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.
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.