Bond portfolio optimization michael puhle springer. In this paper, we apply markowitzs approach of portfolio selection to government bond portfolios. We show that this class of models can also simplify the process of bond portfolio optimization. When we plot the mean portfolio return, p, against the corresponding minimal portfolio volatility standard deviation we obtain the socalled portfolio frontier. Rolling portfolio optimization example i same as previous example, but update wevery quarter 60 periods 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 0. Head of investment analysis at the bank for international settlements in basel, switzerland. Bond immunization is an investment strategy used to minimize the interest rate risk of bond investments by adjusting the portfolio duration to match the investors investment time horizon. Fixed income has received far less attention than equity portfolio optimisation since markowitz original work of 1952, partly as a result of the. Optimization methods in finance gerard cornuejols reha tut unc u carnegie mellon university, pittsburgh, pa 152 usa. The multiasset portfolio properties of corporate bonds therefore depend crucially on the initial equitytreasury mix. Based on the estimates for the vector of expected returns on these bonds and their conditional covariance matrix, optimal meanvariance and minimum variance. Bond portfolio optimization lecture notes in economics and mathematical systems 2008th edition by michael puhle author visit amazons michael puhle page. Exercise 1 solve the meanvariance optimization problem 1.
However, much less is known about portfolio optimization in bond markets. Portfolio optimization modelling with r for enhancing. Managing bond portfolios relies on concepts such as duration, sensibility and convexity, while managing stock portfolios relies on optimization of expected utility. Active bond portfolio management interest rate swaps 1 interest rate sensitivity, duration, and convexity tbond price. Bond portfolio optimization in the presence of duration constraints romain deguest, frank fabozzi, lionel martellini, vincent milhau the journal of fixed income jun 2018, 28 1 626. Excel modeling and estimation in investments third edition. Within your corporate bonds, try to diversify the industries youre exposed to financial, health. Portfolio diversification 198 198 199 203 206 208 3. In this paper we use markowitzs approach to optimize bond portfolios. Pdf this paper describes a new method of bond portfolio optimization based on stochastic string models of correlation structure in bond returns. By periodically rebalancing, investors can diminish. Bond yield maturity rating a 4 3 a 2 b 3 4 aaa 1 the goal is to maximize total return subject to the following limits.
Managing bond portfolios relies on concepts such as duration, sensibility and convexity, while managing stock portfolios relies on optimization. Risk is the chance of exposure to adverse consequences of uncertain fu. Treasuries shows that the proposed portfolio policy outperforms a set of yield curve. Optimizing the allocation of bonds in a portfolio to maximize return. To illustrate the applicability of the proposed estimators of expected bond returns and conditional covariance matrix of bond returns defined in section 2. We derive closed form expressions for the vector of expected bond returns and for their. As a main feature of the analysis, the term structure models is used to estimate expected returns, return variances, and covariances of different bonds. In this paper, we apply markowitzs approach of portfolio selection to govern ment bond. He formulates an optimization problem that minimizes the variance of the loss. The book analyzes how modern portfolio theory and dynamic term structure models can be applied to government bond portfolio optimization problems. A verage price variation index 1r is defined as follows. Equity yield curves, time segmentation, and portfolio.
Bond portfolio optimization by michael puhle, available at book depository with free delivery worldwide. Additionally, in practice, portfolio managers do not usually form an optimal bond portfolio since there 3. The portfolio managers views about the future evolution of the term structure of interest rates translate th selves directly into a positioning relative to his benchmark, taking the risks of these deviations from the benchmark. A general class of dynamic factor models is used to obtain optimal bond portfolios, and to develop a durationconstrained meanvariance optimization, which can be used to improve bond indexing.
Managing credit spread risk in pension investment strategies when constructing a liabilityhedging portfolio for their pension plan, sponsors should consider the funding status risk posed by credit spread volatility in both plan assets and plan liabilities. There is a gap between the traditional approaches to manage bond portfolios and stock portfolios. Sep 05, 2019 dynamic bond portfolio optimization in continuous time 85 also propagate using modern portfolio theory for bond. With an indexing strategy, the portfolio manager attempts to replicate a bond index, such as the standard and poors 500 bond index. C is lower given same t t is larger given same c example text tables.
Two stages our model included an initial bond allocation, a rebalancing of the portfolio at the end of stage 1, and an evaluation of final portfolio value at the end of stage 2. Investor is able to minimize the cost of setting up bond portfolio to. The portfolio managers views about the future evolution of the term structure of interest rates translate th selves directly into. Due to the varied features of bonds, this is a more difficult objective to accomplish than replicating a stock market index. The use of duration and convexity to manage a fixed income portfolio, pension funds, and leveraged bank. He formulates an optimization problem that minimizes the variance of the loss distribution arising from credit risk with the constraints that the expected return of the portfolio not be below the. The multiasset portfolio properties of corporate bonds therefore.
Korn and koziol 2006 pioneered this literature by employing the vasicek 1977 model to perform a meanvariance bond portfolio. Risk measure is a key research component in portfolio optimization xu et al. We think individual bonds are a more efficient way to get exposure, he said. T 1 c yt f t, where y ytm when yields change, bond prices will change. Jun 05, 2018 a bond ladder buys multiple bonds of different durations. Equity yield curves, time segmentation, and portfolio optimization strategies by stephen j.
