could withdraw today without working anymore; also it adds a buffer in case of economic crisis following high increases. These sequences of returns have often appeared in the past. In order to go even further in managing our expectations through retirement, this strategy cap the first retirement year withdrawal by 108% from previous year accrued withdrawal.

If we combine these strategies the retirement date risk is heavily reduced. The S&P500 had 25 times in the past 100 years of returns below 0%. If we go for a percentage withdrawal or a constant dollar strategy, we would experience 25 such reductions. Instead, if we combine capping and smoothing strategies, we only get 4 reductions in withdrawals between the accrued benefit the year prior retirement date versus at the retirement year. Here’s a comparison of these 4 events:


Year
Percentage Withdrawal
(25 events with reduced accrued)
Accumulation-Dynamic Decumulation
(4 events with reduced accrued)
1932
59%
76%
1933
90%
90%
1942
90%
91%
1975
75%
81%



While maintaining the accrued withdrawals is a fine accomplishment, a retiree who needed an extra year of interest would still not be able to retire. The ADD strategy do not adds money where none exist. Instead, it reduces this risk by making more conservative accrued withdrawal estimate prior retirement.

The sequence of return risk

The sequence of return risk for constant dollar withdrawal like the safe withdrawal rule leads to ruin risk. This risk can be avoided using a percentage withdrawal method. This method withdraws a percentage of the fund value each year. With this method or similar method, only the withdrawal fluctuates negatively from a bad sequence of return. Once the sequence returns to average, the fund and withdrawals go back to their original value.  We can also gain the insight that is if the fund loses 5% of its value, the withdrawal only drops by 2.5%.


The Decumulation Phase


In this strategy the main focus is not to manage the fund volatility, but the risk of the withdrawals. Ultimately, the withdrawals are not directly controlled by the market. The retiree decides how much and when he wants to withdraw his fund. A decumulation strategy elaborates a plan to manage them.

In a percentage withdrawal class, there’s no risk of ruin. Using an unsustainable rate of withdrawals will diminish the withdrawals significantly over time, but never to 0. Like demonstrated in the sequence of risk table a 0% return with a 5% withdrawal reduces the withdrawal by 80%. If the return eventually goes back to normal, the withdrawal will return to their original value.

To manage the withdrawal volatility risk, this strategy implements a reserve. 25% of the fund is put in a reserve fund. This fund will serve to pay for the difference between the withdrawal and 95% of any previous withdrawal. If the highest previous withdrawal was 100$ and the new withdrawal would be 80$, the reserve would pay 15$. This means that you need to be prepared that 5% of your withdrawal may not be available next year. For the following few years, you may have to remain at this level until market value returns to normal. To compensate, we increase the withdrawal of the regular fund accordingly. If you wanted to withdraw 6.5%, you need to withdraw at least 6.5%/75%=8.67% from the regular fund. 

A common question is how should the reserve be invested? 25% of the fund is a big portion of the fund. My tests indicate any advantage of being more in bond in the reserve fund. So instead using the same asset allocation than the rest of the fund seems appropriate.

Using a reserve fund has the advantage that we can easily apply a limit on its used. For example, this strategy applies a maximum reserve withdrawal of 10%. This allows for the floor to drop further if the reserve is unable to sustain their uses.  Having a reserve also provides the opportunity to have a significant emergency fund which can be used in time of need. If it is used, the protection erodes. In good time, the reserve is not used the reserve grows since no withdrawal is taken from it. My test showed that the protection is not eroded when we withdraw 50% of the excess above 35% level.

The smoothing and increase cap is also applied in the decumulation phase. The increase cap has to be modified to cap increase at 105% of previous withdrawal after retirement. This lower increase accounts for the withdrawal that is occurring after retirement. Having such a cap provides a great tool to have a constant increase in withdrawals. In case of consistent increase, the cap is increased by 1% each year above the previous mark. This allows recognizing more quickly the sustainable increase.

You may notice that it 105% is lower than the inflation in some of the past years. There’s a strong argument that going forward, the low inflation rate will be maintained. Going forward the US federal bank and bank of Canada has both a target inflation of 2%. The Canadian inflation targets have been stable for the past 25 years and the US for the past 5 years. These targets inflations have been met by both countries since their commitment to them. In the end, 105% increase cap provides another provision for adverse deviation.

Here’s two graphics of the Cash Flows versus Market Value in 1928 and 1965. After 1928, the S&P500 plunged in the great depression and recovered with difficulty in the following decades. By all accounts, it was one of the worst years to retire. 3 combinations are displayed: 100% equity using 6.5% ADD withdrawal; 100% equity using 5.5% ADD withdrawal; 50% equity using 5.5% ADD withdrawal.




A 1965 retiree would have faced better fate in nominal terms. However, the 70’s experience low returns and high inflations. The 80’s and 90’s in the other experience high returns.




Both cases were based on a scenario where 150,000$ were invested 20 years before retirement and 5,000$ with 3% increase each year up to retirement. This is why the initial cash flow is so different between each asset allocation.


For comparison with other decumulation strategy, we will compare them using two metrics. The first metric is the percentage of runs where the one withdrawal year is lower than 80% of any previous year. Under this metric the Safe Withdrawal Rate (SWR) is the safest method. In comparison the Constant Percentage Withdrawal (CPW) is the least safe. The Variable Percentage Withdrawal (VPW) with 50% equity to bonds asset allocation is less risky than the CPW. Otherwise, we can also get a feeling of the importance of each of the sub-strategy. The reserve is the most important strategy in order to reduce this risk. Removing it, allows for dramatic decrease in most of the asset allocation. The smoothing strategy is the least effective strategy. 

