June 2013, Number 13-9THE IMPACT OF INTEREST RATES ON THENATIONAL RETIREMENT RISK INDEX* Alicia H. Munnell is director of the Center for Retirement Research at Boston College (CRR) and the Peter F. Drucker Pro-fessor of Management Sciences at Boston College’s Carroll School of Management. Anthony Webb is a research economistat the CRR. Rebecca Cannon Fraenkel is a research associate at the CRR. The Center gratefully acknowledges PrudentialFinancial for its sponsorship of the National Retirement Risk Index.IntroductionThe National Retirement Risk Index (NRRI) measuresthe share of working-age households who are “at risk”of being unable to maintain their pre-retirement stan-dard of living in retirement. The Index is calculatedby comparing households’ projected replacementrates – retirement income as a percent of pre-retire-ment income – with target rates that would allowthem to maintain their living standard. The Index isthe percent of households for which the projectionfalls short of the target. The NRRI is based on theFederal Reserve’s Survey of Consumer Finances (SCF).The SCF is a triennial survey of a nationally repre-sentative sample of U.S. households, which collectsdetailed information on households’ assets, liabilities,and demographic characteristics. The NRRI resultsshow that, even if households work to age 65 and an-nuitize all their financial assets, including the receiptsfrom reverse mortgages on their homes, more thanhalf of households are at risk.Real – inflation-adjusted – interest rates enter intothe NRRI calculation primarily through the assump-tion that households purchase an inflation-indexedannuity with their assets at retirement. These assetsinclude 401(k)/IRA holdings, financial assets outsideof tax-preferred plans, and the proceeds from access-ing home equity through a reverse mortgage. Thehigher the interest rate, the more income these finan-cial assets produce. This effect is partially reducedby the fact that the portion of the house that can beaccessed through a reverse mortgage varies inverselywith the nominal interest rate. Interest rates do notplay a role during the asset accumulation period,because, as described below, assets at 65 are basedon the steady relationship by age between wealth andincome reported in the SCF. This brief explores thepercent of households at risk under two alternativeinterest rate scenarios: 1) real rates remain at zero ascurrently suggested by the yield on 10-year TreasuryInflation-Protected Securities (TIPS); or 2) real ratesrevert to the 4-percent level experienced when theindexed securities were first introduced in the 1990s.The discussion proceeds as follows. The firstsection describes the nuts and bolts of constructingthe NRRI. The second section discusses the role ofinterest rates in the NRRI and reports the results.The final section concludes that changing interestrates has only a modest effect on the NRRI, and that,regardless of the interest rate, today’s workers face amajor retirement income challenge.By Alicia H. Munnell, Anthony Webb, and Rebecca Cannon Fraenkel*R E S E A R C HRETIREMENT
To calculate projected replacement rates, we alsoneed income prior to retirement. The items that com-prise pre-retirement income include earnings, thereturn on 401(k) plans and other financial assets, andimputed rent from housing. In essence, with regardto wealth, income in retirement equals the annuitizedvalue of all financial and housing assets; incomebefore retirement is simply the return on those sameassets.3Average lifetime income then serves as thedenominator for each household’s replacement rate.Estimating Target Replacement RatesTo determine the share of the population that willbe at risk requires comparing projected replacementrates with a benchmark rate. A commonly usedbenchmark is the replacement rate needed to allowhouseholds to maintain their pre-retirement standardof living in retirement. People clearly need less thantheir full pre-retirement income to maintain thisstandard once they stop working since they pay less intaxes, no longer need to save for retirement, and oftenhave paid off their mortgage. Thus, a greater shareof their income is available for spending. Targetreplacement rates are estimated for different types ofhouseholds assuming that households spread theirincome so as to have the same level of consumptionin retirement as they had before they retired.4Center for Retirement Research2 The Nuts and Bolts of theNational Retirement Risk IndexConstructing the National Retirement Risk Indexinvolves three steps: 1) projecting a replacementrate – retirement income as a share of