Trading Case CA0

Case Objectives

CA0 is a stock trading exercise designed to introduce you to the problem of managing the risk and return of your position. You should use the FTS Portfolio Returns and Efficient Portfolios Module as a trading support system. An important part of the case is to understand how you move from historic prices to risk and return projections plus how you move from theoretical portfolio weights to implementing the portfolio in the market place.

Key Concepts

Markowitz diversification, efficient frontier; managing portfolio risk and return.

Case Description

The environment is based on the actual performance of 6 major US stocks between 1990 and 2001. The companies are: American Express (AXP.N), DuPont (DD.N), Disney (DIS.N), Dow Chemical (DOW.N), United Technologies (UTX.N), and General Electric (GE.N).

Closing monthly prices are provided over the period 1990 to 2001 adjusted for stock splits and dividends. You can examine this file by first launching the FTS Portfolio Returns Module from the Virtual Classroom home page. In step 1 below you can download the spreadsheet containing the supporting price history for trading case ca0. The latest closing prices on this file are:

	AXP.N	DD.N	DIS.N	DOW.N	UTX.N	GE.N
Closing Price	32.91	44.34	20.47	37.50	60.20	38.50

Linking ca0.xls to the FTS Portfolio Management Module

Step 1: Click on the hypertext cao.xls to download the Excel spreadsheet. Launch the module FTS Portfolio Returns and Efficient Portfolios. Click on the button Find Excel Worksheets and select ca0.xls(Sheet1). Next enter 1 for Names are in Row, 2 for First Row with Data, 144 for Last Row with Data, B for First Column with Data and G for Last Column with Data. Keep both Interest Rates and Index Data unchecked and click on the button Initialize. Double click above the name AXP so that all stocks are selected (indicated by a Yes above their name) and finally click OK.

Observe that Step 1 has resulted in getting the price data into the portfolio module.

Step 2: Click on Data Analysis. This will let you compute risk and return statistics for the individual securities.

Step 3: Click on Portfolios this will let you form portfolios and consider the problem of managing return by diversifying risk. You can now verify the following risk and return estimates estimated from the historical price series is as follows. The average return realized from the historical price series is:

Name	AXP	DD	DIS	DOW	UTX	GE
Average Return	0.01485	0.01113	0.00984	0.01018	0.01643	0.01636

The covariance of realized returns is:

AXP	0.00678	0.00226	0.00259	0.00258	0.00305	0.00262
DD	0.00226	0.00509	0.00141	0.00327	0.00262	0.00191
DIS	0.00259	0.00141	0.00654	0.00133	0.00304	0.00215
DOW	0.00258	0.00327	0.00133	0.00592	0.00273	0.00131
UTX	0.00305	0.00262	0.00304	0.00273	0.00626	0.00289
GE	0.00262	0.00191	0.00215	0.00131	0.00289	0.00416

In CA0 the realized end of period price for the stocks will be drawn from the actual risk/return distribution. Your position at the end of the period will be marked at the realized value, and this will determine your actual portfolio return, and therefore your performance.

Using the Sheet Labeled CA0Worksheet (Learning to work from portfolio weights to trading shares)

In the Portfolios subject of the FTS Portfolio Returns module, check Allow Short Sales and leave Risk Free Rate unchecked. Then click on the Plot Frontier button and the Plot Securities button (in that order). This will display the minimum variance frontier with short sales allowed. Now you can click anywhere on the minimum variance frontier to identify the portfolio weights associated the particular, target return/risk portfolio that you have selected. Alternatively, you can enter a target return directly in the text box beside Target.

Beside Weight you will see the portfolio weights for each security associated with the portfolio you constructed.

When you have identified a portfolio with the risk and return properties that you feel comfortable with then click on the Edit menu item and select Copy Weights. This copies the weights to the windows clipboard.

Give focus to Excel and select the second sheet titled CA0Worksheet. Click on cell c8 and then edit paste (or Ctrl V). This pastes the weights into Excel.

Hit the F9 key to manually update if you do not have auto recalc turned on in Excel. The shares to be purchased or sold are now automatically computed for you.

Note it is up to each trader to determine what risk and return combination they are prepared to tolerate when trading in CA0. This is a personal decision.

Trading in CA0

In this economy, you can trade the six stocks for one period, which corresponds to one month of calendar time. There is also a money market, but the interest rate is -100% and borrowing is not allowed. This means that if you have any money left over, you will lose it at the end of the period (so you should try and be fully invested in the stocks by the end of the period). Short selling of stocks is allowed. All trading is done at the closing prices of the stocks shown above.

At the end of the trading period, a new value for each of the stock will be realized, based on the historical distribution of the stock prices.

Initial Trader Endowments

There are two types of traders with the following initial endowment cash and shares:

Trader Data	Cash	AXP	DD	DIS	DOW	UTX	GE
Type 1	100000	21000	25000	23000	38000	-20000	31000
Type 2	331490	-11000	-19000	-80000	85000	-20000	112000

There are (approximately) an equal number of type 1 and type 2 traders. Over different market sessions your trader type can change.

Trading Objective

The object is to earn as much grade cash as possible by managing the risk and return of your position.

Earning Grade Cash

The market is open for one trading period. In calendar time this is the beginning of a month. At the end of the month your position is marked to the market value associated with whatever value is realized for each stock. The trading and the marking of your position is referred to as one trial. Trading will continue over multiple independent trials where you start with a fresh initial position at the beginning of each trial.

Your grade cash in any trial is 0.0001 x market cash. If you end up with negative wealth then you lose grade cash and if you make money then you gain grade cash.

Trading is conducted over a number of independent trials and a record of your cumulative grade cash is maintained.

Trading Support

Your trading support system is the FTS Portfolio Analysis Module combined with the ca0.xls worksheet. If you have not completed step 1 above then you should do so. This binds the module to the ca0 spreadsheet.

Objectives: You need to translate a point on the minimum variance frontier into a position that you trade towards in the FTS markets.

Step 1: Click on the Portfolios button and plot securities and plot frontier with short sales permitted. You will observe the yellow minimum variance frontier computed from the historical price data. The upper part of the minimum variance frontier is referred to as the efficient frontier. Click on this and you can observe that the portfolio weights corresponding to this point are automatically computed. Beside Target in the upper part of the screen you will see a number which is the average monthly return associated with this portfolio given the price history. Similarly, just below Risk Free Share you will see Volatility: and some number. This is the risk associated with the portfolio you have selected. Finally, from the Menu items select Edit, Copy weights.

Step 2: Give the focus to the CA0 spreadsheet and select the sheet labeled CA0Worksheet. You can paste the weights directly into Cell C8. After doing so you will see the target number of shares associated with the portfolio that you selected on the efficient part of the frontier. If this is your desired position then you can adjust your position to approximate this portfolio by trading in the FTS Markets. First, however, you may want to check the risk and return properties of your initial position.

Step 3: What does my initial position look like in terms of risk and return? In the CA0Worksheet you have the portfolio weights provided for both Type I and Type II traders. Mark and copy the weights associated with your type. Give the focus back to the Portfolio Module and click on the button Data Analysis. From the drop down select Depicted Weights and then paste in the weights using Edit Paste Weights. Finally, click on Plot Return Histogram. This will display the risk and return properties associated with your initial position. You can check whether the portfolio you have selected dominates (i.e., has higher return with no greater risk or less risk without less return) your initial position.

Finally, for the purpose of the trading exercise it is your risk and return preferences that determine what portfolio you want to select.