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21.index_short_sales

# 21.index_short_sales - University of California Los Angeles...

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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 β 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 * = σ 2 m N j =1 ( ¯ R j - R f ) β j σ 2 j 1 + σ 2 m N 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.

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21.index_short_sales - University of California Los Angeles...

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