INFORMATION ABOUT RETIREMENT AND THIS TOOL
If you are planning your retirement and you want a simple tool to make some basic calculations, this is your instrument. You don’t need to register or provide personal information. Just use the tool and, then, if you think that you would benefit from professional services, go ahead and hire a certified financial planner (CFP) to help you with planning your retirement. This is not the same as getting help with your investments (Registered Investment Adviser) or with your taxes (Tax Advisor or Tax Consultant).
In Lewis Carroll’s book, Alice in Wonderland, Alice asked the Cat:
“Would you tell me, please, which way I ought to go from here?"
"That depends a good deal on where you want to get to."
"I don't much care where –"
"Then it doesn't matter which way you go.”
We can create an analogy between this conversation and that between an investor and a Financial Planner in which the investor asks the Financial Planner:
“How much money can I spend in retirement?”
“What are your goals for retirement?”
“I don’t have any.”
“Then, you can spend your retirement money any way you want.”
This analogy helps us see that it is not possible to determine how much money you can spend in your retirement unless you know your retirement objectives and goals. Dr. Wade Pfau stated in his book, How Much Can I Spend in Retirement, that, in general, there are four retirement objectives:
 Lifestyle – Keeping the same standard of living that you currently have before retirement or maintaining a certain level of standard of living through retirement.
 Longevity – Making retirement savings last to a certain age.
 Legacy or Bequest – The real value of assets at death, considering that you could die in any year according to the mortality table probabilities.
 Liquidity – Preserving the ability to quickly convert an asset into cash, without losing their value, to pay for regular living and emergency expenses.
These four objectives are interrelated and for most people’s savings, there is a tradeoff between these objectives, so it is necessary to determine the value of each objective to be able to balance them.
The focus in this tool centers on the users’ main goal revolving around their lifestyle spending. The lifestyle spending or standard of living is nothing more than the Retirement Spending (Step 7) in this tool. Once users enter their financial information, they can check the Longevity and Legacy objectives. If the objectives are met, excellent. If not, then the “Whatifs” begin.
The factors that control wealth after retirement, and by extension, the retirement objectives, include the following:
 How much money people have in savings when they retire? See Step 3 – Savings before Retirement, and Step 4 – Current Savings.
 How savings are invested? This really means, at what interest rate is it forecast that savings will grow? See Step 6 – Type of Investment.
 How much money is withdrawn from the portfolio? See Step 7 – Retirement Spending.
 What are the statistics regarding lifetime expectancy? See Figure 4 in Charts, Gompertz  Makeham Probability of Survival (_{t}P_{x}).
These are the factors that users need to play with in the tool to achieve their three retirement objectives.
There are many articles about withdrawing money from your portfolio and several of those strategies are used in this tool and you can select one of them in Step 9 – Type of Portfolio Withdraw Strategy. After making a selection, check to make sure it meets your objectives.
The tool also provides answers about retirement results from different perspectives. For example:

Snapshot – Provides detail portfolio information at particular ages, which can be used to verify the state of the user’s portfolio at specific ages.

When to start Social Security? – The tool answers the following question: “What happens to my portfolio value over time if I change my starting Social Security age? For example, would the yearend balance of my portfolio at 75 years of age go up or down if I start Social Security at 70 instead of 66?

Monte Carlo Simulation – A Monte Carlo simulation analyzes the likelihood of a portfolio being successful by randomizing certain factors and checking the annual result at certain points called percentiles. In this tool, the interest per year changes at random (using the invert of the normal distribution). Then, the simulation is run 500 times each year and the percentiles, 25%, 50%, and 75% are plotted on a graph.

Probability of Retirement Ruin – It is the probability that a fixed spending plan will deplete a retirement nest egg prior to the end of the lifecycle and it is expressed by calculating the Gamma Distribution Function. In Figure 4, the tool shows the Probability of Secure Retirement, which is equal to (1 – Probability of Retirement Ruin).
Money Required To Retire
If you do some research you will find that, in "101 Ways to Build Wealth," Money Magazine article, May 2014, you will need the following:
7.3 x your salary by 55 to retire at 65 and replace 70% of your income.
7.7 x your salary by 55 to retire at 68 and replace 80% of your income.
6.4 x your salary by 55 to retire at 68 and replace 70% of your income.
Or, according to Fidelity, you will need the following level of savings so you won't outlive your savings during 25 years of retirement:
By Age

You Should Have This Much of Your Salary Saved...

