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Question 3: Regression and Event Study(10 marks total as indicated below)

Part 1: Stock Market Reaction to FOMC Announcement

US monetary policy can be measured by changes in the Federal funds rate[ https://en.wikipedia.org/wiki/Federal_funds_rate], which are announced by the Federal Open Market Committee (FOMC) meetings. Given the importance of monetary policy to the whole economy, investors pay special attention to the FOMC announcements. In the attached dataset (“Event Study.csv”), we have collected data on FOMC announcements from 1989 to 2007 and the aggregate stock market reactions to it.[ Bernanke and Kuttner (2005) attached is a good reference. ]

Here is a list of variables:

Date: FOMC announcement date
Return: S&P 500 index return on the announcement date (in percentage)
Total change: change of Federal fund rate (in bps)
Expected: investors’ expected change of Federal fund rate, which is estimated based on the futures contracts written on the Federal fund rate (in bps)
Surprise: the difference between Total change and Expected, which measures the change that is out of expectation of investors (in bps)
Scheduled: equals to 1 if the FOMC is scheduled, and 0 if not.

a)Run three regressions and report the estimation results according.
[Note: please report the coefficient and t-statistics, indicate significance with difference levels, and the adjusted R-squared of the regression. Bernanke and Kuttner (2005) use robust stand errors when calculating t-statistics. Pls follow their approach.
Hint: The following link (http://data.princeton.edu/wws509/r/robust.html) explains how to do that in R. If you cannot figure out how to do it, pls just use the normal t-statistics but one mark will be deducted.] (3 marks) [pls provide your R code]

In the first regression, Y is Return, X is Total change;
In the second regression, Y is Return, X is Expected;
In the third regression, Y is Return, X is Surprise.

b)Comparing the three regression results, which X variable explains Y the best? (1 mark)
Why that is the case? [Note: you may link it with market efficiency and event study] (2 marks)

c)Create a variable which equals to Scheduled*Surprise, and then run a regression in
which Y is Return, the first X variable is Surprise, and the second X variable is Scheduled*Surprise. Report the regression results. (1 mark) [pls provide your R code]

d)Based on the results, is the effect of Surprise on Return dependent on whether the FOMC meeting is scheduled or not? Please explain.(1 mark)

Part 2: Short questions
e) You are running a regression of:

You estimate to be 1.5. How should we interpret the coefficient of ? (1 mark)

g) In the event study, why do we often leave a gap between the “estimation window” and the “event window”?(1 mark)
Question 4: Portfolio Analysis and Optimization (11 marks total as indicated below)

Part 1: Portfolio Analysis

a)An investor can design a risky portfolio based on two shares, A and B. The standard deviation of Share A is 24% while the standard deviation of Share B is 12%. The correlation coefficient between the returns on A and B is -1. The expected return on Share A is 15% while on Share B it is 9%. What is the expected return of the minimum variance portfolio? [1 mark, MCQ, no explanations are needed]
A. 15%
B. 12%
C. 11%
D. 9%

Answer:

b)An investor invests 30% of her wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70% in a T-bill that pays 6%. Her portfolio's expected return and standard deviation are __________ and __________, respectively
[1 mark, MCQ, no explanations are needed]

A. 0.114; 0.12
B. 0.087; 0.06
C. 0.295; 0.06
D. 0.087; 0.12

Answer:

Part 2: Portfolio Optimization
In the folder, there is an .csv file that contains the information of stock prices of three stocks from 2012 to 2018. Pls finish the following tasks using R.
c)Pls calculate the log returns of these three stocks (raw returns, not in percentages) and report their mean values and the variance-covariance matrix. (2 marks) [pls provide your R code]

d)If an investor would like to form a portfolio with a targeted expected return of 0.0008 and achieve the minimized standard deviation by investing in these three stocks. What is the standard deviation of this optimal portfolio given there is no short sale constraint? If the daily risk free rate is 0.0002, what is the Sharpe ratio of this optimal portfolio? [2 marks] [hint: can use the library of “quadprog”] [pls provide your R code used to form the optimal portfolio ]

e)If an investor would like to form a portfolio with a targeted expected return of 0.0008 and achieve the minimized standard deviation by investing in these three stocks. What is the standard deviation of this optimal portfolio given there is short sale constraint (i.e., you cannot short sell the stocks)? If the daily risk free rate is 0.0002, what is the Sharpe ratio of this optimal portfolio? [hint: can use the library of “quadprog”] [2 marks] [pls provide your R code used to form the optimal portfolio ]

f)By comparing your answer in d) and e), is there any difference in their Sharpe ratios? Why that’s the case? [1 mark]

g) Given there is no short sale constraint, pls draw an efficient frontier that satisfies the following conditions: 1. The range of the mean return of the portfolio is from 0.75*min of the mean return of three stocks to 1.25*max of the mean return of three stocks; 2. Pls create 500 optimal portfolios in this range; 3 Then pls plot all the risk-return combination of the 500 optimal portfolios (i.e., the efficient frontier). [2 marks] [Pls provide your R code]

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