Statistics 701: Ponzironi 2, the gambling approach
Announcement
Homework 2 due next time.
Any homework questions?
A point estimate is just a regular estimate.
use y-hat when computing the slope from an elasticity.
draw a picture to convience yourself of this fact.
Faking a good empirical track record
Would a scheme that returned 2% over the market for the last 2
years impress you?
last 10 years?
last 20 years?
last 100 years?
Our goal is to generate such impressive returns without having
to understand actual stocks and bonds.
A Ponzi scheme for quiet customers
Start with 1000 customers who each give 1000 dollars
Each month, tell 10% of them that their account has gone
bust and no longer has any money in it.
Distribute the money of those busted 10% to the remaining
players.
After several rounds, you have a "client list" of
customers each whom has seen 10% returns over the past
several rounds.
After 25 periods you are down to 10 people. The scheme
basically crashes at this point. Notice that these
people have seen a 10% return for 25 rounds. They each now
hold 100,000 dollars!
Problem: The busted part of your client list will complain and
the scheme will be busted by the police.
Principle: Dead people don't talk.
Bettter principle: Non-existant people talk even less!
A Ponzironi scheme (pick one random player from your orginal
list and track their wealth.)
Start with 1 customer who gives 1000 dollars
Each month, place a bet which has a 91% chance of paying
out 10% of the current value and a 9.1% chance of losing
the whole thing.
If lucky, give money to client
If unlucky, tell client that they are busted
You have a 1/100 chance of making as far as 25 rounds
before your one client crashes.
After 25 periods you are down to 10 people. The scheme
basically crashes at this point.
Estimating the probability of rare events.
Suppose you are watching a biathelon (skiing and shooting) and
the shooter has hit 25/25 so far. What is her chance of
missing?
Suppose the true probability of missing is p, then to get 25/25
would have a chance of (1-p)^25. This is a very small
probability IF p > 3/25. But, if p < 3/25, the chance of this
occuring is greater than 5%.
Rule for seeing no misses in n shots so far:
0 < chance of missing < 3/n is 95% confidence interval
0 < chance of missing < 5/n is 99.5% confidence interval
0 < chance of missing < 10/n is 99.995% confidence interval
0 < chance of missing < k/n is 1 - exp(-k) confidence interval
Example:
Suppose you are watching 1000 biathelons in order to possibly
pick one to join your team. The best shooter never misses. How should
you estimate her chance of missing? Use 1 - .05/1000 for confidence
level. That means that k = 10.
How good a record can we fake?
Above scheme requires the possibility of losing everything.
What if the amount we can lose is bounded?
Any instrument for which options exist, can be converted
to having bounded downside. (Of course this lowers the
return.)
Options can be "replicated" as long as the instrument is
publically traded.
So publically traded assest can have their downside
protected.
(Simple rule: sell if price drops more than 10% during
any month. Your sell might not get executed until it
has dropped a bit further. This will depend on market
thickness. Then hold cash for the rest of the month.)
Hedge funds can't have options written against them
since buying and selling only occurs monthly instead of
continuously.
With bounded loss, we are forced to use a smaller disaster.
Hence we can't fake as good performace.
Why read a mutual fund prospectus?
An alternative to using options to bound the loss is to read
the prospectus.
A mutual fund who can use leverage can generate larger swings.
If only stocks can be purchased, downsides can be much lower
If only big stock can be purchase and they must be diversified,
then the downside is lower still.
Buy side: the three disasters rule
Determine what a total disaster would be by one of the
following methods: (listed best to worst)
Use actual options then the downside is legally
determined
Use active trading. Assume you monitor the value of the
fund and anytime it drops by X% you sell. You don't buy
again until next period. Charge yourself Y% for
transaction costs AND how much it might have dropped
past X%. Ideally this requires using tic-by-tic data.
Estimate a disaster drop by reading the prospectus. How
bad might things go?
Use -100% as the definition of a disaster
Make a column of empirical returns
Add three disasters to this column
Test if the average return for this column is higher than
expected.