This is a guest post from Bogleheads® forum member Bobcat2.

## Definition

** Funded ratio** – *The ratio of a pension plan’s assets to its liabilities. A funded ratio above 1.0 indicates that the pension plan is able to cover all payments it is obligated to make. A ratio below 1.0 indicates that it is either unable to make payments or is in danger of not being able to do so.*

Everyone in this room knows what people want for retirement. It is an income. Social security gives an income. DB plans give an income. In DC plans, for some reason, we do not show people the funded ratio. We are showing them the wrong thing, and then we are saying they are making the wrong decisions. We are telling people that risk is the value of their fund, when risk is really how much income they can sustain for retirement. – Jeremy Siegel¹

In planning your retirement strategy before, at, or during retirement how can you check whether you are on track to meet your retirement income goal? One straightforward way to appraise the soundness of your retirement plan is to borrow the method used to assess the viability of DB pension plans – the funded ratio. Pension administrators monitor the financial soundness of their plans by dividing current plan assets by the present value (PV) of all retirement benefits they are obligated to pay to plan participants.

**Funded ratio = Assets/Retirement liability**

This concept can easily be applied to an individual’s retirement plan. Simply divide the value of your assets by the present value of your planned retirement income (your retirement liability). The FR takes into account the current size of your portfolio, your retirement income goal, the current low risk interest rate, and your expected retirement date and life expectancy to produce a single number that indicates how well your retirement income goal is currently funded.

It is important to realize that the funded ratio (FR) is not a forecast. It is instead a point in time measurement that adjusts over time as the size of your portfolio changes, as interest rates change, and as your assumptions about your retirement date and longevity evolve. It is calculated over time and its trajectory indicates whether you are on track through time to meet your retirement income goal, or whether you are in danger of becoming underfunded or, conversely, in the pleasant position of becoming overfunded.

It can also be used to assess projections of future portfolio values and whether they will be sufficient to meet your goal. During retirement the FR should continue to be used to assess whether you are remaining on track or whether you need to cut spending or draw additional assets from your home equity.

To apply the FR you need the following inputs.

Inputs where you decide:

- Your annual retirement income goal;
- Your estimate of when you will begin retirement;
- The length of your planned retirement horizon, how long you plan to be retired.

Market inputs:

- Current value of your retirement portfolio;
- The appropriate current safe market interest rate.

All dollar values are real in terms of current dollars. Because the dollars are real, you need to use a safe real interest rate. Use the real yield that is equal to the duration of the liability. In practical terms that means using the TIPS yield matched to the duration of the liability. If, for example, the duration of the liability is 15 years use the yield on 15 year TIPS. It doesn’t have to be exact; I recommend either rounding to the nearest half percent or rounding up to the nearest half percent. If the funded ratio is above 1.0 as we near retirement, or when we are in retirement, we are in fairly good shape. But ideally we would like to have the ratio between 1.05 and 1.20.

To apply the FR you have to solve time value of money (TVM) calculations for the PV of your targeted retirement income stream – the goal of your retirement plan and the denominator of the FR. TVM problems can easily be solved using a financial calculator, computer spreadsheet, or smart phone app. (See the links at the end of this article for tutorials on solving TVM problems.)

## Three stylized cases of calculating the funded ratio

### Case 1

Judy is retiring in 3 months on her 65th birthday. She wants her 401k retirement portfolio to produce $22,000/year in real income for 25 years to age 90, her retirement planning horizon. The duration of that horizon is approximately 12.5 years. If the current yield on 12.5 year TIPS is 1.21%, we round up to 1.50% for the safe discount rate. The current value of Judy’s 401k account is $515,000. What is Judy’s funded ratio?

First we need to find the PV of her targeted retirement income stream.

n= 25

i= 1.5

pmt= 22,000

FV= 0

PV= ? solution → 455,831

Funded ratio = Assets/Retirement liability = 515,000/455,831 = 1.13

Judy is in good shape to reach her goal of $22,000.

### Case 2

Ricardo is 58 and planning to retire in 8 years at age 66. He wants his retirement portfolio to produce $30,000/year in real income for 26 years to age 92, his retirement planning horizon. The current value of his retirement portfolio is $530,000. The duration of his income liability is 21 years. (The 8 years to retirement and half of the 26 years in his retirement horizon.) The current yield on 21 year TIPS is 1.39%, we round up to 1.50% for the safe discount rate. The current value of his retirement portfolio is $548,000. What is Ricardo’s funded ratio?

To find the PV of Ricardo’s income stream we need to make two TVM calculations. First, find the PV of the income stream at retirement and second, find the PV of that future value now.

