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You are here:  FPA Net  >  FPA Journal  >  Past Issues & Articles  >  2001 Issues  >  2001 May Issue - Article 13  
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Contribution
Rethinking the Family’s Asset Allocation
by William Reichenstein, Ph.D., CFA

Dr. Reichenstein is the Pat and Thomas R. Powers Chair in Investment Management at the Hankamer School of Business, Baylor University, in Waco, Texas. He can be reached at (254) 710-6146. He is a member of the Editorial Review Board of the Journal of Financial Planning.

This article challenges two aspects of the traditional approach to calculating a family’s asset allocation. First, it emphasizes the need to distinguish between before-tax and after-tax funds when calculating the asset allocation. Second, it argues that a family’s portfolio should be broadened to include, at a minimum, (1) the value of retirement income streams, such as Social Security and company pensions and (2) the mortgage as a short position in bonds. As we shall see, a family’s asset allocation varies dramatically depending upon whether we adjust account values for taxes and what we include in the family portfolio.

So, you think you know how to calculate an individual’s or family’s asset allocation? This article challenges the traditional approach to doing this. It extends and refines ideas first expressed in Reichenstein [1998]. Although it may shake readers’ confidence in their current financial planning procedures, it also provides important insights that should help them better serve their clients.

Two Decisions
The financial planner must make two decisions when calculating an individual’s or family’s asset allocation. First, the planner must decide whether to calculate the asset allocation based on accounts’ market values or after-tax values. Second, the planner must decide what assets and liabilities belong in the family portfolio.

Before-tax versus after-tax funds. Steve and Teresa Adams, both 45 years old, are in the 28 percent tax bracket and expect to remain there during retirement. They decide to reduce this year’s consumption by $2,000 and save for retirement. They will each save $1,000 of after-tax funds. Steve invests $1,000 in a Roth IRA. Teresa defers $1,388.89 in her 401(k) plan. The $1,388.89 contribution reduces taxable income by the same amount, which reduces taxes by $388.89. The $1,388.89 of before-tax funds in the deductible pension represents $1,000 of after-tax funds plus the $388.89 tax savings.

They both invest in the same stock or bond mutual fund. It earns nine percent a year for 30 years, at which time the funds are withdrawn and spent on retirement needs. Steve invests $1,000 of after-tax funds this year and it grows to $13,268 at age 75 [$1,000(1.09)30]. Teresa invests $1,388.89 of before-tax funds this year. At age 75, the $1,388.89 is worth $18,427 before taxes and $13,268 after taxes.

At age 45, the $1,388.89 of before-tax funds in Teresa’s 401(k) is equivalent to the $1,000 of after-tax funds in Steve’s Roth IRA. At age 75, the $18,427 of before-tax funds in Teresa’s 401(k) is equivalent to the $13,268 of after-tax funds in Steve’s Roth IRA. Any acceptable method of calculating this couple’s asset allocation must recognize the equivalence of these totals.

The example illustrates the appropriate method of converting before-tax funds in a 401(k) and other deductible pensions to after-tax funds.1 Before-tax funds should be multiplied by (1 – t), where t is the expected tax rate during retirement. At age 45, the $1,388.89 in Teresa’s deductible pension should be treated as $1,000 after taxes, $1,388.89 (1 – 0.28). At age 75, the $18,427 in her deductible pension should be treated as $13,268 after taxes.

Suppose at age 75 Steve transfers the $13,268 in his Roth IRA into a stock fund, Teresa transfers the $18,427 in her deductible pension into a bond fund, and these are their only assets. What is their current asset allocation? If the funds are intended for retirement income needs, I contend it must be 50 percent stocks and 50 percent bonds. In my opinion, the 50 percent stock-50 percent bonds calculation is the only one that is internally consistent in that it recognizes the equivalence between the $13,268 in a Roth and the $18,427 in a deductible pension.

A family may hold assets in several savings vehicles, including deductible pensions, Roth IRAs, nonqualified tax-deferred annuities or taxable accounts. The family asset allocation should be based on these accounts’ after-tax values. The same principle applies: People pay for goods and services with after-tax funds. To compare apples to apples, an individual’s or family’s asset allocation should reflect accounts’ after-tax values. Later in this study, we discuss methods of converting market values to after-tax values for funds held in each savings vehicle.