By Age

You Should Have This Much of Your Salary Saved...

30

1x

50

6x

35

2x

55

7x

40

3x

60

8x

45

4x

67

10x

Again, per Nobel laurate Robert C. Merton, Phd, there are only four ways to improve the chances for achieving a good retirement:
 Save more for retirement and lower lifetime consumption level
 Work longer before retiring
 Take more risk and be prepared for the consequences if the risk is realized
 Improve the income benefits from the assets that are already available
 Annuities, including “tailinsurance” for longevity
 Reverse mortgage
 Goalbased investment strategies
 Redesign employer contribution schedule, for fixed contribution cost
How To Invest Your Savings at Retirement Age
Most people don’t need to time the market, what they need is a professional planner who would invest their money in a simple, well diversified portfolio, with a lowcost, noload index, that does not require market timing. That type of investment is called the “Lazy Portfolio”. If you want to do one yourself, go to https://www.portfoliovisualizer.com, choose one of the lazy portfolios, and it will give you the ticker name, percentage allocation, and its performance over a certain period of time.
Portfolio Withdrawal
There are many portfolio withdrawal strategies and many papers that have been written about them. Some of these are included in this tool. At the end, the portfolio is calculated for every year as follows:
Balance at the End of the Year = Balance at the Beginning of the Year + Interest  Withdrawals
Age and Mortality
What is your remaining lifetime? If you know that you will die before 75, then you will spend more of your retirement, but what about if you live to 95? Maybe you need to spend less.
That is all that counts!
You may ask, what about the income that I have after retirement, such as Social Security, pensions, annuities; also, what about my expenses during retirement, don’t they count? Well, one of the withdrawal strategies, PreRetirement Spending, takes into account these factors by calculating the following:
Portfolio Withdrawals = Expenses + Taxes Social Security Pensions  Annuities
You withdraw money from your portfolio as you need to complement your retirement income to be able to sustain the standard of living that you want.
INPUTS
There are only 9 Steps for entering basic information about your retirement. Steps 1 through 4 refer to your current financial situation. Steps 5 to 9 refer to decisions about your retirement. There are some unlocked boxes where you can enter information, and some other boxes, locked, where the tool does instant calculations and lets you know the results with respect to inputs that you entered in that step. Use Tab to move from one box to another.
Step 1 Date of Birth and Retirement Age
In this tool, retirement age is the age at which you stop working, which is different from the age at which you start collecting Social Security benefits. The Social Security agency uses the word "retirement" as the age at which you start receiving Social Security benefits.
Step 2 Social Security Benefits
In this step, enter the age at which you and your spouse will start collecting Social Security benefits, as well as the Social Security benefits at FRA (full retirement age).
The Social Security full retirement age (FRA) depends on the year that a person was born. At FRA, people receive 100% of their benefits. In the case of early retirement, a benefit is reduced 5/9 of one percent for each month before full retirement age, up to 36 months. If the number of months exceeds 36, then the benefit is further reduced 5/12 of one percent per month. After full retirement age, a benefit is increased by 2/3 of 1% per month or 8% annually. As the date of birth and retirement age are entered in Step 1, the tool calculates the monthly dollar amount of the Social Security benefit.
When a worker files for retirement benefits, the worker's spouse may be eligible for a benefit called Spousal Benefit, based on the worker's earnings. At full retirement age, the Spousal Benefit is 50% of the worker’s earnings. If the spouse begins receiving benefits before "normal (or full) retirement age," the spouse will receive a reduced spousal benefit. See Table 2, in SS Benefits web page.
But, if the spouse is also eligible for a retirement benefit based on his or her own earnings, Social Security pays the higher of the two possible benefits, his/her own earnings or the Spousal Benefit. This amount appears in Spouse 2 Social Security per Month.
If the retirement age is lower than the age when the person starts collecting Social Security benefits, then the Social Security value in the tool is $0.00.
The Full Retirement Age depends on the year the person was born
In 1943  1954