Step 1

n= 26 (projected years of retirement)

i= 1.5

pmt= 30,000

FV= 0

PV= ? solution → 641,959

Step 2

n= 8 ( years until retirement begins)

i= 1.5

pmt= 0

FV= 641, 959

PV= ? solution → 569,874

Funded ratio = Assets/Retirement liability = 548,000/569,874 = 0.96

Ricardo is falling a little short of meeting his retirement income goal. He is close enough to his goal to invest conservatively, but he should probably up his savings rate a few percent between now and retirement. He should continue to monitor his FR to see if his increased saving rate brings his FR above 1.0.

### Case 3

Calculating the Funded Ratio (FR) doesn’t end once you begin retirement. Consider Lucy, who retired at age 61. She planned for a 30 year retirement with $40,000/year in withdrawals from her $1,100,000 retirement portfolio. Her FR was 1.15 at retirement with a safe discount rate of approximately 1.5%. Her portfolio provided reasonable returns for the first four years of retirement, leaving a portfolio balance of $970,000, and a FR of 1.13.

Lucy believed that since she was planning for a long retirement, holding a large proportion of her portfolio in stocks during retirement was prudent, due to their high expected returns in the long-run. Therefore, Lucy had a 70/30 stock/bond AA in her portfolio. But in the 5th of her retirement the stock market has suffered a severe bear market with roughly a 30% stock decline that has left her portfolio balance at $765,000. The FR has fallen from 1.13 to only 0.92, flashing an immediate bright red danger signal to cut withdrawals from the portfolio below $40,000, consider annuitizing more, and perhaps taking some equity out of the house. Lucy can in a sense reverse engineer the FR to see what level of spending is now consistent with a FR of 1.05, which is the lowest she considers prudent.

FR=Assets/Liabilities

Liabilities = Assets/FR = 765,000/1.05 = 728,571

n=25

i= 1.5

PV= 728,571

FV= 0

pmt= ? solution → 35,163

If Lucy wants to get back to a FR of 1.05 solely through reducing income and spending, she will have to go from $40,000/year to approximately $35,200/year in withdrawals from her portfolio. This gets back to important uses of the funded ratio that Robert Merton emphasizes.² In assessing risk in a retirement plan the focus should be on the volatility of the funded ratio, not the volatility of the portfolio. Further, the asset allocation strategy of the portfolio prior to retirement should be based on age, income, and improving the funded ratio at least until it reaches 1.15. The moral of this particular story, however, is once you are retired and your FR is about 1.15, you should de-risk your portfolio by keeping your exposure to equity risk low.

## Social Security and Pension Income

How should one treat annuitized assets such as Social Security (SS) and pensions in the funded ratio? In the case of SS, excluding SS from the FR calculation will affect the FR score. If the FR is above 1 without SS, then including SS in the FR calculation will lower the FR value. How much it lowers the FR depends on the relative sizes of the income coming from SS compared to income withdrawn from the portfolio. The reverse will be true if the FR is below 1. In that case adding SS to the calculation will raise the FR. To avoid an overly optimistic view of your retirement prospects, I would include SS in the FR calculation, or at least do the FR calculation both ways. To include SS in the FR calculation, find its PV the same way you determined the PV of the liabilities. Add the PV of SS to both the numerator and the denominator of the FR.

Most pensions are nominal. If you exclude nominal pension income from the FR you have to deflate that income for every retirement year, and adjust your planning for that shrinking real income. I would include the PV of pensions in the FR calculation.

## Estimating Longevity

In calculating the funded ratio the only forecast is your age of death. A common method to reasonably determine this for retirement planning purposes is your life expectancy plus five years of slack. For example, Dimensional Fund Advisors (DFA) suggests this amount of slack for retirement planning purposes. If you want to be particularly precise for your situation, you can use one of the online personal life expectancy calculators and add five years of slack to that life expectancy. Remember that through time as you continue to survive your age of death becomes older ages. The expected age of death for a 70 year old is later than for a 54 year old. When you are calculating the FR over time continue to update to the current life expectancy.

For anyone extremely worried about retiring at 65 and living 30 years or more to age 95 or beyond, and thereby outliving their assets; then the best solution in that case involves maximizing both SS & DB pension benefits, and heavy annuitization of financial assets with the emphasis on tail insurance, aka longevity annuities.

## Reasons for Using the Market Based Safe Discount Rate

Since the retirement investor’s retirement income goal is known with higher certainty than the return on risky assets, basing a discount rate on the expected return of the investor’s portfolio assets creates a discrepancy between the retirement income goal and the relative uncertainty of the portfolio’s ability to meet the goal.

The funded ratio is silent on the rate of return of the investment portfolio. To put it another way, if I have a $1 million portfolio its PV is $1 million, regardless of whether it is invested in TIPS, emerging market stocks, or the S&P 500 stock index. You don’t get a higher PV for the portfolio because it’s invested in stocks rather than T-bills. Since the FR is concerned only with whether your liability is fully funded now, the FR is unaffected by the expected future rate of return on your investments.

