Business 35150 John H. Coc hraneProblem Set 3Due b y S at 12:00, week 3Part I. Reading questions: These refer to the reading assignment in the syllabus. Please hand inshort answers. Where appropriate, cite the text or tables for your answers. Example:In the introduction, do Fama and French claim that their model explains all the puzzles throw n atit?A: no, p. 56 bottom, "Equation (1), however, cannot explain the continuation of short-term returns."i.e. momentum.These are not deep questions, they’re just “did you get the point of the reading” questions.Fama and French, “Multifactor explanations:”1. In Table I, which kinds of stocks have higher average returns?2. Would a stock with strong earnings growth be a “growth” stock by FF’s definition? Would a stockwith a small number of employees be “small”? (Hin t: This is a tric k question. How do FF definegrowth and value?)3. Does the spread in average returns in Table 1A present a puzzle, by itself? (Hint: why might younot just go buy small value stocks based on the evidence of this table?)4. How are FF’s “SMB” and “HML” factors constructed? (one sentence)5. Which gets better returns going forward, stocks that had great past growth in sales over the last5 years, or stocks that had poor past growth in sales?6. Which results show the “long-term reversal” effect in average returns best? Which show the“momentum” effect best? (Table and line)7. It looks like we should all buy value, but we can’t all buy value, someone has to hold the growthstocks. If we all try to buy value, the value effect will disappear because we drive up the prices.How to Fama and French address this conundrum? (hint, p. 76, 77)FF “Dissecting Anomalies”1. How do FF “Dissecting Anomalies” define “Microcap” and “small” stocks? What percentage ofstocks are “Micro”? What fraction of market value do “micro” stocks comprise? How can thepercentile breakpoint that defines “tiny” be different from the fraction of tiny stocks in the sample?2. Are the average returns in Table II raw, excess, or adjusted somehow? Do they represent returns,or alphas, or something else?3. Which anomalies produce strong average returns for all size groups in Table II? What are the mostimportant numbers in Table II that document your answer?4. Explain what the first two ro ws of MC and B/M columns mean in Table IV.5. “The novel evidence is that the market cap (MC) result draws [size effect] much of its power frommicrocaps.” (p. 1667) What numbers in Table IV are behind this conclusion?1Cochrane, “Discount rates” p. 1053-1064, and 1098-10991. Figure 6 says expected returns are higher for value portfolios. Does the paper say this observationconstitutes the value puzzle?2. What central feature of Figure 6 captures FF’s “explanation” of the value puzzle?3. On p. 1060 I say "Covariance is in a sense Fama and French’s central result.” What table or setof numbers in Fama and French convey this result?4. What kind of regression does “Discount rates” suggest to provide the same information as FF’s Ta-ble 1A, in the same way we forecast returns last week? Write a regression equation that implementsthe “discount rates” idea.5. Does cay help to forecast one year stock returns? How about long run stock returns?6. In the final column of Figure 5, which components of the present value identity also change so thatcay can help to forecast one-year returns without changing the forecast of the long-run dividendyield?Part IIHow m uch of the variation of prices and returns that we have seen over time is due to shocks to newsabout cashflows vs. shocks to news about returns? We’re going to run some regressions and mak e someplots to answer this question. Use the same regressions you ran last week+1= + + +1(1)∆+1= + + +1(2)+1= +  + +1(3)to answer the following questions. Along the way you get some practice in inferring long-run features ofthe data from these sorts of regressions. (You can either use the real dividend growth data or dividendsinferred from the identity. The solutions will use real data.)1. We can use the approximate price-dividend identity− = ∞X=1−1∆+− ∞X=1−1+to decompose the price-dividend ratio at each date into the part due to expected future dividendsP∞=1−1∆+and the part due to expected future returns P∞=1−1+.UsetheVAR(1)-(3) to calculate ³P∞=1−1∆+´³P∞=1−1+´at each date Plot − overtime along with the two terms on the righ t hand side of this equation.(Notes: The formulas all apply to demeaned variables, i.e. − (). We’re interested in howthings vary over time, not the levels. I took out all the means. The answer looks too simpleto be true; eac h term will be some constant times − itself. That’s ok. If you forecast+1=  + + +1then the forecast +1just follows . If we use multiple forecasters on theright hand side, then the terms will not be perfectly correlated, but I wanted to keep it simple. )2. But people use more than dp to forecast. As an opposite extreme, calculate the perfect-foresightdecomposition. (This is a modern version of a Shiller graph):− =X=1−1∆+−X=1−1++ (− )2Use all the available data, i.e. at each date  up to the end of the sample  , i.e. plot each term of− = −X=1−1∆+− −X=1−1++ ( −)(− )To start, plot the left hand side and the sum of the three terms on the right hand side. Thislets you see how well the approximation works. Then, plot − with the return term and finalterm, and − with the dividend term and final term. (I found the graph with all three termsconfusing.)So, if people could forecast dividends and returns so well as to know the actual future, to whatextent do expected future dividends vs. expected future returns account for variation in dividendyields?3. Now, let’s think about the astonishing 20% per year volatility of stock returns. Why are returnsso volatile? Start with