Reference no: EM132846577

ECON1195 Financial Econometrics - RMIT University

Question 1

The dataset assignment capm.csv contains daily returns, it includes the fol- lowing variables:
Mkt RF: excess return on a market portfolio (return on market portfolio minus the risk-free rate);

SMB: measures the "size" factor;

HML: measures the "value" factor;

RF: risk-free rate as the U.S. Treasury Bill rate;

IBM: Continuously compounded returns on IBM stock (tech company);

Coca cola: Continuously compounded returns on Coca-Cola (retail company);

NRG: Continuously compounded returns on NRG (energy company);

(a) If we wish to invest in one stock, which one of these three stocks will you suggest? Give your reasoning (model estimation and R codes are not required in this question).

(b) Estimate the basic CAPM model (only consider the market portfolio in the model) for each stock and write down the estimated models.

(c) Interpret the αˆ and βˆ in the CAPM for IBM.

(d) Is IBM an aggressive or conservative stock? Why?

(e) Compare αˆ from three models. What does it tell you?

(f) If the IBM stock is an independent portfolio (ie. β = 0), do you agree that the percentage of idiosyncratic risk for this stock is 100%? Explain.

(g) Compare and provide an economic interpretation of these three R2 values from the three regression models estimated in (b)?

(h) Fit the Fama-French three-factor model to each stock and write down the estimated models.

(i) Test whether Fama French three-Factor model outperforms the CAPM model.

(j) Write a summary of the market risks based on the results of the CAPM models and three-factor models for three stocks.

Question 2

This question uses the same data given in Question 1. Suppose stock A=IBM, stock B=Coca Cola and stock C=NRG. Let r_A denotes the return of IBM stock, r_B denotes the return of Coca Cola stock and r_C denotes the return of NRG stock, respectively; σ²_A denotes the variance of return of IBM, σ²_B denotes the variance of return of Coca Cola stock and σ²_C denotes the variance of return of NRG, respectively.

We consider the following FOUR possible portfolios: Portfolio 1: 30% stock A and 70% stock B;
Portfolio 2: 50% stock B and 50% stock C;
Portfolio 3: 60% stock A and 40% stock C;

Portfolio 4: 40% stock A and 50% stock B and 10% Treasury Bill (Let assume Treasury Bill is independent of other three stocks);

(a) Compute the expected value of returns and variances of returns for all four portfolios. You need to show the workings, for example:
E(portfolio 9) = E(ax_A + bx_B + cx_C) = aE(x_A) + bE(x_B) + cE(x_C),
= 0.5 × 10% + 0.4 × 12% + 0.1 × 1.5% = 11.3%

(b) If you were a conservative investor, which portfolio would you invest? Explain.

(c) If you were aggressive investor, which portfolio would you invest? Ex- plain.

Question 3
(a) Write down an MA(2) model.

(b) Derive the unconditional mean and unconditional variance for the MA(2) model. You need show all the workings.

(c) The dataset assignment JNJ.csv contains only one variable: JNJ, which is the daily stock price of the JohnsonJohnson Co. Read the data into R and obtain the continuously compounded returns (in % by 100). Construct one line plot and one histogram with appropriate labels and title. In addition, make some comments on these two graphs.

(d) Discuss the efficient market hypothesis (EMH) in detail. Is the return series consistent with the EMH?

(e) Is it reasonable to fit the MA(2) model in (a) to the daily returns of JNJ stock? Explain why or why not (you are not required to fit the model at this stage).

(f) Estimate the MA(2) model and report the estimated model, is it reason- able to fit the MA(2) model? Explain why or why not.

(g) If we wish to improve the model, provide two possible models and give the reason why you think these two models are reasonable.

(h) Estimate the two models you suggest in (g) and write down the estimated models.

(i) Compare all three models and select the best model to the data?

Attachment:- Financial Econometrics.rar