Risk II  <80%
100%/0%
90%/10%
80%/20%
70%/30%
60%/40%
50%/50%
ADD 5,5%
0%
0%
0%
0%
0%
0%
ADD 6,5%
1%
1%
3%
6%
10%
14%
ADD 7%
6%
14%
13%
14%
18%
19%
ADD 7% minus reserve.
100%
100%
100%
100%
67%
64%
ADD 7% minus cap
38%
32%
28%
26%
21%
21%
ADD 7% minus smooth
6%
6%
12%
12%
19%
23%
SWR
0%
0%
0%
0%
0%
0%
VPW
100%
100%
100%
100%
100%
29%
CPW 5,5%
100%
100%
100%
100%
100%
100%


The second metric is the Withdrawal Efficiency Rate (WER) as per Blanchett study. This metrics focus on how much the withdrawal was able to produce out of the fund. It shows if the methods were able to maximize withdrawal. We can see that the ADD strategy is rather efficient at the high withdrawal rate. None of the sub-strategy seems to affect WER negatively.
WER nominal
100%/0%
90%/10%
80%/20%
70%/30%
60%/40%
50%/50%
ADD 5,5%
64%
67%
69%
71%
73%
74%
ADD 6,5%
73%
76%
78%
79%
80%
80%
ADD 7%
77%
79%
81%
81%
82%
81%
ADD 7% minus reserve
77%
80%
82%
84%
85%
85%
ADD 7% minus cap
81%
81%
82%
82%
83%
83%
ADD 7% minus smooth
78%
81%
83%
84%
84%
84%
SWR
51%
54%
56%
58%
61%
63%
VPW
77%
77%
77%
76%
75%
74%
CPW 5,5%
74%
75%
77%
78%
79%
80%

Please consult the full study for further details and insight.

Annexe:

Full parameters list:


General :

a.       Portfolio asset allocation
b.      Accumulation-Dynamic Decumulation withdrawal rate. A higher than usual rate should be used. The sub-strategy reduces the effective withdrawal rate. 
Smoothing – smallest impact on the risk reduction :
a.       Number of years to smooth: 5 years is used. This is in line with economic cycle.
b.      Conservative rate of return: Using expected rate of return minus the variance seems to provide on average smoothed market value equal to the average market value.
c.       Corridor: If the market is very volatile the smoothed market value assessment is at maximum 20% off the real market value.
Increase Cap:

a.       Capping % prior retirement: 115%
b.      Capping % at retirement: 108%
c.       Capping % prior retirement: 105%
d.      Capping % increase: 1%. If the previous year withdrawal is cap, the next year cap is 1% greater than the previous year. This allows compensating more rapidly during high gains.
Reserve:

a.       Initial reserve fund % : 25%
b.      Maximum reserve withdrawal: 10%
c.       Reserve protection : 95% of previous withdrawal
d.       Maximum reserve %: When the reserve is greater than 35%, 50% of the excess is return to the main fund.

Simple example of the smoothing assuming a less than expected return

Data:


Year
2011
2012
2013
2014
2015
Average
Market value
500,000$
480,000$
490,000$
510,000$
530,000$
502,000$
Rate of Return
-4.0000%
2.0833%
4.0816%
3.9216%
N/A
1.7089%

·         Smoothed Value with corridor at 2015 = Min(CorridorMin; Max(CorridorMax; Smoothed Value)) = 558,359$
o   CorridorMin: 530,000*0.8 =  424,000 $
§  [Parameter] Corridor Minimum = 80%
o   CorridorMax: 530,000*1.2 =  636,000 $
§  [Parameter] Corridor Maximum = 120%
o   Smoothed Value = 1/5*500,000*(-(-4%)+5.67%)+2/5*480,000*(-(2.0833%)+5.67%)+3/5*490,000*(-(4.0816)%+5.67%)+4/5*510,000*(-(3.9216)%+5.67%)+530,000 = 558,359$
§  [Parameter] conservative rate of return = 5.67%

Simple example of the reserve

25% reserve covering 95% drop using an ADD withdrawal rate of 8%:
Year
2008
2009
2010
2011
2015
MV BoY
500,000$
286,700$
355,660$
350,162$
328,096$
MV NR BoY
375,000$
210,450$
251,698$
263,981$
247,720$
MV R BoY
125,000$
76,250$
83,962$
86,181$
80,376$






Withdrawal BoY
30,000$
28,500$
28,500$
28,500$
28,500$
Withdrawal NR BoY
30,000$
16,836$
20,136$
21,118$
19,818$
Withdrawal R BoY
0$
11,664$
8,364$
7,382$
8,682$






MV EoY
470,000$
258,200$
307,160$
321,662$
299,596$
MV NR EoY
345,000$
193,614$
231,562$
242,863$
227,902$
MV R EoY
125,000$
64,586$
75,598$
78,800$
71,693$
Rate of Return
-39 %
30%
14%
2%
N/A

Market Value: MV; Reserve: R; Non Reserve: NR; BoY: Begin of Year; EoY: End of Year

As expected in the financial crisis, the fund substantially shrinks during the 4 years. However, we are able to maintain a 95% of the initial withdrawal with relative ease. We can see that the fund value increase substantially after the fabulous year of 2009 & 2010. The 2011 return is 2%, less than the effective withdrawal rate (8%*75% = 6%). This lead to the Non-Reserve fund shrunk in 2012. The reserve would be able to withstand about 10 years at the end of 2012 regardless of future recovery.




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