GMWB Modelling- Morningstar

March 22, 2018 | Author: jitenparekh | Category: Asset Allocation, Retirement, Annuity (American), Pension, Mutual Funds
Share
Report this link


Comments



Description

Retirement Portfolio and Variable Annuity with Guaranteed Minimum Withdrawal Benefit (VA+GMWB) Sponsored By Nationwide Financial® Ibbotson Associates, Inc. October 2007 ©2007 Ibbotson Associates, Inc. All rights reserved. The information in this document is the property of Ibbotson Associates. Reproduction or transcription by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar, Inc. Correspondence should be sent to: Ibbotson Associates 225 North Michigan Avenue Suite 700 Chicago, IL 60601-7676 Phone: 312 616 1620 Fax: 312 616 0404 About Ibbotson Associates Ibbotson Associates opened its doors in 1977 to bridge the gap between modern financial theory and real-world investment practice. Professor Roger G. Ibbotson, the company founder, pioneered the collection of the requisite historical data used in asset allocation and quantified the benefits of diversification. Ibbotson continues to provide solutions to investment and finance problems for a diverse set of markets. Entrusted to create asset allocation models for many of the largest companies in the finance and investment industries, Ibbotson Associates is a leading provider of retirement advice programs and investment consulting services to institutions. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar, Inc. VA+GMWB, October 5, 2007 © 2007 Ibbotson Associates. All rights reserved. The information in this document is the property of Ibbotson Associates. Reproduction or transcription by any means, in whole or part, without the prior written consent of Ibbotson Associates, is prohibited. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar, Inc 2 Executive Summary The total assets under management (AUM) for variable annuity accounts at the end of 2006 reached $1.36 trillion, an increase of 38.2% since the end of 2001. The dominant sales driver for variable annuities in recent years was the guaranteed minimum withdrawal benefit (GMWB). Part of the reason is that the shift from Defined Benefit (DB) plans to Defined Contribution (DC) plans has created a void for retirees – the loss of guaranteed income in retirement, therefore, retirees need to find other guaranteed income sources. In this paper, we introduce a basic variable annuity (VA) product with a guaranteed minimum withdrawal benefit (GMWB), and use empirical analysis and Monte Carlo simulations to study the benefits and costs of including VA with GMWB in a retirement income portfolio. This continues our studies on incorporating insurance products into an investor’s overall portfolio (e.g., Chen and Milevsky 1 (2003), Chen, Ibbotson, Milevsky, and Zhu (2006 & 2007)). We have developed a hypothesis that the GMWB will help improve the overall retirement income levels without increasing income risk levels. We employed the income risk or income semi-deviation, which is defined as the standard deviation on negative income changes over the last period, for a series of simulation analyses across three scenarios: 1) a diversified asset allocation VA account with GMWB; 2) a diversified traditional non-annuity portfolio (such as mutual funds); and 3) a combination of VA+GMWB products and non-annuity products in a portfolio context. In the combined portfolio, a portion of the fixed income /cash allocation is replaced with a more aggressively allocated VA, which will leave the remaining mutual fund portfolio with a higher equity allocation than the original mutual fund portfolio. The analysis compared the traditional mutual fund portfolio with the combined portfolio assuming a fixed percentage withdrawal rate (5%) on the non-VA portion of the portfolios, and a fixed 5% on the benefit base of the VA portion. Both empirical results and Monte Carlo simulations show that the combined portfolios have lower average negative income return, lower semi-deviation, higher average income return, and higher total income withdrawals. (See VI Appendix C for Glossary.) 1 The research was conducted by Ibbotson and sponsored by Nationwide Financial®. Special thanks go to Nationwide Financial, specifically, John M. Kawauchi, Harold C. Schafer and Antonio E. Morello, CFA for helpful discussions on this white paper, especially on applying the concept of semi-deviation on income amount as a measurement of income risk and developing the hypothesis that the GMWB will help improve the overall retirement income levels. Ibbotson would also like to thank Roger Ibbotson, Frank O’Connor, and Moshe Milevsky for valuable comments. VA+GMWB, October 5, 2007 © 2007 Ibbotson Associates. All rights reserved. The information in this document is the property of Ibbotson Associates. Reproduction or transcription by any means, in whole or part, without the prior written consent of Ibbotson Associates, is prohibited. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar, Inc 3 VA+GMWB. as we increase the equity exposure of the traditional non-annuity investments. we did not specifically incorporate default risks on these VA contracts into our analysis. and the combined portfolios have a higher equity allocation which contributes to an increase in total income. moderate conservative. for a 30-year horizon.In general. since almost all VA contracts are offered by insurance companies with very high credit standings. October 5. the guaranteed VA portion has no income risk so it helps to lower the income risk for the overall combined portfolios. We believe the default risk would lower the amount of the VA+GMWB benefit in a retirement portfolio. That is. adding VA+GWMB to the conservative. without the prior written consent of Ibbotson Associates. the portfolio provides higher total income with higher semi-deviation (thus higher income risk). All rights reserved. but it would not have necessarily changed the main analytical results. in whole or part. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. We then analyzed the shortfall income risk and average or median sustainable income level for the three scenarios over a 30-year horizon. Therefore. We found that all combined portfolios have higher median income levels and lower shortfall income risk than stand-alone traditional mutual fund portfolios. is prohibited. The addition of VA+GMWB to the retirement portfolios (replacing cash or fixed income allocations) increases total income while it decreases income risk. Inc 4 . and moderate portfolios is beneficial in that it increases the average sustainable income and decreases the shortfall income risk. Reproduction or transcription by any means. The information in this document is the property of Ibbotson Associates. Although there is potential risk that insurance companies could default on these VA guarantees. 2007 © 2007 Ibbotson Associates. October 5. not only face market risk. total assets under management (AUM) for variable annuity accounts at the end of 2006 reached $1. We developed the analytical framework regarding the measurement of income risk. Reproduction or transcription by any means. a portion of the fixed income /cash is replaced with a more 2 We assume that there is no default risk in VA+GMWB contracts. Inc 5 . The information in this document is the property of Ibbotson Associates. VA+GMWB. but also retirement income risk.2% since the end of 2001. an increase of 38. most retirement assets are invested in traditional mutual fund portfolios. that can help investors hedge market risk and retirement income risk. longer life expectancies. All rights reserved. and they don’t offer effective protections against market downturn or retirement income risk.36 trillion. and 3) a combination of VA products and non-annuity products in a portfolio context.I. medical advancements. and more specifically. who rely on their own personal savings in retirement. We also do not consider the scenario that an investor might need to withdraw the VA investment in a lump sum. Today. and the graphical presentation of the results. