Journal of Financial Planning: August 2011
William Reichenstein, Ph.D., CFA, is the Powers Professor of Investments at Baylor University, and head of research at Retiree Income.
In Reichenstein (2009), I examined the structure of indexed annuities (IAs) including equity-indexed annuities (EIAs). I concluded that “because of their design, IAs must underperform returns on similar risk portfolios of Treasuries and index funds.” In this column, I present the logic to readers of the Journal of Financial Planning. Separately, I discuss a recent critique of my study by VanderPal, Marrion, and Babbel (2011).
To assess the competitiveness of indexed annuity returns and specifically equity-indexed annuity returns, I used two frameworks. First and foremost, I looked at their structure. I concluded that because of their structure “all indexed annuities must produce below-market, risk-adjusted returns.” Second and less important, I examined hypothetical historical returns on four EIA contract designs and 13 contracts for 1957–2008.
Structure of IAs
Let’s review how an insurance firm would hedge the investment risk in an equity-indexed annuity. Consider the one-year annual reset EIA strategy (sometimes called one-year point to point). Each year, the interest credited is: Max(0, min(((It+1 – It)/It), cap rate)), where It is the index level at the beginning of the year, It+1 is the index level at the end of the year, and the cap rate places a cap on the return that year. Therefore, if the index level falls, the interest credited for the year is zero. If the index level rises, the return is the lesser of the price appreciation return on the index, (It+1 – It)/It, or the cap rate.
In this strategy and assuming a 5 percent yield, per $100 premium the insurance firm would invest about $95.18 in high-grade bonds [$100/(1.025)2, where 1.025 is one plus the semi-annual yield]. Of the remaining $4.82, the insurance firm may take $2.10 to pay for commissions, other expenses, and to provide a profit margin, and invest the remaining $2.72 in options; this $2.10 or 2.10 percent of premium is sometimes called a spread.
Suppose the S&P 500 Index is at 1,300. The insurance firm may set the cap rate at 5 percent on the one-year annual reset contract. The 5 percent would be selected because, based on option prices, the insurance firm would be able to use the $2.72 to buy enough at-the-money call options and sell enough call options with a 1,355 exercise price to provide the return should the index price rise for the year. Thus the investor receives up to 5 percent price appreciation, but is assured against a loss. Because interest rates and options’ implied volatilities change, the insurance firm would retain the right to set at its discretion the cap rate at the beginning of each contract year subject only to some minimum cap rate.
As discussed by Reilly and Brown (2009, p. 549), to try to add value compared with a passive investment strategy, active managers use one of three generic themes: (1) market timing; (2) overweighing stocks by sectors/industries, overweighing value or growth stocks, or overweighing stocks by size; and (3) through security selection. All attempts to beat a market index on a risk-adjusted basis use one or more of these three themes.
By design, indexed annuities cannot add value with any of these themes. By design, (1) they do not attempt market timing, (2) they do not make sector/industry/style/size bets, and (3) they do not try to add value through security selection. Furthermore, because hedging strategies usually require long and short positions in options contracts, the industry cannot argue that indexed annuity strategies beat the market because option values are consistently undervalued or overvalued. So, I concluded that the risk-adjusted returns on indexed annuities must trail the risk-adjusted returns available in marketable securities by the sum of their spread plus their transaction costs.
In short, because of their design, indexed annuities cannot add value to offset their substantial embedded costs. They buy high-grade bonds and a portfolio of options. A risk-appropriate benchmark portfolio for an indexed annuity contains (1 – b)Treasuries + (b)index, where b denotes the IA’s beta. By design, the IA will produce returns that trail this benchmark portfolio’s returns by the sum of their spread plus their transaction costs.
I give credit for this insight and conclusion to Nobel laureate William Sharpe (1991). He says,
If “active” and “passive” management styles are defined in sensible ways, it must be the case that (1) before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar, and (2) after costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar. These assertions will hold for any time period. Moreover, they depend only on the laws of addition, subtraction, multiplication, and division. Nothing else is required.