66

In 1955

66 + 2 Months

In 1956

66 + 4 Months

In 1957

66 + 6 Months

In 1958

66 + 8 Months

In 1959

66 + 10 Months

In 1960 

67

When a person creates an account at the SS agency, the agency provides the dollar amount of the benefits at "Full Retirement Age." Using Table 1 on the SS Benefits webpage, the tool calculates the percentage of the Full Retirement Age Benefit (FRA) that would be received based on the user’s birthday year, and the age when the retiree would like to star receiving the benefit, anywhere from age 62 to 70. Then, the tool multiplies that percentage by the FRA entered by the user, and that is the Social Security benefit that would be received per month.
Source of Tables 1, 2, and 3 on the Social Security webpage in this tool: Author calculations based on above IRS guidelines.
Step 3 Savings before Retirement
When users are saving from their salaries, the total saving at any future time is calculated as a constant periodic investment at a constant interest rate where the periodic investment is per month. Then, these savings are added to the Portfolio (Non IRA and IRA accounts) to calculate the Ending Balance. The value stops showing when the person retires.
The future value of these savings is calculated using the following formula:
Where:
FVA = Future value of the annuity  savings
R = Periodic payment in an annuity savings per month
I = is the interest rate per month
N = Number of months
Step 4 Current Savings
Current Savings is divided into two groups, Taxable (NonIRA) and TaxDeferred IRA accounts.
Taxable accounts, also called nonqualified or nonIRA retirement accounts, are regular accounts in which income taxes have already been paid prior to the investment, and taxes are paid only on growth, earnings and withdrawals during the year that they are received.
TaxDeferred IRA accounts, also called qualified investment accounts, are the traditional IRA accounts, 401K, 403(b)(7) in which you don’t pay income tax (taxdeferred) until you make a withdrawal. For tax purposes, traditional IRA distributions are considered ordinary income. The amount of the IRA distribution is added to other sources of income to determine the adjusted gross income; taxes are paid according to the person’s tax bracket.
A person can’t use a Roth IRA contribution as a deduction on a tax return, but the required minimum distribution (RMDs) doesn’t have to be taken during his/her lifetime. So, if Roth IRA accounts are part of the portfolio, include them as taxable accounts in the tool. Remember that there is a 10% federal penalty tax on withdrawals taken before age 59½.
https://investor.vanguard.com/ira/rothvstraditionalira
The tool uses IRA Minimum Required Distribution percentages to determine the amount by which each IRA account needs to be reduced after age 70 to calculate taxes. Taxes increase annual total expenses.
The portfolio current savings future value, which increases at a constant interest, is calculated using the following formula:
Where:
FV is the future value of the current portfolio account
PV is the present value of the investment portfolio account
i is the interest rate per year
is the number of years, from today’s year to retirement
Step 5 Other Incomes After Retirement
Enter here any pension plan or annuity that will be received after retirement.
Step 6 Type of Investments
The tool provides three types of investment strategies: Conservative, Moderate, and Aggressive, based on Portfolio Investment Strategies (From Money Magazine, November 2011).
 Conservative: 40% stocks, 40% bonds, 20% Cash;
 Moderate: 60% stocks, 40% bonds;
 Aggressive: 80% stocks, 20% bonds.
Then, a tool at Portfolio Visualizer,
https://www.portfoliovisualizer.com/backtestassetclassallocation, is used to determine the 10year Compund Annual Groth Rate (CAGR) between 20082017, as well as the Standard Deviation Risk Volatility, for these investment strategies. The rate of return and volatility selection apply for both before and after retirement.
The following figures show The Portfolio Visualizer results of calculating the 10year CAGR between 20082017, as well as the Standard Deviation Risk Volatility, for these Conservative, Moderate and Aggressive investment strategies. The Portfolio Visualizer also shows the portfolio allocations used in this tool.
Step 7 Inflation Adjusted PreRetirement Spending at Retirement Age Spending
By entering your current, preretirement annual expenses in the tool, it can then calculate the future value of those expenses at retirement age based on the cost of living. When you select “PreRetirement Spending” as the withdrawal strategy, the tool calculates how much money is required to withdraw from your savings to pay for your inflationadjusted spending, also called Standard of Living at retirement.
Step 8 Type of Spending over Lifetime
A common approach to estimating the total amount of spending over retirement is to say, “I would like to maintain a lifestyle during retirement similar to the one I have right now.” Or, to put it in another way, how much of my lifestyle do I want to keep? Once you decide on a figure, you enter your preretirement expenses in Step 8 and the tool calculates your spending based on inflation.
There are several articles that have been written indicating that in reality, spending over retirement does not remain the same, or increase each year by inflation or by some otherwise static percentage. In this tool, we use the findings of David Blanchett, Head of Retirement Research at Morningstar Investment Management company in his paper, “Estimating the True Cost of Retirement,” to determine spending during retirement. In his analysis, David Blanchett and his associates created an equation to determine the change in real annual spending as a function of age and the aftertax total expenditure target (ExpTar), which, in this tool, is called preretirement expenses.
Where:
ΔAS = Change in real annual spending
ExpTar = Aftertax total expenditure target of a retiree
The retirement spending curve looks like a smile, “the retirement spending smile,” as they called it in the paper, whereby the expenditures actually decrease in real terms at the beginning and then increase toward the end. See the chart, Annual Real % Change in Consumption.
In this tool, there are two types of strategies for spending during retirement:
 Constant Spending + Inflation: The current spending increases over the years by the rate of inflation, but in today's dollars, the amount is the same.
 Blanchett's Retirement Spending Smile: Spending is not the same over retirement. Over time, it changes by a percentage depending on the person’s age and his initial spending, using the formula from David Blanchett’s paper, "Estimating the True Cost of Retirement."
Step 9 Select your Portfolio Withdrawal Strategy
Once you are retired, if your income at retirement is lower than your expenses, you will need to start taking withdrawals from your retirement portfolio.
In this tool, users can select from seven types of withdrawal strategies to accomplish this.