The discount factor comes into play on the liabilities side – the PV of your targeted retirement income stream. A basic principle of finance is that if you want to hit a financial target with high probability, in this case your targeted retirement income stream goal, then the discount rate applied to those liabilities must be safe. This has nothing to do with the portfolio’s expected return. To repeat, there is no connection between the portfolio’s expected return and the discount rate applied to the liabilities.

For a safe discount rate the duration of the asset must match the duration of the liability. Furthermore, since in this case the targeted retirement income stream is real, the matched asset needs to also be real. For US investors that matching asset is a long-term TIPS bond. Currently to the nearest half percent the return on long-term TIPS is 1%. That is how the 1% discount rate is derived. It is the safest discount rate in this case. Since we want to hit the goal with high probability we need to use a safe discount rate. If we instead use the expected return on a portfolio with a heavy allocation to stocks then we have roughly a 50% to 60% chance of reaching the target. Since we want to meet the income goal – instead of meeting it about 50% of the time – using the higher expected return of a risky portfolio as the discount rate is not appropriate.

Here is a quote from an article by financial planner Paula Hogan that addresses this issue succinctly.³

First, when planning for retirement, set yourself up for clear decision-making. Separate the exercise of determining the cost of safely funding your income in retirement from the exercise of deciding how to invest your portfolio. When planning for retirement income, use as your base case a plan that does not rely on stock performance for success. Then, look at the range of possibilities implied as you increase risk from that base income projection. As you increase portfolio risk beyond the base case scenario, you are in essence indicating that you are able and willing to accept a reduced future standard of living if necessary in return for having a chance of obtaining a higher standard of living.

Or, perhaps you will decide to increase portfolio risk even though you are unable or unwilling to reduce your future standard of living if investments don’t work out as planned.If you take this route, and like a pension fund use current accounting guidelines rather than a fair-market valuation approach, you are in essence relying on the future-taxpayer/white-knight scenario as your ultimate financial safety net in retirement.

## Dealing with Couples

Determining the retirement horizon in the case where we are dealing with a couple rather than a single individual is a more difficult set of FR calculations, because it involves joint mortality probabilities both in terms of first and last to die. This is particularly tricky if they have pensions that are only for the pensioner and not the partner, and either only one such pension or life annuity, or one that is much bigger than the other. In such cases you definitely have to look at more than one scenario. I would also suggest keeping or slightly lowering the shorter life expectancy and more significantly extending the longer life expectancy. The base scenario would use the two life expectancies and the conditions that would pertain if those expectations were met. Examples of the different scenarios would require a separate article, given the extra considerations that need to be taken into account in these possible states of the world.

## Notes

- Some authors use the term
*funding ratio*instead of*funded ratio*. - DB – Defined Benefit
- DC – Defined Contribution

## References

¹ Q Group Panel Discussion: Looking to the Future – with Lo, Merton, Ross, and Siegel

² Challenges and Solutions in Retirement Funding and Post-Retirement Payout – Robert C. Merton

³ Are Public Pension Plans Your Model For Retirement Planning? – Paula Hogan

**Funded Ratio and general retirement**

*Retirement Security In a Single Number*– Eleanor Laise, Kiplinger*3600 Retirement Planning*– Morgan Stanley*Tips to Manage Spending in Retirement*– Paul Sullivan, New York Times*Funded Ratio: What is it and what’s yours?*– Russell Investments*Your model to successful individual retirement investment plans*– Tim Noonan

### Market Based Discount Rate

*Money to burn – The muddle-headed world of American public-pension accounting–*The Economist*UNDERSTANDING THE ARGUMENT FOR MARKET VALUATION OF PUBLIC PENSION LIABILITIES*– Andrew Biggs and Kent Smetters – AEI*Logical Implications of GASB’s Methodology for Valuing Pension Liabilities*– Robert Novy-Marx*Why Discount Rates Should Reflect Liabilities: Best Practices for Setting Pension Fund Discount Rates*– Truong Bui and Anthony Randazzo, Reason Foundation*Daily Treasury Real Yield Curve Rates*– US Treasury

### Time Value of Money and Funded Ratio – tutorials and spreadsheets

*TVMCalcs.com – “Time Value of Money Calculations” and “Time Value of Money Calculators”)*– source for financial calculators, time value of money mathematics, and Microsoft Excel tutorials on the Internet.- Time value of money calculations on your phone – Google
*Bogleheads Wiki on Present Value*- “Funding ratio”, a Google spreadsheet for calculating a funding ratio, by Bogleheads forum member
*cametomysenses.*Available for LibreOffice Calc (**ods**) and Microsoft Excel (and**xlsx****xlsm**).