In a short piece, Fama and French (2009) summarize Sharpe’s argument. They conclude that we do not need empirical tests to conclude that the average active fund must underperform the appropriate risk-adjusted benchmark portfolio by the average expense ratio. The arithmetic of equilibrium accounting ensures this outcome.
To put this argument in the context of indexed annuities, we do not need empirical tests to ensure that IAs underperform their risk-adjusted benchmark portfolio’s returns. Because their structure prevents them from adding value compared to this benchmark return, they must underperform this benchmark return by the sum of their spread plus their transaction costs. Proof completed! In Reichenstein (2009), I relied primarily on this framework presented by three academic giants—Sharpe, Fama, and French—to reach my conclusion that IAs cannot offer competitive risk-adjusted returns.
Empirical Analysis
Separately, I also examined whether EIAs offered competitive long-run returns. However, as stated in Reichenstein (2009), my conclusion rests primarily on the argument presented in the prior section. Using returns data from Ibbotson Associates, I examined historical returns on four EIA contract designs and 13 contracts for 1957–2008. The contracts came from a 1998–2005 database containing $19 billion of real-world annuities from AmerUS and affiliates. Because Reichenstein (2009) presents the results of these analyses, I will not go through these results in depth here.
However, I note the following points. In the first sentence of that section, I called these results “hypothetical long-run returns on EIA contracts” because EIA contracts have not been around since 1957. The beginning date was chosen because the S&P 500 began in March 1957. I used the 1957–2008 period to assess whether these products offer competitive ex ante returns. I used a long-run period because, as Sharpe (1990) says, “While fairly recent historic data can provide useful estimates of asset risks and correlations, recent history is typically of little (if any) use when predicting expected returns. Instead, the analyst must both (1) rely on experience over very long periods and (2) take into account reasonable relationships among expected returns, risks, and correlations.”
From the conclusions section, I said,
I modeled hypothetical returns on 13 EIA contracts for 1957–2008…. The average beta on these contracts was about 0.15. None of these contracts could match returns available on one-month Treasury bills. Based on alphas and Sharpe ratios, none of the contracts could produce competitive market-based returns. Moreover, EIAs impose several risks that are not present in market-based investments, including surrender fees, loss of return on funds withdrawn before the end of the term, and default risk. The evidence suggests that these index-linked EIAs would have produced long-run returns that would have failed to match returns available on competitive market-based assets. Given the substantial costs built into these contracts and the inability of indexed annuities to add value through security selection, this conclusion is inevitable.
VanderPal, Marrion, and Babbel (2011) compared the performance of EIA returns from their data set to returns on portfolios containing (1) 100 percent S&P 500 and (2) 50 percent Treasury bills and 50 percent S&P 500. They did not compare returns on EIAs to a 15 percent Treasury bill and 85 percent S&P 500 portfolio, which my study suggests would have been the risk-appropriate benchmark portfolio’s returns for a typical EIA. They considered returns for five-year periods ending 2002–2010. Not surprisingly, their results confirmed the obvious conclusion that lower-beta-risk EIAs will outperform higher-beta portfolios during bear markets and underperform during bull markets. But their results do not compare the returns on EIAs to similar-risk portfolios. Moreover, as they state, their “data reflect results across a very small spectrum of time.”
Critique of Critique
VanderPal, Marrion, and Babbel (2011) made general statements critiquing studies by Lewis (2005), McCann (2008), Collins, Lam, and Stampfli (2009), and Reichenstein (2009). These statements include, first, that the studies did not include real-world EIAs and, second, they assumed crediting formulas rarely used. Criticism of my specific study was as follows:
He assumes that a particular annuity whose terms were observed in the late 1990s would have had similar parameters beginning in 1957 and continuing for almost 40 years before the first [fixed-index annuity] arrived on the scene. (Indeed there were not even any index funds available to individual investors until 1977, yet his study assumes that individual investors would have secured better returns over that period by investing in them. His study also assumes that these funds were held together with five-year Treasury bonds that were held for only one month and then liquidated, replacing them with new five-year bonds every month for 52 consecutive years.)
