AIN3220 Investment and Risk Analysis Assignment (Total: 40 Marks)

  1. The total mark for this assignment is 40.

2. It counts for 20% of your total course grade.

3. Due date: 5:00 PM, 04 December 2023 (MONDAY). 4. NO late submissions will be accepted.

5. Be sure to follow the instructions below:

1. The assignment computations are done in EXCEL, but your solutions are presented in WORD in form of an assignment report.

2. Demonstrate your rationale behind each calculation, not simply displaying your solution. Use complete sentences for analysis and explanations.

3. Your assignment report, including all text, tables and figures, should be in A4-paper format with font size of 11. Make sure all text, tables and figures are clearly displayed and labelled in your report.

4. Deposit your assignment report in the box marked “AIN3220: Assignment Box” located in front of Room D609 in Building D.

5. Submit your Excel file and a soft copy of your assignment report (Use your student ID as your file name) electronically in Moodle.

6. Marks are given for both accuracy and clarity in your EXCEL and WORD submissions.

Tip: For all Excel commands used in this Assignment, please consult all Excel demon- strations done in class.

In this assignment you will analyze various risks and develop an investment strategy (along with other tasks) based on mean-variance portfolio theory, the Capital Asset Pricing Model (CAPM), risk factor analysis, and risk measures. Six stocks have been chosen for you and the historical data can be found in Data.xlsx on Moodle (Your stocks are the ticked ones located on the right of your name in Allocation of Data.xlsx). It contains weekly price data for the stocks listed in the Hang Seng Index (HSI), as well as weekly values of the HSI, for the past eleven years. Assume that there are 52 trading weeks in one year.

1

You have landed on a job in an asset management firm in Hong Kong specializing in Hong Kong equities. After taking AIN3220, you decide to employ some of the tools you have learned in assessing risks and constructing your very first portfolio.

Your boss has also set you a strict 15% expected target return per annum on any port- folio you construct, given the six stocks provided. Use the first ten years of weekly data (from 03 SEP 2012 to 29 AUG 2022) to estimate the expected weekly return and and the weekly variance-covariance matrix of the available assets. (Hint: What’s the correspond- ing weekly expected target return?)

1. (Total: 10 Marks) You decide to construct a minimum variance portfolio according to the theory you learned in AIN3220. Recall the 15% expected target return per annum imposed by your boss and assume that short sale is allowed. To do so, you need to perform the following tasks:

(a) Using the resulting returns data, estimate and report the vector of the weekly ex- pected returns for the six shares, as well as the weekly variance-covariance matrix of these returns.

(b) Compute and report the values of A, B, C and ∆.

(c) Find and report the portfolio weights (of the six stocks), expected return, and standard deviation of the global minimum variance portfolio (GMVP). What does the GMVP mean? Does it involve short selling of any stocks? Why is it useful? Explain.

(d) Determine and report the portfolio weights for the efficient portfolio that achieves expected target return of 15% per annum. Find also the standard deviation of the returns of this efficient portfolio. Does your efficient portfolio involve any short-selling? Explain.

(e) Plot the minimum variance set (MVS), i.e., the combination line. Your figure should also indicate the six stocks, the GMVP, and the efficient portfolio in Q1(d). Label the axes correctly.

2. (Total: 10 Marks) Now, in addition to the six stocks, you realize that you can also invest in a risk-free asset. You quickly call the fixed-income desk and determine that the appropriate risk-free rate to use is 2% per annum. (Hint: What’s the corresponding weekly risk-free rate?) Perform the following tasks to adjust your portfolio weights:

(a) Determine and report the optimal portfolio weights for the efficient portfolio with the expected target return of 15% per annum, when the risk-free asset is available. Does your efficient portfolio involve any short-selling? Do you have to lend or borrow any risk-free asset? Report also the standard deviation of the weekly return of this optimal portfolio. Are you better off, in terms of lower portfolio risk, when a risk-free asset is available? Explain.

2

(b) Find and report the portfolio weights, expected return, and standard deviation of weekly returns of the tangency portfolio. Explain the meaning behind the tan- gency portfolio. Does the tangency portfolio contain any risk-free asset? Explain.

(c) Determine the new portfolio weights for the efficient portfolios with the expected returns of (15 + i)%, where i = 1, ..., 10, per annum. Also calculate the corre- sponding weekly standard deviation of returns of these portfolios. Report your answers in a table. Explain the rationale behind your construction of these new portfolios.

(d) When the risk-free asset is available, what is the GMVP in this case? What are the expected return and the standard deviation of returns of the GMVP? Explain.

(e) Plot the minimum variance set with the risk-free asset. Your figure should also include the combination line with risky assets only in Q1(e). Also display the six stocks in this figure. Use the same ranges of the axes as in Q1(e). Locate the tangency portfolio in Q2(b) and the efficient portfolio in Q2(a) with the expected target return of 15% per annum only on the plot.

3. (Total: 8 Marks) Following your portfolio recommendation, your boss also wants you to provide some analysis on the fair pricing of these stocks. Using your knowledge on CAPM, perform the following tasks:

(a) Using the HSI as a proxy for the market portfolio, estimate and report the betas of the six shares based on the standard capital asset pricing model (CAPM), with risk-free borrowing and lending to be rF = 2% per annum. Explain the meaning behind these betas.

(b) Using the HSI as the proxy for the market portfolio, state the equations of the capital market line (CML) and the security market line (SML) based on the given data set. Plot the CML and the SML, and indicate the positions of the six stocks as well as that of the MP. Label all axes correctly.

(c) Based on your figures in Q3(b), identify and explain the stocks that are overvalued, correctly valued, and undervalued. Explain your rationale.

(d) Calculate and report the Sharpe and Treynor ratios of the six stocks. Explain the meaning behinds these ratios for these stocks.

4. (Total: 6 Marks) Next, your boss also wants you to identify the systematic and unsystematic risks of these six stocks. By using the HSI as the single risk factor, perform the following:

(a) Calculate the pricing errors for each of the six stocks on the given data. (You do not have to report these here.) Calculate and report the systematic and unsys- tematic risks for the six stocks. Explain the meanings behind the systematic and unsystematic risks of these stocks.

3

(b) Calculate and report the total risk and R2 for the six stocks. Explain the meaning behind the R2 for each stock.

(c) Based on your answers in Q4(b), which of the six stock(s) you think would be unreliable to have their expected returns to be estimated by the return of the HSI alone? Explain.

5. (Total: 6 Marks) Finally, your boss wants you to assess the performance of your optimal portfolio in Q1(d) with an expected target return of 15% per annum against the one-sixth portfolio, i.e., xj = 1/6, for j = 1, ..., 6, via some risk measures. Calculate the weekly returns of your optimal portfolio based on the weekly returns of your six stocks from 5 SEPT 2022 to 28 AUG 2023. Using the concepts of risk measures you learned in AIN3220, perform the following tasks:

(a) Calculate and report the 90% and 95% weekly Value-at-Risk for your optimal portfolio and the one-sixth portfolio in a table. Based on your understanding of the Value-at-Risk, compare and interpret the performance of your optimal portfolio against that of the one-sixth portfolio if you are given $100 million to invest into each of these portfolios.

(b) Calculate and report the 90% and 95% weekly expected shortfall for your optimal portfolio and the one-sixth portfolio in a table. Based on your understanding of the expected shortfall, compare and interpret the performance of your optimal portfolio against that of the one-sixth portfolio if you are given $100 million to invest into each of these portfolios.

4