Many retirees spend thirty years or more in retirement. In current retirement planning practice, we assume an “average” portfolio growth rate and an “average” inflation rate for the entire time horizon. The reality is that all asset values fluctuate. Many naively think that if they use historical averages, then everything will be fine in the long run.
Unfortunately, this is not the case. There is always a permanent loss owing to the fluctuations in a distribution portfolio due to the luck factor. After any fluctuation, large or small, not only do you need to recover from the market losses, but you also need to recover from the differential losses between the original plan and the actual portfolio value while you are withdrawing income. In many cases, these losses can cut the portfolio life by half of what a standard retirement calculator forecasts. That is why many pension funds appear to be in a downward spiral in recent years. The pension administrators and managers routinely blame markets, demographics and other factors for what is actually their failure to incorporate the concept of “Time Value of Fluctuations” in their forecast.
Since this is one of the most misunderstood concepts in retirement planning, it is well worth looking into it at this point.
Root Causes of Time Value of Fluctuations:
The time value of fluctuations exists only if money goes into or out of the portfolio periodically. If there are no withdrawals from or deposits to a portfolio, then there is no time value of fluctuations, just fluctuations.
If there are periodic withdrawals from the portfolio then any fluctuations shorten the portfolio life. There are two types of contributors to the time value of fluctuations: The first one is fluctuations in the growth rate. An analogy can be made to gas mileage when driving: If you drive along a straight road with no hills, you will use less gas than if you were to drive an identical distance with many curves, hills and valleys. Similarly, the more a portfolio fluctuates, the more money is exhausted going up and down the fluctuations, for lack of a better term, “friction losses”.
The second contributing factor to the time value of fluctuations is caused by fluctuations in cash outflow. The further inflation deviates from the assumed “average”, the more money is exhausted.
Figure 13.1: Components of the time value of fluctuations in distribution portfolios
Calculating the Time Value of Fluctuations in Distribution Portfolios:
How can we measure the time value of fluctuations (TVF) in a distribution portfolio? We know the present value of the assets and we know the time horizon. We plan for zero future value of assets. Starting with these, we go through the following steps:
Step 1: Calculate the benchmark withdrawal rate:
Assume there are no fluctuations in the growth rate of assets or in the indexation of withdrawals. Calculate the annuitized withdrawal rate that leaves zero assets at the end of the time horizon. This is the benchmark.
Step 2: Calculate the sustainable withdrawal rate:
We want to make sure that portfolio assets survive, even for the unlucky outcome, which is defined as the bottom decile (bottom 10%) of all observations. By trial and error, we calculate the withdrawal rate where the unlucky portfolio lasts exactly as long the benchmark portfolio calculated in the first step.
Step 3: Calculate the Time Value of Fluctuations:
TVF is the difference in withdrawal rates, with and without fluctuations. Since we use the entire market history, this calculation reflects all effects of all possible events, i.e. the entire luck factor.
The formula for the TVF for a distribution portfolio is:
TVF = AWR – SWR10 (Equation 13.1)
Additional capital required to overcome the effect of the TVF is calculated using the following formula:
AWR is the annuitized withdrawal rate
SWR10 is the sustainable withdrawal rate based on 90% portfolio survival ACR is the additional capital required, over and above the calculated
value using the average and steady growth rate of the portfolio and steady indexation of withdrawals; i.e. annuitized withdrawal rate
Example 13.1
Ron is 65 years old. He is retiring this year. He expects to die at age 95. His retirement savings are valued at one million dollars. His asset allocation is 40% DJIA, 60% fixed income.
On the equity side, he assumes an average annual growth rate of 7.3%, which happens to be the average annual growth rate of DJIA between the years 1900 and 2006. He expects an average dividend of 2% annually, but it will all be spent for management fees and portfolio expenses. On the fixed income side, he assumes a net yield of 5.2% after expenses, which also happens to be the average interest rate on a 6–month CD plus one half of one percent premium. Therefore, his average portfolio growth rate is 6.04%
after all expenses.
Step 1: What is Ron’s annuitized withdrawal rate? Calculate the annuitized withdrawal rate, using a spreadsheet. By trial and error, a withdrawal rate of $52,221 in the first year, indexed to inflation by 3% annually thereafter, lasts exactly 30 years.
Age Year Begin Value $ Growth $ Withdrawal $ End Value $
Assuming there are no fluctuations of the portfolio growth rate and indexation of the withdrawals, the annuitized withdrawal rate is 5.22% in the first year of retirement, calculated as $52,221 divided by $1 million expressed as a percentage. This is the benchmark.
Step 2: How much can Ron take out based on actual market history? I use my retirement calculator based on market history. The chart below depicts the portfolio value for all retirement years between 1900 and 2006. It also shows the annuitized withdrawal rate and at the sustainable withdrawal rate.
The sustainable withdrawal rate for the unlucky portfolio (90% probability of survival) using actual market history is calculated as $37,600 in dollars, or 3.76%.
Step 3: What is the time value of fluctuations? The time value of fluctuations is the difference between the withdrawal rates with and without fluctuations, i.e. the annuitized and sustainable withdrawal rates.
TVF = 5.22% – 3.76% = 1.46%
• In real life, with savings of $1 million at age 65, Ron’s withdrawals must be 28% lower than the annuitized withdrawal rate (52,221), calculated as
1.46%
×100%
5.22% , for his money to last 30 years.
• In real life, if Ron wants the same income as the annuitized withdrawal rate ($52,221) for life, the additional capital he needs is:
ACR = (5.22% - 3.76%) × 100%
3.76% = 38.8%
Ron needs 38.8% more than the $1 million he has, or $1,388,000 savings to start with, if he wants $52,221 at age 65 indexed to actual inflation until age 95.
Portfolio Value at Annuitized Withdraw al Rate Portfolio Value at Sustainable Withdraw al Rate
Table 13.1 depicts the ACR, the additional capital required, using S&P500 as the equity proxy for various asset mixes and time horizons.
Table 13.1: Additional capital required to overcome TVF in distribution portfolios for different asset mixes and time horizons
If the asset mix is not at its optimum, i.e. if the portfolio volatility is too high or too low, then this creates a higher time value of fluctuations. This debunks another myth in our business: “If you want higher returns, you need to take a higher risk!” This is the wrong advice for all distribution portfolios.
Table 13.2 displays the ACR for different markets and time horizons for an asset allocation of 40% equity and 60% fixed income.
Table 13.2: Additional capital required to overcome TVF in distribution portfolios for different markets
Market:
Table 13.3 depicts the historical average growth rates used in calculating the annuitized withdrawal rates for Table 13.2.
Table 13.3: Average growth rates, net after portfolio expenses
Market:
Average Growth Rate
DJIA (1900 – 2006) 7.3%
S&P500 (1900 – 2006) 7.0%
Nikkei 225 (1914 – 2006) 10.9%
FTSE All Shares (1900 – 2006) 6.0%
SP/TSX (1919 – 2006) 7.3%
Fixed income (1900 – 2006) (historical 6–month CD interest plus 0.5%)
5.2%
If you like formulas, I have developed a formula based on empirical data to calculate the TVF approximately as a function of the time horizon. This formula applies only to distribution portfolios with optimum asset mix and only to DJIA, S&P500 and the SP/TSX indices.
TVF = 20
N0.735 (Equation 13.3)
where:
N is the number of years, any number between 10 and 40
Time Value of Fluctuations in Accumulation Portfolios:
In accumulation portfolios, there are several forces at work:
• In secular bullish trends, asset values surge up; the luck factor works for you.
• In secular sideways trends, the dollar–cost–averaging (DCA) works for you.
However, the benefit of DCA does not compensate for the adverse luck factor in such trends.
• In secular bearish trends, if you have the patience and fortitude to continue investing, dollar–cost–averaging and rebalancing create a positive outcome eventually. Keep in mind that most of us do not have the discipline and the patience for that.
The logic for calculating the TVF in accumulation portfolios is the mirror image of that of distribution portfolios. We know the present value of the assets, the time horizon and the desired future value of assets.
Step 1: Calculate the benchmark deposit rate:
Calculate the benchmark deposit rate, which is the first year’s savings as a percentage of the future target amount of the median portfolio. Assume a constant growth rate of the portfolio with no fluctuations of deposits over the entire time horizon.
Step 2: Calculate the deposit rate based on market history:
Using the actual market history by trial and error, calculate the deposit rate that you need.
This is the dollar amount you need to save periodically to reach the desired median portfolio value over the same time horizon as the benchmark.
