Hi,I don't have a sense of how much uncertainty practicioners would accept in real-world applications of financial models.Let's consider a simple example. Denote with x the expected return on an asset. This can be an input of either a simple Markowitz model or a super complicated model.In both cases x is a random variable and, in principle, one should deal with its uncertainty.Assume you estimate the expected return such that x is the sample average but you have information about the whole distribution.I was thinking of a very simple metric such as z = [q(95) - q(5)] / q(50), where q(i) is the ith percentile. That is the length of the 5%-95% confidence interval standardized by the median. I would have a sense of which numbers for z are considered acceptable or not.Thanks.

In my experience, if you need a number you need a number. Your particular example is probably unnecessarily complicated by q(50) being very close to zero... I doubt anybody can provide a useful answer, because the question is simultaneously too open-ended and too specific.

There's no standard value for z because one can so readily convert any z into any other larger or smaller z via leverage or allocation. And if one hedges (which does come with a host of potential dangerous assumptions), then one might not care about z at all because one are not exposed to the uncertainty. Finally, different customers (or customer applications) have different risk tolerances.That said, you might want to research Sharpe ratios which is a inverted version of your z.

QuoteOriginally posted by: frameLet's consider a simple example. Denote with x the expected return on an asset. This can be an input of either a simple Markowitz model or a super complicated model.I would just add that this is why Markowitz portfolio optimization, as originally proposed, was essentially a failure. The sensitivity of the allocations (of single names) to the expected returns is orders of magnitude beyond what can actually be estimated, whereyou are lucky to estimate the sign correctly. In other words, the confidence intervals needed to actually use that particular theory are, let's say, 100xsmaller than the real-world plausible confidence intervals that you might get through the best financial analysis possible.Of course, the theory morphed, through Sharpe and others into one of the rationales for indexing and wide diversification. In general, confidence intervals are hugely important in finance --but like all statistics, are easily abused or rendered meaningless becausethey are computed under poor assumptions.