15-Diversification I

15-Diversification I - BKM: Chapter 6 Efficient...

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Unformatted text preview: BKM: Chapter 6 Efficient Diversification Portfolio Theory We want to maximize Sharpe ratios . We want to understand: 1. How does the Sharpe ratio change as we change our portfolio weights ? 2. How can we determine if the portfolio of our Sharpe ratio is the highest possible? 1. Should we “tilt towards” some asset (increase our weight in that asset)? 2. Should we “tilt away” from some asset (decrease our weight in that asset)? 0.000 0.050 0.100 0.150 0.200 0.250 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 Standard Deviation Expected Return 0.000 0.050 0.100 0.150 0.200 0.250 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 Standard Deviation Expected Return 100% in asset A 100% in asset B In this range, you are short B. The weight on A >1. In this range you are short A. The weight on B >1. 0.000 0.050 0.100 0.150 0.200 0.250 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 Standard Deviation Expected Return The location of the optimal risky portfolio, also called the tangency portfolio. This curve is called the “efficient frontier”. Portfolio Rule #1: Two assets (e.g., two funds) If the correlation between the two funds equals +/-1, you cannot increase Sharpe ratio by diversifying. the efficient frontier becomes “V” shaped The “V” touches the y axis at the risk-free rate, The efficient frontier overlaps the CAL lines for the 2 funds If the correlation is +1: The two funds have the same Sharpe ratio. Either is MSRP If the correlation is -1: One fund has Sharpe Ratio>0, the other has a Sharpe ratio<0. The fund with Sharpe ratio>0 is MSRP Tangency portfolio How can we tell if the portfolio we hold is the tangency portfolio, or if we should change our portfolio weights to do better?...
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This note was uploaded on 03/01/2012 for the course BUS M 410 taught by Professor Brianboyer during the Fall '10 term at BYU.

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15-Diversification I - BKM: Chapter 6 Efficient...

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