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題名 不同風險偏好下多期投資策略之研究
Dynamic asset allocation for long-term investors diverse risk preference
作者 林佳華
Lin, Chia-Hua
貢獻者 張士傑
Chang, Bill
林佳華
Lin, Chia-Hua
關鍵詞 利率風險
共同基金理論
風險中立
interest rate risk
mutual fund
martingale
Markovian processes
exchange rate risk
日期 2003
上傳時間 18-Sep-2009 19:24:08 (UTC+8)
摘要 對一些退休基金或是壽險基金來說,因為它們的金額都相當龐大,進而影響的層面也相當廣泛;它們影響著金融市場的發展、有價證券的價格和市場的報酬。
所以,對現今市場投資在這樣長期資產的投資策略而言,以下我們要討論的議題將是非常重要。
以前的退休基金管理計畫是建立在單期的假設當中。根據目前所持有所有資產的部位、目前市場的狀況與對未來報酬的期望,基金管理人將尋求對下期的最適投資決策。傳統的方法都是用期望值-變異數方式(Mean-Variance approach)去極大化投資的報酬,以求取最適部位。但是單期的期望值-變異數方式(Mean-Variance approach)面對了二個問題:
一、 集合各個單期最適決策用多期的眼光來看不一定是最適。
二、 單期最適決策並不能同時處理投資面與集資面的問題。例如:退休基金同時間有每月的收入與每月的投資面。
不像單期的投資方式,使用多期的投資方法比較能符合這樣的投資問題與要求,也比較具有合理性。
投資在長期資產的部位與報酬率,最容易受到利率變動的影響。換句話說,利率變化是影響投資在長期性資產的最大變因。因此,我們將討論的問題:在利率是隨機變動時,以Vasicek (1977)的利率模型為主,加入投資人風險偏好的共同基金的分配原則。這樣的理論下,我們將利用風險中立的方法求出最適的投資組合,以滿足在長期投資觀點下避險與套利的需求。其中投資人的風險偏好是以Merton (1973)提出的常數相關風險偏好(Constant Relative Risk Aversion;CRRA)的效用函數去討論;在文章最後,我們將針對投資人的風險偏好做一些討論,包括:改變CRRA的參數、自然對數的效用函數(Logarithmic utility function)。
以往的研究都採用動態程式設計(Dynamic programming approach)的方法來解決這樣多期投資的問題,但是這樣的方法運用的計算相當複雜,也不一定求的出最適部位解;而利用Cox and Huang (1989)提出的風險中立方法(Martingale approach)將完全的解決以上遇到的問題。
In this study, we investigate the dynamic mutual fund separation theorem applied to portfolio management for constant relative risk averse investors where, in particular, the interest rate risks are incorporated. Within this economy, the real interest rates and stock prices are assumed to follow the Markovian processes whose drifts and diffusion parameters are driven by certain state variables. Our approach involves the use of the martingale methodology developed by Cox and Huang (1989) as proposed in the work of Deelstra et al. (2003). Following their framework, we consider the economy of the investors that consists of cash, bond fund and stock indices. Adding to the previous works, we investigate the obtained optimal strategies through numerical examples in order to be compared to the allocations of popular advice and clarify the hedge and arbitrage demands in financial decision from long-term perspective. Finally, certain mutual funds are constructed to validate the validity of the popular advice.
參考文獻 Bajeux-Besnainou, 2003. Dynamic asset allocation for stocks, bonds, and cash. Journal of Business 76, 263-287.
Barberis, N., 2000. Investing for the long run when returns are predictable. Journal of Finance 55, 225-264.
Breeden, D., 1979. An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7, 265—296.
Chang, S. C. and H. Y. Cheng. 2002. Pension valuation under uncertainty: implementation of a stochastic and dynamic monitoring system, Journal of Risk and Insurance, 69, 171-92.
Cox, J. and Huang, C. F., 1989. Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory 49, 33-83.
Cox, J. and Huang, C. F., 1991. A variational problem arising in financial economics. Journal of Mathematical Economics 20, 465-487.
Devolder, P., Princep, M. B., Fabian, I. D., 2003. Stochastic optimal control of annuity contracts, Insurance: Mathematics and Economics 33, 227-238.
Deelstra, G., Grasselli, M. and Koehl, P. F., 2000. Optimal investment strategies in a CIR framework. Journal of Applied Probability 37, 936-946.