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. without the prior written consent of Ibbotson Associates. Introduction The growing number of retiring baby boomers. and the fees do not change in the future. we concentrate our effort on analyzing variable annuities with lifetime guaranteed withdrawal benefit (GMWB for life). for example variable annuities and payout annuities. According to the latest issue of Annuity Market News. In this paper. In the combined portfolio. The dominant sales driver for variable annuities in recent years was the guaranteed minimum withdrawal benefit (GMWB). which could incur surrender charges and loss of the guaranteed withdrawal benefits. and increased uncertainty surrounding Social Security benefits dramatically increase the burden of retirees to finance retirement spending. We ran a series of simulation analyses across three investment scenarios: 1) stand-alone VA products with these guarantees.2 Our hypothesis is that GMWB in VA products can potentially improve the overall retirement income levels without increasing income risk levels. the paradigm shift away from defined benefit pensions to defined contribution pensions. in whole or part. Many retirees. The income return is defined as the income change in percentages in two consecutive years. the modeling of portfolios. we use empirical analysis and Monte Carlo simulations to study the benefits and costs of including VA with lifetime GMWB in a retirement income portfolio. In this paper. is prohibited.the semi-deviation on income changes or income returns over the last period. There are some instruments. we study the role of variable annuities with a lifetime guaranteed minimum withdrawal benefit (GMWB) in managing market and retirement income risk. 2) stand-alone traditional non-annuity products (such as mutual funds). We introduced the income risk-. 2007 © 2007 Ibbotson Associates. without the prior written consent of Ibbotson Associates. Inc 6 . 2007 © 2007 Ibbotson Associates. to continue exploring more efficient ways to help investors build retirement income portfolios that maximize average sustainable income levels while minimizing shortfall income risk. in whole or part. The rest of the paper is organized as follows. Section III introduces the hypothesis. which will leave the remaining mutual fund portfolio with a higher equity allocation than the original mutual fund portfolio.aggressively allocated VA. VA+GMWB. Both empirical results and Monte Carlo simulations showed that the combined portfolios had lower average negative income return and semideviation. All rights reserved. Glossary is presented in section VI Appendix C. Section II introduces VAs with lifetime GMWB. The shortfall income risk is defined as the risk of running out of income when the market has performed poorly for an extended period of time. We see this framework as an extension of the work by Chen and Milevsky (2003). is prohibited. October 5. The analysis compared the traditional mutual fund portfolio with the combined portfolio assuming a fixed percentage withdrawal rate (5%) on the non-VA portion of the portfolios. We believe that this framework is also more important in examining the “portfolio risk-return” in retirement income setting than the traditional mean-variance framework. That is. Reproduction or transcription by any means. we examined the average sustainable income level versus the shortfall income risk relationship for the above-mentioned three scenarios. (See VI Appendix C for Glossary. The conclusions are given in section V. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. Section IV presents empirical analysis and Monte Carlo simulation results.) In the other framework. to effectively evaluate the risk-return tradeoff of different retirement income patterns. The information in this document is the property of Ibbotson Associates. and higher average total income return and total income withdrawals. We found that all studied combined portfolios have higher average income levels and lower income shortfall risks than stand-alone traditional mutual fund portfolios. suppose that John's initial investment was $1. Table 1 illustrates characteristics of the VA+GMWB. respectively. By 2006. • A payout of remaining contract value to beneficiaries at death. 2007 © 2007 Ibbotson Associates. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. The benefit base will be reset to $1. 5%) of the benefits base each year until death. The benefit base is the high-water mark of the contract value on the rider anniversary date. in whole or part.578. • An Annual rider fee. What is VA + Lifetime GMWB? A recent innovation in the variable annuity products is the guaranteed minimum withdrawal benefit (GMWB) rider on variable annuities (VA+GMWB). We will focus on the GMWB rider for life in this study.806. if the net return is a 20% gain instead of a 20% loss. In summary. The best aspect of this guarantee is that it protects annuitants against any nominal investment losses that would have been incurred without losing the benefit of upside gain. The information in this document is the property of Ibbotson Associates. he will still be able to withdraw $50.000 on the next anniversary day so that John is able to withdraw at least $60.II. or for life. Inc 7 . the annuitant pays a fee each year. i. The benefits base can step up and will be reset to the high-water mark of the contract value on the rider anniversary date when market has performed well.g.000 each year thereafter. Therefore.651. 20 years).g.000. 5%) on the benefit base.558 and $2. is prohibited. mainly due to the strong market performance over 28 years (1979—2006).000.200. This put-option-like rider can be purchased for a fixed term (e. For example. which typically ranges from 0.000 each year no matter if the loss were 20% or 50%. it steps up whenever the contract value exceeds the previous year’s benefit base. the investment suffers a 20% loss the next year and the contract value decreases to $800. the contract value would be $1.000. Due to downturns in the economy. which removes the investor concern about giving up liquidity to the heirs. With the VA+GMWB products. The GMWB rider for life gives annuitants the ability to protect their retirement investments against downside market risk by allowing the annuitant the right to withdraw a fixed percentage (e.35% to 0. VA+GMWB.e. In exchange for this benefit. Reproduction or transcription by any means. some typical features of the GMWB rider for life include: • A guaranteed lifetime withdrawal rate (e. Note that the benefits base is the high-water mark of the contract value. the guaranteed withdrawal or income never decreases.200. • A step-up feature allowing the investor to lock in a higher amount for the benefit base guarantee on the rider anniversary date. October 5. However.g. automatic annual resets are available after the contract is purchased. without the prior written consent of Ibbotson Associates.75% of the benefits base. All rights reserved. The remaining contract value at death will be paid to beneficiaries. Since John had purchased a guaranteed minimum withdrawal benefit with a rate of 5%.831. The GMWB is often referred to as a benefit rider. the income would have reached $191.000. assuming that one purchased the contract at the beginning of 1979. The benefit base and the remaining contract value at the end of 2006 would have been $3. 230.558 $ 3.392.544.558 $ 3.788 $ 2. and the guarantee keeps the income level flat.082.831.264 $ 2.463.47% -2.40% 27.831.037 $ 1.570 $ 2.379) (112. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.578) (191.582 $ 2.251.651.106) (62.000. October 5.618.582 $ 2.067.024 $ 2.439 $ 1.551) (62.640 $ 2.024 $ 2.572 $ 2.493) $ (7.392.30% 18.531) $ (15.000) $ (6.53% 23.000.024 $ 2.861 $ 2.779 $ 2.081) $ (22.989) $ (22.247.558 Total: $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Guaranteed Income (50. Inc 8 .46% -10.927.230 $ 2.082) (103.130.582 $ 2.558 $ 3.717 $ 3.000 $ 1.46% 15.000 $ 1.989) $ (22.989) $ (22.189 $ 2.831.551) (69.405) $ (13.13% 23. It is noted that the nominal income level steps up and never decreases.831.305) * The net returns are calculated based on a moderate aggressive portfolio (see table 2A) with the assumed fee structure shown in table 2D.86% 13.63% 14.383.251.562.71% 11.352) $ (10.529) (175. 