# I high average returns that are unrelated to the

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I High average returns that are unrelated to the market I Why? Don’t need a fund manager to get market exposure ! simply invest in S&P 500 fund How to quantify this? Compute alpha from r p - r f = p + β p ( r m - r f ) + " p For hedge funds, the goal is to produce alpha, returns unrelated to the market What makes a good manager? Generally speaking a manager that has an alpha over a couple of percentage points is doing a good job. 41 / 77
BCSIX - Is statistically significant? Using data on monthly total returns Aug 2013 - July 2016 with Morningstar Small Growth TR as the market index: Russell 200 Growth TR as the market index: In both cases, (here, monthly) is not statistically significant... 42 / 77
Today’s lecture 1 Recap: portfolio theory 2 Applying mean-variance analysis 3 CAPM 4 Performance evaluation 5 Testing CAPM 6 APT 43 / 77
Testing CAPM empirically CAPM predicts a linear ("cross-sectional") proportional relation between the risk premium RP k (long-run average excess return) on an asset ( k ) and its β Idea of the test: I work with portfolios (Can measure β ’s more accurately) I choose portfolios with wide range of β ’s I do second regression with portfolio risk premia (left hand side) and portfolio β ’s (right hand side) Questions: I Is the slope significant? (i.e., do β ’s explain any of the di ff erence in risk premia between portfolios?) I Is the intercept zero? (i.e., is the risk premium for assets with a zero beta actually zero?) This is the approach taken in early tests, e.g., by Black, Jensen and Scholes (1972) 44 / 77 Aste calculate B 's of portfolios choose a wide range of B 's CAR N : Rp - rt =o + Bp MRP Bi = O Ri = rt t.sk#2.Sep a n Rp rt - Atf Bps LHS = - RHS =
Testing CAPM empirically 45 / 77 - r g s J - 0 #
Testing CAPM empirically 46 / 77 * of "
Testing CAPM empirically 47 / 77 Book - to - market = Bvequily Mr equity BM I low - o Growth fi firm T ygo line undopotom relative to CAPM £ outperform high Value - firm w f relation * O O a > o " value Premium - E l A Rp¥Rma - rft
Testing CAPM empirically Average returns vs market β - 25 size and BE/ME sorted stock portfolios 48 / 77 sine : !
Why doesn’t β work? Wrong theory? Behavioural biases No relation between return and marginal risk Friction-less market assumption in CAPM is invalid ! Leverage? Non-tradable risks? Wrong test? Tests don’t capture the correct market portfolio If you had the right portfolio, you’d see the risk priced 49 / 77 I Rolliscrtigne
Does CAPM hold?
How do we create a size or a book-to-market factor?
How do we interpret the return on the factor?