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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 cut-off point C * . This cut-off 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 cut-off 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