You're right that it's an arbitrary interval, but the math is still valid if you assume (as I cautioned against) that each investment is a coin flip relative to

You're right that it's an arbitrary interval, but the math is still valid if you assume (as I cautioned against) that each investment is a coin flip relative to the market. In that case, over any time period your relative performance is the sum of a series of coin flips, i.e. a binomial distribution with mean 0. This has a 50% chance of outperformance regardless of the interval -- what changes as a function of interval is the total variance, not the median result. One consequence of this is that the probability of outperforming each day over 40 days is the same as outperforming each year over 40 years. The latter sounds more impressive, but it actually isn't. The former would be impressive too if the null hypothesis really is a series of coin flips (but again, it's not).