Click here for printer friendly page
Does my beta look big in this?23/05/2008. Source: Burns Statistics. Patrick Burns
 Simulations are performed which show the difficulty of actually achieving realised market neutrality. Results suggest that restrictions on the net value of the fund are particularly ineffective. A negative correlation, that is, market negativity, is proposed as a more reasonable target, both on theoretical and practical grounds. Random portfolios, portfolios that obey given constraints but are otherwise unrestricted, prove themselves to be a very effective tool to study issues such as this, writes Patrick Burns of Burns Statistics.
1 Introduction
How should I constrain my portfolio's beta in order to achieve market neutrality? That is the practical question to be answered. Market neutrality is a very useful feature, and is well worth pursuing. The value of a fund to an investor is partly based on the return that it generates, and partly based on its correlation to the rest of the investor's portfolio - the lower the correlation, the more valuable it is. As [Beliossi, 2000] points out, a fund that claims market neutrality but doesn't deliver it, will evoke disappointment. Thus a methodology to produce market neutrality should be of keen interest to the fund manager. Section 2 discusses correlation -perhaps the most natural measure of market neutrality- and its relation to beta. Experiments with various constraints aiming for market neutrality are shown in Section 3. Section 4 moves to market negativity, and Section 5 concludes.
2 Betas and Market Correlation
An asset's beta is defined as the slope coefficient in a linear regression in which market returns explain the returns of the asset. One approach to computing the beta is to manipulate elements of the variance matrix of the asset and the market. Specifically beta is equal to the covariance between the asset and the market.divided by the variance of the market, see, for example, [Weisberg, 1980]. We can use this definition to establish the relationship between a portfolio's beta and its correlation with the market.
Click here to view the full document (pdf 347KB) You need Adobe Acrobat to read this document. If you do not have it, you can download it free from www.adobe.com/products/acrobat/readstep.html
Burns Statistics is the consulting and software vehicle for Patrick Burns. For more information go towww.burns-stat.com.
|
