In this paper we model and solve a retirement consumption problem with differentially taxed accounts, parameterized by longevity risk aversion. The work is motivated by some observations on how Canadians de-accumulate financial wealth during retirement — which seem rather puzzling. While the Modigliani lifecycle model can justify a variety of (pre-tax) de-accumulation or draw down rates depending on risk preferences, the existence of asymmetric taxes implies that certain financial accounts should be depleted faster than others. Our analysis of data from the Survey of Financial Security indicates that Canadian retirees maintain approximately two-thirds of their financial wealth in tax-sheltered accounts and a third in taxable accounts regardless of age. The ratio of taxable to tax-sheltered wealth increases slightly or remains relatively constant depending on household income which is not what one would expect from the lifecycle model. Indeed, using our model we cannot locate a plausible tax function that justifies a constant “account ratio” regardless of age. For example under flat rates taxable accounts should be depleted well before tax-sheltered accounts are ever touched. The account ratio should go to zero quite rapidly in the absence of government mandated withdrawals. We also demonstrate that under progressive income taxes withdrawals are made from both accounts but at different rates depending on account size, pension income and longevity risk preferences. Again, the “account ratio” should eventually decline. We postulate that this sort of behavior is likely due to irrational considerations linked to mental accounting, etc. It remains to be seen whether this will persist over time and under a more careful analysis of Canadian cohorts or if retirees in other countries exhibit the same behavior.
{"title":"Longevity Risk and Retirement Income Tax Efficiency: A Location Spending Rate Puzzle","authors":"Huang Huaxiong, M. Milevsky","doi":"10.2139/ssrn.1961698","DOIUrl":"https://doi.org/10.2139/ssrn.1961698","url":null,"abstract":"In this paper we model and solve a retirement consumption problem with differentially taxed accounts, parameterized by longevity risk aversion. The work is motivated by some observations on how Canadians de-accumulate financial wealth during retirement — which seem rather puzzling. While the Modigliani lifecycle model can justify a variety of (pre-tax) de-accumulation or draw down rates depending on risk preferences, the existence of asymmetric taxes implies that certain financial accounts should be depleted faster than others. Our analysis of data from the Survey of Financial Security indicates that Canadian retirees maintain approximately two-thirds of their financial wealth in tax-sheltered accounts and a third in taxable accounts regardless of age. The ratio of taxable to tax-sheltered wealth increases slightly or remains relatively constant depending on household income which is not what one would expect from the lifecycle model. Indeed, using our model we cannot locate a plausible tax function that justifies a constant “account ratio” regardless of age. For example under flat rates taxable accounts should be depleted well before tax-sheltered accounts are ever touched. The account ratio should go to zero quite rapidly in the absence of government mandated withdrawals. We also demonstrate that under progressive income taxes withdrawals are made from both accounts but at different rates depending on account size, pension income and longevity risk preferences. Again, the “account ratio” should eventually decline. We postulate that this sort of behavior is likely due to irrational considerations linked to mental accounting, etc. It remains to be seen whether this will persist over time and under a more careful analysis of Canadian cohorts or if retirees in other countries exhibit the same behavior.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131335865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Bucciol, L. Cavalli, Igor Fedotenkov, P. Pertile, Veronica Polin, N. Sartor, Alessandro Sommacal
The paper presents a large scale overlapping generation model with heterogeneous agents, where the family is the decision unit. We calibrate the model for three European countries - France, Italy and Sweden - which show marked differences in the design of some public programs. We examine the properties in terms of annual and lifetime redistribution of a number of tax-benefit programs, by studying the impact of removing from our model economies some or all of them. We find that whether one considers a life-cycle or an annual horizon, and whether behavioral responses are accounted for or not, has a large impact on the results. The model may provide useful insights for policy makers on which kind of reforms are more likely to achieve specific equity objectives.
