nhaehnle's reply contains the fundamental error in your post, but there is another issue, which is that variance doesn't go away when you take the long run. Option 2 has more variance, and this doesn't get averaged out in the long run. Each year adds more variance to your wealth, which is a bad thing.
Sure, the variance on the yearly rate of return will shrink as the time horizon grows. But because the yearly rate is compounded, this doesn't prevent the total variance in returns from growing with time.
Long term investment doesn't cure the risk from volatile investments.
Sure, the variance on the yearly rate of return will shrink as the time horizon grows. But because the yearly rate is compounded, this doesn't prevent the total variance in returns from growing with time.
Long term investment doesn't cure the risk from volatile investments.