pre-retirementincome – for each member of a nationally represen-tative sample of U.S. households; 2) constructing atarget replacement rate that would allow each house-hold to maintain its pre-retirement standard of livingin retirement; and 3) comparing the projected andtarget replacement rates to find the percentage ofhouseholds “at risk.”Projecting Household Replacement RatesThe exercise starts with projecting how much retire-ment income each household will have at age 65.Retirement income is defined broadly to include theproceeds from all of the usual suspects plus housing.1Retirement income from financial assets and hous-ing is derived by projecting assets that householdswill hold at retirement, based on the stable relation-ship between wealth-to-income ratios and age that isevident in the 1983-2010 SCFs. As shown in Figure 1,wealth-to-income lines from each survey rest virtuallyon top of one another, bracketed by 2007 values onthe high side and 2010 values on the low side. Thissteady relationship is surprising given the shift fromdefined benefit to defined contribution plans, becauseaccrued wealth in defined benefit plans is not includ-ed in the SCF data while defined contribution assetsare included. As a result, an increasing reliance ondefined contribution plans would have been expectedto show up as more wealth accumulation over time.In addition to the pension shift, other factors wouldalso have been expected to lead to increased house-hold wealth over time, such as longer lifespans,higher health care costs, and lower returns. Despiteall these developments, though, the wealth-to-incomeratios have remained quite stable.2Sources of retirement income that are not de-rived from SCF-reported wealth need to be estimateddirectly. For defined benefit pension income, the pro-jections are based on the amounts reported by surveyrespondents. For Social Security, benefits are calculat-ed directly based on estimated earnings histories foreach member of the household. Once estimated, thecomponents are added together to get total projectedretirement income at age 65.Figure 1. Ratio of Wealth to Income by Age fromthe Survey of Consumer Finances, 1983-2010Source: Authors’ calculations based on U.S. Board of Gov-ernors of the Federal Reserve System, Survey of ConsumerFinances (SCF), 1983-2010.024620-22 26-28 32-34 38-40 44-46 50-52 56-58 62-641995199820011992198319861989200420072010Age
-1%0%1%2%3%4%5%1997 1999 2001 2003 2005 2007 2009 2011 201310 year TIPS constant maturity rate: actual10 year TIPS constant maturity rate: estimatedIssue in Brief 3Calculating the IndexThe final step in creating the Index is to compareeach household’s projected replacement rate withthe appropriate target. Households whose projectedreplacement rates are more than 10 percent below thetarget are deemed to be at risk of having insufficientincome to maintain their pre-retirement standardof living. The Index is simply the percentage of allhouseholds that are more than 10 percent short oftheir target.The NRRI under AlternativeInterest Rate ScenariosInterest rates play a role in the NRRI calculationbecause households are assumed to purchase aninflation-indexed annuity with their financial assets– 401(k)/IRA holdings, financial assets outside oftax-preferred plans, and the proceeds from a reversemortgage. The gain (loss) from higher (lower) inter-est rates is slightly offset by the fact that the portionof the house that can be accessed through a reversemortgage varies inversely with the interest rate.5Asjust discussed, interest rates do not play a role on theaccumulation side, because assets at 65 are based onthe steady relationship by age between wealth andincome observed in the SCF over almost 30 years.This analysis considers two alternative interestrate scenarios. The first scenario has the real interestrate at zero percent for the full period,6as suggestedby the current yield on Treasury Inflation-ProtectedSecurities (TIPS) (see Figure 2). The second scenarioconsiders a robust recovery, with the real interestrate slowly climbing from its 2010 level to a rate of 4percent, the approximate level after TIPS were intro-duced in the 1990s.7These alternatives are comparedwith the 2010 baseline scenario, where interest ratesare tapered from 2010 rates for households approach-ing retirement to 2004 rates (2.2 percent) for youngercohorts.8The year 2004 is used because it representsthe most normal economic period and stable interestrate environment experienced in recent years.The results of the exercise show relatively littlechange in the NRRI overall. It rises slightly, from 53percent