{"title":"Public Policies over the Life Cycle: A Large Scale OLG Model for France, Italy and Sweden","authors":"A. Bucciol, L. Cavalli, Igor Fedotenkov, P. Pertile, Veronica Polin, N. Sartor, Alessandro Sommacal","doi":"10.2139/ssrn.2707193","DOIUrl":"https://doi.org/10.2139/ssrn.2707193","url":null,"abstract":"The paper presents a large scale overlapping generation model with heterogeneous agents, where the family is the decision unit. We calibrate the model for three European countries - France, Italy and Sweden - which show marked differences in the design of some public programs. We examine the properties in terms of annual and lifetime redistribution of a number of tax-benefit programs, by studying the impact of removing from our model economies some or all of them. We find that whether one considers a life-cycle or an annual horizon, and whether behavioral responses are accounted for or not, has a large impact on the results. The model may provide useful insights for policy makers on which kind of reforms are more likely to achieve specific equity objectives.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128255764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we extend the traditional life cycle model of saving and portfolio choice to allow for possible long-term unemployment spells to have permanent effects on subsequent labor income prospects. The risk of losing future labor income could imply strong human capital erosion for the investor at any age, dampening the incentive to invest in risky stocks. The resulting optimal portfolio share invested in stocks may be relatively flat in age, more in line with the available evidence and contrary to the predictions of traditional life-cycle models.
{"title":"Life-Cycle Asset Allocation and Unemployment Risk","authors":"F. Bagliano, C. Fugazza, G. Nicodano","doi":"10.2139/ssrn.2744761","DOIUrl":"https://doi.org/10.2139/ssrn.2744761","url":null,"abstract":"In this paper we extend the traditional life cycle model of saving and portfolio choice to allow for possible long-term unemployment spells to have permanent effects on subsequent labor income prospects. The risk of losing future labor income could imply strong human capital erosion for the investor at any age, dampening the incentive to invest in risky stocks. The resulting optimal portfolio share invested in stocks may be relatively flat in age, more in line with the available evidence and contrary to the predictions of traditional life-cycle models.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131767441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We compare the performance of the commonly nominated default retirement investment option, the lifecycle fund, to alternative investment strategies during retirees' decumulation phase. Under different shortfall risk measures, we find balanced portfolios with constant exposure to equities, equity dominated portfolios as well as 'reverse lifecycle' portfolios that increase exposures to equities over time to consistently outperform the conventional lifecycle portfolio. While an increasing equity glidepath improves the performance of an investment strategy, the starting asset allocations are equally important. Using a utility-of-terminal wealth approach which allows for loss aversion as discussed in prospect theory by Kahneman and Tversky (1979), we find the Growth portfolio to dominate the alternative strategies at low and moderate thresholds. With increasing wealth threshold levels, a strategy with all equity allocations become dominant. The lifecycle portfolio is dominated by the 'reverse lifecycle' portfolio at all threshold levels.
{"title":"Portfolio Strategies in Decumulation Phase: Does Lifecycling Fail?","authors":"Osei K. Wiafe, A. Basu, E. Chen","doi":"10.2139/ssrn.2480293","DOIUrl":"https://doi.org/10.2139/ssrn.2480293","url":null,"abstract":"We compare the performance of the commonly nominated default retirement investment option, the lifecycle fund, to alternative investment strategies during retirees' decumulation phase. Under different shortfall risk measures, we find balanced portfolios with constant exposure to equities, equity dominated portfolios as well as 'reverse lifecycle' portfolios that increase exposures to equities over time to consistently outperform the conventional lifecycle portfolio. While an increasing equity glidepath improves the performance of an investment strategy, the starting asset allocations are equally important. Using a utility-of-terminal wealth approach which allows for loss aversion as discussed in prospect theory by Kahneman and Tversky (1979), we find the Growth portfolio to dominate the alternative strategies at low and moderate thresholds. With increasing wealth threshold levels, a strategy with all equity allocations become dominant. The lifecycle portfolio is dominated by the 'reverse lifecycle' portfolio at all threshold levels.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121607375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I investigate a dynamic life-cycle strategic asset allocation and consumption problem under model uncertainty, where both inflation rate and income growth rate are assumed to be estimated with errors. I present a feasible boundary for the uncertainty aversion parameter, which measures the investor's preference for robustness using econometric theory. I derive a closed-form solution for a robust investor characterized by min-max utility preference to insure against the worst case scenario. Robustness dramatically increases the demand for the long-term bonds when the instantaneous inflation rate is low.
{"title":"How Much Should Life-Cycle Investors Adapt their Behavior when Confronted with Model Uncertainty?","authors":"Sally Shen","doi":"10.2139/ssrn.2475803","DOIUrl":"https://doi.org/10.2139/ssrn.2475803","url":null,"abstract":"I investigate a dynamic life-cycle strategic asset allocation and consumption problem under model uncertainty, where both inflation rate and income growth rate are assumed to be estimated with errors. I present a feasible boundary for the uncertainty aversion parameter, which measures the investor's preference for robustness using econometric theory. I derive a closed-form solution for a robust investor characterized by min-max utility preference to insure against the worst case scenario. Robustness dramatically increases the demand for the long-term bonds when the instantaneous inflation rate is low.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"87 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124325644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mortality models are fundamental to quantify mortality/longevity risks and provide the basis of pricing and reserving. In this article, we consider a family of mortality jump models and propose a new generalized Lee–Carter model with asymmetric double exponential jumps. It is asymmetric in terms of both time periods of impact and frequency/severity profiles between adverse mortality jumps and longevity jumps. It is mathematically tractable and economically intuitive. It degenerates to a transitory exponential jump model when fitting the US mortality data and is the best fit compared with other jump models.
