RE: What Constitutes Acceptable System Performance?

["Gray, Gabriel" <Gabriel.Gray@xxxxxxxxxxxxxxxxx>]

Gary, Dennis, and all,

First, there is a difference between qualitatively looking at Sharpe and
optimizing your system to maximize Sharpe. The later, I think Alex has
convincingly demonstrated to be a mistake. Second, Sharpe does punish
upward volatility in some circumstances. Since you are maximizing a
ratio, at some points the consistency of returns can dominate the
magnitude of the returns themselves. This is easy to see with only
positive returns. 
Assume the risk free rate is 0. Imagine a distribution where you make 4%
one month and 6% the next. Your average return is 5%, but your standard
deviation is just .0104 for a Sharpe of 4.7. Take another distribution
of returns of 1% a month for 9 months, 20% the next, 50% the next, and
70% the last. Your average return is 12.4%, your standard deviation is
.23, but your Sharpe is just .53. The first distribution returns 79%,
but the second 234% with no drawdowns! 

Admittedly, this is an extreme example, but I think it shows why you
wouldn't optimize a system to maximize Sharpe. Such an optimization will
attempt to remove any large positive returns far from the mean. 

Gabriel



-----Original Message-----
From: Gary Fritz [mailto:fritz@xxxxxxxx] 
Sent: Thursday, January 22, 2004 3:54 PM
To: omega-list@xxxxxxxxxx
Subject: Re: What Constitutes Acceptable System Performance?


> I'm not sure I buy that hypothesis or the whole notion that Sharpe 
> "punishes" upward volatility. There are two terms in the Sharpe
> formula: profit and stddev of profit. Downward volatility decreases 
> profit; upward volatility increases profit. Upward volatility gives a 
> higher Sharpe ratio every time.

Bingo.

I constructed a spreadsheet that calculates Sharpe ratio on 
monthly returns.  Then I fed it a 1% monthly return and a 0% 
Tbill rate.  Result:  infinite Sharpe, since there is zero 
volatility.

Then I added volatility to the results:  Each 4th month 
alternated between 1% + 2% = 3% and 1% - 2%.  Other months stayed 
at 1%.  Equal volatility upward and downward.  Result:  12-month 
sharpe alternated between 3.93 (after the 3% months) and 2.80 
(after the -1% months).

Next I changed each 4th month to be 1% - 2% = -1% -- only 
negative volatility.  Result:  12 month Sharpe = 1.90.

Next I changed each 4th month to be 1% + 2% = 3% -- only positive 
volatility.  Result:  12 month Sharpe = 5.80.

Finally I experimented with somewhat more realistic volatility.  
Every 4th month flipped between -2 / +3 (pos & neg volatility 
with a negative bias) and -1 / +4 (pos & neg volatility with a 
positive bias).  Result:  negative bias Sharpe = 1.66/3.01, 
positive bias Sharpe = 2.56/3.39.

So clearly positive volatility is NOT punished, at least not as 
compared to negative or mixed volatility.  Increased volatility 
IS punished, so ideally the Sharpe seeks out zero volatility.  
But in real-life system performance, you're not going to see zero 
volatility.  Given similar levels of volatility, a system with 
positive volatility will get a higher Sharpe score than a system 
with mixed or negative volatility.  And that high-Sharpe system 
is exactly the one you want to trade.

Gary