PreRetirement spending  This strategy uses a constant dollaradjusted amount for inflation or a variable overtime adjustment according to David Blanchett’s paper, “Change in Real Annual Expending.” See Step 8.

Spending Annual Earnings Only  The idea is to leave the principal untouched and spend only the portfolio annual interest earnings.

Withdrawals Based on Life Expectancy  This strategy is to spend all financial assets over your life expectancy or to an age at which there is a low probability of surviving using the following annuity formula.
Where:
r= Riskfree interest rate on the investments
t= Remaining life expectancy.
IP= Investment Portfolio balance in that year.

Percent Rule (Bengen’s SAFEMAX)  A fixed percentage is spend; the default is 4% (Bengen 1994), of the initial portfolio value, and the withdrawal amount is adjusted by the rate of inflation every year. The percentage can be changed in the tool when this strategy is selected.

Required Minimum Distribution (RMD)  Withdrawals are based on the IRS's Required Minimum Distributions. However, this strategy results in relatively low consumption early in retirement, at ages when retirees are better able to enjoy possibilities for travel and other leisure activities.

Modified RMD (RMD + Interest)  Wei Sun and Anthony Webb, in their paper, "Can Retirees Base Wealth Withdrawals on the IRS' Required Minimum Distribution?" compared the above withdrawal strategies using a measure called Strategy Equivalent Wealth (SEW). They concluded that the optimal withdrawal was really to consume interest and dividends in addition to the RMD.

Blanchett’s Dynamic Complex Formula The Dynamic Complex Formula determines the withdrawal percentage for a given target probability of success, portfolio equity allocation, expected retirement period, and fees (or alpha). Several Monte Carlo simulations were conducted, each consisting of 10,000 runs, to devise a formula that will approximate the withdrawal rate that would be determined through solving a Monte Carlo simulation for the target parameters.
Percentage of Wealth = 0.195  0.037 x ln(Years) + 0.0126 x (Equity%)^0.5  0.0447 x Probability of Success + 0.507 x Alpha
Where:
Years: Retirement Period (In this tool, 30 Years)
Equity%: Equity Allocation in percentages (In this tool, 40%)
PoS: Probability of Success target (In this tool, 90%)
Alpha: Fees (In this tool, 1%)
These strategies are derived from five papers: