Question 1 (60 points) Four graduates from the Graham School of Management at Saint Xavier University (i.e., Amy, Brad, Chris, and Dale) have been hired by a white-shoe firm headquartered in Chicago. The first task that they receive is a complex one: the CFO of that white-shoe firm requests them to proceed with a complete analysis of three stocks, namely K, E, and Y. In fact, they have the mission to construct a new portfolio that will be sold to institutional clients: the KEY Portfolio. More information on stock returns is provided below.

State of the Economy -Probability-Stock K -Stock E -Stock Y

Catastrophic 2.00% -31.75% -10.50% -3.25%

Bad 24.50%. - 7.25% -3.75%. -1.00%

Normal 46.25% 2.50% 1.00%. -0.50%

Good 25.75% 4.50% 5.25% 3.25%

Exuberant 1.50% 15.75% 25.75% 4.50%

1a. Please compute the expected return and the standard deviation pertaining to each of the three stocks.

1b. Please compute the expected return and the standard deviation pertaining to the KEY Portfolio (note: the capital allocation is equally weighted).

Question 2 Illinois Financial Theory Orb (IFTO) is a consulting firm specialized in corporate training. In fact, IFTO is currently preparing a special learning material on aspects pertaining to time series and probability theory for an important client: the Federal Reserve. Because of your sound knowledge in principles of finance, the CEO of IFTO has decided to hire you to help them complete that document.

2a. Assume that you have historical data on stock S. In particular, you have stock returns pertaining to the last five trading days. If we intend to compute its historical variance, why is it necessary to use N- 1 in the denominator of the formula? Please explain. 2b. In probability theory, what is the set? Please explain.