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Description
One necessary condition for the two-pass risk premium estimator to be consistent and asymptotically normal is that the rank of the beta matrix in a proposed linear asset pricing model is full column. I first investigate the asymptotic properties of the risk premium estimators and the related t-test and Wald test statistics when the full rank condition fails. I show that the beta risk of useless factors or multiple proxy factors for a true factor are priced more often than they should be at the nominal size in the asset pricing models omitting some true factors. While under the null hypothesis that the risk premiums of the true factors are equal to zero, the beta risk of the true factors are priced less often than the nominal size. The simulation results are consistent with the theoretical findings. Hence, the factor selection in a proposed factor model should not be made solely based on their estimated risk premiums. In response to this problem, I propose an alternative estimation of the underlying factor structure. Specifically, I propose to use the linear combination of factors weighted by the eigenvectors of the inner product of estimated beta matrix. I further propose a new method to estimate the rank of the beta matrix in a factor model. For this method, the idiosyncratic components of asset returns are allowed to be correlated both over different cross-sectional units and over different time periods. The estimator I propose is easy to use because it is computed with the eigenvalues of the inner product of an estimated beta matrix. Simulation results show that the proposed method works well even in small samples. The analysis of US individual stock returns suggests that there are six common risk factors in US individual stock returns among the thirteen factor candidates used. The analysis of portfolio returns reveals that the estimated number of common factors changes depending on how the portfolios are constructed. The number of risk sources found from the analysis of portfolio returns is generally smaller than the number found in individual stock returns.
ContributorsWang, Na (Author) / Ahn, Seung C. (Thesis advisor) / Kallberg, Jarl G. (Committee member) / Liu, Crocker H. (Committee member) / Arizona State University (Publisher)
Created2011
Description
In this paper, we propose an autonomous throwing and catching system to be developed as a preliminary step towards the refinement of a robotic arm capable of improving strength and motor function in the limb. This will be accomplished by first autonomizing simpler movements, such as throwing a ball. In this system, an autonomous thrower will detect a desired target through the use of image processing. The launch angle and direction necessary to hit the target will then be calculated, followed by the launching of the ball. The smart catcher will then detect the ball as it is in the air, calculate its expected landing location based on its initial trajectory, and adjust its position so that the ball lands in the center of the target. The thrower will then proceed to compare the actual landing position with the position where it expected the ball to land, and adjust its calculations accordingly for the next throw. By utilizing this method of feedback, the throwing arm will be able to automatically correct itself. This means that the thrower will ideally be able to hit the target exactly in the center within a few throws, regardless of any additional uncertainty in the system. This project will focus of the controller and image processing components necessary for the autonomous throwing arm to be able to detect the position of the target at which it will be aiming, and for the smart catcher to be able to detect the position of the projectile and estimate its final landing position by tracking its current trajectory.
ContributorsLundberg, Kathie Joy (Co-author) / Thart, Amanda (Co-author) / Rodriguez, Armando (Thesis director) / Berman, Spring (Committee member) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
A systematic top down approach to minimize risk and maximize the profits of an investment over a given period of time is proposed. Macroeconomic factors such as Gross Domestic Product (GDP), Consumer Price Index (CPI), Outstanding Consumer Credit, Industrial Production Index, Money Supply (MS), Unemployment Rate, and Ten-Year Treasury are used to predict/estimate asset (sector ETF`s) returns. Fundamental ratios of individual stocks are used to predict the stock returns. An a priori known cash-flow sequence is assumed available for investment. Given the importance of sector performance on stock performance, sector based Exchange Traded Funds (ETFs) for the S&P; and Dow Jones are considered and wealth is allocated. Mean variance optimization with risk and return constraints are used to distribute the wealth in individual sectors among the selected stocks. The results presented should be viewed as providing an outer control/decision loop generating sector target allocations that will ultimately drive an inner control/decision loop focusing on stock selection. Receding horizon control (RHC) ideas are exploited to pose and solve two relevant constrained optimization problems. First, the classic problem of wealth maximization subject to risk constraints (as measured by a metric on the covariance matrices) is considered. Special consideration is given to an optimization problem that attempts to minimize the peak risk over the prediction horizon, while trying to track a wealth objective. It is concluded that this approach may be particularly beneficial during downturns - appreciably limiting downside during downturns while providing most of the upside during upturns. Investment in stocks during upturns and in sector ETF`s during downturns is profitable.
ContributorsChitturi, Divakar (Author) / Rodriguez, Armando (Thesis advisor) / Tsakalis, Konstantinos S (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2010
Description
This thesis lays down a foundation for more advanced work on bipeds by carefully examining cart-inverted pendulum systems (CIPS, often used to approximate each leg of a biped) and associated closed loop performance tradeoffs. A CIPS is characterized by an instability (associated with the tendency of the pendulum to fall) and a right half plane (RHP, non-minimum phase) zero (associated with the cart displacement x). For such a system, the zero is typically close to (and smaller) than the instability. As such, a classical PK control structure would result in very poor sensitivity properties.It is therefore common to use a hierarchical inner-outer loop structure. As such, this thesis examines how such a structure can be used to improve sensitivity properties beyond a classic PK structure and systematically tradeoff sensitivity properties at the plant input/output. While the instability requires a minimum bandwidth at the plant input, the RHP zero imposes a maximum bandwidth on the cart displacement x.
Three CIPs are examined – one with a long, short and an intermediately sized pendulum. We show that while the short pendulum system is the most unstable and requires the largest bandwidth at the plant input for stabilization (hardest to control), it also has the largest RHP zero. Consequently, it will permit the largest cart displacement x-bandwidth, and hence, one can argue that the short pendulum system is easiest to control. Similarly, the long pendulum system is the least unstable and requires smallest bandwidth at the plant input for stabilization (easiest to control). However, because this system also possesses the smallest RHP zero it will permit the smallest cart displacement x-bandwidth, and hence, one can argue that the long pendulum system is the hardest to control. Analogous “intermediate conclusions” can be drawn for the system with the “intermediately sized” pendulum. A set of simple academic examples (growing in plant and controller complexity) are introduced to illustrate basic tradeoffs and guide the presentation of the trade studies.
ContributorsSarkar, Soham (Author) / Rodriguez, Armando (Thesis advisor) / Berman, Spring (Thesis advisor) / Marvi, Hamidreza (Committee member) / Arizona State University (Publisher)
Created2021
Description
The focus of this project investigates high mobility robotics by developing a fully integrated framework for a ball-balancing robot. Using Lagrangian mechanics, a model for the robot was derived and used to conduct trade studies on significant system parameters. With a broad understanding of system dynamics, controllers were designed using LQR methodology. A prototype was then built and tested to exhibit desired reference command following and disturbance attenuation.
ContributorsKapron, Mark Andrew (Author) / Rodriguez, Armando (Thesis director) / Artemiadis, Panagiotis (Committee member) / Industrial, Systems & Operations Engineering Prgm (Contributor) / Electrical Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05