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() 

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. 

it's not only about r_a ≥ r_g, 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).