2007 © 2007 Ibbotson Associates.377) $ (16.101) (126.024 $ 2.831.233.255.461 $ 2.251.051.379) (103.52% 27.023 $ 1.46% 5.558 $ 3.831.562.101) (126. in whole or part.250 $ 2.570 $ 2.000 starts at the beginning of 1979.101) (128.22% 5.506) $ (7.578 by 2006.513.522.781.578) (3.989) $ (22.854. All rights reserved.522. VA+GMWB.23% 4.391.255.151.602) (69.831.89% 15.251.101) (126.831.729 $ 2.578) (191. the income level would remain flat in the future till the contract value exceeds the benefit base.922 $ 2.132) $ (15.578) (191.578) (191.578 $ 3.989) $ (444.383) $ (21.067.558 $ 3.831.30% -1.761) (126.330) $ (12.721. ** The withdrawal is assumed at the beginning of each year.50% 16.405) $ (12.024 $ 2.078) (146.702.551) (62.377) $ (15.067.937 $ 2.06% -15.562.80% Contract Value $ 1.63% 22.139) (128. without the prior written consent of Ibbotson Associates.392.037 $ 1.423.388 $ 1.989) $ (22.788 $ 2.956 $ 1.06% 33.689) $ (17.927.506) $ (8.506) $ (7.788 $ 2. Note the contract value in 2006 is still below the guaranteed base. The first payment of $50.578) (191.522.126 $ 1.566) $ (19.132) $ (15. The VA+GMWB contract value and benefit base are plotted in Chart 1B.505 $ 3.578) (191.522.386) (161.505 $ 3.640 $ 2.352) $ (8.717 $ 3. and reaches $191.12% 16.Table 1.721.023 $ 1.578 $ 3.230 $ 2.87% 2.602) (86.781. Chart 1A plots the guaranteed income levels shown in table 1.558 $ 3.49% 18.806 Benefit Base $ 1.132) $ (15.082.563. therefore.558 $ 3.558 $ 3. is prohibited. The information in this document is the property of Ibbotson Associates.023 $ 1.675) (191.34% -11.367. Conceptual Illustrations of VA+GMWB VA+GMWB Net Return 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 14.037 $ 1.989) $ (22.540) Rider Fee $ (6.21% 15.01% 11.578) (191.132) $ (15.989) $ (22. Reproduction or transcription by any means.126 $ 1.230.513.903 $ 2.139) (139.023 $ 1.522. The stock market crash from 2000 did not reduce the income.52% -5.000) (54. 578 * The assumed fee structure is shown in table 2D.000 $2. Reproduction or transcription by any means.000 $100.000 $4.Chart 1A. Guaranteed Withdrawal from 1979 to 2006 for VA+GMWB VA+GMWB Income. Inc 9 . All rights reserved. Contract Value and Benefit Base for VA+GMWB from 1979 to 2006 Contract Value and Benefit Base for VA+GMWB from 1979 to 2006 $5.000 $200. Chart 1B. from 1979-2006 $250. The information in this document is the property of Ibbotson Associates.000 $3. without the prior written consent of Ibbotson Associates.000.000. VA+GMWB. in whole or part.000.000. October 5. is prohibited.000 $1975 1980 1985 1990 1995 2000 2005 2010 $191. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.000 $50.000.000 $1975 1980 1985 1990 1995 2000 2005 2010 Contract Value Benefit Base * The assumed fee structure is shown in table 2D.000 $1. 2007 © 2007 Ibbotson Associates.000 Income $150. resulting in a slightly more aggressive combined portfolio. the income risk decreases. in whole or part. 3 3 In this paper. The information in this document is the property of Ibbotson Associates. The income risk describes the downside volatility of the change in income from year to year. Our hypothesis is that adding VA+GMWB to traditional portfolios will improve the overall retirement income levels without increasing income risk levels.III. The idea is to replace some fixed income or cash allocation in a traditional portfolio with VA+GMWB. is prohibited. as the allocation to VA+GMWB increases. traditional mutual fund portfolios may suffer from market downside risk and jeopardize retirement income. We will show that the VA+GMWB has no income risk which helps to lower the income risk for the combined portfolios. without the prior written consent of Ibbotson Associates. A real (as opposed to nominal) analysis will result in guaranteed payments possibly falling over time for VA+GMWB. VA+GMWB. Reproduction or transcription by any means. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. Furthermore. which allows the income to only go up and never go down. A VA+GMWB by itself carries no income risk due to the high-water-mark feature. Hypothesis of Adding VA+GMWB to a Retirement Portfolio As we know. We did not explicitly consider inflation. All rights reserved. October 5. Inc 10 . we presented results in nominal terms. which creates a higher downside volatility or semi-deviation. and the combined portfolios have higher equity weight which contributes to increase total retirement income over time. 2007 © 2007 Ibbotson Associates. the moderate aggressive allocation has 80% equity and 20% fixed income (80/20).S. impact of different asset allocations. moderate. we can analyze the risk information. one can specify a probability distribution for variables such as market returns. volatilities and covariance. and moderate aggressive—are adopted in this paper. Inc 11 . Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. Asset Allocation Portfolios Asset Classes U. The moderate model portfolio has 60% equity and 40% fixed income (60/40). The beginning year VA+GMWB. Table 2A. In one simulation path. Con. Monte Carlo simulation is generally considered a better tool to provide comprehensive analysis than the deterministic method. October 5.IV. a path of random market returns for each asset class is generated. Therefore. and the probability of reaching retirement goals. Aggregate Bonds Short-term Bonds Cash Benchmark Russell 1000 Russell MidCap Russell 2000 MSCI EAFE LB Aggr. Bond LB 1-5 Yr Gvt/Credit CG U. in whole or part. All rights reserved.000) are tabulated to determine the outcomes over broad spectrum of risk and return scenarios. The detailed asset allocations for the four model portfolios are shown in table 2A. Model Portfolios and Capital Market Returns Four diversified asset allocation portfolios—conservative. 20% 10% 0% 10% 35% 15% 10% Moderate 30% 10% 5% 15% 25% 10% 5% Mod. Small Cap Stocks International Stocks U. Aggr. moderate conservative. The information in this document is the property of Ibbotson Associates. The portfolio value is calculated by following equation (1) or (2) in Appendix A. Reproduction or transcription by any means. Based on the outcomes.S. Empirical Analysis Monte Carlo Simulations We employ Monte Carlo simulation to study the dynamics of VA+GMWB and traditional mutual fund portfolios over various market return scenarios.S. The VA+GMWB is assumed to be invested in a moderate aggressive allocation throughout the study. etc. 3 Mo Tbill Conservative 10% 5% 0% 5% 40% 25% 15% Mod.S.S. Large Cap Stocks U. A large number of paths (5. The moderate conservative model portfolio has 40% equity and 60% fixed income (40/60). 2007 © 2007 Ibbotson Associates. Table 2B shows the historical returns and standard deviations during1979-2006 and Ibbotson’s forward-looking returns and standard deviations for the seven asset classes. 35% 15% 5% 25% 15% 5% 0% The conservative model portfolio has 20% equity and 80% fixed income (20/80). With Monte Carlo simulations. without the prior written consent of Ibbotson Associates. Mid Cap Stocks U. Table 2C shows the historical correlation matrix (1979—2006) for the seven asset classes. Each path represents one possible investment horizon experience.and worstcase scenarios. Monte Carlo simulation allows us to view projections of best. Finally. is prohibited. 48% Ibbotson STD 19.86% 9.47% 5.1979 was chosen for the empirical study.6% GMWB rider fee. it is consistent to use annual instead of monthly returns to estimate standard deviations for asset classes.54% 21. Large Cap Stocks U. in whole or part.46% 15.10% 3. VA+GMWB.14% 6. and Ibbotson forecasted standard deviations are estimated from annual returns.61% 14. Inc 12 .34% Ibbotson E[R]* 11.73% 11. in particular. and Ibbotson’s forecasted returns and forecasted standard deviations for the seven asset classes.S. while annual returns give a cash standard deviation of 3.03% 12.83% 13. October 5.90% 8. 1979--2006 Arithematic Average Return U. The historical standard deviations shown in table 2B are calculated from annual returns instead of monthly returns.4% VA M&E fee. Also. Small Cap Stocks International Stocks U. It is known that serial correlations among time-series returns tend to lower the standard deviation of returns. while the other fees are based on the contract value. Mid Cap Stocks U.S. therefore.26% * Ibbotson forward-looking annual expected return (arithmetic).97% 14.49% 22. For the VA+GMWB. the Monte Carlo simulations are conducted annually.25% 6. cash standard deviation is only 0. For mutual fund portfolios.24% 4.39% 5.05% 4. and 0. Using monthly returns. 1% advisor fee.30% 14. The historical returns and standard deviations (1979-2006).67% 7. All rights reserved.34%.61% 15. monthly cash returns are highly serial correlated.96%. is prohibited.4 Table 2D shows the fee structure assumed in this study. The GMWB rider fee is based on the benefit base. Reproduction or transcription by any means.62% 7.S.31% 13. 2007 4 © 2007 Ibbotson Associates.04% 3. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.07% 8.28% 28. Table 2B. the total fees of 3% include 1% underlying fund management fee.09% 18.21% 1979-2006 STD 15.74% 24. We believe that our forward-looking return estimates are more realistic returns for today’s investors than historical returns from 1979 to 2006.33% 11. 