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Optimal trading strategies and risk in the government bond market : two essays in financial economics Koster, Hendrik Aaldrik Jan


The two main questions arising from the problem of optimal bond portfolio management concern the formulation of an optimal trading rule and the specification of an appropriate dynamic risk measure in which to express portfolio objectives. We study these questions in two related essays: (l) a theoretical study of optimal trading policies in view of, as yet unspecified, portfolio objectives when trading is costly; and (2) an empirical, comparative study of several bond risk measures, proposed in the literature or in use by practitioners, for the government or default-free bond market. The theoretical study considers a delegated portfolio management setting, in which the manager optimizes a cumulative reward over a finite time period and where the reward rate increases with portfolio value and decreases with deviations from the given risk objectives. Trading is then often not worthwhile, as the possible gains from smaller objective deviations are offset by losses on account of transactions costs. This setting obviates the need for separate ex post performance evaluation. The trading problem is formulated as one of optimal impulse control in the framework of stochastic dynamic programming; this formulation improves upon prior results in the literature using continuous control theory. A myopic optimal trading rule is characterized, which is also applicable to time-homogeneous problems and more general preferences. An algorithm for its use in applications is derived. The empirical study applies the usual methods of stock market tests to the returns of constant risk bond portfolios. These portfolios are artificial constructs composed, at varying risk levels, of traded bonds on the basis of six different one or two dimensional risk measures. These risk measures are selected in order to obtain a cross-section of term structure variabilities; they include duration, short interest rate risk, long (13-year) interest rate risk, combined short and consol rate risks, duration combined with convexity, and average time-to-maturity. The sample period is the 1970s decade, for which parameter estimates for the risk measures— where necessary—are available from source papers. This period is known to be one with wide-ranging term structure movements and is therefore ideally suited for the tests of this paper. Portfolios are formed at two levels of diversification: bullet and ladder selection. We confirm that all of these risk measures are reasonably effective in capturing relevant bond market risk: the state space of bond returns has in all cases a low dimension (two or three), with only a single factor significantly priced. Best fit is found for portfolios selected by duration, the 13-year spot yield risk, and the two-dimensional short/consol rate risk, all of which consist predominantly of "long" rate risk. The short rate-based risk measure does not explain portfolio returns as well: it has difficulty discriminating between portfolios with long remaining times-to-maturity. Convexity, furthermore, adds nothing to the explanatory power of duration. Average time-to-maturity compares reasonably well with the above risk measures, provided the portfolios are well-diversified across the maturity spectrum; this lends some support to the use of yield curves. A strong diversification effect has also been found, to the extent that the returns on ladder portfolios are practically linear combinations of two or three of the portfolios, typically the lowest and highest risk portfolios in the one dimensional risk cases, with an intermediate portfolio added in the two-dimensional cases. Provided that diversified portfolios are used, the comparatively easy to implement duration measure is as good as any of the risk measures tested.

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