about me
game theory
... more
Subscribe Weblog

Ernest Chan (blog) writes in his book Quantitative Trading - How to Build Your Own Algorithmic Trading Business:
Here is a little puzzle that may stymie many a professional trader. Suppose a certain stock exhibits a true (geometric) random walk, by which I mean there is a 50-50 chance that the stock is going up 1 percent or down 1 percent every [day]. If you buy this stock, are you most likely--in the long run and ignoring financing costs--to make money, lose money, or be flat?
Most traders will blur out the answer "Flat!," and that is wrong. The correct answer is that you will lose money, at the rate of 0.005 percent (or 0.5 basis points) every [day]! This is because for a geometric random walk, the average compounded rate of return is not the return μ, but is g = μ - σ^2/2.
For this very reason, geometric Brownian Motion is often written as
bmwhere "μ - σ^2/2" is the expected return and "μ" is the return of the expected prices, i.e. ln(E[St]/E[St-1]).

If you lose 50 percent of your portfolio, you have to make 100 percent to get back to even... that's what everybody knows. But it's also interesting to see how mild volatiltiy hurts over time. Here are ten (random - no cherry picking) realizations of a geometric Brownian Motion with a daily volatility of 1% (i.e. a yearly volatility of 16% when having 252 trading days) over the period of 100 years:
R Development Core Team (2008). R: A language and environment for statistical computing.

PS: Hey, this looks promising:
OneEyedMan (guest) meinte am 26. Dec, 16:17:
What you described isn't Brownian motion
Because increments of all scales are not normally distributed. The distribution you described has the exact geometric mean of 0.
ln (1+g) = 1/2 ln (.99)+1/2 ln (1.01)
->2 ln (1+g) = ln (.99 * 1.01) = ln(1) = 0 -> g =0 
Mahalanobis antwortete am 26. Dec, 19:28:
First, we are talking here about geometric Brownian motion. If a stockprice follows geometric Brownian motion, its returns are normally distributed but the increments (the absolute changes in the stock price) are log-normally distributed. Chan used a binomial model but it can be shown that the distribution of a stock that follows a binomial model converges to the distribution of a stock that follows a geometric Brownian motion. For my simulation, I drew from a normal distribution.

Second, you made a computational error: 0.99*1.01 does not equal one, it's (1-0.01^2).

S(t) = S(0)*Z(1)*Z(2)*Z(3)...Z(n)
log(S(t)/S(0)) = log(Z(1))+log(Z(2))+...+log(Z(n))

E(log(Z(s))) = 0.5*log(0.99) + 0.5*log(1.01)
E(log(Z(s))) = 0.5*(log(0.99*1.01))
E(log(Z(s))) = 0.5*(log(0.9999))

Since log(0.9999) < 0, S(t) goes to minus infinity. QED

NB: log() = ln() 
OneEyedMan (guest) antwortete am 27. Dec, 23:19:
Point taken on the arithmetic error. My mistake and since my point turned on it, it was a big mistake.

Is Chan's point just that you shouldn't confuse the arithmetic and geometric mean return? That's a critical fact that all asset managers should know.

Is he making a point about the second order aproximation to the geometric mean using mean and variance? If so, I don't get it. Because why would you use the approximation when the exact answer is so readily available. 
Mahalanobis antwortete am 28. Dec, 10:44:
it's not only about ra ≥ rg, but also about the extent of the difference.

I think these days most asset managers look at VAMI charts and compounded rates of return since that is what their software (e.g. PerTrac) gives them anyway. I worked as a Hedge Fund Analyst until recently (Woops) and the track record of most funds was somewhere between 2 and 5 years (monthly data). And especially when having such short time series, one shouldn't assume μ and σ fixed. It's more about how much those parameters can vary given certain environments. (And in case the funds do mark-to-model, you can forget most of the statistical analysis anyway ;-D).

Chan's book is more about "How to build your own algorithmic trading business" than on "quantitative trading". Take a look at the table of contents (Amazon). For somebody who comes straight out of University and has no practical experience, it is probably a good read and the price is really ok too (< $40). 
kimcil (guest) antwortete am 7. Apr, 13:12:
Years later, while wrapping up her Ph.D., Oster stumbled onto a seemingly unrelated fact: a small medical literature suggesting that women with hepatitis B were far more likely to give birth to boys. What followed was a series of sophisticated natural experiments, the upshot of which was to demonstrate that 100 million women hadn't gone missing after all. Instead, unusually high rates of hepatitis B had arranged it so that Asian mothers were producing far more boys than nature's track record would suggest.
alfamart official partner merchandise fifa piala dunia brazil 2014
Unit Link Terbaik di Indonesia Commonwealth Life Investra Link 
measurement data collectors (guest) antwortete am 27. Jun, 07:52:
There are ten major categories, such as “independent shorts”, “tv commercials / public service announcements” or “music videos”, which are further divided into sub categories.measurement data collectors 
Netzwerkkamera (guest) antwortete am 23. Aug, 13:44:
VIVOTEK IP8131, Kompakte Outdoor Netzwerkkamera, 1 Megapixel,IR-LED und H.264 Kompression für den Aussenbereich MIT Synology DiskStation DS213j inkl. 1TB Festplatte und Surveillance Station Software 
deviyudis antwortete am 25. Mar, 00:26:
Your information is really interesting. Thank you very much for taking the time to share with us. iklan baris gratis 
nickgogerty (guest) meinte am 28. Jan, 21:45:
FYI it is called Siegels paradaox