0. The information in this document is the property of Ibbotson Associates. Aggregate Bonds Short-term Bonds Cash 1979--2006 Geometric Average Return 13.21% 2.S. the total fees of 2% include 1% management fee and 1% advisor fee. without the prior written consent of Ibbotson Associates.56% 16.83% 8. simply because of the availability of data. Reproduction or transcription by any means. Bonds S/T Bonds Cash Mid Cap Small Cap International Aggr. Historical correlation matrix (1979—2006) for the seven asset classes Large Cap Large Cap Mid Cap Small Cap International Aggr. Assumed Fee Structure for Traditional Mutual Fund Portfolio and VA+GMWB Mutual Fund Portfolio VA+GMWB Fees Catogory5 Fund Management Fee 1% 1% Advisor Fee* 1% 1% VA M&E Fee N/A 0. in whole or part. All rights reserved. without the prior written consent of Ibbotson Associates. 2007 5 © 2007 Ibbotson Associates. The information in this document is the property of Ibbotson Associates.4% GMWB Rider Fee N/A 0. October 5. The fees on both variable annuities and traditional mutual funds can vary greatly from product to product.6% Total Fees 2% 3% * Advisor fee is the service fee charged by a financial advisor.Table 2C. Inc 13 . We assume that both the traditional portfolio and the VA+GMWB are serviced through a financial advisor. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. Bonds S/T Bonds Cash 100% 95% 83% 57% 24% 17% 1% 95% 100% 93% 55% 23% 17% -1% 83% 93% 100% 52% 14% 8% -2% 57% 55% 52% 100% 16% 13% -5% 24% 23% 14% 16% 100% 96% 11% 17% 17% 8% 13% 96% 100% 23% 1% -1% -2% -5% 11% 23% 100% Table 2D. is prohibited. VA+GMWB. we generate seven random numbers for the seven asset classes. and meanwhile the fees are paid. This process will be repeated for 28 years for the empirical study or 30 years in the forward looking study. Reproduction or transcription by any means. i. table 7D in Appendix VI section B shows the implied returns at the various percentiles for the VA+GMWB over a 28year horizon).000 when the market has tumbled for an extended period of time. in whole or part. The information in this document is the property of Ibbotson Associates. this completes one simulation path. VA+GMWB. the detailed formulas are shown in Appendix A. without the prior written consent of Ibbotson Associates.e. The historical income levels shown in chart 1A fall slightly above the 90th line in chart 2. 2007 © 2007 Ibbotson Associates. (For readers not familiar with percentiles in Monte Carlo simulation. Inc 14 . The average ending income after 28 years is $72. The asset allocation in the VA+GMWB account is moderate aggressive (80/20). the 50-percentile income curve indicates the average income from VA+GMWB. The retirement income is withdrawn at the beginning of the period. are used in the simulations. All rights reserved.000 times to complete the entire simulation. Simulated Guaranteed Income for VA+GMWB Chart 2 shows the Monte Carlo simulated guaranteed income for the VA+GMWB assuming an initial investment of $1 million at age 65.770. while the 10th percentile is the worst scenario.VA+GMWB Modeling We followed Milevsky (2006) in modeling the dynamics of the traditional mutual fund portfolio value and the VA+GMWB contract value. October 5. and we then calculate the portfolio return over the period. In each period. much higher than the 50th percentile simulated income. Ibbotson’s forward-looking asset returns and standard deviations. In chart 2. the income is at least $50. The withdrawal rate is set at 5% of the benefits base. The process is repeated 5. is prohibited. which are shown in table 2B. The reason is that our forecasted future returns are much lower than the historical returns from 1979 to 2006 shown in table 2B. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. 770 $55. Simulated Income $200.000 10% 25% 50% 75% 90% VA+GMWB. 80/20. Income for 100% VA+GMWB 100% VA+GMWB. Inc 15 .000 $172. The information in this document is the property of Ibbotson Associates.573 $150.000 $50. October 5. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.000 $0 65 70 75 80 Age 85 90 $110. 2007 © 2007 Ibbotson Associates. is prohibited.000 Income $100.789 $50.546 $72.Chart 2. without the prior written consent of Ibbotson Associates. Reproduction or transcription by any means. All rights reserved. in whole or part. moderate conservative.S. All rights reserved. the 40/45/15 has a higher risk than the moderate conservative portfolio (40/60). we replace a portion of the fixed income/cash of the allocation with a more aggressively allocated VA. but a lower risk than the moderate portfolio (60/40).Semi-Deviation Measurement of Income Return In this section. Reproduction or transcription by any means. Ibbotson’s forward-looking asset returns and standard deviations were used to generate the efficient frontier. The combined portfolios are slightly more aggressive than their corresponding model portfolios. The assumed fee structure is shown in table 2D. October 5. Chart 3A-B show the traditional efficient frontier for the seven asset classes. along with the four model portfolios and some selected combined portfolios. respectively.S. and moderate). in whole or part. The information in this document is the property of Ibbotson Associates. is prohibited. The combined portfolio has an allocation of 40/45/15 (equity / fixed income / VA+GMWB). In each model portfolio. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. the remaining model portfolio will have 40% equity and 45% fixed income. The asset allocation for the VA+GMWB will be fixed at 80/20 (moderate aggressive). aggregate bonds. moderate conservative portfolio has an asset allocation of 40/60 (equity/fixed income). Inc 16 . For example. The pure U. For example. we study three model portfolios (conservative. which will leave the remaining mutual fund portfolio with a heavier equity allocation than the original mutual fund portfolio. in which 20% bonds were replaced with 20% VA+GMWB. The gross returns and net returns for the model portfolios and combined portfolios are shown in chart 3A and chart 3B. the remaining model portfolio becomes slightly more aggressive (40/60 47/53). The combined 20/60/20 portfolio. We will then study the impact of replacing some percentages of fixed income with the VA+GMWB on the average total income returns and semi-deviation of income returns for each model portfolio. VA+GMWB. 2007 © 2007 Ibbotson Associates. without the prior written consent of Ibbotson Associates. In other words. aggregate bonds and the pure large-cap stocks are plotted for comparisons. or effectively 47/53 in a scale of 100%. is only slightly more aggressive than the pure U. If 15% of the fixed income is replaced with 15% VA+GMWB. is prohibited. Reproduction or transcription by any means. as we mentioned above. Table 3 illustrates the calculation of income returns for the moderate conservative model portfolio as well as the combined portfolio (40/45/15) in which 15% VA+GMWB replaces bonds. All rights reserved. The combined portfolios have a higher underlying equity allocation than the original moderate conservative model portfolio. Inc 17 . in whole or part.Chart 3A. For the VA+GMWB portion. VA+GMWB. The information in this document is the property of Ibbotson Associates. Traditional Efficient Frontier (Net Returns) Portfolio Risk and Return 16 14 12 10 8 6 4 2 0 0 Expected Return (%) LC Stock 40/60 60/40 80/20 60/30/10 40/45/15 20/80 20/60/20 Bond 5 10 15 Standard Deviation (%) Model Portfolios US Bonds 20 Combined Portfolios 25 Efficient Frontier Large-Cap Stocks * The assumed fee structure is shown in table 2D. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. 2007 © 2007 Ibbotson Associates. the income is the guaranteed 5% of the benefits base. without the prior written consent of Ibbotson Associates. Traditional Efficient Frontier (Gross Returns) Portfolio Risk and Return (Gross Returns) 16 14 12 10 8 6 4 2 0 0 Expected Return (%) 80/20 40/60 20/80 60/40 60/30/10 LC Stock 40/45/15 20/60/20 Bond 5 10 15 Standard Deviation (%) Model Portfolios US Bonds 20 Combined Portfolios 25 Efficient Frontier Large-Cap Stocks Chart 3B. We assume that the retirement income is from a fixed 5% withdrawal based on the beginning balance for each model portfolio. due to a slightly more aggressive allocation in the combined portfolios and the guaranteed withdrawals from the VA+GMWB. October 5. We will show next that the combined portfolios have lower income risk and higher total income returns than the moderate conservative portfolio. The income return is defined as the percentage change in income for two consecutive years. At the end of 2006. and ending assets are 3.03%. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. and income returns for each year for the combined 40/45/15 portfolio. October 5. Reproduction or transcription by any means. a $1 million initial investment was made in a hypothetical moderate conservative portfolio as well as in a combined 40/45/15 portfolio. Columns 5-7 show the portfolio principals. respectively. is prohibited. All rights reserved. and income returns for each year for the moderate conservative portfolio.In table 3.891. and ending assets) are higher in the combined 40/45/15 portfolio. The average income return. total incomes.349. $3. and $2. and $2. in whole or part. VA+GMWB. without the prior written consent of Ibbotson Associates. incomes. It can be seen that all three numbers (average income return. incomes. The information in this document is the property of Ibbotson Associates. respectively. Columns 2-4 show the portfolio principals.950.656 for the combined 40/45/15 portfolio. Inc 18 . $2. total income.146.607 for the moderate conservative portfolio. total income. and ending assets are 4. 2007 © 2007 Ibbotson Associates.522. the average income return.53%.454. at the beginning of 1979. 94% 1.74% 3. Historical Illustration of Income Return for the Moderate Conservative Portfolio (40/60).14% 7.977 $112.87% 12.03% 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 VA+GMWB.324 $107.244.34% 1.82% 2. and the Combined Portfolio (40/45/15) from 1979 to 2006.077.52% -3.296 $1.88% 2. Inc 19 .771 $99.644 $125. without the prior written consent of Ibbotson Associates. is prohibited.673 $2.207.76% 19.888 $138.723 $1.280 $142.662.455 $1.873.013 $111.011.059 $1.285.542 $2.884 $93.087.531 $2.412.044 $1.000 $52.396 $62.714.503 $108.811 $93.360.455 $68.614.696 $113.969.546 $140.93% 13.166.996.30% -1.656 40/45/15 Income $50.34% -9.91% -5.376 $80.71% -2.828 $55.17% -1.050.473 $2.28% 6.388.271 $2.526 $96.98% 3.420 $2.147.930.511 $1.454 40/45/15 Inc.667.569 $2.572.000.Table 3.65% 10.708 $127.58% 1.473.402 $69.154 $1.595 $2.458.13% 9.000 $1.921 $1.479.627 $103.823 $54.205.031 $1.72% -5.248.574 $118.577 $120. 2007 © 2007 Ibbotson Associates.835 $3.896.474 $88.764.823 $58.704 $2.476 $1. 3.75% Average: 4.858 $2.48% 8.095 $63.401.146.793 $123.903 $2.671 $1.10% 6.824 $2.459 $1.801 $2.264 $2.423 $2.399 $2.11% 7.08% -1.232.721 $122.950 40/60 Inc.53% Average: 3.74% 4. 40/60 Principal $1.773 $2.555 $1.570.517.833 $138.741 $2.038 $139.486 $57.097 $1.11% 2.610 $2.40% 12.52% 40/45/15 Principal $1.40% 14.664.76% 5.318.913 $120.702 $138.820.552 $157.349.03% 5.17% 2. Ret.036. Ret. in whole or part.042 $150.675.015.87% -3.58% 8.820 $110.443 $102.312 $2. October 5.358 $151.608 $83.351.588 $2.000 $51.443 $121.868.49% -5.000 $1.183 $2.58% -0.215 $66.66% 7.56% 14.607 40/60 Income $50. All rights reserved.085 Total: $3.690 $2.367.227 $1.656 $90.257 $141. Reproduction or transcription by any means.109 $94.116.045 $3.368.534 $135.837 $2.606 $123.98% -1.020 $2.157 $2.777.857 $2.522.188 $1.96% 12.664 Total: $2.809.512 $1.434.98% 4.135 $68.250.266 $111.25% -0. 5.96% 10.125 $2.547 $2.035 $2.37% 6.329.095 $128.169.22% -7.244 $2.72% -2.459 $1.891.264 $2.242 $133.127.69% -7.262.89% 17. The information in this document is the property of Ibbotson Associates.871 $130. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.130 $1.863 $2.07% -6.570.065 $2.38% 10.718 $114.605.45% 10.30% 8.291 $103.15% -9.145.25% 0.000.132 $2.890 $117.056.613. the income risk only comes from the non-VA portion of the portfolios. in whole or part. 2007 © 2007 Ibbotson Associates. The information in this document is the property of Ibbotson Associates. one could argue that the history might not repeat. Inc 20 . the VA+GMWB has zero downside risk for the income returns due to the guaranteed minimum incomes.e. average total income return. respectively. and the simulated results along with empirical results are shown in tables 4–6. or 10th percentile concepts.98% for the moderate conservative portfolio. Monte Carlo simulations with Ibbotson forward-looking returns and standard deviations are conducted for three model portfolios and their corresponding combined portfolios. All five measurements are attractive for the VA+GMWB combined portfolios. To help understand the 90. total incomes. thus the ending value is less when the market has performed worse than average for an extended period of time. and two combined portfolios (20/60/20 and 20/40/40) are shown in table 4A. which is our hypothesis. the average loss income return and semi-deviation are 4. 75. All rights reserved. i.43% and 2. The average loss income return and semi-deviation are 4. Therefore.. By design. 25. and such a strong market performance may not sustain long in the future. The reason is that a more aggressive portfolio suffers more.1% and 2. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. while the average loss income return and loss semi-deviation are lower for the combined portfolios. and ending assets are higher. Monte Carlo simulations with forward-looking expectations shown in table 4B largely support the abovementioned hypothesis in all percentiles. The empirical data analysis shown in table 3 suggests that VA+GMWB will help improve the overall retirement income levels without increasing income risk levels. respectively. The empirical results using historical returns from 1979-2006 for the conservative portfolio (20/80). and 10th percentiles. However. 25.97% for the combined 40/45/15 portfolio. The higher the VA+GMWB replacement ratio. One can see that the average loss income return is lower in the 40/45/15 portfolio and semi-deviations are almost same for the 40/60 and 40/45/15 portfolios.The average loss income return is defined as the average of negative income returns and the semi-deviation is defined as the standard deviation of negative income returns. except that the ending assets are lower for the combined portfolios for the 50. To continue with the above-mentioned moderate conservative portfolio and the combined 40/45/15 portfolio shown in table 3. Reproduction or transcription by any means. VA+GMWB. without the prior written consent of Ibbotson Associates. is prohibited. To test this hypothesis. the more attractive are the five measurements. Appendix B presents the implied portfolio returns for each percentile for all model portfolios and the corresponding combined portfolios. October 5. 50. 26% lossSTD 2. The empirical results for the moderate conservative portfolio (40/60).94% -1. endAsset is the ending assets of the portfolios.42% -4. except that the ending assets are lower for the combined portfolios for the 50.02% 1.173 $268.058 $1.48% -0.04% 1.647.075.41% -1. The average loss returns are lower in the combined 40/45/15 and 40/25/35 portfolios. 2007 © 2007 Ibbotson Associates.263 $1.74% totalWithdrawal $2.35% 3. totalWithdrawal is the total income amounts over the entire 28 years.363.830 100%TA Conservative 80%TA/20%VA 60%TA/40%VA *Ending assets are the total of VA+GMWB contract value and traditional portfolio value for the combined portfolios.04% 3.31% 0.77% -3. without the prior written consent of Ibbotson Associates.92% -4.27% 1.79% 2.895 $123.00% -1.460 100%TA 80%TA/20%VA 60%TA/40%VA * lossAvg is the average of negative income returns.523.78% 4.50% 1.349.34% -0.14% -0. during which the stock market crashed while the bond market performed well.200.14% -3. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.15% 0. is prohibited.908 $1.275.180 $339.60% -2. avgReturn is the average of both positive and negative income returns.72% 3.019 $1.28% 1.07% 2.709.98% -4.09% 1.330.030.651 $1.38% -1.338 $973.459 $1. in whole or part.090.060 $1. total incomes.386. Monte Carlo simulations on forward-looking market expectations shown in table 5B once again largely support the above-mentioned hypothesis in all percentiles.920 $433.95% -3. The semi-deviation is slightly higher in the 40/25/35 combined portfolio because of the significant losses from 2000 to 2002.199. Inc 21 .689.607.895. and ending assets are all higher in the combined portfolios.197. and 10th percentiles (ending value in a more aggressive portfolio suffers more when the market performed worse than average). and two combined portfolios (40/45/15 and 40/25/35) are shown in table 5A. 25. lossPeriodsIncome is the average income in the periods that have negative income returns.269 $581.52% -6.49% 1. All rights reserved. The results are basically similar to the conservative portfolio shown in table 4B.807 $1.882.096.653 $872.569 $3.892 $780.90% lossPeriodsIncome $104.567 $2.864 $1.31% -1.86% totalWithdrawal $1.900 $423.55% -3. Reproduction or transcription by any means.96% -5. The 40/45/15 portfolio was discussed before. Monte Carlo Simulations for Conservative Model Portfolio and Combined Portfolios percentiles 90% 75% 50% 25% 10% 90% 75% 50% 25% 10% 90% 75% 50% 25% 10% lossAvg -3.58% 2.918 lossSTD 2.307.05% -2.356 $1.16% -0.892 $2.Table 4A.35% -2.080 endAsset $1.43% -0.763 $1.39% 2.067 $1.30% -2.18% 1. the average income during the income-loss periods is higher for 40/25/35 although its semi-deviation is higher.95% 3.98% -2.513 $505.201 $1.896 $997.509.30% avgReturn 2.967 $2.691 $630.198 $504. so that the semi-deviation is slightly higher for 40/25/35. VA+GMWB.891.02% 2.21% 3.025 $1. Conservative Model Portfolio and Combined Portfolios from 1979 to 2006 lossAvg -2.754 $1.63% -2. Note that in table 5A.27% avgReturn 0.117 $138.36% 2. The information in this document is the property of Ibbotson Associates.195 endAsset $955. The average total income return. October 5.055 $352. Table 4B.76% 2. 