Wharton Undergraduate Division is once sponsoring (with the
Tutoring Center)...free of charge....Wednesday until December
8, from 6:30 - 8:30, in room 104/105 Vance Hall.
Finanacial simulation
Show of hands: Who liked: Green? Red? White?
White is like T-Bills/cash.
Green is like the market
Red is like an "internet stock."
What was your final wealth for white/green/red?
Make a histogram of each (0 - 2000 for white, 0 - 20,000 green)
Red mostly goes to zero, but someone will prob. be lucky (billions of dollars final wealth)
(either do this on the blackboard or in JMP)
Growth is determined not just by the mean but also by the variance
Joe's boss gets mad at him, and cuts his pay 10%
The next day, his boss says he isn't mad anymore and so gives him a 10% raise.
Why isn't Joe completely happy about this?
Notice: Joe is behind 1 percent from where he started
True growth rate = mean - 1/2 variance
Sometimes called the log-growth rate
Related to a utility function that looks like a log
To tame distribution of red, compute the log(final wealth)
either use base 10 logs (to make the ploting easier) or base
e logs (to make the drift rate meaningful) But make sure that
everyone in class is useing the same base!
Have each group compute their three logs of final wealth
Sketch new histograms for each color (or compute logs in JMP)
red is much more spread out, but drifts left
Work out what should happen for Pink
via example, show that the mean of pink is about 1/2 that of
read (in other words, the mean of white is about zero)
Via example, show that the standard deviation of Pink is
about 1/2 that of Red (In other words, the variance of white is
almost zero)
compute the expected log growth rate for pink (mean - 1/2 variance)
If using log-base-e, "guess" where a typical groups final pink wealth should be
collect pink data on log scale
Moral: Need both the mean and the variance to evaluate a stock /
bond / portfolio / option / derivative product.
Next class we will discuss how to compute variances for combinations of stocks