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Chicago Booth BUSF 35150 - Problem Set 6 answers

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Business 35150 John H. CochraneProblem Set 6 answersPart ICarhart:The introduction summarizes his conclusions:• Momentum in stocks accounts for momentum in funds. Funds that did well last y ear have stocksthat went up and those stocks will keep rising a bit. It is not persistent skill, or good returns formomentum funds. Momentum funds do poorly after transactions costs. There is some persistentunder performance. Important: Survivor bias free data — includes funds that die. (Lots of hardwork by Carhart, and another great CRSP dataset.) (p. 58)We need to look for the facts! Find the facts behind these assertions in the paper.Now Questions1. Carhart defends the four-factor model as a performance attribution model.(a) Wh y is it OK to use a “momentum factor” even if that is not a “state variable for investmentopportunities?”(b) What question are we using the multifactor model to answer, and how is that question differentfrom Fama and French’s question?A: To measure stock picking ability, performance relative to mechanical portfolios is enough,whether or not it is a “true” multifactor model. What you want to know is whether you canreplicate the fund’s performance with (cheap) index or mechanical strategies, not whether thereturns from such a strategy or “style” are justified from fundamental risk. Thus, Carhart’s modelis market, sml, hml, momentum, and we don’t argue about whether momentum is a “real” factoror not. An ything that you could (and might have!) realistically programmed a computer to do onthe righ t hand side goes here.Even better see Fama and French p.1918 pp2 prose.2. (Hint: Table III is the most important. Spend most of y our time to understand it.) How doesCarhart form portfolios of m utual funds - -what are Portfolio 1A 1B...10C in column 1 of TableIII?A: Re-formed once per y ear based on the previous year’s performance.. Then look at monthlyreturns in the portfolios. Again, we have to form portfolios, then watch. Keep in mind, all ofCarhart’s evidence is about portfolios of funds (or average behavior of funds of a given type),not individual funds.3. Do the funds that went up last year always continue to go up? How much risk is there in thisin vestment strategy? To quantify these questions, what is the c hance that portfolio 1A will earna positiv e return in a typical month of next year?A: For risk, std dev column. 1A is 0.75% with  =545%. Thus, the chance of going up at all isΦ(075545) = 5547%. So this is still a 55 up / 45 down phenomenon, and that is among a groupof funds in the highest 1/10 of performance for the previous year!9And that’s for the portfolio of funds — individual funds in the portfolio are even more v olatile, sothe chance of an individual winner fund doing well next year is eve n lower. Just a reminder thatreturns ha ve a lot of risk with them! Don’t confuse alpha with arbitrage opportunity. Alpha meansan average return, but not a good return every year.Also, as with momentum, this is not a “new phenomoneon” it’s a “new way of looking at somethingwe knew all along.” There is no conflict here with the conventional wisdom that funds who wonlast year are almost 50% likely to fall this year. If you can wrap your mind around that, you willhave really understood the first column!4. How do the CAPM R2values compare to those for stocks you hav e seen before? What accountsfor the difference?A: Especially in the middle, they’re huge. Individual companies get about 40%; FF stock portfoliosgot about 65%, here we’re seeing 98%. Portfolios of active funds are almost exactly replicating themarket index.Notethe2tail off as we go up and down the table. To be extreme, you have tostray far from the benchmark. The 1 and 10 portfolios actually have very low 2meaning hugetrac king errors, for funds.5. Are all the alphas zero after the 4 factor model is done, or is there a puzzle? Who seems still tobe outperforming and who is underperforming?A: Alphas from -0.1% (1% / y ear, as before) to -0.2% (9). Then a big increase in the bottom endto an amazing  = −064%! Puzzle — how can you lose money in a diversified portfolio?? Efficientmarkets mean you can’t do this either (or you and I short what they are long). Expenses? Comingup.Note: negative alphas is not that surprising. The indices do not include transactions costs. Real-world performance is usually less than the index.Note: FF4F have no transactions costs or short costs (hml is perpetually short small gro wth stocks,without an y cost), and assume you buy at midpoint of b/a. Some negative alpha is natural.6. Fund managers claim that fees and turnover do not reduce returns to investors. How could c hargingmore money not reduce returns to investors? (Try to be a good salesperson for a high-turnoverhigh-fee fund. Why should I give you my money? Then try to be a good supply-demand economist.What should the equilibrium relationship be between fees, expenses and returns to investors?)A: the claim is that fees pay for superior abilit y, and that turnover is losing dogs and buying goodstocks so helps. Standard S=D economics says we should see zero effect. It is a surprise to see anyeffect! .7. (Table V. Make sure you understand how this table was created. How are Table IV and Table Vdifferent?) What does Carhart find about fees and turnover? Ho w much does a 1% c hange in feesc hange returns to investors? How much does turnover — selling one stock and buying another —change returns to investors?A: Table V. and p. 67. Table V is based on individual funds, while Table IV looks at the portfoliosof Table 1. Expenses and turnover are all bad. Expenses are more than 1-1 bad. Turnovercorresponds to a 0.95bp/transaction cost. (Seems large; more than 1-1 as with expenses). I thinkthis is a big puzzle, we should see zeros here in a market in equilibrium! You can’t say “investorsare dumb” in mutual funds but “investors are smart” in trading!8. What is the point of Figure 2? (Hint: what would it look like if the sort on one year performanceindicated skill?)10A: Skill shouldn’t disappear, so the fact that returns seem to revert (2 year return is worse than1 y ear return) suggests momentum in stocks (which does dissipate over time). If it were skill, thelines would be flat. This is the crucial evidence that it’s momentum in underlying stocks, not skill.Also p. 71, 80% turnover in top funds each year.9. What does Carhart say


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