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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Short sales allowed, risk free asset exists Single index model - Ranking stocks The calculation of optimal portfolios is simplified by using the single index model to rank securities based on the excess return to beta ratio defined as follows: Excess return to beta = R i- R f i . After stocks are ranked using the above ratio the optimum portfolio (point of tangency) consists of investing in all stocks: Those for which the excess return to beta is greater than the cut-off point C * will be held long. Those for which the excess return to beta is smaller than the cut-off point C * will be held short. This cut-off rate is computed as follows: C * = 2 m N j =1 ( R j- R f ) j 2 j 1 + 2 m N j =1 2 j 2 j . where R j Expected return on stock j . R f Return on a riskless asset. j Change in the rate of return of stock j associated with a 1% change in the market return. 2 m Variance in the market index . 2 j Variance of the error term. Also known as unsystematic risk....
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This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.
- Spring '11