{"title":"A Family of Mortality Jump Models Applied to U.S. Data","authors":"Hua Chen","doi":"10.2139/ssrn.1911688","DOIUrl":"https://doi.org/10.2139/ssrn.1911688","url":null,"abstract":"Mortality models are fundamental to quantify mortality/longevity risks and provide the basis of pricing and reserving. In this article, we consider a family of mortality jump models and propose a new generalized Lee–Carter model with asymmetric double exponential jumps. It is asymmetric in terms of both time periods of impact and frequency/severity profiles between adverse mortality jumps and longevity jumps. It is mathematically tractable and economically intuitive. It degenerates to a transitory exponential jump model when fitting the US mortality data and is the best fit compared with other jump models.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128827994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I solve the life-cycle portfolio allocation problem of a disappointment averse (DA) agent. DA agents overweight disappointing outcomes. Unlike expected utility investors, DA investors drastically cut their allocation to stocks around retirement due to a distinct effect associated with the drop in income risk. The effect is driven by the changing comovement between returns and the disappointment/elation realization. The allocations are consistent with empirical evidence on portfolio shares and the allocation rules of target-date retirement funds. Sufficiently disappointment-averse agents abstain from investing in stocks after retirement, which is consistent with the observed low rates of stock market participation among retirees.
{"title":"What Drives Risky Investments Lower Around Retirement?","authors":"R. Khanapure","doi":"10.2139/ssrn.2308751","DOIUrl":"https://doi.org/10.2139/ssrn.2308751","url":null,"abstract":"I solve the life-cycle portfolio allocation problem of a disappointment averse (DA) agent. DA agents overweight disappointing outcomes. Unlike expected utility investors, DA investors drastically cut their allocation to stocks around retirement due to a distinct effect associated with the drop in income risk. The effect is driven by the changing comovement between returns and the disappointment/elation realization. The allocations are consistent with empirical evidence on portfolio shares and the allocation rules of target-date retirement funds. Sufficiently disappointment-averse agents abstain from investing in stocks after retirement, which is consistent with the observed low rates of stock market participation among retirees.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126335224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Historical tontines promised enormous rewards to the last survivors at the expense of those who died early. While this design appealed to the gambling instinct, it is a suboptimal way to manage longevity risk during retirement. This is why fair life annuities making constant payments -- where the insurance company is exposed to the longevity risk -- induces greater lifetime utility. However, tontines do not have to be designed using a winner-take-all approach and insurance companies do not actually sell fair life annuities, partially due to aggregate longevity risk. In this paper we derive the tontine structure that maximizes lifetime utility, but doesn't expose the sponsor to any longevity risk. We examine its sensitivity to the size of the tontine pool; individual longevity risk aversion; and subjective health status. The optimal tontine varies with the individual's longevity risk aversion $gamma$ and the number of participants $n$, which is problematic for product design. That said, we introduce a structure called a natural tontine whose payout declines in exact proportion to the (expected) survival probabilities, which is near-optimal for all $gamma$ and $n$. We compare the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity's advantage over tontines, is minimal. We also review and analyze the first-ever mortality-derivative issued by the British government, known as King Williams's tontine of 1693. We shed light on the preferences and beliefs of those who invested in the tontines vs. the annuities and argue that tontines should be re-introduced and allowed to co-exist with life annuities. Individuals would likely select a portfolio of tontines and annuities that suit their personal preferences for consumption and longevity risk, as they did over 320 years ago.
