For example when estimating a norwegian funds alpha

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For example, when estimating a Norwegian fund’s alpha, should we use the OBX (25 most liquid Norwegian stocks) or Oslo All Shares (OSEAX) or maybe the world portfolio? 21
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What should we use as the benchmark portfolio when estimating alpha? What does the CAPM say? In practice, most often the benchmark is used and not the market portfolio. What are the implications of this practice? Suppose we run the following regression: 22
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What should we use as the benchmark portfolio when estimating alpha? 23 p f m p p pb b pb f m b pb b pb pb pb b f m b b pb pb f p pb f b pb pb f p b f m b b f b r r r r r r r r r r r r r r r r so and
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What should we use as the benchmark portfolio when estimating alpha? So a manager can be better than the benchmark but the benchmark itself might be overpriced (negative alpha) such that the overall alpha of the fund is negative. In this case we might want to underweight the benchmark but overweight the manager’s fund within the index. Comment: the benchmark might still offer a positive expected excess returns so we do not necessarily want to short it. It might be sufficient to underweight it. In order to decide what to do with the benchmark we need to do portfolio optimization.
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Treynor’s measure There is still some problem in Jensen’s alpha. What if the manager obtained the positive alpha by investing in high beta stocks? In this case investing in that fund might increase the volatility of our overall portfolio. 25
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Treynor’s measure Treynor’s measure for portfolio P is defined as: For example: 26 P f P P r r E T ) (
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β A M B 1 2 0.5 2 % 1 % A* T A T B SML * E(r) - r f
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Example: Which portfolio is better, P or Q? Market Portfoli o Q Portfoli o P ? 1.60 0.90 β 10% 19% 11% E(r)-r f ? 3% 2% α 28
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Note: the slope is Treynor’s measure β M 1 10% 1.6 19% 16% α= 3% 0.9 11% Q P SML* 9% 29 f r r E ) (
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Assume we are quite risk averse and want a beta of no more that 0.9. We can invest in portfolio P and have an alpha of 2%. Alternatively we can mix portfolio Q with the risk free asset to obtain a new portfolio Q * which also has a beta of 0.9: 30 5625 . 0 6 . 1 9 . 0 ) 1 ( * * Q P P Q Q f Q Q x x r x xr r
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So and portfolio P is preferrable. 31
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Many active funds try to “beat the benchmark” by having a large position in the benchmark and a small position in what they perceive as mispriced securities.
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