Optimal Decentralized Investment Management

We study a decentralized investment problem in which a CIO employs multiple asset managers to implement and execute investment strategies in separate asset classes. The CIO allocates capital to the managers who, in turn, allocate these funds to the assets in their asset class. This two-step investment process causes several misalignments of objectives between the CIO and his managers and can lead to large utility costs on the part of the CIO. We focus on i) loss of diversification ii) different appetites for risk, iii) different investment horizons, and iv) the presence of liabilities. We derive an optimal unconditional linear performance benchmark and show that this benchmark can be used to better align incentives within the firm. The optimal benchmark substantially mitigates the utility costs of decentralized investment management. These costs can be further reduced when the CIO can screen asset managers on the basis of their risk appetites. Each manager%u2019s optimal level of risk aversion depends on the asset class he manages and can differ substantially from the CIO%u2019s level of risk aversion.

Coronal disturbances and their effects on the dynamics of the heliosphere

The Sun blows out the solar wind which propagates into the interplanetary medium and forms the heliosphere about 100 AU across. The solar activity causes various types of time-dependent phenomena in the solar wind from long-lived corotating interaction regions to shorter on duration but more extreme events like coronal mass ejections. As these structures propagate outward from the Sun, they evolve and interact with each other and the ambient solar wind. Voyager 1 and 2 provided first unique in-situ measurements of these structures in the outer heliosphere. In particular, Voyager observations in the heliosheath, the outermost region of the heliosphere, showed highly variable plasma flows indicating effects of solar variations extending from the Sun to the heliosphere boundaries. Most surprisingly, Voyager 1 data shows shocks and pressure waves beyond the heliosphere in the interstellar medium. Important questions for the future Interstellar Probe mission are (1) how do the heliosphere boundaries respond to solar variations? (2) how do disturbances evolve in the heliosheath? and (3) how far does the Sun influence extend into the interstellar medium? This talk will review observations and recent modeling efforts demonstrating highly variable and dynamic nature of the global heliosphere in response to disturbances originated in the Sun's atmosphere.https://ui.adsabs.harvard.edu/abs/2019EPSC...13.1229P/abstractPublished versio

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a state-of-the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.delayed differential equations, delayed optimal control, numerical optimization, time-to-build

On the Timing and Pricing of Dividends

We present evidence on the term structure of the equity premium. We recover prices of dividend strips, which are short-term assets that pay dividends on the stock index every period up to period T and nothing thereafter. It is short-term relative to the index because the index pays dividends in perpetuity. We find that expected returns, Sharpe ratios, and volatilities on short-term assets are higher than on the index, while their CAPM betas are below one. Short-term assets are more volatile than their realizations, leading to excess volatility and return predictability. Our findings are inconsistent with many leading theories

Numerical Solution of Optimal Control Problems with Constant Control Delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a state-of-the-art direct method by applying Bock's direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic example

On the Transition from Instantaneous to Time-Lagged Capital Accumilation: The Case of Leontief Type Production Functions

We formulate an optimal control capital accumulation model with a Leontief-type production function and an exogenously given time-lag between investment and the accumulation of the capital stock, to analyze the qualitative and quantitative influence of time-lags on the system dynamics. As known from the time-to-build literature, optimal investment paths for positive and finite time-lags are in general cyclical, in contrast to the monotonic optimal paths for instantaneous capital accumulation. We show that the transition between instantaneous and time-lagged capital accumulation is continuous, in the sense that the greater is the time-lag between investment and capital accumulation, the more likely and more pronounced becomes cyclical behavior of the optimal paths. --cyclical optimal paths,numerical optimization,time-lagged optimal control,time-to-build

Decentralized Decision Making In Investment Management

The article addresses the investment problem of a pension fund in which a centralized decision maker, the Chief Investment Officer (CIO), employs multiple asset managers to implement investment strategies in separate asset classes. The investment management division of pension funds is typically structured around traditional asset classes such as equities, fixed income, and alternative investments. The asset allocation decisions are made in at least two stages. Firstly, the CIO allocates capital to the different asset classes, each managed by a different asset manager. Secondly, each manager decides how to allocate the funds made available to him, that is, to the assets within his class. The CIO of the fund therefore faces a tradeoff between the benefits of decentralization, driven by the market timing and stock selection skills of the managers, and the costs of delegation and decentralization. The optimal portfolio of the asset managers can be decomposed into two components. The first component is the standard myopic demand that optimally exploits the risk-return trade-off. The second component minimizes the instantaneous return variance and is therefore labeled the minimum-variance portfolio. The minimum variance portfolio substitutes for the riskless asset in the optimal portfolio of the asset manager. The two components are then weighted by the risk attitude of the asset manager to arrive at the optimal portfolio

Unambiguous determination of spin dephasing times in ZnO

Time-resolved magneto-optics is a well-established optical pump probe technique to generate and to probe spin coherence in semiconductors. By this method, spin dephasing times T_2^* can easily be determined if their values are comparable to the available pump-probe-delays. If T_2^* exceeds the laser repetition time, however, resonant spin amplification (RSA) can equally be used to extract T_2^*. We demonstrate that in ZnO these techniques have several tripping hazards resulting in deceptive values for T_2^* and show how to avoid them. We show that the temperature dependence of the amplitude ratio of two separate spin species can easily be misinterpreted as a strongly temperature dependent T_2^* of a single spin ensemble, while the two spin species have T_2^* values which are nearly independent of temperature. Additionally, consecutive pump pulses can significantly diminish the spin polarization, which remains from previous pump pulses. While this barely affects T_2^* values extracted from delay line scans, it results in seemingly shorter T_2^* values in RSA.Comment: 11 pages, 10 figure

On the Timing and Pricing of Dividends

We recover prices of dividend strips on the aggregate stock market using data from derivatives markets. The price of a k-year dividend strip is the present value of the dividend paid in k years. The value of the stock market is the sum of all dividend strip prices across maturities. We study the properties of strips and find that expected returns, Sharpe ratios, and volatilities on short-term strips are higher than on the aggregate stock market, while their CAPM betas are well below one. Short-term strip prices are more volatile than their realizations, leading to excess volatility and return predictability.