This theoretical approach for bond portfolio selection was first introduced by wilhelm 1992. Simulation approach to twostage bond portfolio optimization. In an application to sovereign bonds in the eurozone, we find that the use of portfolio optimization techniques based on robust estimators for risk parameters generates an improvement in investor welfare compared with the use of ad hoc bond benchmarks such as equally weighted or capweighted portfolios. An empirical application involving two large data sets of u. Request pdf on jun 11, 2018, romain deguest and others published bond portfolio optimization in the presence of duration constraints. Bond portfolios are nowadays mainly managed by a comparison of portfolio 3 4 risk measures vis a vis a benchmark. Bond portfolio optimization using dynamic factor models. A bond ladder buys multiple bonds of different durations. Robust portfolio optimization and management frank j. Chapter 1 introduction to portfolio theory updated. Stephen boyd ee103 stanford university december 8, 2017. As a main feature of our analysis, we use term structure models to estimate expected returns, return variances, and covariances of different bonds. Bond portfolio management 12 example 1 consider the value of a bond portfolio consisting of one 7year annual coupon bond.
Two pathways of modeling potential catastrophe bond losses are analyzed. Caldeira and others published bond portfolio optimization using dynamic factor models find, read and cite all the research you need on researchgate. Dynamic bond portfolio optimization in continuous time 85 also propagate using modern portfolio theory for bond. The author studies the necessary adjustments, examines the models with regard to the plausibility of their results and compares the outcomes to portfolio selection techniques used by practitioners. Fixed income portfolio management interest rate sensitivity. May 23, 2018 lionel martellini, director of edhecrisk institute discusses the key challenges involved in bond portfolio optimization and nathalie pistre, head of quantitative research, support and development. Bond portfolio optimization using dynamic factor models, journal of empirical finance, elsevier, vol.
A broad knowledge has been accumulated about the performance, the strengths, and the weaknesses of this approach when applied to equity portfolios. Bond portfolio optimization in the presence of duration. Try to build your bond portfolio with a diverse mix of maturities oneyear, fiveyear, 10year, 30year and bond types treasury, municipal, corporate, high yield. The author proposes a portfolio selection method to manage market risk and credit risk in a corporate bond portfolio relative to its benchmark. Bond portfolio optimization the journal of fixed income. Pdf by using a risk model to analyze a portfolio, managers gain insight into risk and exposures. The portfolio approach pioneered by markowitz is one of the cornerstones of modern portfolio management. Psf portfolio optimization conservative available through pacific life variable annuity products benchmark. Bond portfolio optimization in the presence of duration constraints. Lionel martellini, director of edhecrisk institute discusses the key challenges involved in bond portfolio optimization and nathalie pistre, head of quantitative research, support and development. In this article, the authors apply markowitzs approach of portfolio selection to government bond portfolios. Pdf fixedincome portfolio optimization researchgate. Bond portfolio optimization, according to the meanvariance framework. Excel modeling and estimation in investments third.
One basic use of the solver is to correctly divide a bond portfolio among bonds of different yield, maturity, and risk or in order to maximize yield or minimize risk. By periodically rebalancing, investors can diminish the tendency for portfolio drift, and thus potentially. Dynamic bond portfolio optimization in continuous time. Assistant professor of finance at university of mannheim in mannheim, germany. The authors empirical study for the german market shows that a small number of risky bonds is sufficient to reach very promising. Bond portfolio optimization lecture notes in economics. Our empirical study for the german market shows that a small number of risky bonds is sufficient to reach very promising predicted risk. Existing literature shows few references suggesting the use of a meanvariance approach to bond portfolio selection. Edhecrisk ostrum bond portfolio optimization youtube. As one bond matures, you reinvest the principal in a new bond. Inori this is an increasing function of tj, so that larger risk is associated with a bond with longer maturity. Feb 27, 2015 the use of duration and convexity to manage a fixed income portfolio, pension funds, and leveraged bank. A variety of bond portfolio optimization problems of institutional investors are formulated as linear andor bilinear fractional programming problems and algorithms to solve this class of problems are discussed. Full professor of corporate finance at whuotto beisheim school of management in vallendar, germany.
We show why and how the markowitz model has to be adapted in order to be useful for the selection of bond portfolios. Consider the case of y 10% scenario i, and also consider an. Fixed income has received far less attention than equity portfolio optimisation since markowitz original work of 1952, partly as a result of the need. Lecture notes in economics and mathematical systems, 605. Investor is able to minimize the cost of setting up bond portfolio to cover random obligations with our model. This chapter describes static bond portfolio optimization based on the meanvariance framework of markowitz 1952. First, we consider bond portfolio optimization problem under stochastic optimization structure.
Bond portfolio optimization lecture notes in economics and. A factor allocation approach to optimal bond portfolio, cirje fseries cirjef494, cirje, faculty of economics, university of tokyo. This chapter introduces modern portfolio theory in a simpli. Finmod 11 fixed income banking portfolio optimization. Managing credit risk in a corporate bond portfolio the. Analysis and optimization of a portfolio of catastrophe bonds. As with mutual funds, overlap can occur with buying individual bond securities.
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