ECON3016: Problem Set 2
ANSWER 3 QUESTIONS OUT OF THE 4 QUESTIONS
Instructions: Please write your answers in the spaces provided and upload a scanned pdf of this sheet as your submitted work. The spaces provided are sufficient for what is expected from each question (handwriting is ine). If you prefer to use a word-processor to submit your answers please also retype the questions on top of your answers.
(Q1) Using the monthly squared returns of a stock market index (T = 250 observations) you have obtained the following irst 6 sample autocorrelations: ˆ(ρ)1 = 0:25 , ˆ(ρ)2 = 0:15, ˆ(ρ)3 = 0:08, ˆ(ρ)4 = 0:02, ˆ(ρ)5 = -0:09, ˆ(ρ)6 = 0:01.
(i) Using a suitable test argue whether the return series is characterised by volatility clustering patterns. Note: to be complete your answer should state the null and alternative hypotheses, the test statistic and its distribution and the inal decision rule.
(ii) Do your indings in part (i) contradict the e伍cient markets hypothesis? Why or Why not? Explain.
(Q2) Suppose that the following environment holds: rt = μ + et with E[etjIt-1] = 0, E[et(2)] = σe(2) and where rt+1 = ln(Pt+1/Pt) = pt+1 - pt. We also let rt;t+2 = ln(Pt+2/Pt) = pt+2 - pt denote the 2-period continuously compounded returns.
(i) Are the rt’s (single period returns) serially correlated? Why or why not? Justify your answer.
(ii) Are the rt;t+2’s serially correlated? Why or why not? Justify your answer.
(iii) Using your answers to (i) and (ii) briely discuss the dangers of using long-horizon returns for assessing the weak form of the efficient markets hypothesis.
(Q3) The data ile PS2 market data.xlsx provides historical annual returns (1927-2020) on the aggregate US market (RM), the risk free rate (RF) and the excess returns here deined as (RM-RF). We want to use this latter quantity to evaluate the US equity premium (i.e., the expected return on stocks in excess of the risk-free rate).
Note: you do not need to provide an additional spreadsheet with calculations. Just report the numerical outcomes in the space provided below.
(i) Estimate the expected US equity premium using its historical average, say EQPn.
(ii) Estimate the standard deviation of the equity premium, say ˆ(σ)(EQP).
(iii) Obtain the standard error of EQPn as ˆ(σ)EQP = ˆ(σ)(EQP)/pn with ˆ(σ)(EQP) obtained in part (ii) above and evaluate the t-ratio EQPn/ˆ(σ)EQP . Comment.
(iv) You wish to forecast the EQP using historical averages. At any time t your forecast for t + 1 is EQPj(t)=1 EQP/t) i.e., you compute a historical average up to time t and use this as your forecast for t + 1.
Starting from t=1950 generate your forecasts up to t=2020 and obtain the mean, variance and irst few sample autocorrelations of your forecast errors. Comment on the quality of your forecasts.
(Q4) How would you backtest an investment strategy that aims to select irms that have generated strong stock market returns over the past 6 months. Your answer should include the following details: (i) data requirements, (ii) methodology, (iii) potential shortcomings of your methodology.