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題名 因子投資與固定指數連動年金設計
Factor investing and the design of fixed index annuity
作者 陳可為
貢獻者 謝明華
陳可為
關鍵詞 因子投資
固定指數連動型年金
年金
日期 2017
上傳時間 10-Aug-2017 09:48:56 (UTC+8)
摘要 近年來，隨著學者提出除了市場投資組合以外，影響證券資產變動的因子後，因子投資的概念與理論慢慢被奠定，不僅如此，相關的應用也在業界中發酵。年金商品為其中之一，固定指數連動年金商品，在2010年首次將因子投資的策略放入指數編制中，發行眾多的Smart Beta指數供連結，其主要以波動控制、超額報酬與多資產策略的方式，以增加商品的吸引力。然而，過去皆以歷史回測的方式比較指數連結帳戶與固定利率帳戶的年化報酬，以判斷何種方式較優，較無其他比較基準，甚至忽略了下方風險(downside risk)風險值。因此，本文提出兩種評估該商品的指標，一為期望超額報酬，二則是年化平均報酬小於固定利率的機率 ()，並透過蒙地卡羅方法抽樣計算該值。其結果顯示有些Smart Beta指數優於S&P500。本文更近一步延伸這兩種指標，提出有別於其他商品的商品設計，即最適化權重連結帳戶。其概念為商品提供保戶能以任意權重的方式連結帳戶，保戶能夠在給定一定期望超額報酬水平下，極小化所得的權重。結果顯示最適化權重能優化商品設計，讓保戶在獲得與連結單一指數同樣的期望報酬下，可降低 高達95%所承擔的風險。
For the past few years, as many academic have found that in addition to market portfolio, there’re other factors which determine the changes in assets prices, the concept of factor investing has been established gradually and the related application has been widely used in the industries. Fixed index annuity is one of them. In 2010, the first smart beta index which is the strategy of factor investing was launched and provided for consumers to credit. From then on, there are about 40 kinds of smart beta indices. To make products more attractive, main concerns of FIA’s indices are volatility control, excess return and multi-asset strategy. However, most only adopted historical annualized returns to compare between fixed credit method and index credit method in the past, and even ignored the downside risk of products. We propose two innovative way to assess. The First one is the expected returns exceeding fixed rate, and the second is the probability of return below fixed rate, called p-downside. We calculated both of them by Monte Carol methods. The results show that some smart beta indices are better than S&P500. Additionally, we also propose new design of FIA, optimization linking weight. The idea is to optimize the best linking weight to minimize the downside risk. In our simulation, it can reduce almost 95% downside risk, benefit the insured and improve the products.
參考文獻 中文部分
王儷玲. (2000). 退休財務規劃與年金保險. 退休基金季刊, 1(2), 9-28.
英文部分
Alexander, C. (2000a). Orthogonal methods for generating large positive semi-definite covariance matrices.
Alexander, C. (2000b). A primer on the orthogonal GARCH model. manuscript ISMA Centre, University of Reading, UK, 2.
Alexander, C. (2002). Principal component models for generating large GARCH covariance matrices. Economic Notes, 31(2), 337-359.
Allianz. (2011). Understanding crediting methods. Minneapolis: Allianz Life Insurance Company of North America.
Ang, A. (2014). Asset management: A systematic approach to factor investing: Oxford University Press.
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The cross‐section of volatility and expected returns. The journal of finance, 61(1), 259-299.
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2009). High idiosyncratic volatility and low returns: International and further US evidence. Journal of financial economics, 91(1), 1-23.
Asness, C. S., Frazzini, A., & Pedersen, L. H. (2014). Quality minus junk.
Averting the old age crisis: Policies to protect the old and promote growth. (1994). A World Bank Policy Research Report.
Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as limits to arbitrage: Understanding the low-volatility anomaly. Financial Analysts Journal, 67(1), 40-54.
Bali, T. G., & Cakici, N. (2008). Idiosyncratic volatility and the cross section of expected returns. Journal of Financial and Quantitative Analysis, 43(01), 29-58.
Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of financial economics, 9(1), 3-18.
Basu, S. (1977). Investment performance of common stocks in relation to their price‐earnings ratios: A test of the efficient market hypothesis. The journal of finance, 32(3), 663-682.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
BlackRock. (2016). The Rise of Factor Investing.
Blitz, D. C., & Van Vliet, P. (2007). The volatility effect. The Journal of Portfolio Management, 34(1), 102-113.
Breeden, D. T. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of financial economics, 7(3), 265-296.
Chen, N.-F., Roll, R., & Ross, S. A. (1986). Economic forces and the stock market. Journal of business, 383-403.
Chiu, Y.-F., Hsieh, M.-H., Tsai, C.-H., & Chen, W.-K. (2011). Valuation of Ratchet Equity-Indexed Annuities. Journal of Financial Studies, 20(4), 89.
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological methods, 4(3), 272.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), 3-56.
Garcia-Feijóo, L., Kochard, L., Sullivan, R. N., & Wang, P. (2015). Low-Volatility Cycles: The Influence of Valuation and Momentum on Low-Volatility Portfolios. Financial Analysts Journal, 71(3), 47-60.
Gerber, H. U., & Shiu, E. S. (2003). Pricing lookback options and dynamic guarantees. North American Actuarial Journal, 7(1), 48-66.
Glasserman, P. (2013). Monte Carlo methods in financial engineering (Vol. 53): Springer Science & Business Media.
Golub, B. W., & Tilman, L. M. (2000). Risk management: approaches for fixed income markets (Vol. 73): John Wiley & Sons.
Hardy, M. (2003). Investment guarantees: modeling and risk management for equity-linked life insurance (Vol. 215): John Wiley & Sons.
Hardy, M. (2004). Ratchet equity indexed annuities. Paper presented at the 14th Annual International AFIR Colloquium.
Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of economic theory, 20(3), 381-408.
Harrison, J. M., & Pliska, S. R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic processes and their applications, 11(3), 215-260.
Hsieh, M.-h., & Chiu, Y.-f. (2007). Monte carlo methods for valuation of ratchet equity indexed annuities. Paper presented at the Simulation Conference, 2007 Winter.
Hsieh, M.-h., Kuo, W., Li, Y.-c., & Tsai, C. (2014). Generating Economics Scenarios for the Long-Term Solvency Assessment of Life Insurance Companies: The Orthogonal ARMA-GARCH Method.
Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The journal of finance, 48(1), 65-91.
Jegadeesh, N., & Titman, S. (2001). Profitability of momentum strategies: An evaluation of alternative explanations. The journal of finance, 56(2), 699-720.
Johnson, R., & Wichern, D. (2007). Applied multivariate correspondence analysis: Prentice-Hall, Upper Saddle River, NJ, USA.
Johnson, R. A., & Wichern, D. W. (2014). Applied multivariate statistical analysis (Vol. 4): Prentice-Hall New Jersey.
Lee, H. (2003). Pricing equity-indexed annuities with path-dependent options. Insurance: Mathematics and Economics, 33(3), 677-690.
Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The review of economics and statistics, 13-37.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
Marrion, J. (2006). Variable annuity & index annuity market growth parallels. Retrieved from Mcknney, TX:
Marrion, J. (2016). Fixed Index Annuity Vol-Controlled Indices. Retrieved from McKinney, TX:
Marrion, J. (2017). Fixed Index Annuity Volatility Controlled Indices. Retrieved from McKinney, TX:
Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica: Journal of the econometric society, 867-887.
Mitchell, G., & Slater Jr, J. (1996). Equity-Indexed Annuities: New Territory on the Efficient Frontier. Society of Actuaries Study Note Number, 441, 99-96.
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica: Journal of the econometric society, 768-783.
Peterson, D. R., & Smedema, A. R. (2011). The return impact of realized and expected idiosyncratic volatility. Journal of Banking & Finance, 35(10), 2547-2558.