nice demonstration. 
Mahalanobis antwortete am 29. Jan, 09:24:
I've actually blogged about it already. 
maskodok antwortete am 15. Jan, 01:54:
Interesting topic for a blog. I have been searching the Internet for fun and came upon your website. Fabulous post. Thanks a ton for sharing your knowledge! It is great to see that some people still put in an effort into managing their websites. I'll be sure to check back again real soon.
Mobil Sedan COrolla,Idrpoker.com agen Texas poker Online Indonesia Terpercaya, Mobil Sedan COrolla, Cipto Junaedy 
kurasakisan meinte am 30. Sep, 22:27:
It's my first visit and yet, totally great for first coming. Thank you for prividing useful content. Don't forget to visit some of my profiles like Eterna Profiles - Scoop It - Pocket Knowledge Profile - Cyberlaw Harvard - Hong Kong Protest via cnn 
ahmedomar meinte am 1. Oct, 21:11:
wow! nice post!
هناك العديد من المهام التي يقوم بها اللاعب في لعبة صب واي سيرفرس، احيانا يكون عليك أن تجمع عدد محدد من العملات، أو المفايتح، وأحيانا يجب عليك أن تقفز لعدد معين، والعديد من المهام الاخري، التي تميز لعبة صب واي سيرفرس، وكلما نجحت في انهاء المهام كلما تقدمت في اللعبة بشكل افضل واسرع اود ان اشير ايضاً الي العاب ك من سيربح المليون و زوما و جاتا
ttlwu meinte am 12. Nov, 10:14:
This is a great inspiring article.I am pretty much pleased with your good work.You put really very helpful information. Keep it up. Keep blogging. Looking to reading your next post.
usb 3 flash drive 
ttlwu meinte am 8. Dec, 11:43:
I found that site very usefull and this survey is very cirious, I ' ve never seen a blog that demand a survey for this actions, very curious...
gamesr3d meinte am 30. Dec, 20:54:
woow i love it

???? ?? ????? ???????
?????? ??????? ??? ???????? ?? ???????? ??????? ???? ?? ????? ??????? ???? ??? ???? ??? ???? mbc ?? ???????? ??????? ???? ?????? ???? ????? ??? ?? ???? ????? ???? ??? ???? ????????
??? ?????? ??????? ??? ?? ????
?? ????? ???????
?? ?? ???? ??? ??????? ?????? ???? ????? ??? ?????? ??? ???? ????? ??? ???? ???? ???? ????? ?????? ?? ????? ???????? ??? ?????? ??? ??????? ????? ??? ??????? ???? ??????? ?? ??? 4 ?????? ??? ???? ?? ????? ?????? ?????? ????? ????? ???? ????? ??????? ??????? ???? ????? ????? ????? 98% ??? ??? ????? ??? ??????? ????? ???????? ???? ???? ?? ???? ??? ?????? ??? ???? ??? ?????? ????????? ??????? 100% ????? ???? ?? ?? ?????? ??????? ??? ??? ?????? ?????? ?????? ???? ???? ????? ??? 
gamesr3d meinte am 30. Dec, 20:55:
I like this very much,very good post.
good games her subway


?? ???
???? ????? ??? ????? ???? ????? ??? ??????? ?? ???? ????? ??? ??? ???????? ????? ??????

???? ?? ???
???? ???????? 
gamesr3d meinte am 23. Jan, 19:28:
very nice post brother, hopefully it's news can be received by many people.


spider2016 meinte am 12. Mar, 03:59:
تعتبر العاب تلبيس بنات من اشهر الانواع في هذا المجال وهي بدورها تتضمن عدة اصناف جميلة ويعشقها الكتير وخاصة البنات منها العاب تلبيس ومكياج التي تمزج بين التلبيس وكذلك الميك اب في آن واحد هذا الامر الدي يزيد من جمالها وتجعل كل من يلعبها يستمتع بذلك زد على ذلك العاب تلبيس باربي التي تعرف شعبية كبيرة لانها شخصية مشهورة ويعرفها الصغير والكبير ولهم ذكريات جميلة معها لانها اشتهرت في عالم الكارتون والان اصبح الامر كذلك في مجال الالعاب وغير هذا هناك كذلك نوع آخر مميز ايضا وهو العاب تلبيس عرائس فالجميع يحلم ان يقوم بتلبيسهما لانها تذكرهم بهذه المناسبة الجميلة الا وهي الزواج التي تعتبر اهم مرحلة في حياة الانسان وهناك انواع مغايرة لها جمهور كبير في كل انحاء العالم وهي العاب قص الشعر ليس هي فقط بل توجد ايضا العاب طبخ التي يمكن للجميع لعبها سواء كانوا اولادا او بناتا وهي الاكتر طلبا في النت ويحبها الجميع ومعها ايضا العاب باربي التي تكلمنا عليها بكل انواعها