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# You will each be given a dataset of the behaviour of a gambler playing a form of roulette.

INSTRUCTIONS TO CANDIDATES

(1) Risk Taking by Gamblers (50%) – complete on eviews

You will each be given a dataset of the behaviour of a gambler playing a form of roulette. This will be a clean dataset which will save you substantial time that you can dedicate to your modelling. This data shows the gambles taken in a long sequence of games: (i) the amount gambled, (ii) the outcome bet upon (red/black/green), and (iii) the resulting gain or loss. The gambler thus makes two decisions each round: how much to gamble and whether to take a low or high-risk bet. A bet on red or black pays \$2 for every \$1 staked (a net gain of \$1). A bet on green pays \$14 (a net gain of \$13).  Red and black each occur with probability 46.65%, green 6.7%.

Construct an econometric model of how the gambler’s risk-taking varies in response to their experience in previous rounds. As a minimum, you need to construct a well-specified model of the amount bet each round as a function of previous betting levels and previous wins/losses.

Consider your modelling approaches very carefully, using the tools available in your econometrics software. It is very easy to produce bad econometric models! Explain the choices that you made to arrive at your preferred model (what potential problems did you identify and how were you able to deal with them?).  Discuss the strengths and weaknesses of your preferred model(s), and interpret what your results tell us about the behaviour of this gambler.

Now extend your analysis of the dataset to derive further interesting results and test further hypotheses. For example, you could construct a model of the level of upside risk taken each round (this will be different from the downside risk if the gambler bets on green). Compare this with your model of downside risk. Which appears to represent a more satisfactory model of gambler behaviour, and why?

Additional econometric analysis could be more challenging, so use this as the opportunity to try to impress me and earn correspondingly high marks. For example:

Does your roulette gambler show evidence of the “gambler’s fallacy”? This would require a discrete choice model.

Alternatively, consider the gambler as simultaneously making two decisions (i) whether to choose a high-risk (green) or low-risk (red or black) gamble and (ii) how much to bet.  This would suggest modelling these two variables as part of a single system, such as a Vector AutoRegression (VAR).

Finally, consider other ways in which further work could extend your analysis of this dataset.

(2) The Disposition Effect (15%) – complete on excel

I will give each of you a dataset of the daily profit/loss generated by traders in the foreign exchange market. These have been standardised, so that each represents the dollar profit/loss on a single trade in which the trader buys (goes long) \$100 of a chosen currency, and then closes the trade later that day. The data records the profit/loss on each of the days that this trader trades (think of these as first trading day…second trading day… rather than particular dates, since they are likely to correspond to completely different dates for different traders).

Every day each trader chooses when to close the trade. Leaving the trade open a long time might increase the variance of the profit/loss. It might also introduce the disposition effect. Each trade involves a small fixed transaction cost.

Assume that exchange rates follow a simple Brownian motion. This means that if, for example, a trader decided in advance “I will open the trade at 09.30 and then close it at 12.30”, then her P&L would be distributed symmetrically. If instead her decision to close the trade depends on how much profit she has made on this trade, then the distribution of profits could be skewed. By analogy, suppose that I flip a coin repeatedly, counting +1 for each head and -1 for each tail (simple Brownian motion). I continue flipping until my cumulative total reaches either +1 or -2. The distribution of possible outturns will have +1 with two thirds probability and -2 with one third probability (hence mean zero).

Calculate the skewness of the return distribution for each of the traders in your sample and use this to assess whether they tend to exhibit the disposition effect. Is this effect significant?  How powerful is your test?  Are there any other aspects of this data that are noteworthy?

The trades you have been given are in chronological order. Does investor behaviour change over time (consider total risk-taking and skewness) in response to (a) increased experience (a larger number of previous trades), (b) whether they made profits or losses in their first 25 trades? Is this effect significant?  In addition to discussing your conclusions, submit a spreadsheet containing your calculation

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