Case Objective

Market efficiency and diffuse information.

You can trade two stocks over two months. The assessed (independent) distributions of future stock prices are associated with the nature of quarterly earnings' reports released at the end of the second month. Possible reports are: bearish, normal and bullish (equally likely) as follows:

Stock 1’s assessed chances (as %’s) of future marked values given earnings reports are:

Stock 2’s assessed chances (as %’s) of future marked values given earnings reports are:

The interest rate each month is 0.5%. You can borrow and sell stocks short.

Private Information

Private sample information is provided to you from the true distribution. Suppose the true distribution is Bear for stock 2: You are more likely to have state l or m or n realized than states x or y or z. You will receive private state information from two independent drawings from the underlying true distribution.

Example 1: At the beginning of the first trading period you receive: p, s. This implies that from two independent drawings, with replacement, states p and s were realized.

Based upon this information you can update your expected earnings report which is equivalent to updating your forecast of the future stock value distribution.

At the beginning of period 2 you will receive another clue in this manner. That is, by the start of the second period you will have four independent clues, two from period 1 and two from period 2.

You have an Excel prior information support system that you can modify if desired. Loading in RE4SUP.XLS ready for use. Linking instructions, described below, bring real time market prices into the market data section of this spreadsheet. The calculation of the posterior probabilities and expected value of your current position is displayed by clicking on the Bayes calculator button. This lets you compute conditional expected values given your private information.

The initial screen for this calculator appears as below. If this screen is different it can be initialized by selecting blanks under Input Information for Stock 1, followed by clicking on the Calculate button. Similarly, you can repeat these steps for Stock 2.

You input your private information for stock 1 by matching your information with your drop down selections. If your sample consists of two clues then the remaining two drop down selections should be blank. After you have entered all clues for stock 1 and then stock 2 the expected value of your current position, conditional on your private information, is displayed in the bottom right hand corner. You can then translate this information into your trading strategy.

To create the appropriate link to Wtrader run the spreadsheet titled re4sup.xls. Then click on the edit menu in Wtrader and select either automatic or manual link. If your trading station is fast enough then you will not experience any machine delay on automatic link and your spreadsheet will be continuously updated. If your trading station is slower, then manual link is recommended. In this case, to update your spreadsheet you will have to click on manual link each time you want to view current price and position information.

If you click on either Automatic Link or Manual Link a screen will appear with a find button that lets you find any Excel worksheet that you have currently opened. If the title RE4SUP.XLS does not immediately appear beside the Find button click on the Find button and use the drop menu to the right of Find to locate RE4SUP.XLS. Double click on this name to complete the link and then click OK. Note if you cannot locate If the name RE4SUP.XLS be sure that you have Excel open with this spreadsheet.

Finally click on the button OK to initiate the link. You will see your endowments come into the spreadsheet once the link is made.