Date: Fri, 18 Feb 2005 09:02:08 -0600 Daniel Sharp "SAS(r) Discussion" Daniel Sharp Re: Homework Exercise /Finance/Probability text/plain; charset=ISO-8859-1

I recall problems like this in portfolio theory,and it was my first exposure to SAS way back when, and I used punchcards for doing this because I had no idea how to use one of the terminals. The issue then was creating a frontier of tradeoffs between risk and return (forgot what its called) based upon various portfolios that can be constructed. Then, given that, there is a straight line that can be defined by making assumptions about what is the risk free return and the tradeoff between the risk-free return and the risky return as the portfolio make-up is varied. This goes back to the portfolio theory work that was done by Markowitz and others.

I did this eons ago and have had no further experience with it since I took the class back in the last century when I was young and had still had hair and it hadn't turned grey yet-probably 1979 or 80. However, there is a method to this and was well described in out text, so that our homework involved implementing the procedure that would calculate the optimal portfolio frontier (of risk vs return) and then calculating the slope of the straight line that ranged from the risk free return (return on the y-axis, risk on the x-axis, so this is the Y-intercept) then through the point where the line is just tangent to the risk-return frontier.

This done, pick a return and you have determined the risk associated with it by finding the corresponding point on the line from risk-free through the tangent to the risk-return frontier.

Regards,

Dan Sharp Research Analyst Research and Planning Madison Area Technical College

>>> "Choate, Paul@DDS" <pchoate@DDS.CA.GOV> 02/17/05 01:44PM >>> Nick -

Seems like voodoo to me. :)

Paul Choate DDS Data Extraction (916) 654-2160

-----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Nick . Sent: Thursday, February 17, 2005 11:09 AM To: SAS-L@LISTSERV.UGA.EDU Subject: Homework Exercise /Finance/Probability

Hello SAS experts, A kid (well, he's 30 yrs old, kid compared to me) here at work sent me this homework exercise to help him with. I already have some ideas on this problem but I wish to get your input on this as well. Maybe my ideas and yours can help him out on his homework:

1. Letıs say your fund has \$17 million to invest. Each of the 11 companies in which you might invest has a 40% chance of yielding tenfold returns and a 60% chance of going out of business. These probabilities are independent for the different companies because they are in different industries. Your investors want at least a .60 probability that the fund will yield \$60 million or more, and you want to keep \$5 million in reserve for other opportunities. How should you allocate the \$12 million among the 11 companies?

Extra Credit (optional): Suppose that instead of asking for a .60 probability of attaining \$60 million, you are willing to make that probability as low as 1/3; but you also want to reduce your chances of losing (at all) to below .05. Now how would you invest?

NICK