94% 0.454 $1.25% 4.742 $1. Monte Carlo simulations show that the semi-deviation is lower for the combined 40/25/35 portfolio.89% 5.75% 4.492 $1.120.28% -7.72% -5.000 possible scenarios.43% -4. All observations in both empirical results and Monte Carlo simulations are similar to the moderate conservative portfolio (40/60) and the combined 40/45/15 and 40/25/35 portfolios.28% -5.607 $2.461.419.368 $145. Moderate Conservative Portfolio and Combined Portfolios from 1979 to 2006.563 $652.705. Monte Carlo simulation results are shown in table 6B.27% avgReturn 3.49% 2.27% 3.492 $2.21% avgReturn 1.97% 3.82% -4.486.216.14% -4. Reproduction or transcription by any means.390.49% 2.66% -4.216.158 $1. is prohibited.388 $436.589 $2.656 $2.39% -1.878 $2. All rights reserved.999 $1.692.039.450 $2. Monte Carlo Simulations for Moderate Conservative Model Portfolio and Combined Portfolios 100%TA Mod.146.04% 3.75% 2.54% -6.48% -0.871 $1.195.80% 0.614 $131.281.718 $590.607 endAsset $1.362 $1.349. Table 5A.491.02% -0.725 $822. in whole or part.10% -0.78% -3.10% -3.12% 0. VA+GMWB.45% 2. whereas the empirical semi-deviation is over just one historical scenario which may suffer from random fluctuations and extreme events.22% -4.954 endAsset $2.In contrast to empirical results.730 $1.337.857.79% 3.67% totalWithdrawal $2.86% -5.72% 4.35% 2.62% totalWithdrawal $1. lossAvg -4. without the prior written consent of Ibbotson Associates. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.52% 4.77% -1.322.891.344 $865. Con.454 $3.762.645 $493.11% -7. percentiles 90% 75% 50% 25% 10% 90% 75% 50% 25% 10% 90% 75% 50% 25% 10% lossAvg -4.628.22% 3.943. 2007 © 2007 Ibbotson Associates.49% 0.155 $1.27% 3.216.906 $1. Inc 22 .45% -6.280 $1.98% 0. The reason is that Monte Carlo-simulated semi-deviation is the median semi-deviation over 5.74% 4.950 $3.32% 4.447 $893.291 $1.03% 4.038 $342.47% 1.451 $1.495 $502.522.999.98% 2.87% lossPeriodsIncome $120.908. The information in this document is the property of Ibbotson Associates. October 5.675 $1.540.755 lossSTD 2.82% 3.79% -5.954 100%TA 85%TA/15%VA 65%TA/35%VA Table 5B.88% lossSTD 3.876 85%TA/15%VA 65%TA/35%VA The empirical results for the moderate portfolio (60/40) and two combined portfolios (60/30/10 and 60/15/25) are shown in table 6A.13% -6.199 $1. 51% -5.983.152.57% -9. which were discussed previously.083.398 $1.48% 1. The information in this document is the property of Ibbotson Associates.107 $3.218 $148.758.54% 6.326 $3.221.57% -6. October 5. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.322.615 $561.03% 5.225 $1. The empirical period is from the beginning of 1979 to the end of 2006.02% 2.16% -5.82% -6. total income.60% 2.92% 4.76% 1.152 $1.97% 5.150 $2.202.399 $3. VA+GMWB.02% 6.369.77% 4.04% -9.58% 5. without the prior written consent of Ibbotson Associates.032 $3.73% 4.80% 5.243 $3.539. All rights reserved.300 $1.128 $426.952 $1.33% 7.828 $3.Table 6A. Inc 23 .15% -6.127.24% 1.386 $1.71% 5.846 $513.672.79% 6.876.12% -10.77% 3.02% 5. 50 and 10th percentiles are plotted for comparison purposes and the period covered is 28-years.78% 0.305 lossSTD 4.597.461 $1. The Monte Carlo simulations for the five parameters in the 90.085 endAsset $2. is prohibited.130.36% 5.717 $2.05% -0. and ending assets for the moderate conservative (40/60) portfolio and combined portfolios (40/45/15 and 40/25/35).06% -9.51% -0.779.27% 6.231.24% avgReturn 4.895.67% -7. average loss income return.24% 0.460.29% -6. Moderate Portfolio and Combined Portfolios from 1979 to 2006 lossAvg -6.236.09% 3.961 $1.894 $1.71% 3.080 $759.313.626.60% -8.10% -7.911. in whole or part.823 $1.926 $805.233 $1.442.227.46% 0.599 $1.52% avgReturn 3.316 $3.17% -8.553 $1.14% 4.04% lossSTD 4.220 $2.081 $2.319 100%TA Moderate 90%TA/10%VA 75%TA/25%VA Chart 4 A-E shows the average income return.49% totalWithdrawal $2. 2007 © 2007 Ibbotson Associates.556 100%TA 90%TA/10%VA 75%TA/25%VA Table 6B. semi-deviation.194.32% -7.81% 4.49% totalWithdrawal $3.492 endAsset $3.744.772 $3.026.690 $144.445.942 $686. Reproduction or transcription by any means.94% 4.28% lossPeriodsIncome $141.095.990 $1.03% -8.24% -0.787. Monte Carlo Simulations for Moderate Model Portfolio and Combined Portfolios percentiles 90% 75% 50% 25% 10% 90% 75% 50% 25% 10% 90% 75% 50% 25% 10% lossAvg -6. Con. 50%.00% 3.00% 8. Average Total Income Return. 5. Mod.00% 2. in whole or part. Con.00% 90% 50% 10% 1979-2006 100% TA 85%TA / 15%VA 65%TA / 35%VA VA+GMWB. October 5. The information in this document is the property of Ibbotson Associates. is prohibited. Average Income Return Loss.00% 4.Chart 4A.00% 0. without the prior written consent of Ibbotson Associates.00% 1.00% -2.00% -1. 2007 © 2007 Ibbotson Associates. Chart 4B. 40/45/15.00% 90% 50% 10% 1979-2006 100% TA 85%TA / 15%VA 65%TA / 35%VA *90%. Average Total Income Returns for the 40/60. and 10th percentiles results for the Monte Carlo Simulations. Average Loss Income Returns for the 40/60.00% 2. 40/45/15. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. and 10% are the 90. and 40/25/35 Portfolios. and 40/25/35 Portfolios.00% 0. Mod. 50.00% 4. 10. All rights reserved. Reproduction or transcription by any means. Inc 24 .00% 6. 000 $3.00% 4. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. and 40/25/35 Portfolios.00% 90% 50% 10% 100% TA 85%TA / 15%VA 65%TA / 35%VA 1979-2006 * Note that for historical analysis. 40/45/15.00% 3.00% 0.000 $2. Semi-Deviations of Income Returns for the 40/60. Con.000.Chart 4C.000 $1. 40/45/15. Mod.000 $0 90% 50% 10% 1979-2006 100% TA 85%TA / 15%VA 65%TA / 35%VA VA+GMWB.500.500. Total Incomes for the 40/60.000.000 $500. the historical average income during the income-loss periods is $145.00% 2. without the prior written consent of Ibbotson Associates.000.755 for 40/25/35 (higher than $120. Moderate Conservative $4. is prohibited. The information in this document is the property of Ibbotson Associates.614 for 40/60) although its semi-deviation is slightly higher. in whole or part. and 40/25/35 Portfolios.000 $1.00% 5.000 $2. Chart 4D. Total Income.000 $3. 2007 © 2007 Ibbotson Associates.000. 6. Inc 25 .00% 1. All rights reserved. October 5. Semi-Deviation of Income Returns.500. Reproduction or transcription by any means. Ending Asset. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. is prohibited. Reproduction or transcription by any means.000. Moderate Conservative $3.000 $2.000 $2. All rights reserved.000 $500. The information in this document is the property of Ibbotson Associates. without the prior written consent of Ibbotson Associates.000 $1. 2007 © 2007 Ibbotson Associates.000.500. Ending Assets for the 40/60. October 5.500. 40/45/15.Chart 4E. in whole or part.000 $0 90% 50% 10% 1979-2006 100% TA 85%TA / 15%VA 65%TA / 35%VA VA+GMWB.000. and 40/25/35 Portfolios. Inc 26 .000 $1. 400. in whole or part. Reproduction or transcription by any means. The information in this document is the property of Ibbotson Associates. That is. October 5. however. and their corresponding combined portfolios are summarized in Chart 5.000 0% 1% 2% 3% 4% 5% 6% Income Loss Semi-Deviation 20/40/40 20/60/20 20/80 60/15/25 60/30/10 40/45/15 40/60 60/40 40/25/35 *The assumed fee structure is shown in table 2D. additions of VA+GMWB will shift the income-risk curve in Chart 5 up and left. It plots the 50th percentile of total income and semi-deviation from the Monte Carlo simulations with forward-looking market expectations over the 28 years. Monte Carlo Simulations for Total Income and Semi-Deviation Total Income and Semi-Deviation. 2007 © 2007 Ibbotson Associates. and the combined portfolios have more equity allocation which contributes to an increase in the total income.000 $1.000 $800.600. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. moderate conservative.000. without the prior written consent of Ibbotson Associates. 