What "counts" in the family portfolio? The second decision that a financial planner must make is what assets and liabilities to include in the family portfolio. In my opinion, Scott [1995] presents a good framework for answering this question. She says the family "portfolio should consist of financial assets that you would be willing to sell for spending money or that generate some form of spending money, either now or sometime in the future" (p.15). In short, she includes assets that affect cash flows. As such, she includes the present value of retirement income streams such as Social Security payments. I expand her framework to include the mortgage, because it, too, affects cash flows.

I recommend that financial planners include, at a minimum, the after-tax present value of retirement income streams as a long bond position and include the mortgage as a short bond position. I leave unresolved other issues, including whether the family portfolio should include the value of the personal residence as real estate and whether the cash value of life insurance policies should be included as a long bond.2

Studies that examine families’ preparedness for retirement consider Social Security and other retirement income streams.3 Yet, the traditional approach to calculating a family’s asset allocation excludes retirement income streams. This is inconsistent! In my opinion, the value of retirement income streams belongs in the portfolio. I know a retired couple in their upper forties. Both partners are retired from the military. Without their inflation-adjusted military pensions, they would not be retired today. They clearly understand that retirement income streams "count" in their family portfolio. It is time for the financial professions to recognize what others already understand.

To repeat, Scott does not consider the mortgage in the family portfolio. Yet, since it affects cash flows, it would appear to meet her criterion. Suppose a 50-year-old couple has a $140,000 mortgage and $140,000 bonds held in a taxable account (the cost basis and market value of the bonds are $140,000). On Tuesday, they liquidate the taxable bond account and prepay the mortgage. On Wednesday, they take out a $140,000 mortgage and invest in bonds held in a taxable account. They are in the same financial position after Wednesday as before Tuesday. If the bond fund is included but the mortgage is not, the family appears to decrease its bond exposure the first day and increase it the second. It seems logically inconsistent to exclude the mortgage. In my opinion, the mortgage should be considered a short bond position.

The next section examines issues related to the valuation of retirement income streams.

Issues Related to Valuation of Retirement Income Streams

Social Security, military retirement and company pensions provide retirement income streams. There are at least three issues that must be addressed in valuing these streams. First, we estimate the present value of their after-tax cash flows because goods and services are purchased with after-tax funds. Second, for this paper we estimate the value of cash flows through life expectancy. The third issue is the appropriate discount rate. When valuing Social Security and military retirement, we use today’s yield on the Treasury Inflation Protection Security (TIPS) with maturity nearest the life expectancy. Like Social Security and military retirement, payments from TIPS are government guaranteed and increase each year with the consumer price index (CPI) inflation.

In contrast, a company pension usually promises a fixed dollar amount each month for the ex-employee’s life. Assuming the pension fund is well funded (and most are), the discount rate can be set at today’s nominal Treasury yield with maturity nearest the life expectancy. Social Security and military retirement’s constant annual stream of real income can be discounted at today’s real Treasury yield, while, if well funded, a company pension’s constant annual stream of nominal income can be discounted at today’s nominal Treasury yield.4

Suppose Hank is 65, single, and will receive Social Security payments of $1,433 a month, inflation adjusted, for the rest of his life. The Internal Revenue Service’s unisex mortality tables assume that a 65-year-old has a life expectancy of 20 years. Based on today’s long-term TIPS yield of 3.75 percent, the present value of a $17,196 ($1,433 x 12) annuity due for 20 years is about $248,000. Assuming taxes at 28 percent, the after-tax value is about $178,500.5

Social Security and other retirement income streams are different from financial assets. They are contingent income streams in that the income is contingent upon someone living (or his or her spouse living). Hank will receive $1,433 a month inflation adjusted for the rest of his life. This is different from a guaranteed inflation-adjusted $1,433 a month for his 20-year life expectancy. If Hank dies this month, the payments cease. And the payments continue as long as he lives, which may be well beyond 20 years.

Suppose, due to a child from a previous marriage, that Hank wants to convert Social Security’s contingent value into a guaranteed value. By buying term life insurance with a $178,500 death benefit, he can convert the contingent value into a guaranteed value. Each year, he can renew the term life policy for the then-current, after-tax present value of Social Security payments through his life expectancy. Despite the contingent nature of retirement income, I believe Social Security should be considered a $178,500 bond in Hank’s portfolio. However, the client and financial planner should be aware of the distinction between its contingent value and guaranteed value.

The next section presents a detailed example that incorporates this paper’s topics.

