SEMESTER 2 TAKE-HOME FINAL ASSESSMENT 2022-23
ECON3016 Empirical Finance
Duration: 8 HOURS:
START: 9:00 am, XX/5/2023 - END: 5:00 pm, XX/5/2023
This paper contains 5 questions
- Answer 3 out of 5 questions.
- All questions are equally weighted.
- Explain concisely all steps you undertake to answer the questions. Please write clearly, only readable parts will be taken into account.
- This is an open book assignment. You may use notes, books, online resources or software when answering these questions. You must always use your own words and calculations and you may not communicate to others or get help from any person be it private or online.
- Once you have inished, you should upload your answers as a single pdf ile on the Assessment section of the ECON3016 Blackboard site. Your answers may be hand-written or typed. A submission is only complete with a submission number.
- The submission deadline is 5:00 pm on XX/5/2023. Your work must be up- loaded onto the Blackboard website before this deadline. See blackboard for detailed submission instructions.
- Submission of this work acknowledges that you have answered the questions in- dividually and in accordance with University guidance on Academic Integrity.
Question 1
(a) A bank quotes the nominal annual rate of 6%, and it compounds interest every two months. What is the value of one pound deposited in this bank after a year?
(b) What is the quarterly rate that is equivalent to an annual return of 10%?
(c) What is the value of $1 after 50 days if the continuous annual rate is 10%? (assume 365 days in a year)
(d) A fund requires investors to pay an equal amount each year for 3 years, with the irst installment to be paid immediately. At the end of the 3 years,a lump sum will be paid back to investors. If the APR is 5% what is the amount of the installment so that the investor can get back ↔10000?
(e) On October 1987 the SP500 index dropped more than 15% in one day. Let r denote the daily returns and assume that they are normally distributed with mean 0.000532 and standard deviation 0.012098. What is the probability of such a crash occurring?
(f) The current price of a stock is P0 = 75. The associated continu- ously compounded returns are modeled as rt = 0.035 + et with et ’s independent across time and et N (mean = 0, variance = 0.09). Find the probability that the time-4 stock price P4 exceeds today’s stock price P0. Hint: recall that rt is such that Pt = Pt-1 ert .
(g) Suppose that the current stock price is given by P0 rt ) with Dt denoting dividends and r the discount rate. Dividends are assumed to grow at a constant rate g so that Dt+1 = (1 + g)Dt. If the irm distributes its entire earnings E as dividends so that D1 = E1 what is its PE ratio if r = 0.10 and g = 0.03?
(h) Suppose that log stock prices evolve according topt = α+β pt-1 +et where the et ’s are “news” shocks. Set β = 1 and assume α > 0. (i) Do these stock prices contain a deterministic trend, stochastic trend, or both? (ii) How would your answer to question (i) change if β = 0.5?
(i) Under the eicient markets hypothesis current stock returns cannot be predicted from past macroeconomic data even if expected returns are time varying. True, False or Uncertain? Explain.
(j) Suppose that stock prices follow the random walk Pt = Pt-1 + et.
Assume that the e'ts are normally and independently distributed with mean 0 and some variance σe(2). What is the probability that the stock price tomorrow will be lower than the stock price today?
Question 2
(a) For each of the following statements state whether they are True, False or Uncertain and briely justify your answer.
(i) If returns are serially correlated we have a violation of the ei- cient markets hypothesis.
(ii) If there is volatility clustering in returns then squared returns are predictable from their past.
(iii) Under the eicient markets hypothesis stock prices should not be predictable.
(iv) For any two random variables Y and X , Cov[Y, X] = 0 implies that E[YjX] = 0.
(v) Under the eicient markets hypothesis excess returns must have zero unconditional expectation.
(b) Let et = rt - rt(*) denote excess returns with rt the actual returns andrt(*) the expected returns. We also let It denote the information
set up to and including time t with It = fet , et-1 , et-2 , . . .g.
(i) Assume E[et jIt-1] = 0. Show that in such an environment excess returns (the et ’s) must be serially uncorrelated.
(ii) Does the assumption that E[et jIt-1] = 0 imply that you cannot make money in such an environment?
(iii) Assume E[et jIt-1] = 0 and E[et(2)jIt-1] = σe(2) for all t. Does such en environment allow for volatility clustering to occur?
Question 3
(a) Using the monthly squared returns to abroad equity index you obtain the following sample autocorrelations up to order 6: ˆ(ρ)1 = 0.60, ˆ(ρ)2 = 0.40, ˆ(ρ)3 = 0.20, ˆ(ρ)4 = 0.10, ˆ(ρ)5 = 0.05 and ˆ(ρ)6 = 0.02. The sample size that has been used is T=500. What can you conclude about the presence of volatility clustering in this series? Note: you may implement your test using a 5% signiicance level.
(b) Is it reasonable to argue that your data in question (a) does not support the weak form of the eicient markets hypothesis? Why or Why not? Explain.
(c) A trader argues that stock returns exhibit return reversals. Stocks that have generated a weak performance relative to the market at a given time tend to revert and outperform in subsequent periods and vice-versa. You have access to historical monthly return data on each stock.
(i) Explain how you would test for the presence of such efects.
(ii) Briely propose an investment strategy that takes advantage of such patterns.
Question 4
(a) Describe the stock market anomaly known as the value premium.
(b) You are provided with historical monthly returns on the performance of a style index that follows a value investment strategy. Explain how you would assess whether the investment strategy has generated abnormal proits.
(c) An investor argues that the value anomaly is entirely driven by Jan- uary returns. Explain how you would extend the model(s) you have considered in question (b) to test this claim.
(d) If value stocks outperform growth stocks then we have a violation of the Eicient Markets hypothesis. True, False or Uncertain. Explain.
Question 5
(a) An investor argues that her portfolio has generated a positive CAPM based alpha over the past few years and uses this to justify high management fees. Is this a convincing argument for the investor to make? Why or why not? Discuss.
(b) You wish to launch an investment fund that selects cheap value stocks with certain quality characteristics (e.g., good levels of prof- itability as measured by ROE or some other related quality indica- tor). As part of your fund brochure you want to present the out- comes of a backtest that illustrates the performance of your strategy over the past 10 years. Provide a step by step explanation on how you would design and implement your backtest.