212 Inv Game scoring

Investment Project Assessment

The investment project runs over three months: September through November, but only October and November will be scored.

You will earn points for the assignment based on the value of your portfolio at the end of the month. My objectives when designing the mechanism to calculate your project score (out of 300 remember) were:

1. I do not want students competing against each other, so this precludes referencing your performance to that of the class, through an average, say.

2. I want your score to reflect your performance relative to some average, so that you can “do better” or “do worse” depending on your efforts.

3. I do not want you to be penalized by forces beyond your control, such as the general movements of the market. For example, I don’t want every one to fail just because the stock market crashed.

4. I do not want the investment project to take on an excessive value. I am willing for the project to earn you more than 300 points (like extra credit), but I will avoid excessively large scores (such as 400/300).

The resulting scoring system is (based on an initial investment of $100,000 as an example):

1. The base score for the project is 225/300 (75%).

2. Your raw project multiplier is the ratio of the end value of your portfolio to the starting value. Eg. Your portfolio is worth $125,000 at the end of the month, your raw project multiplier is:

, i.e. your portfolio grew by 25%.

3. Your relative project multiplier is the ratio of your performance to that of the market, as measured by the change in the S&P500 index. Eg, if the S&P500 increased by 10% over the month, then your relative project multiplier would be:

, i.e. you did nearly 14% better than the market.

4.       If your relative multiplier is greater than 1.0 your score is calculated as follows:
(a)    Subtract 1 from your multiplier, then divide by 0.125 to get your “Z” (e.g. (1.136-1)/0.2 = 0.68)
(b)     Find the Normal probability of getting your Z (e.g. Pr(Z£.0.68) = 0.75)
(c)     Subtract 0.5 from this number (e.g. 0.75 - 0.5 = 0.25). This is your project multiplier score.
(d)     Multiply the project multiplier score by 240 and add to 225, the base score. (e.g. 225 + (0.25 x 250) = 287.5). This is your project score.

5.       If your relative multiplier is less than 1.0 your score is calculated as follows:
(a)     Subtract 1 from your multiplier, then divide by 3.0 to get your “Z” (e.g. (0.864-1)/3 = - 0.045)
(b)     Find the Normal probability of getting your Z (e.g. Pr(Z£- 0.045) = 0.48)
(c)     Subtract 0.5 from this number, then take absolute value (e.g. 0.48 - 0.5 = 0.02). This is your project multiplier score.
(d)   Multiply the final project multiplier by 600 and subtract from 225, the base score. (e.g. 225 - (0.02 ´ 600 = 213). This is your project score.

I will do these calculations for you (but you can do them in Excel also if you want), and will determine your project score using the rules above (please note that the multipliers are slightly different in order to give larger scores in a bear market!). The rules allow for a maximum score of 350/300 for the project, and a minimum score just below 200/300, and you’d have to lose a whole bag of your money to get that low a score! The scoring rules above produce an asymmetric Gaussian distribution that looks like:

Your October and November scores will be calculated separately, and an overall 2-month score, then I will choose the highest score as your project score.

You are required to submit a final report for each month to register your investment project and receive a score. You will be assessed a penalty of 5% of your project score for failure to submit both reports.

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