The Sanchez Family Portfolio

Table 1 presents the family portfolio of José and Maria Sanchez. They are both 65 years old and have two children, both grown and financially independent. They are in the 28 percent ordinary income tax bracket and 20 percent capital gains tax bracket and expect to remain there. The market value of their financial assets totals $400,000. In addition, they each receive $10,000 a year in Social Security payments. Their personal residence is worth $300,000 and there is a $140,000 mortgage on it. What is their current asset allocation?

Table 1: Sanchez Family Portfolio in Market and After-Tax Values

The first decision is to convert market values to after-tax values. They have $10,000 in bonds held in a Roth IRA. Since distributions from a Roth IRA generally are tax exempt, its after-tax value is identical to its market value.

They have a bond fund held in a taxable account with a market value of $110,000 and cost basis value of $114,000. If they liquidate the fund this year, the $4,000 short-term capital loss can be used to offset capital gains. Assume they realize the loss this year and have no other capital gains or losses. They reduce this year’s taxable income by $3,000 and they carry the remaining $1,000 loss forward to the next year. They reduce taxes this year by $740 [$3,000 (0.28)], and the $1,000 loss carried forward reduces taxes by $280 next year. The present value of $280 one year hence is about $260. So, the $4,000 unrealized loss has an after-tax value of about $1,000. The bond fund’s after-tax value is thus $111,000 or $110,000 + $1,000 tax savings.

José and Maria own $30,000 of an individual stock with a cost basis of $10,000. There is no one "right way" to handle the built-in long-term capital gain. Table 1 assumes the funds will be liquidated this year and they will pay capital gain taxes of $4,000 (20 percent of the $20,000 gain). The after-tax value is thus $26,000.

Other tax treatments are possible. There are two possibilities: first, the stock will be sold several years later and, second, the stock will be held until the first spouse dies. Assume the stocks will be sold in, say, five years. The following example suggests that assuming the capital gains are realized this year is an acceptable tax treatment even if the stock will not be sold for several years. In five years, the tax liability will be 20 percent of the capital gain at that date. A reasonable expectation may be a projected total stock return of ten percent, including eight percent capital gain. This implies a projected sales price of about $44,000 [$30,000(1.08)],5 which implies a projected capital gain of $34,000 and projected tax liability of $6,800 (20 percent of the projected gain.) The present value of $6,800 when discounted at ten percent, which reflects the stock’s risk, is $4,222. The $4,222 is close to the $4,000 tax liability if the stock is sold today. Thus, assuming that the capital gains are realized this year appears to be an acceptable tax treatment even if the stock will not be sold for several years.

The second possibility is that the couple plans to hold the stock until the first spouse dies, at which time the surviving spouse will liquidate the stock. At death, the stock’s cost basis is increased to its fair market value; that is, the stock receives a step-up in cost basis. There will be no capital gains taxes. In this case, the stock’s current after-tax value is $30,000.

In summary, there is no one right way to handle the tax treatment of the built-in capital gain. The client and financial planner should discuss the issue and decide on an acceptable assumption. The financial planner provides a valuable service by educating the client about the tax issue.

The Sanchez family has a nonqualified tax-deferred annuity with a market value of $50,000 and a cost basis of $30,000. Suppose they funded this account six years ago with a $30,000 original investment. The additional $20,000 is tax-deferred returns. Eventually, the deferred returns will be taxed as ordinary income. Table 1 assumes that they are taxed immediately, which reduces the account’s after-tax value to $44,400 [$50,000 – 0.28($20,000)]. Suppose they do not plan to liquidate the annuity for several years. As with the tax treatment of the built-in capital gain, the assumption that they liquidate the annuity this year probably provides a reasonable tax treatment of the deferred returns.6

Their deductible pension contains stock worth $200,000 before taxes and, based on an expected 28 percent tax bracket during retirement, $144,000 after taxes. By ignoring taxes, the traditional approach implicitly assumes the retirement tax bracket will be zero. Thus, even though this conversion requires an estimate, it is easy to improve upon the traditional approach’s implicit assumption that the tax rate will be zero. The difference between market value and after-tax value is larger for families that expect to be in higher retirement tax brackets. Since most families have substantial assets in deductible pensions, the traditional approach’s failure to adjust for taxes is both a common and significant problem.

