Final Exam 2020, MGMTMFE 407 Empirical Methods in Finance Prof. . Lochstoer
You are only free to consult your lecture notes, homeworks, and the textbook (Tsay) when answering this exam. You are not allowed to discuss the exam with anyone else. Please be clear and concise. Good luck!
1. Time: 180 minutes, 11:30am to 2:30pm. Emails must be sent by 2:45pm, which gives you 15 minutes extra for scanning.
2. There are a total of 4 longer questions (100 points in total). Please answer all questions. To get credit you must show your work.
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3. Write your anwers on blank sheets of paper, number each page.
4. When done, you have to scan your pages and email them back to the MFE o¢ ce as a pdf Öle with title: EmpiricalYOURFULLNAME.pdf. YOURFULLNAME = last name and Örst name as in LochstoerLars or ZhangDanyu. The Örst page should have your name, student id, and the sentence “I acknowledge my obligations under the UCLA Honor Code” with your signature following.
1. Autocorrelation and ARMA models
(a) Consider the following ARMA-model:
yt+1 = 0:5 + 0:9yt 0:25″t + “t+1; (1)
where “t is i.i.d. standard Normal for each t.
i. What are the unconditional mean and variance of this process? ii. Assume yt = 0:3 and “t = 1. What are Et [yt+1] and Et [yt+2]?
(b) You have a sample of the return on equity for Google. The unconditional mean of roe is 0:1. The unconditional variance is 0:22. The Örst, second, and third order autocorrelations are (rounded to two decimal places) 0:9, 0:81, and 0:66.
i. What is the most parsimonious ARMA process that captures this pattern? (Example: AR(1), AR(2), MA(1), MA(2), ARMA(1,1) or other?) Explain how you got to your answer.
ii. Write down the ARMA model you choose, including the values of all coef- Öcients in the model (similar to Equation 1 given above).
(c) Assume monthly ináation follows an AR(1) process with autocorrelation 0:99. Due to seasonalities you want to estimate a model using 12-month sums of ináation overlapping monthly. That is, if the Örst observation is the sum of monthly ináation January through December, the second observation is the sum from February through January, etc.
Ignoring the intercept term, give the ARMA process this data follows, includ- ing the value of the coe¢ cients. Remember to show your work.
2. VAR models, return predictability and the present-value restriction
(a) Write down a VAR(1) that has two state-variables: log market returns (rt) and
the log price-dividend ratio (pdt). Clearly deÖne all variables and parameters.
(b) Explain in words how you would estimate the parameters of this VAR.
(c) Using the VAR you wrote down in 2.a, derive the formulas for the following expectations:
i. Et (rt+1), Et (rt+2) :
ii. E P1 jr P, where jj < 1. t j=1 t+j (d) DeÖne DRt = Et j=1 rt+j . Derive a formula that uses your VAR to get an expression for the cash áow component of the pd-ratio: CFt = Et 1j=1 jdt+j. (e) Now, you want to instead estimate a VAR(2) using the same variables (returns and pd-ratio). Write this 2-variable VAR(2) in the form of a 4-variable VAR(1). 3. Volatility models (a) Give the three main stylized facts about market return volatility? (b) Let 2t Et 1 ["2t ] : Explain why an AR(1) process for "2t is not appropriate for modeling 2t . (c) Consider the GARCH(1,1) process 2t+1 = 0:1 + 0:08"2t + 0:92t . If 2t = 0:22 and "2t = 0:12, what is Et 2t+2? (d) What di§erentiates an EGARCH(1,1) from a GARCH(1,1)? 4. Factor models You are evaluating a long-short equity hedge fund and are given the below regression results: Re =0:05+0:5MKT 0:8HML +0:8SMB +0:1"; (2) fund;t t t t t where the factors are the FF3 factors and where " is a standard Normal error term. Assume all coe¢ cients are signiÖcant. (a) What investment ístylesíwould you say characterizes this fund? (b) Describe in detail how you would construct a factor-neutral version of this fund. Give the expression for the return on this factor-neutral fund (denote the ensuing return Rt ). (c) What is the expected return and Sharpe ratio of this factor-neutral fund? (d) Assume your existing portfolio has excess returns Rpe;t = 0:5 MKTt 0:8 HMLt + 0:8 SMBt. The expected excess return on this portfolio is 6% and the standard deviation is 10%. Assuming you could buy the factor-neutral version of the hedge fund with returns Rt , what is the mean-variance e¢ cient combination of Rpe;t and Rt that achieves an unconditional standard deviation of 15%? 程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com