CiteULike: pdlug's asset

On the probability distribution of stock returns in the Mike-Farmer model

Gao-Feng Gu — 2008-05-27T02:34:16-00:00

(23 May 2008)

Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not only the well-known power-law tails, together with several other important stylized facts. There are three key ingredients in the Mike-Farmer (MF) model: the long memory of order signs characterized by the Hurst index $H_s$, the distribution of relative order prices $x$ in reference to the same best price described by a Student distribution (or Tsallis' $q$-Gaussian), and the dynamics of order cancelation. They showed that different values of the Hurst index $H_s$ and the freedom degree $α_x$ of the Student distribution can always produce power-law tails in the return distribution $f(r)$ with different tail exponent $α_r$. In this paper, we study the origin of the power-law tails of the return distribution $f(r)$ in the MF model, based on extensive simulations with different combinations of the left part $f_L(x)$ for $x<0$ and the right part $f_R(x)$ for $x>0$ of $f(x)$. We find that power-law tails appear only when $f_L(x)$ has a power-law tail, no matter $f_R(x)$ has a power-law tail or not. In addition, we find that the distributions of returns in the MF model at different timescales can be well modeled by the Student distributions, whose tail exponents are close to the well-known cubic law and increase with the timescale.

Asset Allocation: Management Style and Performance Measurement

William Sharpe — 2008-04-25T04:08:31-00:00

Journal of Portfolio Management, (1992), pp. 7-19.

It is widely agreed that asset allocation accounts for a large part of the variability in the return on a typical investor's portfolio. This is especially true if the overall portfolio is invested in multiple funds, each including a number of securities. Asset allocation is generally defined as the allocation of an investor's portfolio among a number of "major" asset classes. Clearly such a generalization cannot be made operational without defining such classes. Once a set of asset classes has been defined, it is important to determine the exposures of each component of an investor's overall portfolio to movements in their returns. Such information can be aggregated to determine the investor's overall effective asset mix. If it does not conform to the desired mix, appropriate alterations can then be made. Once a procedure for measuring exposures to variations in returns of major asset classes is in place, it is possible to determine how effectively individual fund managers have performed their functions and the extent (if any) to which value has been added through active management. Finally, the effectiveness of the investor's overall asset allocation can be compared with that of one or more benchmark asset mixes. An effective way to accomplish all these tasks is to use an asset class factor model. After describing the characteristics of such a model, we illustrate applications of a model with twelve asset classes to analyze the performance of a set of open-end mutual funds between 1985 and 1989.

Robust Portfolio Management

E Erdogan — 2007-12-10T21:35:04-00:00

In this paper we present robust models for index tracking and active portfolio management. The goal of these models is to control the e#ect of statistical errors in estimating market parameters on the performance of the portfolio. The proposed models allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta, limits on cash exposure, etc. The optimal portfolios are computed by solving second-order cone programs. Since the...

The Cross-Section of Expected Stock Returns

Eugene Fama — 2007-03-20T04:50:59-00:00

The Journal of Finance, Vol. 47, No. 2. (1992), pp. 427-465.

Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market β, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in β that is unrelated to size, the relation between market β and average return is flat, even when β is the only explanatory variable.