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27.rho_short_sales

# 27.rho_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 Constructing the optimal portfolios - Constant correlation model Short sales allowed The calculation of optimal portfolios is simplified by using the constant correlatation model to rank securities based on the excess return to standard deviation ratio. Excess return to standard deviation = ¯ R i - R f σ 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 point is computed as follows: C * = ρ 1 - ρ + N X j =1 ¯ R j - R f σ j where ¯ R j Expected return on stock j . R f Return on a riskless asset. σ j Standard deviation of the returns of stock j .

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