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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Short sales not 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 β i . After stocks are ranked using the above ratio the optimum portfolio consists of investing in all stocks for which the excess return to beta is greater than the cutoff point C * . This cutoff rate is computed as follows: C * = σ 2 m ∑ i j =1 ( ¯ R j R f ) β j σ 2 j 1 + σ 2 m ∑ i j =1 β 2 j σ 2 j . where ¯ R j Expected return on stock j . R f Return on a riskless asset. β j Change in the rate of return of stock j associated with a 1% change in the market return. σ 2 m Variance in the market index . σ 2 j Variance of the error term. Also known as unsystematic risk. To find C * we compute all C i ’s using portfolios that consist with the first ranked stock, the first and second ranked stocks, the first, second, and third ranked stock etc. We know we have found the cutoff poit C * when all stocks used in calculating C i satisfy: ¯ R...
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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
 Nicolas
 Statistics

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