The second decision is what to include in the family portfolio. The family’s "other assets and liabilities" include Social Security payments of $20,000 this year, a personal residence worth $300,000 and a $140,000 mortgage. In the case of Social Security, they will each receive a constant annual real income of $10,000 for the rest of their lives. For purposes here, we estimate the value of Social Security as the present value of after-tax payments through their 20-year life expectancy. The present value of a 20-year, $20,000-a-year annuity when discounted at 3.75 percent is about $288,300. Its after-tax value is $207,600 [$288,300 (1 – 0.28)].

José and Maria Sanchez bought the house seven years ago for $200,000 and have lived there since. Since they file jointly and have owned and occupied the house as a principal residence for an aggregate of at least two of the prior five years, they can exclude from income up to $500,000 in capital gains from its sale or exchange. Thus, there is no tax liability on the $100,000 built-in gain. The residence’s market and after-tax values are $300,000.

A single person who satisfies the ownership and occupation requirements can exclude from income up to $250,000 in capital gains. The exclusion can apply to one sale or exchange every two years; this is not a once-per-lifetime exclusion. Moreover, the capital gain exclusion is pro-rated for periods shorter than two years. Thus, if José and Maria realized a $100,000 capital gain from a principal residence that they owned and occupied for 18 months, they could exclude three-fourths (18/24 months) of the gain.7

Table 1 assumes that the mortgage’s face value and market value are $140,000; that is, their mortgage rate equals the current mortgage rate. If the interest rate on their fixed-rate mortgage is below the current fixed rate, then the financial planner may record the market and after-tax values of the mortgage at less than face value. Suppose José and Maria have a seven percent fixed-rate mortgage with 23 years remaining, and today’s fixed mortgage rate is nine percent. Their monthly principal and interest payment is $1,021.89.8 Based on today’s nine percent interest rate, the present value of the $1,021.89 monthly payment is $118,926. If José and Maria expect to retain their seven percent mortgage for the 23 years, then the $118,926 figure would be the appropriate market and after-tax value. If, however, they expect to sell their home and pay the mortgage within a few years, then the current face value is a reasonable estimate of the current market and after-tax value. Note that the value of a below-market interest rate depends upon how long they expect to retain the mortgage.

Six Views of the Sanchez Family’s Asset Allocation

The bottom section of Table 1 presents six views of the stock portion of the Sanchez family’s asset allocation. Three views rely on accounts’ market values and three on after-tax values. There are three views or opinions about what counts in the portfolio. The narrow view counts financial assets only. A middle view also includes the present value of Social Security. A broad view counts financial assets, Social Security and the mortgage, where the mortgage is considered a short bond position.9

The traditional approach to calculating the family asset allocation is the market-value narrow view. According to this view, the Sanchez family portfolio contains 72 percent stocks, $280,000/$400,000, and 28 percent bonds. Since I believe the asset allocation should reflect after-tax values, I limit discussion to the three after-tax views. According to the after-tax narrow view, they have a 64 percent stock allocation, [$214,400/$335,400]. According to the after-tax middle view, they have 39 percent in stocks, in thousands [$214.4/ ($335.4 + $207.6)]. According to the after-tax broad view, they have 53 percent in stocks, in thousands [$214.4/($335.4 + $207.6 – $140)].

It is instructive to compare the traditional view to each of the after-tax views. The traditional view says the Sanchez portfolio contains 72 percent stocks, while the after-tax narrow view says it contains 64 percent stocks. This family follows the advice of Reichenstein [2000] and Shoven and Sialm [1998], among others, and holds stocks in tax-favored retirement accounts. Bodie and Crane [1997] report that the stock portion of most individuals’ retirement accounts indeed exceeds the stock portion of their other investment accounts. The traditional approach will likely substantially overstate these families’ true stock allocation. And the higher their ordinary-income tax rate, the larger the measurement error.

Next, compare the Sanchez family’s 72 percent stock allocation as measured by the traditional view to the 39 percent allocation as measured by the after-tax middle view. If the family has already paid the mortgage (or if the financial planner decides to exclude the mortgage from the family portfolio), I believe the 39 percent stock allocation would be correct. The traditional approach’s measurement error would be a whopping 33 percent, or 72 percent minus 39 percent! The traditional approach contains two errors, both of which cause it to overstate the "true" stock allocation: It overweighs the value of assets in deductible pensions and it excludes Social Security. The traditional approach’s measurement error is likely to be largest for families that hold stocks in tax-favored retirement accounts and have no mortgage, a situation that depicts many families near retirement or in retirement.