28-Years $2. the guaranteed income from VA+GMWB has no income risk which helps to lower the overall income risk. 50th Percentile. Chart 5. is prohibited.000 $1. All rights reserved.000 Total Income $2.200.Proof of Hypothesis The total income and semi-deviation for conservative. more aggressive model portfolios have higher total income and higher semi-deviation (thus higher income risk). moderate portfolios. In general. Inc 27 . VA+GMWB. The information in this document is the property of Ibbotson Associates. It differs from the previously discussed semi-deviation analysis in that the income withdrawal in this framework is in constant or slightly increasing dollar amounts.000 (=$50. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. the shortfall income is $0 because the income is at least 5% of the initial investment of $1. without the prior written consent of Ibbotson Associates. The annual fixed 5% of withdrawal rate based on the portfolio value is assumed in the semi-deviation framework.000 -$2. All rights reserved. 30 years. October 5.000 VA+GMWB 40/45/15 80/20 60/40 40/60 20/80 $8.000 $6.000 $50.300 (=$50.650.000 $4. the income is only $40. thus the shortfall income is $9. The 5th percentile is chosen to represent the “worst” market return scenario for the portfolio performance.e. Inc 28 . The average sustainable income level is the annual income that can sustain for 30 years at the 50th percentile. and more precisely. shortfall income risk. e. 30-Year Horizon Median Income Level $80. 2007 © 2007 Ibbotson Associates. For the conservative portfolio.000-$40. The average or median sustainable income level for stand-alone VA+GMWB is simply the average income payout at the 50th percentile for the 30-year horizon. However. is prohibited. The shortfall income risk is defined as the shortage of income compared to a target income of $50. the average income levels are calculated by binary searches.g. it is the median sustainable income level. average sustainable income level vs.700). i. in whole or part.000 20/60/20 $0 $2. Expected returns and standard deviations for the seven asset classes used in the simulation analysis are forecasted by Ibbotson Associates and shown in table 2B. we introduce another framework.000 $10. Chart 6 shows the average or median sustainable income level and shortfall risk for a 30-year horizon for three sets of portfolios: 1) stand-alone VA products with these guarantees (VA+GMWB). two conditions are satisfied for apples-to-apples comparisons: (a) the ending total portfolio value is equal to the ending contract value of the stand-alone VA+GMWB at the 50th percentile and (b) the income stream shape is the same as the standalone VA+GMWB at the 50th percentile shown in Chart 2.000 60/30/10 $70.000. and in addition. and 3) a combination of VA products and non-annuity products. instead of a fixed 5% based on the portfolio value in each year.000 $60. Chart 6. at the 5th percentile. For stand-alone traditional asset portfolios or combined portfolios. Reproduction or transcription by any means. 2) stand-alone traditional non-annuity products (such as mutual funds). Median Income Level and Shortfall Risk for 30-Year Horizon Median Income Level (50th Percentile) and Shortfall Income Risk (5th Percentile).000 at the 5th percentile for a given investment horizon. VA+GMWB.000).000 Shortfall Income Risk (Target $50K) VA+GMWB Combined Traditional Assets For stand-alone VA+GMWB.Average Sustainable Income Level and Shortfall Income Risk In this section. in the combined 20/60/20 (20% bonds were replaced by 20% VA+GMWB in the conservative portfolio) the shortfall income declined to $6.700 for a 30-year horizon. Reproduction or transcription by any means. is prohibited. without the prior written consent of Ibbotson Associates. All rights reserved. On the other hand. different withdrawal patterns or income curves result in different ending portfolio values. however the benefit might not be as much as those illustrated in this paper. The information in this document is the property of Ibbotson Associates. in whole or part. adding VA+GMWB to the conservative. The above-mentioned condition (a) considers the impact on positive remaining contract value. Inc 29 . October 5. and for conservative. and condition (b) takes it into account.766.The amount of income withdrawn from VA+GMWB is dynamically determined by the benefits base. the average sustainable income level increased to $56. and moderate portfolios. and after 30 years. Investors needing much higher or much lower percentage of withdrawal from their portfolio to sustain retirement income would still benefit from including VA+GMWB.068. 6 These findings suggest that adding VA+GMWB to the retirement portfolio can be beneficial. Chart 6 clearly shows that all combined portfolios have higher average income levels than stand-alone traditional mutual fund portfolios. In other words. For the conservative 20/80 portfolio. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. 2007 © 2007 Ibbotson Associates. . additions of VA+GMWB even lead to a reduction in shortfall income risk due to the guaranteed income feature in the VA+GMWB. 7 VA+GMWB. moderate conservative. We intend to address how much an investor should put into VA+GMWB in a retirement portfolio in a separate analysis. while for the combined 20/60/20 portfolio. the same average ending assets and the same income stream shape allow unbiased average income levels to be calculated for the traditional and combined portfolios. moderate conservative. the average sustainable income level is $53. the VA+GMWB may still have positive remaining contract value. Therefore. and moderate model portfolios enhances average income and reduces shortfall risk for investors needing roughly 5% from their portfolios to 67 sustain retirement income for 30 years or more . First. the guaranteed income from VA+GMWB has no income risk which helps to lower the overall income risk. we believe this risk is very small. However. and 3) a combination of VA products and non-annuity products in a portfolio context. However. Third. more aggressive model portfolios provide higher total income with higher semi-deviation (thus higher income risk). the benefit of GMWB will be lower for investors needing a much lower percentage of withdrawal (i.g. In other words. An example would be investors with significant defined benefit pension income in retirement. 2) stand-alone traditional non-annuity products (such as mutual funds). Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. the study does not consider the default risk in VA contracts. who have a significant probability of living pass age 85 and 90. for investors with existing market risk and retirement income risk coverage. VA+GMWB. we analyzed the shortfall risk and median sustainable income level for the three model portfolios and the combined portfolios over the 30-year horizon. both empirical results and Monte Carlo simulations show that the combined portfolios have lower average negative income return and semi-deviation and higher average total income return and total income withdrawals. due to the more aggressive allocation and the guaranteed withdrawals in the VA+GMWB. the ending portfolio assets are likely to be higher in the combined portfolios. Assuming a fixed percentage withdrawal rate (5%) on the model portfolios. 2007 © 2007 Ibbotson Associates.. However. Reproduction or transcription by any means.e. October 5. Conclusions We applied the semi-deviation measurements on income returns for a series of simulation analyses across the three scenarios: 1) stand-alone VA products with these guarantees. is prohibited. which we believe is the typical planning horizon for retirees today and in the future. and the combined portfolios have more equity allocation which contributes to increase total income. The information in this document is the property of Ibbotson Associates. to be precise). the benefit will be smaller. All rights reserved. 30+ years). the benefits will be greater than those presented in this study. On the other hand. the study assumes the investor has a retirement income period of 25 years or longer (28 in the income risk analysis and 30 years in the income shortfall risk analysis.V. we focus on investors needing roughly 5% from one’s portfolios. in whole or part. ultra high net worth investors). We found that all combined portfolios have higher average income levels and lower shortfall income risk than stand-alone traditional mutual fund portfolios. if the market performed better than average. While presenting the benefit of a VA+GMWB from the results. Inc 30 . a VA+GMWB may not be as beneficial. which will leave the remaining mutual fund portfolio with a heavier equity allocation than the original mutual fund portfolio. That is. This probability is particular high for married couples. Second. without the prior written consent of Ibbotson Associates. a portion of the fixed income /cash is replaced with a more aggressively allocated VA. In an alternative framework. we need to keep in mind a few caveats of this study. The tradeoff is that the ending portfolio assets are lower in the combined portfolios when the market performed worse than average for extended periods of time. The combined portfolios have a slightly more aggressive allocation than the original moderate conservative model portfolio. In the combined portfolio. For an investor with a shorter horizon. for investors with even longer horizons (e. The addition of VA+GMWB helps to increase total income while reducing income risk.. Lastly. we have shown that the combined portfolios have lower income risk and higher total income returns than the corresponding portfolios. adding VA+GMWB to the conservative and moderate conservative model portfolios enhances average sustainable income while reducing shortfall income risk. and reduce the amount of income risk. in whole or part. Reproduction or transcription by any means. This can potentially increase the amount of income generated from the entire portfolio (especially during poor market performance periods). For the typical retiree. All rights reserved. Inc 31 . without the prior written consent of Ibbotson Associates. Similar to payout annuities. VA+GMWB offers a secured lifetime income that is not available through traditional investment products. For the typical investor in or near retirement.Overall. 2007 © 2007 Ibbotson Associates. The information in this document is the property of Ibbotson Associates. it is beneficial to look into investing a portion of their assets into VA+GMWB. we believe VA+GMWB offers protection both in terms of market downturns and more importantly retirement income risk. is prohibited. VA+GMWB. there is a good amount of value by investing a portion of his or her investment asset into VA+GMWB. October 5. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. which provides a guaranteed income level through retirement. The g value can be age-dependent (e. The information in this document is the property of Ibbotson Associates.e.g. i.5% if income starts at age 67. Inc 32 . The constant ε is the management fees for the VA account including underlying fund fees. 2007 © 2007 Ibbotson Associates. assuming a constant withdrawal rate (e. for a traditional mutual fund portfolio. σ is the volatility of the VA account. Mt is the maximum of the contract value from initial purchase to current period.0 ≤ s ≤ t ) Incomet = gM t (1) Where Vt and Mt are the VA account or contract value and benefits base at time t. The constant f is the GMWB rider fee (e.) In contrast. October 5.g.g. VA+GMWB. The constant g is the guaranteed withdrawal rate (e. The spending or income is stepped up each time the contract or account value reaches a new maximum. 5% of the initial deposit). Appendix A. without the prior written consent of Ibbotson Associates. σ is the volatility of the mutual fund portfolio. VA+GMWB Modeling The dynamics of the VA+GMWB contract value is (Milevsky 2006): dVt = ( µ − ε )Vt + σVt dBt − fM t dt − gM t dt M t = max(Vs . Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. All rights reserved. is prohibited. 5% if income starts at age 60. Reproduction or transcription by any means.VI. The constant g is the withdrawal rate on the beginning balance of the mutual fund portfolio (5%) in each period.6%). the dynamics of the portfolio value is: dVt = ( µ − ε )Vt + σVt dBt − gVt dt Incomet = gVt (2) The constant ε is the mutual fund management fees. 5%) on the beginning balance of the portfolio in each period. 0. and 5. in whole or part.g. Bt denotes a standard Brownian motion with mean zero and variance t. the highwater mark of the contract value. respectively. 13% 6. Implied Returns To give an estimate on how an average portfolio (at 50th percentile) or the worst scenario portfolio (at 10th percentile) performed over a 28-year horizon.32% 7. without the prior written consent of Ibbotson Associates. 2007 © 2007 Ibbotson Associates.49% Table 7A-D shows the implied returns for the four model portfolios and the corresponding combined portfolios. in whole or part.56% 3.31% 2.87% VA+GMWB. Assuming no intermediate cash flows and initial $1 million investments. The assumed fee structure is shown in table 2D. Reproduction or transcription by any means. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.610. The implied returns for the conservative model portfolio and the corresponding combined portfolios over a 28-year horizon Percentile 90% 75% 50% 25% 10% Conservative 5.42% 2.02% 3.46% 4.04% 3.38% 5. Table 7A.72% 2. For example.66% 6. we calculate the implied returns for each percentile based on the wealth distribution at the end of 28 years. for the moderate aggressive model portfolio at the 10th percentile. The information in this document is the property of Ibbotson Associates. the ending portfolio is $2. The implied returns for the moderate conservative model portfolio and the corresponding combined portfolios over a 28-year horizon Percentile 90% 75% 50% 25% 10% Moderate Conservative 7.94% 40/45/15 8.64% 6.45% 4.31% 4. All rights reserved. October 5.15% 5.58% 20/40/40 7.00% 4.79% 2.87% 2.98% 40/25/35 9. is prohibited.33% 20/60/20 6.09% 2. we performed Monte Carlo simulations on the four model portfolios and some combined portfolios to get a wealth distribution at the end of 28 years.80% 5.61)^(1/28) – 1 = 3.63% Table 7B. and the implied return over the 28-year period is: (2.B.47% 5.016. Inc 33 .46% 3.96% 2.24% 6. 17% 2.18% 4.44% 4.80% 3.09% 9.17% 3. All rights reserved. Reproduction or transcription by any means. The information in this document is the property of Ibbotson Associates.16% 4.15% 6.84% 8.69% 8.16% 5.71% 3.Table 7C.74% 6. The implied returns for the moderate aggressive model portfolio and VA+GMWB over a 28-year horizon Percentile 90% 75% 50% 25% 10% Moderate Aggressive 11.73% 6. 2007 © 2007 Ibbotson Associates.12% Table 7D.26% 60/15/25 10. is prohibited.63% 3.16% 6.81% 4.15% 7. without the prior written consent of Ibbotson Associates. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar.49% VA+GMWB 10.32% 60/30/10 9.49% VA+GMWB. Inc 34 . The implied returns for the moderate model portfolio and the corresponding combined portfolios over a 28-year horizon Percentile 90% 75% 50% 25% 10% Moderate 9. October 5.09% 8.26% 7. in whole or part. in whole or part. Inc 35 . Semi-Deviation: standard deviation of negative income returns. year. VA+GMWB: variable annuity with a guaranteed minimum withdrawal benefit. VA+GMWB. October 5.g. Implied Return at 50th Percentile: a fixed compound return required to accumulate the wealth equals a Monte Carlo simulated wealth at the 50th percentile for a given period. The information in this document is the property of Ibbotson Associates. without the prior written consent of Ibbotson Associates. 30 years).C. Income Risk: the downside volatility (or semi-deviation) of the change of income from year to Income Shortfall Risk: the shortage of sustainable income to a target income over a given period (e. Reproduction or transcription by any means. Glossary Benefit Base: a high-water mark of the VA+GMWB contract value. All rights reserved. Income Return: the change of income in percentage from year to year. is prohibited. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. which is used to calculate the withdrawal income and rider charge. 2007 © 2007 Ibbotson Associates. in whole or part. Reproduction or transcription by any means. Chen. no. and Ken X. Ibbotson Associates is a registered investment advisor and wholly owned subsidiary of Morningstar. 2006. Cambridge University Press. Ibbotson. October 5. Roger G. 62. Moshe A. “Human Capital. and Ken X. Peng. Milevsky. Journal of Financial Planning. All rights reserved. Zhu. 2007. Zhu.VII. is prohibited. Ibbotson. without the prior written consent of Ibbotson Associates. Inc 36 . “Lifetime Financial Advice. ”Merging Asset Allocation and Longevity Insurance: An Optimal Perspective on Payout Annuities“. 2003. Milevsky. Asset Allocation. and Moshe A. Chen. (June): 64-72. 1 (January/February):97–109. VA+GMWB. Moshe “The Calculus of Retirement Income”. Reference Chen. The information in this document is the property of Ibbotson Associates. 2007 © 2007 Ibbotson Associates. Milevsky.” Financial Analysts Journal. and Life Insurance. 2006.” CFA Institute Research Foundation Monograph. Peng. Milevsky. Roger G. Peng. Moshe A. vol.
Copyright © 2024 DOKUMEN.SITE Inc.