{"title":"Optimal Retirement Tontines for the 21st Century: With Reference to Mortality Derivatives in 1693","authors":"M. Milevsky, T. Salisbury","doi":"10.2139/ssrn.2271259","DOIUrl":"https://doi.org/10.2139/ssrn.2271259","url":null,"abstract":"Historical tontines promised enormous rewards to the last survivors at the expense of those who died early. While this design appealed to the gambling instinct, it is a suboptimal way to manage longevity risk during retirement. This is why fair life annuities making constant payments -- where the insurance company is exposed to the longevity risk -- induces greater lifetime utility. However, tontines do not have to be designed using a winner-take-all approach and insurance companies do not actually sell fair life annuities, partially due to aggregate longevity risk. In this paper we derive the tontine structure that maximizes lifetime utility, but doesn't expose the sponsor to any longevity risk. We examine its sensitivity to the size of the tontine pool; individual longevity risk aversion; and subjective health status. The optimal tontine varies with the individual's longevity risk aversion $gamma$ and the number of participants $n$, which is problematic for product design. That said, we introduce a structure called a natural tontine whose payout declines in exact proportion to the (expected) survival probabilities, which is near-optimal for all $gamma$ and $n$. We compare the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity's advantage over tontines, is minimal. We also review and analyze the first-ever mortality-derivative issued by the British government, known as King Williams's tontine of 1693. We shed light on the preferences and beliefs of those who invested in the tontines vs. the annuities and argue that tontines should be re-introduced and allowed to co-exist with life annuities. Individuals would likely select a portfolio of tontines and annuities that suit their personal preferences for consumption and longevity risk, as they did over 320 years ago.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122349912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The decision about how much to save for retirement is likely to be dependent on when an individual plans to be retired, and vice versa. Yet, the established literature on hyperbolic discounting and life-cycle saving behavior has for the most part abstracted from choice over retirement. Two notable exceptions are Diamond and Koszegi [1] and an important follow-up study by Holmes [2], which demonstrates that time-inconsistent retirement timing is impossible when saving behavior is explicitly modeled in a stylized three-period setting. In this paper, we build upon the framework of Diamond and Koszegi [1] and Holmes [2] by generalizing the assumptions about initial income and assets. We show analytically and via simple numerical examples that time-inconsistent retirement can exist in a three-period life-cycle model of consumption and saving.
{"title":"Quasi-Hyperbolic Discounting and the Existence of Time-Inconsistent Retirement","authors":"T. Findley, J. Feigenbaum","doi":"10.4236/TEL.2013.32019","DOIUrl":"https://doi.org/10.4236/TEL.2013.32019","url":null,"abstract":"The decision about how much to save for \u0000retirement is likely to be dependent on when an individual plans to be retired, \u0000and vice versa. Yet, the established literature on hyperbolic discounting and \u0000life-cycle saving behavior has for the most part abstracted from choice over \u0000retirement. Two notable exceptions are Diamond and Koszegi [1] and an important \u0000follow-up study by Holmes [2], which demonstrates that time-inconsistent \u0000retirement timing is impossible when saving behavior is explicitly modeled in a \u0000stylized three-period setting. In this paper, we build upon the framework of \u0000Diamond and Koszegi [1] and Holmes [2] by generalizing the assumptions about \u0000initial income and assets. We show analytically and via simple numerical \u0000examples that time-inconsistent retirement can exist in a three-period \u0000life-cycle model of consumption and saving.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132259970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-21DOI: 10.2470/rf.v2012.n3.full
Z. Bodie, Laurence B. Siegel, Lisa Stanton
The third conference on the future of life-cycle saving and investing, entitled “Financial Education and Consumer Financial Protection,” was held at the Boston University School of Management on 23–25 May 2011. Like the previous two conferences, it was organized by Professor Zvi Bodie of Boston University and financially supported by the Research Foundation of CFA Institute, the Federal Reserve Bank of Boston, and Boston University. Also as in the previous conferences, speakers from a wide variety of disciplines, not just finance, offered their perspectives.
{"title":"Life-Cycle Investing: Financial Education and Consumer Protection","authors":"Z. Bodie, Laurence B. Siegel, Lisa Stanton","doi":"10.2470/rf.v2012.n3.full","DOIUrl":"https://doi.org/10.2470/rf.v2012.n3.full","url":null,"abstract":"The third conference on the future of life-cycle saving and investing, entitled “Financial Education and Consumer Financial Protection,” was held at the Boston University School of Management on 23–25 May 2011. Like the previous two conferences, it was organized by Professor Zvi Bodie of Boston University and financially supported by the Research Foundation of CFA Institute, the Federal Reserve Bank of Boston, and Boston University. Also as in the previous conferences, speakers from a wide variety of disciplines, not just finance, offered their perspectives.","PeriodicalId":151802,"journal":{"name":"ERN: Life Cycle Models (Topic)","volume":"32 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116378383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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