Reinganum, M. R. (1981). Misspecification of capital asset pricing: Empirical anomalies based on earnings` yields and market values. Journal of financial economics, 9(1), 19-46.
Rejda, G. E. (2011). Principles of risk management and insurance: Pearson Education India.
Roll, R. (1977). A critique of the asset pricing theory`s tests Part I: On past and potential testability of the theory. Journal of financial economics, 4(2), 129-176.
Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of economic theory, 13(3), 341-360.
Roy, A. D. (1952). Safety first and the holding of assets. Econometrica: Journal of the econometric society, 431-449.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The journal of finance, 19(3), 425-442.
Sheldon Lin, X., & Tan, K. S. (2003). Valuation of equity-indexed annuities under stochastic interest rates. North American Actuarial Journal, 7(4), 72-91.
Srivastava, V. (2015). Evolution of indexing in fixed index annuities. Retrieved from Chicago, IL:
Tiong, S. (2000). Valuing equity-indexed annuities. North American Actuarial Journal, 4(4), 149-163.
Treynor, J. L. (1961). Toward a theory of market value of risky assets. Unpublished manuscript, 6.
Tsay, R. S. (2005). Analysis of financial time series (Vol. 543): John Wiley & Sons.
描述 碩士
國立政治大學
風險管理與保險學系
104358029
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0104358029
資料類型 thesis
dc.contributor.advisor 謝明華zh_TW
dc.contributor.author (Authors) 陳可為zh_TW
dc.creator (作者) 陳可為zh_TW
dc.date (日期) 2017en_US
dc.date.accessioned 10-Aug-2017 09:48:56 (UTC+8)-
dc.date.available 10-Aug-2017 09:48:56 (UTC+8)-
dc.date.issued (上傳時間) 10-Aug-2017 09:48:56 (UTC+8)-
dc.identifier (Other Identifiers) G0104358029en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/111752-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險學系zh_TW
dc.description (描述) 104358029zh_TW
dc.description.abstract (摘要) 近年來，隨著學者提出除了市場投資組合以外，影響證券資產變動的因子後，因子投資的概念與理論慢慢被奠定，不僅如此，相關的應用也在業界中發酵。年金商品為其中之一，固定指數連動年金商品，在2010年首次將因子投資的策略放入指數編制中，發行眾多的Smart Beta指數供連結，其主要以波動控制、超額報酬與多資產策略的方式，以增加商品的吸引力。然而，過去皆以歷史回測的方式比較指數連結帳戶與固定利率帳戶的年化報酬，以判斷何種方式較優，較無其他比較基準，甚至忽略了下方風險(downside risk)風險值。因此，本文提出兩種評估該商品的指標，一為期望超額報酬，二則是年化平均報酬小於固定利率的機率 ()，並透過蒙地卡羅方法抽樣計算該值。其結果顯示有些Smart Beta指數優於S&P500。本文更近一步延伸這兩種指標，提出有別於其他商品的商品設計，即最適化權重連結帳戶。其概念為商品提供保戶能以任意權重的方式連結帳戶，保戶能夠在給定一定期望超額報酬水平下，極小化所得的權重。結果顯示最適化權重能優化商品設計，讓保戶在獲得與連結單一指數同樣的期望報酬下，可降低 高達95%所承擔的風險。zh_TW
dc.description.abstract (摘要) For the past few years, as many academic have found that in addition to market portfolio, there’re other factors which determine the changes in assets prices, the concept of factor investing has been established gradually and the related application has been widely used in the industries. Fixed index annuity is one of them. In 2010, the first smart beta index which is the strategy of factor investing was launched and provided for consumers to credit. From then on, there are about 40 kinds of smart beta indices. To make products more attractive, main concerns of FIA’s indices are volatility control, excess return and multi-asset strategy. However, most only adopted historical annualized returns to compare between fixed credit method and index credit method in the past, and even ignored the downside risk of products. We propose two innovative way to assess. The First one is the expected returns exceeding fixed rate, and the second is the probability of return below fixed rate, called p-downside. We calculated both of them by Monte Carol methods. The results show that some smart beta indices are better than S&P500. Additionally, we also propose new design of FIA, optimization linking weight. The idea is to optimize the best linking weight to minimize the downside risk. In our simulation, it can reduce almost 95% downside risk, benefit the insured and improve the products.en_US
