Trading Case RP2

 

Case Objectives

To understand the relationship between spot prices, expected returns and market efficiency.

 

Key Concepts

Market efficiency, capital market line and the market price of risk, security market line, expected utility theory, diversification and price discovery.

 

Case Description

You can trade stock in three companies: Company A, B and C for the first trading day of the current period.  During the trading day you are allowed borrow cash (at 1% for the period) and sell stocks short.  If you sell a stock short and don’t cover your position by the end of the trading day you will have to cover the value of this short position from your money market account at the end of the period. 

 

The timing of the events work as follows:  At the end of the trading day time “flashes by” to the end of the period at which time one path is realized for the economy.  Your position is marked-to-market at the values associated with the realized path for the economy.  That is, first interest is accrued or paid on the end of trading day balance in your money market account at the rate of 1% for the period.  If you have borrowed cash during the trading day, so your money market balance is negative, you pay 1% interest otherwise you receive 1% interest.  Second, your stock position is liquidated at the values associated with the realized path in the table below.  That is, after interest is settled, one of 9 paths for the economy is realized.  Each path determines a final or liquidated value for each company as provided below and your portfolio is marked to market at these values.  This means that the number of shares you own times the liquidated value per share is added to (or subtracted from if you have sold stock short) to your money market account for each of the three stock markets open.

 

For example, suppose you own 10,000 shares in Co. A and path 7 is realized.  From the table below this would result in 10,000*19.642 = $196,420 being added to your money market account.

 

To permit the trading crowd to go down the learning curve of trading experience multiple independent trading trials will be conducted.  The realized path for each trial is randomly generated from a distribution where each path is equally likely.

 

The task of the trading crowd each trial is to discover the spot price for each stock.  Each trader can act both as a market maker (i.e., submit limit orders (bids to buy or offers to sell some specified quantity)) or a market taker (i.e., submit market orders to buy from the existing ask or sell to the existing bid some specified quantity).  That is, all trades are executed at the bids and asks that either you or another trader in the trading crowd submit.  

 

Fundamentals and Economic Data

 

The possible paths for the economy, and the corresponding end-of-period realized values for the general market index and the three companies are shown here.   The average value is also shown.

 

Path

1

2

3

4

5

6

7

8

9

Average

Co. A

39.112

34.786

30.459

28.295

23.969

22.238

19.642

17.478

13.157

25.459556

Co. B

43.218

40.762

38.306

37.078

34.623

33.64

32.167

30.939

28.483

35.468444

Co. C

39.889

44.777

49.665

52.109

56.997

58.953

61.886

64.33

69.218

55.313778

Index

1400

1300

1200

1150

1050

1010

950

900

800

1084.4444

 

The spot index value is 1068.925 and therefore the expected return from the stock index is as follows:

 

Path

1

2

3

4

5

6

7

8

9

Average

Index Return

0.3097

0.2162

0.1226

0.0758

-0.0177

-0.0551

-0.1113

-0.1580

-0.2516

0.01452

 

In this trading exercise only the three stock markets are open (the stock index cannot be traded).  Prices discovered by the market determine the realized return distribution for each stock and therefore how returns co-vary among themselves and with the market index. 

 

The return associated with any realized path is defined as follows (e.g., suppose path 3 is realized):

 

Let p(1), p(2), and p(3) be the spot prices of the three stocks.  Suppose path 3 is realized then the realized return from each stock is:

 

Realized Return (Path  3) = (30.459 – p(1))/p(1), (38.306 – p(2))/p(2), (49.665 – p(3))/p(3), (1200 – 1068.925)/1000 =0. 1226

 

As you can see the prices you discover in the market determine the risk and expected return from each security across the possible set of paths for the economy.  In turn this determines the realized return distribution for each stock and therefore how these returns covary among themselves and with the general market index.

 

Trading Objective

 

The object is to earn as much grade cash as possible by managing both the risk and return of your portfolio.  The market is open for one trading period.  At the end of the period your position is marked to the market value associated with the realized path for the economy.  Trading will continue over multiple independent trials where in each trial you start with a fresh initial position.  The conversion from market cash to grade cash is as follows:

 

Grade Cash = 1000*Ln(Market Cash) where Ln(Market Cash) is the natural logarithm of the total marked value of your position at the end of the period.

 

If market cash finishes at zero or below, your grade cash will equal zero.  Your grade cash is cumulated across trials.

 

Initial Trader Endowments

 

Each trader will commence with a position that has an expected future value of a little over $1 million.  You will start with some endowment of cash and stocks but different traders can start with different initial endowments.

 

Private News Information

You will receive unbiased forecasts of the end of period’s realized stock index value throughout the trading day.  That is, the information will be in the form of the “true realized index number” plus or minus some error.  The expected value of the error is zero but the realized error can be positive or negative.  Different trader types get different unbiased forecasts so that in aggregate the market as a whole always has better information than any individual forecast.  In addition, information is such that you receive forecasts with smaller errors as the period progresses.

 

In the information text box (a single click on the first security, Co. 1, reveals the information in the information text box) you may observe the following (number provided for illustrative purposes only):

 

Forecast Time: 57 Private analyst forecast is 1100.

 

This means that the forecast became available 57-seconds after the start of the market and reveals that an unbiased estimate of the realized path is 1100 = true index number +/- realized error.

 

Forecasts become finer throughout the trading day and since the forecast error is independently generated with an expected value equal to zero multiple forecasts provide a smaller forecast error.  Similarly, because forecast errors are independent among different trader types then the market in aggregate always has finer information than any individual trader’s analyst information.  Trader types here is defined relative to initial endowments.