According to the recommended after-tax broad view, the traditional approach overestimates the family’s stock allocation by 19 percent (72% – 53%). Although smaller than the prior measurement error, it is substantial. A frequent rule of thumb says a portfolio deviates significantly from its target portfolio if one of its asset class weights is at least ten percent from its target weight. By this standard, the method of calculating a family’s asset allocation is clearly significant.

Does the Portfolio View Matter?

One may ask if it really matters how we calculate the family asset allocation. After all, the Sanchez family’s true financial position is the same regardless of what we include in their portfolio and whether we use market values or after-tax values. I believe it matters a great deal because, among other reasons, it affects investment decisions. Suppose Maria inherits $100,000 after taxes, and they ask a financial planner to help them invest the funds. Based on their risk tolerance, assume that their target asset allocation calls for a 50 percent stock allocation. Should the $100,000 be invested in stocks or bonds? As we shall see, it depends upon the portfolio view.

According to the traditional market-value narrow view, none of the inheritance should be invested in stocks. According to the after-tax narrow view, she should invest $3,300 in stocks. According to the after-tax middle view, she should invest the full $100,000 in stocks. According to the after-tax broad view, she should invest $37,000 in stocks. Depending upon one’s view of the portfolio, she should invest anywhere from none to all of the $100,000 in stocks. Any decision that affects investment decisions is indeed important.

Investment Lessons

This analysis provides several investment implications. A financial planner who has been calculating a family’s asset allocation using the traditional market-value, narrow approach has made the following systematic errors.

  • He or she has overweighed the value of deductible pensions. If the family expects to be in the 28 percent tax bracket during retirement, then $1,000 in a deductible pension should be counted as $720 of after-tax funds. After paying deferred taxes, a $1,000 withdrawal from a deductible pension will buy only $720 of goods and services.
  • If the family primarily holds stocks in deductible pensions and nonqualified tax-deferred annuities, then it has likely overstated its true stock allocation. If the family primarily holds bonds in these tax-favored accounts, then it has likely understated its true stock allocation.
  • If the planner has not considered the value of retirement income streams, then he or she has underestimated the amount of "bonds" in the family portfolio. Most families expect to receive monthly Social Security payments, and these promised payments are like having an inflation-indexed Treasury bond in the family portfolio.
  • Similar to Social Security, a company pension plan and military retirement provide a bond-like exposure that the planner may not have considered. The value of these retirement income streams is often a substantial portion of the family portfolio, especially for less wealthy families.
  • Every financial planner has encountered clients who are hesitant to invest as much in stocks as the planner believes is appropriate. The planner can explain that Social Security (and a company pension and military retirement payments) is like a big bond in their portfolio. Thus, the client currently has a larger portion of his or her portfolio in bonds than the traditional approach suggests.
    To achieve the client’s desired true stock allocation, they may need to reallocate financial assets from bonds to stocks. For example, Maria and José may consider the 72 percent stock exposure (as measured by the traditional approach) as too risky, and decide they prefer a 60 percent stock allocation. The financial planner can point out that their true stock allocation is only 53 percent when measured using the after-tax broad view. To attain their desired asset allocation, they must reallocate funds to stocks.
  • The traditional approach severely overstates the stock allocation of families that have no mortgage and hold stocks in deductible pensions and nonqualified annuities. The traditional approach ignores the value of Social Security and other retirement income streams and overstates the value of stocks in these tax-favored accounts. Both errors cause the traditional method to overstate the family’s true stock allocation.
  • The mortgage is essentially a short position in bonds. Planners who have ignored the mortgage have likely overstated the family’s net bond exposure. In fact, a young family probably has a net negative bond position, meaning it has a larger mortgage than investment in bonds. I am not arguing that this form of leverage is inappropriate. Indeed, most young families hold a leveraged portfolio of stocks and real estate, where the latter includes the personal residence.
  • The "typical" retired family or individual has paid the mortgage. If it has not, the mortgage represents a short bond position, and the family’s true bond exposure is less than the sum of its bond investments. For example, the Sanchez’ true financial position would be substantially better if it did not have the mortgage. Failure to include the mortgage in their portfolio results in an exaggerated net bond position, an exaggerated net worth and an overstatement of the standard of living they can maintain during retirement.