to 54 percent, when rates are low and fallsslightly when rates are high (see Table 1).Figure 2. Real Interest Rates on 10-year TIPS,1997-2013Note: The interest rate from 1/1/03 onward is that on the10-year constant maturity TIPS. The interest rate prior to1/1/03 is the authors’ estimate of the 10-year constant matu-rity rate, based on TIPS market data.Source: Federal Reserve Bank of St. Louis (2013).Table 1. Percent of Households “At Risk” at Age65 by Income Group and Interest RateSource: Authors’ calculations.Income group Real interest rate0% 4%All 54% 53% 51%Lowest third 61 61 61Middle third 56 54 51Highest third 46 44 40The change in the percentage at risk for all house-holds is surprisingly small, given the large changesin real interest rates. The explanation is threefold.First, changes in interest rates have a muted effect onannuity income. One’s initial thought might be thatBaseline (about 2%)
a doubling of interest rates would lead to a doublingof retirement income. But annuity payouts consistof a return of principal along with interest earnings.Since changes in interest rates only affect the interestportion of the annuity payout, the impact on the fullannuity payout is much smaller. Hence, a retireewith $100,000 will receive $507 per month from aninflation-indexed annuity when the real interest rateis 4.0 percent compared to $324 per month when it is0 percent.9Second, financial assets for most householdsare only a modest portion of their total wealth. Forexample, as shown in Figure 3, financial assets areonly 10 percent of total wealth (including the presentdiscounted value of Social Security and benefits fromdefined benefit pensions) for households aged 55-64in the middle third of the income distribution. And,those in the lowest third, who rely heavily on SocialSecurity for their retirement income, have minisculelevels of financial assets.Third, housing wealth is a significant asset formany households. But, as described below, the im-pact of changes in interest rates on the payout from areverse mortgage is partially offset by changes in theamount that can be borrowed.The change in the percent of households at riskby age group shows that the households age 50-59 areless affected by the shift to a zero-percent rate thantheir younger counterparts (see Table 2). The reasonis that the change from the baseline rate is smallerfor older households than for younger householdsbecause their baseline rate is lower.Center for Retirement Research4Figure 3. Financial Wealth as a Percent of Total Wealth by Income Group, Households 55-64, 2010Note: The values reflect the mean of the middle 10 percent of each income tercile.Source: Authors’ calculations based on the 2010 SCF.Lowest third Middle third Highest thirdTable 2. Impact of Changing Interest Rate by AgeGroupSource: Authors’ calculations.AgegroupReal interest rate0% 4%All 54% 53% 51%30-39 64 62 6040-49 57 55 5250-59 44 44 42Interest Rates and Reverse MortgagesAs noted, one complication in the simple story thathigher interest rates produce more income and viceversa is the fact that interest rates also directly influ-ence the amount that can be borrowed. For example,under the federal Home Equity Conversion Mortgageprogram for reverse mortgages, at a real interestrate of zero, 64 percent of the value of the house canbe borrowed. At 4 percent, only 30 percent can beborrowed.10The reason for this variation is that, athigher interest rates, interest on the original amountborrowed cumulates more rapidly. To prevent anunacceptable increase in the risk of the loan, plusaccumulated interest, exceeding the sale proceeds ofthe house, the lender must reduce the amount of theoriginal loan. Thus, the change in the portion of thevalue of the house that can be borrowed offsets thePrimary housing DB SS 401(k), IRA, and financial assets Other non-financial and business assets3%3%14%8%72% 55%32%28%18%16%6%17%14%4%10%Baseline (2%)
Issue in Brief 5direct effect of interest rates on annuity income. Forexample, an interest rate of zero increases the shareof households at risk by 1.4 percentage points, which(with rounding) is the net effect of a 2.7-percentage-point increase due to lower annuity rates and a1.3-percentage-point decrease due to the ability to bor-row more against the house (see Figure 4).ConclusionThis NRRI analysis shows that, as of 2010, morethan half of today’s households will not have enoughretirement income to maintain their pre-retirementstandard of living even if interest rates rise substan-tially above their current low. Households are lessvulnerable than expected to today’s historically lowinterest