MSB Trading - 2019, page-569

" if MSB went up $1 per week for the next 2 years - the average weekly return would be $1 and the standard deviation (a measure of volatility) would be zero."

Dude, you are wrong. A price series that goes up by $1 per week for the next two years does not have a standard deviation of zero. The weekly return is not constant but experiences a relative decline, which in functional form looks like this:- f(x) = [x(x - 2)] / (x - 2)^2 {where x is weeks; and f(x) is the relative change in return at week x}

For example, if we started at x = $1 then return in the first week would be 100% ($1 to $2); in the second week would fall to 50% ($2 to $3); and in the third decline further to 33% ($3 to $4). This series, even expressed in infinite form does not have a standard deviation of zero. In fact, in the case you mention i.e. a series that starts at $1.36 and grows by $1 a week for two years, the annualised standard deviation of returns over the two-year period is approx 65%!

I think what you were trying to say, was that if the price went up by (x%) per week then the standard deviation would be zero.