Duffie, J. D. and Huang, C. F., 1985. Implementing Arrow-Debreu equilibria by continuous trading of few long-lived ecurities, Econometrica, 53, 1337-1356.
El Karoui, N. and Huang, S. J., 2001. A dynamic maximum principle for the optimization of recursive utilities under constraints. Annual of Applied Probability 11,
664—693.
Karatzas, I., 1989. Optimization problems in the theory of continuous trading. Journal of Control and Optimization 27, 1221-1259.
Karatzas, I. and Shreve, S., 1991. Brownian Motion and Stochastic Calculus, Seconded. Springer-Verlag, Berlin. Long, J.B., 1990. The numeraire portfolio. Journal of Financial Economics 26, 29—69.
Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time case. Journal of Economy Theory 3, 373-413.
Merton, R. C., 1969. Lifetime portfolio selection under uncertainty: The continuoustime case. Review of Economics and Statistics 51, 247—257.
Markowitz, H., 1959, Portfolio Selection: Efficient Diversification of Investment, John Wiley, New York.
Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373—413.
Merton, R. C., 1973. An intertemporal capital asset pricing model. Econometrica 41, 867—887.
Pliska, S., 1986. A stochastic calculus model of continuous trading: optimal portfolios. Mathematics of Operations Research 11, 371—382.
描述 碩士
國立政治大學
風險管理與保險研究所
91358020
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091358020
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.advisor Chang, Billen_US
dc.contributor.author (Authors) 林佳華zh_TW
dc.contributor.author (Authors) Lin, Chia-Huaen_US
dc.creator (作者) 林佳華zh_TW
dc.creator (作者) Lin, Chia-Huaen_US
dc.date (日期) 2003en_US
dc.date.accessioned 18-Sep-2009 19:24:08 (UTC+8)-
dc.date.available 18-Sep-2009 19:24:08 (UTC+8)-
dc.date.issued (上傳時間) 18-Sep-2009 19:24:08 (UTC+8)-
dc.identifier (Other Identifiers) G0091358020en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/36733-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 91358020zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 對一些退休基金或是壽險基金來說,因為它們的金額都相當龐大,進而影響的層面也相當廣泛;它們影響著金融市場的發展、有價證券的價格和市場的報酬。
所以,對現今市場投資在這樣長期資產的投資策略而言,以下我們要討論的議題將是非常重要。
以前的退休基金管理計畫是建立在單期的假設當中。根據目前所持有所有資產的部位、目前市場的狀況與對未來報酬的期望,基金管理人將尋求對下期的最適投資決策。傳統的方法都是用期望值-變異數方式(Mean-Variance approach)去極大化投資的報酬,以求取最適部位。但是單期的期望值-變異數方式(Mean-Variance approach)面對了二個問題:
一、 集合各個單期最適決策用多期的眼光來看不一定是最適。
二、 單期最適決策並不能同時處理投資面與集資面的問題。例如:退休基金同時間有每月的收入與每月的投資面。
不像單期的投資方式,使用多期的投資方法比較能符合這樣的投資問題與要求,也比較具有合理性。
投資在長期資產的部位與報酬率,最容易受到利率變動的影響。換句話說,利率變化是影響投資在長期性資產的最大變因。因此,我們將討論的問題:在利率是隨機變動時,以Vasicek (1977)的利率模型為主,加入投資人風險偏好的共同基金的分配原則。這樣的理論下,我們將利用風險中立的方法求出最適的投資組合,以滿足在長期投資觀點下避險與套利的需求。其中投資人的風險偏好是以Merton (1973)提出的常數相關風險偏好(Constant Relative Risk Aversion;CRRA)的效用函數去討論;在文章最後,我們將針對投資人的風險偏好做一些討論,包括:改變CRRA的參數、自然對數的效用函數(Logarithmic utility function)。
以往的研究都採用動態程式設計(Dynamic programming approach)的方法來解決這樣多期投資的問題,但是這樣的方法運用的計算相當複雜,也不一定求的出最適部位解;而利用Cox and Huang (1989)提出的風險中立方法(Martingale approach)將完全的解決以上遇到的問題。
zh_TW
dc.description.abstract (摘要) In this study, we investigate the dynamic mutual fund separation theorem applied to portfolio management for constant relative risk averse investors where, in particular, the interest rate risks are incorporated. Within this economy, the real interest rates and stock prices are assumed to follow the Markovian processes whose drifts and diffusion parameters are driven by certain state variables. Our approach involves the use of the martingale methodology developed by Cox and Huang (1989) as proposed in the work of Deelstra et al. (2003). Following their framework, we consider the economy of the investors that consists of cash, bond fund and stock indices. Adding to the previous works, we investigate the obtained optimal strategies through numerical examples in order to be compared to the allocations of popular advice and clarify the hedge and arbitrage demands in financial decision from long-term perspective. Finally, certain mutual funds are constructed to validate the validity of the popular advice.en_US