Let me address these critiques. First, as noted, my study used real-world contracts that represented contracts in the marketplace from 1998–2005. By comparison, Marrion, VanderPal, and Babbel (2011) used two data sets. According to the authors, the main limitation of the first data set is that the data “are derived from carriers that chose to participate and that chose the products for which they reported returns.” Carriers could decide whether to provide returns data and, if they provided data, then they could provide the returns data they chose to provide. I would bet these returns data were not audited. I leave it to the reader to decide if that data set is unbiased. Their second data set reflects “actual real-world total five-year returns credited to annuity owners from an annual point-to-point with cap-structured index annuity…. [The data are] not intended to be representative of anything except itself.” In addition, their returns data do not reflect real-world features of annuity contracts including surrender penalties, loss of interest on funds withdrawn before the end of the crediting period, market-value adjustments, and default risk.
Concerning the specific criticisms of my study, I repeat that my major conclusion was primarily based on the framework presented by Sharpe. In the empirical section, I modeled four contract designs, and for each design I considered a range of specific contract terms. Yes, I assumed that at least one of these would have been appropriate had EIAs been around in 1957. For a given contract, the terms do not change except that the insurance firm has the right to set parameters for the next crediting period at its discretion subject only to a minimum; in the one-year annual reset EIA example, the insurance firm can set the cap rate at the beginning of each year at its discretion subject only to the requirement that the cap rate must be at least 4 percent. The contract entered into in 1957 might have been different than the contract terms at another date. But for a given contract, the terms cannot be changed.
I used the Ibbotson Associates data set. This data set has been used in hundreds if not thousands of studies. As an aside, before Marrion, VanderPal, and Babbel criticize a well-respected data set, they should make sure their criticism is accurate. As stated in each year’s Classic Yearbook, Ibbotson (2011) says, “One-bond portfolios are used to construct the intermediate-term government bond index. The bond chosen each year is the shortest noncallable bond with a maturity not less than five years, and it is ‘held’ for the calendar year.” The Yearbook also provides a table indicating the one bond used for each year. Ibbotson does not (and I did not) “assume that these funds were held together with five-year Treasury bonds that were held for only one month and then liquidated, replacing them with new five-year bonds every month for 52 consecutive years.” Their criticism failed to get this simple stuff right.
Challenge
I end this note with an open challenge to VanderPal, Marrion, Babbel, and anyone else. Given the structure of indexed annuities and their embedded expenses, explain to me how they can produce competitive risk-adjusted long-run returns. That is, how can they add value compared with a risk-appropriate benchmark portfolio to more than offset the sum of their spread and transaction costs? In my opinion, their structure ensures that they cannot meet this hurdle.
References
Collins, P. J., H. Lam, and J. Stampfli. 2009. “Equity Indexed Annuities: Downside Protection, But at What Cost?” Journal of Financial Planning 22, 5 (May): 48–57.
Fama, E. F., and K. R. French. 2009. “Why Active Investing Is a Negative Sum Game.” www.dimensional.com/famafrench/2009/06/why-active-investing-is-a-negative-sum-game.html.
Ibbotson Associates. 2011. Ibbotson Stocks, Bonds, Bills, and Inflation 2011 Classic Yearbook. Chicago: Morningstar Inc.
Lewis, W. Cris. 2005. “A Return-Risk Evaluation of an Indexed Annuity Investment.” Journal of Wealth Management 7, 4.
McCann, C. 2008. “An Economic Analysis of Equity-Indexed Annuities.” Working paper submitted to North American Securities Administrators Association (September 10).
Reichenstein, W. 2009. “Financial Analysis of Equity-Indexed Annuities.” Financial Services Review 18 4: 291–311.
Reilly, F. K., and K. C. Brown. 2009. Investment Analysis and Portfolio Management. 9th ed. Florence, KY: Cengage Learning.
Sharpe, W. F. 1990. “Asset Allocation.” In Managing Investment Portfolios: A Dynamic Process. 2nd ed. J. L. Maginn and D. L. Tuttle, eds. 7–40.
Sharpe. W. F. 1991. “The Arithmetic of Active Management.” Financial Analysts Journal 47, 1: 7–9.
VanderPal, G., J. Marrion, and D. F. Babbel. 2011. “Real-World Index Annuity Returns.” Journal of Financial Planning 24, 3: 50–59.