Applied Portfolio Management
Select 5 Australian listed companies in the ASX200 or 5 US companies in the S&P500 and download their monthly adjusted closing prices. The adjusted closing price is adjusted for dividends, stock splits and so on.
This makes the adjusted closing price reflect total returns, not capital returns only. A good source of adjusted closing prices is Yahoo Finance. Ensure that each of the companies have at least 120 months of adjusted closing price data so that the GFC which started in 2007 is included. Do not mix US and Australian companies since we don't want to complicate the assignment with foreign exchange considerations.
If you chose Australian stocks, download the ASX200 accumulation index or if you chose US stocks, download the S&P500 accumulation index monthly closing prices provided on MQ ilearn. Each countries' government bond yields are also provided. Match the accumulation index, government bond yields and stock data so that the dates correspond. There is a demonstration spreadsheet on MQ ilearn called ‘vlookupExample.xlsx' which might help you start.
The shares you selected will be referred to as the shares, the ASX200 or S&P500 as the market portfolio, and the Australian or US federal government bonds as the bond. All of them will be referred to as the assets, so there are 7 assets (5 stocks, the market portfolio and the bond).
Question 1: Convert the assets' monthly adjusted closing prices (or yields to maturity in the case of the bonds) into discretely compounding monthly returns compounding per month, also called monthly net discrete returns or effective monthly returns (r_(eff monthly) = r_(discrete monthly)=(p_1-p_0)/p_0 ).
Do not use monthly continuously compounding returns. Report the discrete monthly returns' historical arithmetic average, geometric average, standard deviation and variance for each of the assets. Report your results in a clearly labelled table with units. For this and all of the following questions, use the discretely compounded monthly returns.
Note that the Australian and US government bond yields provided by Bloomberg are expected future annual yields to maturity (YTM's), not past historical prices.
Therefore you should convert the annual YTM's into monthly past historical returns. For an example of how to do that. The ‘approximate solution' using the duration-bond-price-change formula will suffice.
Question 2 : Report the assets' covariance of returns matrix in a table. Also report the assets' correlation of returns matrix in a table. Note that the assets include the stocks, market portfolio and bond.
Question 3a : Comment on the bond's risk and discuss if it can be seen as a risk free security. Consider the different risks that Australian or US government bond investors are exposed to and which are or aren't significant. Use academic references to support your answer.
Question 3b : For the purpose of an investor trying to make a portfolio allocation decision using Markowitz mean-variance optimization, a risk free rate is needed. What risk-free rate would you recommend that the investor use? Outline the rationale for your decision. Use academic references to support your answer.
Question 4a :Graph two Markowitz bullets on the same chart using the stocks only, and then all assets (stocks, market and bond). Do not assume that the bond is risk free. Label each portfolio possibility frontier (Markowitz bullet) appropriately. Depict the stocks, market portfolio and bond as points on the graph and label them too. Assume that all assets can be short-sold.
Question 4b: Repeat with short selling not allowed.
Question 5: From this question onwards, assume that the bond is a risk free security in the sense that its standard deviation of returns is zero. Use the risk free rate that you recommended in the prior question.
Question 5a: Construct a tangency portfolio using the stocks only. Ignore the market portfolio. Assume that the bond is risk free and short selling is allowed. Repeat with short selling not allowed.
Report the return, standard deviation, variance, Sharpe ratio and weights in each stock using a table with one row or column for each the three portfolios: short-selling allowed tangency portfolio; non-short selling tangency portfolio; and the market portfolio. You can leave the weights of the stocks in the market portfolio (ASX200 or S&P500) blank or include the adjusted weights calculated in the Black-Litterman question.
Question 5b: Plot the three Capital Allocation Lines (CAL's) from the bond through the two tangency portfolios (short and non-short selling) and the market portfolio (ASX200 or S&P500) on a graph of return versus standard deviation.