dc.description.tableofcontents 1 Introduction 1
1.1 Multiperiod financial planning 2
1.2 Bond and stock holding 3
1.3 Literature Reviews 5
2 Financial framework 6
2.1 The growth-optimum portfolio 9
2.2 The Optimization Program 9
3 The solution with CRRA utility function 11
4 Numerical analysis 15
5 Conclusion and remarks 25
Reference
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091358020en_US
dc.subject (關鍵詞) 利率風險zh_TW
dc.subject (關鍵詞) 共同基金理論zh_TW
dc.subject (關鍵詞) 風險中立zh_TW
dc.subject (關鍵詞) interest rate risken_US
dc.subject (關鍵詞) mutual funden_US
dc.subject (關鍵詞) martingaleen_US
dc.subject (關鍵詞) Markovian processesen_US
dc.subject (關鍵詞) exchange rate risken_US
dc.title (題名) 不同風險偏好下多期投資策略之研究zh_TW
dc.title (題名) Dynamic asset allocation for long-term investors diverse risk preferenceen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Bajeux-Besnainou, 2003. Dynamic asset allocation for stocks, bonds, and cash. Journal of Business 76, 263-287.zh_TW
dc.relation.reference (參考文獻) Barberis, N., 2000. Investing for the long run when returns are predictable. Journal of Finance 55, 225-264.zh_TW
dc.relation.reference (參考文獻) Breeden, D., 1979. An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7, 265—296.zh_TW
dc.relation.reference (參考文獻) Chang, S. C. and H. Y. Cheng. 2002. Pension valuation under uncertainty: implementation of a stochastic and dynamic monitoring system, Journal of Risk and Insurance, 69, 171-92.zh_TW
dc.relation.reference (參考文獻) Cox, J. and Huang, C. F., 1989. Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory 49, 33-83.zh_TW
dc.relation.reference (參考文獻) Cox, J. and Huang, C. F., 1991. A variational problem arising in financial economics. Journal of Mathematical Economics 20, 465-487.zh_TW
dc.relation.reference (參考文獻) Devolder, P., Princep, M. B., Fabian, I. D., 2003. Stochastic optimal control of annuity contracts, Insurance: Mathematics and Economics 33, 227-238.zh_TW
dc.relation.reference (參考文獻) Deelstra, G., Grasselli, M. and Koehl, P. F., 2000. Optimal investment strategies in a CIR framework. Journal of Applied Probability 37, 936-946.zh_TW
dc.relation.reference (參考文獻) Duffie, J. D. and Huang, C. F., 1985. Implementing Arrow-Debreu equilibria by continuous trading of few long-lived ecurities, Econometrica, 53, 1337-1356.zh_TW
dc.relation.reference (參考文獻) El Karoui, N. and Huang, S. J., 2001. A dynamic maximum principle for the optimization of recursive utilities under constraints. Annual of Applied Probability 11,zh_TW
dc.relation.reference (參考文獻) 664—693.zh_TW
dc.relation.reference (參考文獻) Karatzas, I., 1989. Optimization problems in the theory of continuous trading. Journal of Control and Optimization 27, 1221-1259.zh_TW
dc.relation.reference (參考文獻) Karatzas, I. and Shreve, S., 1991. Brownian Motion and Stochastic Calculus, Seconded. Springer-Verlag, Berlin. Long, J.B., 1990. The numeraire portfolio. Journal of Financial Economics 26, 29—69.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time case. Journal of Economy Theory 3, 373-413.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1969. Lifetime portfolio selection under uncertainty: The continuoustime case. Review of Economics and Statistics 51, 247—257.zh_TW
dc.relation.reference (參考文獻) Markowitz, H., 1959, Portfolio Selection: Efficient Diversification of Investment, John Wiley, New York.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373—413.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1973. An intertemporal capital asset pricing model. Econometrica 41, 867—887.zh_TW
dc.relation.reference (參考文獻) Pliska, S., 1986. A stochastic calculus model of continuous trading: optimal portfolios. Mathematics of Operations Research 11, 371—382.zh_TW