Trading Case RP1

Case Objectives

To understand the relationship between spot prices and expected returns, mean-variance efficiency; to understand how CAPM applies to stock prices.

Key Concepts

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	24.459
Co. B	43.218	40.762	38.306	37.078	34.623	33.640	32.167	30.939	28.483	35.469
Co. C	39.889	44.777	49.665	52.109	56.997	58.953	61.886	64.330	69.218	53.314
Index	1400	1300	1200	1150	1050	1010	950	900	800	1084.444

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

The volatility of the index is 17.177% over the period.

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.