dc.description.tableofcontents 第一章 緒論 1
第一節 研究動機與背景 1
第二節 研究目的 3
第三節 研究架構 4
第二章 文獻探討 6
第一節 因子投資與Smart Beta指數 6
第二節 個人年金保險介紹 9
第三章 固定指數連動年金商品與Smart Beta 指數 15
第一節 商品介紹 15
第二節 評價與避險策略 25
第三節 Smart Beta 指數 31
第四節 商品評估 35
第四章 模型設定 37
第一節 最適化權重商品設計 37
第二節 證券資產動態過程 39
第三節 蒙地卡羅方法 46
第五章 數值例子 49
第一節 資料敘述與參數估計 49
第二節 模擬假設 56
第三節 數值結果 58
第六章 結論與建議 68
參考文獻 71		zh_TW
dc.format.extent 3300885 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0104358029en_US
dc.subject (關鍵詞) 因子投資zh_TW
dc.subject (關鍵詞) 固定指數連動型年金zh_TW
dc.subject (關鍵詞) 年金zh_TW
dc.title (題名) 因子投資與固定指數連動年金設計zh_TW
dc.title (題名) Factor investing and the design of fixed index annuityen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 中文部分
王儷玲. (2000). 退休財務規劃與年金保險. 退休基金季刊, 1(2), 9-28.
英文部分
Alexander, C. (2000a). Orthogonal methods for generating large positive semi-definite covariance matrices.
Alexander, C. (2000b). A primer on the orthogonal GARCH model. manuscript ISMA Centre, University of Reading, UK, 2.
Alexander, C. (2002). Principal component models for generating large GARCH covariance matrices. Economic Notes, 31(2), 337-359.
Allianz. (2011). Understanding crediting methods. Minneapolis: Allianz Life Insurance Company of North America.
Ang, A. (2014). Asset management: A systematic approach to factor investing: Oxford University Press.
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The cross‐section of volatility and expected returns. The journal of finance, 61(1), 259-299.
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2009). High idiosyncratic volatility and low returns: International and further US evidence. Journal of financial economics, 91(1), 1-23.
Asness, C. S., Frazzini, A., & Pedersen, L. H. (2014). Quality minus junk.
Averting the old age crisis: Policies to protect the old and promote growth. (1994). A World Bank Policy Research Report.
Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as limits to arbitrage: Understanding the low-volatility anomaly. Financial Analysts Journal, 67(1), 40-54.
Bali, T. G., & Cakici, N. (2008). Idiosyncratic volatility and the cross section of expected returns. Journal of Financial and Quantitative Analysis, 43(01), 29-58.
Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of financial economics, 9(1), 3-18.
Basu, S. (1977). Investment performance of common stocks in relation to their price‐earnings ratios: A test of the efficient market hypothesis. The journal of finance, 32(3), 663-682.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
BlackRock. (2016). The Rise of Factor Investing.
Blitz, D. C., & Van Vliet, P. (2007). The volatility effect. The Journal of Portfolio Management, 34(1), 102-113.
Breeden, D. T. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of financial economics, 7(3), 265-296.
Chen, N.-F., Roll, R., & Ross, S. A. (1986). Economic forces and the stock market. Journal of business, 383-403.
Chiu, Y.-F., Hsieh, M.-H., Tsai, C.-H., & Chen, W.-K. (2011). Valuation of Ratchet Equity-Indexed Annuities. Journal of Financial Studies, 20(4), 89.
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological methods, 4(3), 272.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), 3-56.
Garcia-Feijóo, L., Kochard, L., Sullivan, R. N., & Wang, P. (2015). Low-Volatility Cycles: The Influence of Valuation and Momentum on Low-Volatility Portfolios. Financial Analysts Journal, 71(3), 47-60.
Gerber, H. U., & Shiu, E. S. (2003). Pricing lookback options and dynamic guarantees. North American Actuarial Journal, 7(1), 48-66.
Glasserman, P. (2013). Monte Carlo methods in financial engineering (Vol. 53): Springer Science & Business Media.
Golub, B. W., & Tilman, L. M. (2000). Risk management: approaches for fixed income markets (Vol. 73): John Wiley & Sons.
Hardy, M. (2003). Investment guarantees: modeling and risk management for equity-linked life insurance (Vol. 215): John Wiley & Sons.
Hardy, M. (2004). Ratchet equity indexed annuities. Paper presented at the 14th Annual International AFIR Colloquium.
Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of economic theory, 20(3), 381-408.
Harrison, J. M., & Pliska, S. R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic processes and their applications, 11(3), 215-260.
Hsieh, M.-h., & Chiu, Y.-f. (2007). Monte carlo methods for valuation of ratchet equity indexed annuities. Paper presented at the Simulation Conference, 2007 Winter.
Hsieh, M.-h., Kuo, W., Li, Y.-c., & Tsai, C. (2014). Generating Economics Scenarios for the Long-Term Solvency Assessment of Life Insurance Companies: The Orthogonal ARMA-GARCH Method.
Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The journal of finance, 48(1), 65-91.
Jegadeesh, N., & Titman, S. (2001). Profitability of momentum strategies: An evaluation of alternative explanations. The journal of finance, 56(2), 699-720.
Johnson, R., & Wichern, D. (2007). Applied multivariate correspondence analysis: Prentice-Hall, Upper Saddle River, NJ, USA.
Johnson, R. A., & Wichern, D. W. (2014). Applied multivariate statistical analysis (Vol. 4): Prentice-Hall New Jersey.
Lee, H. (2003). Pricing equity-indexed annuities with path-dependent options. Insurance: Mathematics and Economics, 33(3), 677-690.
Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The review of economics and statistics, 13-37.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
Marrion, J. (2006). Variable annuity & index annuity market growth parallels. Retrieved from Mcknney, TX:
Marrion, J. (2016). Fixed Index Annuity Vol-Controlled Indices. Retrieved from McKinney, TX:
Marrion, J. (2017). Fixed Index Annuity Volatility Controlled Indices. Retrieved from McKinney, TX:
Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica: Journal of the econometric society, 867-887.
Mitchell, G., & Slater Jr, J. (1996). Equity-Indexed Annuities: New Territory on the Efficient Frontier. Society of Actuaries Study Note Number, 441, 99-96.
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica: Journal of the econometric society, 768-783.
Peterson, D. R., & Smedema, A. R. (2011). The return impact of realized and expected idiosyncratic volatility. Journal of Banking & Finance, 35(10), 2547-2558.
Reinganum, M. R. (1981). Misspecification of capital asset pricing: Empirical anomalies based on earnings` yields and market values. Journal of financial economics, 9(1), 19-46.
Rejda, G. E. (2011). Principles of risk management and insurance: Pearson Education India.
Roll, R. (1977). A critique of the asset pricing theory`s tests Part I: On past and potential testability of the theory. Journal of financial economics, 4(2), 129-176.
Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of economic theory, 13(3), 341-360.
Roy, A. D. (1952). Safety first and the holding of assets. Econometrica: Journal of the econometric society, 431-449.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The journal of finance, 19(3), 425-442.
Sheldon Lin, X., & Tan, K. S. (2003). Valuation of equity-indexed annuities under stochastic interest rates. North American Actuarial Journal, 7(4), 72-91.
Srivastava, V. (2015). Evolution of indexing in fixed index annuities. Retrieved from Chicago, IL:
Tiong, S. (2000). Valuing equity-indexed annuities. North American Actuarial Journal, 4(4), 149-163.
Treynor, J. L. (1961). Toward a theory of market value of risky assets. Unpublished manuscript, 6.
Tsay, R. S. (2005). Analysis of financial time series (Vol. 543): John Wiley & Sons.		zh_TW