Endnotes

  1. A deductible pension is any account where the investment amount is deductible in the contribution year, returns grow tax deferred and withdrawals are fully taxable at ordinary income tax rates. Examples include 401(k), 403(b), Keogh and SEP-IRA.
  2. Scott excludes the personal residence under the argument that, if a family sells its house, it would likely buy another. If and when a family downsizes to a smaller house, she believes the portfolio should include the freed funds. In essence, she views the personal residence as prepaid housing, but for asset-allocation purposes it is not treated as part of the family portfolio.
  3. See Poterba, Venti and Wise [1994]; Kennickell, Starr-McCluer and Sunden [1997]; Yuh, Hanna and Montalto [1998]; and Tacchino and Saltzman [2001].
  4. See Jennings and Reichenstein [2000] for a more detailed discussion of issues related to the valuation of retirement income streams.
  5. Social Security payments are assumed to be fully taxable, while they are usually at least partially tax free. As such, this study may underestimate the value of Social Security and understate the importance of including the value of Social Security in the family portfolio. In a later study, I will try to better estimate the taxes associated with Social Security payments.
  6. The applicable tax rate is the expected tax rate at withdrawal. If they are currently in the 36 percent ordinary income tax bracket but expect to be in the 28 percent bracket during retirement, the 28 percent tax rate applies.
  7. The $500,000 exclusion for a married couple filing jointly applies if at least one spouse satisfies the ownership test and neither spouse is ineligible for exclusion due to a sale or exchange within the prior two years.
  8. Insert into a financial calculator, PV = ($140,000), i = 7%/12 or 0.583333%, n = 23(12) = 276, FV = $0, and calculate the payment of $1,021.89. The P&I (principal and interest) payment is $1,021.89. Their full monthly payment is higher due to taxes and insurance.
  9. 9. A fourth view, which is not reflected in Table 1, includes financial assets, Social Security, mortgage and personal residence. See Reichenstein [1998] for a discussion of this view.

References

  1. Zvi Bodie and Dwight B. Crane, "Personal Investing: Advice, Theory, and Evidence," Financial Analysts Journal, November/December 1997, pp. 13–23.
  2. Jean Brunel, "Why Should Taxable Investors Be Cautious When Using Traditional Efficient Frontier Tools?" Journal of Private Portfolio Management, Vol. 1, No. 3, Winter 1998, pp. 35–50.
  3. Steve P. Fraser, William W. Jennings and David R. King, "Strategic Asset Allocation for Individual Investors: The Impact of the Present Value of Social Security Benefits," U.S. Air Force Academy, working paper, 1999.
  4. William W. Jennings and William Reichenstein, "Valuing Retirement Income Streams: The Value of Military Retirement," Baylor University, working paper, 2000.
  5. Arthur B. Kennickell, Martha Starr-McCluer and Annika E. Sunden, "Family Finances in the U.S.: Recent Evidence from the Survey of Consumer Finances," Federal Reserve Bulletin, January 1997, pp. 1–24.
  6. James M. Poterba, Steven F. Venti and David A. Wise, "Targeted Retirement Saving and the Net Worth of Elderly Americans," American Economic Review, Vol. 84, No. 2, 1994, pp. 180–185.
  7. William Reichenstein, "Calculating a Family’s Asset Mix," Financial Services Review, Vol. 7, No. 3, 1998, pp. 195–206.
  8. William Reichenstein, "Calculating the Asset Allocation," Journal of Private Portfolio Management, Vol. 3, No. 2, Fall 2000, pp. 20–25.
  9. Maria Crawford Scott, "Defining Your Investment Portfolio: What Should You Include?" AAII Journal, Vol. 17, No. 10, November 1995, pp. 15–17.
  10. John B. Shoven and Clemens Sialm, "Long Run Asset Allocation for Retirement Savings," Journal of Private Portfolio Management, Vol. 2, No. 2, Summer 1998, pp. 13–26.
  11. Kenn B. Tacchino and Cynthia Saltzman, "Should Social Security be Included When Projecting Retirement Income?" Journal of Financial Planning, Vol. 14, No. 3, March 2001, pp. 98–112.
  12. Yoonkwung Yuh, Sherman Hanna and Catherine Phillips Montalto, "Mean and Pessimistic Projections of Retirement Adequacy," Financial Services Review, Vol. 7, No. 3, 1998, pp. 175–193.

Acknowledgment: I thank three anonymous reviewers for their constructive reviews.


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