Step 3: Calculate the Time Value of Fluctuations:
The difference between the two deposit rates is the time value of fluctuations, which reflects the gains, or the losses as the case might be, due to the fluctuations in asset value and inflation over the entire time period.
The formula for the TVF in an accumulation portfolio is:
TVF = RDR – ADR (Equation 13.4)
The following formula is for calculating the additional periodic savings required to overcome the effect of the TVF:
ASR = (RDR- ADR) × 100%
ADR (Equation 13.5)
where:
ADR is the deposit rate, first year’s deposits as a percentage of the future target amount, where growth rate and indexation rate are constant RDR is the deposit rate required, first year’s savings as a percentage of the
future target amount of the median portfolio, growth rate and inflation varies using actual market history
ASR is the additional periodic savings required, over and above the ADR
Example 13.3
Steve wants to accumulate $2 million in his portfolio in 30 years. He wants to start saving right now, and increase his annual saving amount by 3% each year. Currently, he has nothing in his account. His asset allocation is 60% DJIA and 40% fixed income.
On the equity side, he assumes an average annual growth rate of 7.3%, which happens to be the average annual growth rate of DJIA between the years 1900 and 2006. He assumes an average dividend of 2% annually which will be spent entirely for management fees. On the fixed income side, he assumes a net yield of 5.2% after expenses, which is the historical average interest rate on a 6–month CD plus 0.5% premium. Therefore, he calculates his average portfolio growth rate is 6.46% after all expenses.
Step 1: What is his deposit rate?
Use a spreadsheet. By trial and error, we calculate an accumulation rate as $15,506 in the first year, indexed by 3% annually thereafter.
Year Begin Value $ Growth $ End of Year
Therefore, assuming there are no fluctuations of growth rate, the deposit rate is 0.775%, calculated as $15,506 divided by $2 million (the final–year target amount).
This is the benchmark, ADR.
Step 2: How much should Steve deposit based on market history? He increases his deposits each year by the same amount as inflation. He is targeting a total portfolio value of $2 million in 30 years.
Using my retirement calculator based on market history. I calculate that Steve needs to deposit $18,470 in the first year, indexed to actual inflation for the next 30 years, to accumulate $2 million in his median portfolio. The required deposit rate (RDR) is 0.924%, calculated as $18,470 / $2,000,000 X 100%.
Here is the aftcast:
What is the time value of fluctuations? The time value of fluctuations is the difference between the deposit rates with and without fluctuations.
TVF = 0.924% – 0.775% = 0.149%
If the portfolio growth rate were steady, Steve would need to deposit $15,506, indexed by 3% annually. In real life, both the growth rate and inflation fluctuate.
How much more does he need to deposit periodically?
The additional periodic savings required is calculated using equation 13.5:
ASR = (0.924% - 0.775%)
× 100%
0.775% = 19.2%
Steve needs to save periodically 19.2% more than he calculated using the steady growth and inflation rates for the next 30 years to accumulate $2 million in the median portfolio.
Table 13.4 depicts the ASR, the additional periodic savings required, using S&P500 as the equity proxy for various asset mix and time horizons. Generally, if your asset mix is near the optimum, the dollar amount of your deposits is the lowest to achieve the same target.
Table 13.4: Additional periodic savings required in an accumulation portfolio
Asset Mix:
Time Horizon
20 years 30 years
Additional Periodic Savings Required to account for TVF:
100% Equity – S&P500 1% 10%
2% 9%
60 / 40 –1% 5%
40 / 60 5% 10%
20 / 80 5% 18%
100% Fixed Income 7% 19%
Conclusion:
The Time Value of Fluctuations is defined as losses created by long and short–term market fluctuations and inflation. It is the missing link between the annuitized (steady) withdrawal rate and the sustainable withdrawal rate in distribution portfolios. The TVF describes and quantifies the chronic losses which are outside the control of the investor.
It is essential to understand that it exists. It is especially important if you are preparing retirement plans or administering pension funds. You don’t need to remember the formulas or memorize the tables in this chapter; the TVF has a more qualitative use than a quantitative one. In Chapter 16, we will use this knowledge as our starting point for optimizing the asset allocation process. But first, we need to discover the flaws of the tool that is most commonly used for optimization, the efficient frontier.