workshop answer for unit 4 PDF

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REVISION WORKSHOP Unit 4 SOLUTIONS Workout Michael Jensen and “Jensen’s Alpha”. • Describe the investment opportunities here. A offers a return higher than the market (appropriately levered) is offering. B offers less. • Suppose you take one of these investment opportunities. What market movements are you exposed to? How might you think about protecting yourself against market conditions?. A and B have the same beta risk as the (appropriately levered) market. They might also have idiosyncratic risk. Suppose we bought A and sold market short. We’d be pocketing the difference, a number Jensen spotted as equivalent to alpha in the market index model. If CAPM is true, every asset lies on SML not above or below so Alpha should be zero. What did he find? For 115 funds, alpha was really rather negative.

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Overtime You are analyzing the stock of Shelbyville Fiberoptics (SF ). You have 60 monthly observations of returns on SF stock (rSF ), the T-Bill (rf ), and the S&P 500 index (rSP 500 ). You assign a capable and competent assistant to fit the market model to this data; she gives you this (correct) output from her Excel software: SUMMARY OUTPUT

ANOVA df

Regression Statistics Regression Multiple R 0.4692 Residual R Square 0.2201 Total Adjusted R Square 0.2067 Standard Error 0.0953 Observations 60 Intercept S&P500

1 58 59

SS 0.1486 0.5265 0.6751

MS 0.1486 0.0091

F 16.3731

Coefficients Std. Error t-Stat P-value 0.0277 0.01340 2.0645 0.0434 1.2554 0.31020 4.0464 0.0002

1. What are the x− and y− variables in the regression? —x is the index excess return (realized risk premium), and y is the stock excess return 2. What is the equation of the fitted line? yˆ = α ˆ + βˆ × x yˆ = 0.0277 + 1.2554x 3. Is there any strong evidence of mispricing in SF stock? —yes since t(α ˆ ) = 2.06, there is strong suspicion of underpricing. 4. What is the sample standard deviation of the y− variable? s2 = Total SS ÷ df = 0.6751 ÷ 59 s = .10697 5. Comment briefly on the goodness of this fit—can the index explain a lot of the movement in SF ? Is there an unusual amount of unsystematic risk? Plenty of observations, adjusted R2 of 22%, so plenty of unsystematic variance but certainly nothing unusual for an individual stock. A portfolio with R2 this low would make us highly suspicious of the quality of our model.

Penalty Shootout 1. You say Qantas is a good investment because its alpha is 2.0%. I say Qantas is a bad investment with an alpha of -2.0%. (a) How do we know who is correct? I don’t know which investment opportunities are available to each of us, so it’s impossible to answer this question completely. If you can only trade the S&P500, Qantas really IS better than other investments available to you. If you can trade the ASX, however, Qantas is not as good as a levered position in ASX (i.e., buying the ASX on margin).

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(b) Suppose that I now fit an index model for S&P relative to ASX. I tell you that: rSP = −0.002 + 0.95 ∗ rASX + ǫSP What could you do with this information? Again, there are 3 basic possibilities. If I have to choose between the two, I would prefer $95 of ASX and $5 of risk-free investment to $100 of S&P. If I wanted to get really fancy, I could short sell $100 of the S&P500 and match it with a $95 of ASX and $5 of lending. I could also plausibly hold a portfolio of ASX and S&P to get better risk-return tradeoffs (like the international example in class). However, the correlation is pretty high, so my benefits from this are likely small. 2. “Betting against Beta.” Recent research from Frazzini and Pedersen (2014 JFE) suggests an interesting way to better understand the index model approach.1 • Suppose you cannot borrow money; where would the usual SML stop for you? (At beta = 1; you can’t just lever up the market anymore if you want a higher return)

• If you have very low risk aversion, and you cannot borrow, what is your best response now to get expected higher returns than E[rm ]? the only way to get high returns is high beta risk, so high beta stocks in your portfolio must be overweighted relative to the market • The authors argue that if some people want to over-weight high-risk stocks, prices will rise and expected returns will decrease for those stocks. • This suggests the relationship between beta and expected returns (the SML, taking account of all this) will change. How? if these people bid up the prices of high beta stocks, expected returns for a given beta (> 1) must fall and so the SML is less steep up in this high beta region

1 http://www.sciencedirect.com/science/article/pii/S0304405X13002675. The Journal of Financial Economics is one of our top journals for scientific study in finance.

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