rates, but higher interest rates would alsoprovide no real cure to the problem of inadequateretirement saving.Three factors explain the modest effect of inter-est rates on retirement security. First, changes ininterest rates never hit annuity payouts with full force,because the principal portion of the payout is unaf-fected by interest rates. Second, most householdshave relatively little financial wealth. Finally, hous-ing wealth is significant for many households, butthe impact of movements in interest rates is partiallyoffset by changes in the amount that can be borrowedthrough a reverse mortgage.Figure 4. Impact of Reverse Mortgages on thePercent at RiskNote: To decompose the change in percent at risk, the pro-jections are run sequentially. First, the change from annuityrates is calculated by holding the percent of the value ofthe house available to borrow constant at the baseline level.Second, the percent of the house available is also allowed tovary, giving the net change. The change from reverse mort-gages is the difference between these two numbers.Source: Authors’ calculations.1.4%-2.2%2.7%-3.6%-1.3%1.4%-4%-3%-2%-1%0%1%2%3%Baseline to zero percent Baseline to 4 percentNet change in % at risk Change from annuity ratesChange from reverse mortgages1.4%-2.2%2.7%-3.6%-1.3%1.4%-4%-3%-2%-1%0%1%2%3%Baseline to zero percent Baseline to 4 percent-2.2%-3.6%%1.4%ent Baseline to 4 percent
Center for Retirement Research6Endnotes1 The Index does not include income from work,since labor force participation declines rapidly aspeople age.2 For more detail on this analysis, see Delorme,Munnell, and Webb (2006) and Munnell (2012).3 Interest on both mortgage debt and non-mortgagedebt is subtracted from the appropriate componentsof both retirement income and pre-retirement in-come.4 To ensure a stable replacement rate target, theanalysis assumes that households calculate theirtargets based on expected rates of return when theyenter the workforce. An alternative approach, whichwould be consistent with a life-cycle savings model,would be for households to continually update thosetargets based on realized returns and revisions toexpectations of future returns.5 The income obtainable on an inflation-indexed an-nuity depends on the real interest rate. The amountthat a household can access through a reverse mort-gage depends on the nominal interest rate.6 The period of the analysis ends in 2045, when theyoungest members of the NRRI sample turn 65 andare assumed to retire.7 The 4-percent interest rate is fully phased in by2021, so that younger households benefit more.Households retiring from 2016-2020 receive annu-ity income that is a blended average of the incomepayable when the interest rate is 4 percent and theincome payable when the interest rate is at the 2010level of 0.9 percent.8 In the baseline scenario, the interest rate climbsfrom 0.9 to 2.2 percent over the period 2015-2038.9 This example is for an individual born in 1956 andretiring in 2021. The year 2021 was chosen becauseit is when the 4-percent rate is fully phased in. Thecalculation is made by determining the expectedpresent value of a joint life and two-thirds survivorannuity using the 10-year TIPS interest rate and thencalculating annuity rates at other interest rates, usingthe same expected present value. In practice, insur-ance companies offering inflation-linked annuitiesdo not completely hedge their liabilities by investingexclusively in TIPS, and the duration of annuitiesexceeds ten years. But calculations based on an as-sumption that insurers price annuities by reference tothe yield on 10-year Treasury bonds provide reason-able estimates of the effect of changes in interest rateson annuity rates.10 The calculations are before mortgage insurancepremium, closing costs, and servicing cost set-aside.They assume a 2.5 percent inflation rate and a 2.5percent lender’s margin, so the nominal rates are 5percent for the low-interest-rate scenario and 9 per-cent for the high-interest-rate scenario.ReferencesDelorme, Luke, Alicia H. Munnell, and AnthonyWebb. 2006. “Empirical Regularity SuggestsRetirement Risks.” Issue in Brief 41. Chestnut Hill,MA: Center for Retirement Research at BostonCollege.Munnell, Alicia H. 2012. “2010 SCF Suggests EvenGreater Retirement Risks.” Issue in Brief 12-15.Chestnut Hill, MA: Center for Retirement Re-search at Boston College.Federal Reserve Bank of St. Louis. 2013. Yields onSelected 10- and 30-Year Treasury Inflation-IndexedSecurities. 1997-2013. St. Louis, MOU.S. Board of Governors of the Federal ReserveSystem. Survey of Consumer Finances, 1983-2010.Washington, DC.