Measure the expected return and risk of an equally weighted portfolio of the stocks

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Task 1

According to the CAPM, the market is the only source of risk and excess return on a security (risk premium) should only be explained by systematic risk; that is the security’s sensitivity to the changes in the market, which is a well-diversified portfolio. To test this argument, collect monthly prices and dividend (or DY) for 30 stocks from any stock market over the last 5 years. Collet monthly values of the relevant stock market index and its dividend (or DY), as well as the risk free rate (e.g. 3-month US T-Bill). Finally, collect market cap, earnings, and total debt for the 30 stocks you have chosen.

1- Calculate monthly returns for each stock over the past 5 years and estimate the mean and standard deviation of returns for each company, as well as stock index.

2- To investigate the sensitivity of stock returns to the market, we use CAPM and estimate the following regression for each stock where, rt is return on stock, rf,t is risk free rate, rm,t is the market return at time t. α and β are coefficients of the regression, and σ2 is the variance of estimated residuals.

3- You should obtain 30 alphas, 30 betas, and 30 sigmas. Find the average of the estimated coefficients.

4- To assess the validity of CAPM, we can estimate the following cross-sectional regression where Ci, EPi, and DEi are market capitalization, earning to price ratio, and debt to equity ratio for stock, i.

5- Test the significance of each coefficient (γ0, γ1, γ2, γ3, γ4 , γ5) and comment on your results, including the goodness of fit. [25 Marks]

Task 2

Download monthly prices for a commodity of your choice or shipping freight rate for a single shipping route over the past 20 years (end of the data should be Feb 2022).

1- Partition your sample into estimation and ex-post periods, with ex-post being 4 years. Use the observations in the estimation period to estimate 3 different models, e.g. Econometric Model, ARMA, Exponential Smoothing, etc. Perform diagnostic tests, present the final estimation outcome and the diagnostics for each model, and discuss the results.

2- Use appropriate techniques to compute forecast values for 1 to 48 months ahead, over the ex-post period (last 4 years; i.e. March 2018 to February 2022) of the sample with the

3 models you have estimated in part 1. 3- Use appropriate statistics to evaluate the forecasting performance of each model and compare forecasting performance of models.

4- Choose the best model and prepare a short report including forecast values on how freight rates are going to behave over the next 12 months, March 2022 to February 2023 and present your forecast. [25 Marks] ( ) ( ) ; ~ iid(0, ) 2 rt − rf ,t = +  rm,t − rf ,t +  t  t  ( ) ˆ ; ~ iid(0, ) ˆ 2 ri − rf =  0 +  1i +  2 i +  3Ci +  4EPi +  5DEi +  i  t  2

Task 3

Collect daily returns for 15 stocks from any stock market over the last year. Assuming you are going to invest £1m in these stocks, use Excel to perform the following analyses, assuming no short selling. If you are investing in non UK markets convert the amount using the current FX rate.

1- Measure the expected return and risk of an equally weighted portfolio of the stocks,

2- Measure the correlation between the stocks in your portfolio,

3- Measure the one-week 5% VaR of an equally weighted portfolio of stocks using the variances and correlation between stocks,

4- Find the optimum weight for each stock included in the portfolio in order to minimise the variance of portfolio given 3 different levels of expected returns (e.g. 5% per year, 10% per year and 15% per year; or 2%, 5% and 8% per year, etc),

5- Find appropriate weights to optimize risk-return of the portfolio,

6- Measure the one-week 5% VaR of the portfolio of stocks with minimum risk using the variances and correlation between stocks,

7- Find the 5% ETL of the portfolio of stocks with minimum risk using the variances and correlation between stocks,

8- Comment on your results in terms of risk management of this portfolio.

Attachments:

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme