I wish there was a Strunk and White for mathematics.
While by no means logically incorrect, it feels inelegant to setup a problem using variables A and B in the first paragraph and solve for X and Y in the second (compounded with the implicit X==B, and Y==A).
This is why Markowitz isn't used much in the industry, at least not in a plug-and-play fashion. Empirical volatility, and the variance
-covariance matrix more generally speaking, is a useful descriptive statistic, but the matrix has high sampling variance, which means Markowitz is garbage in garbage out. Unlike in other fields, you can't just make/collect more data to reduce the sampling variance of the inputs. So you want to regularize the inputs or have some kind of hybrid approach that has a discretionary overlay.
What a weird way to write the harmonic average.
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Write v_i = Var[X_i]. John writes
But if you multiply top and bottom by (1 / \prod_{m=1}^n v_m), you just get No need to compute elementary symmetric polynomials.If you plug those optimal (t_i) back into the variance, you get
where `H = n / (\sum_{k=1}^n 1/v_k)` is the Harmonic Mean of the variances.I wish there was a Strunk and White for mathematics.
While by no means logically incorrect, it feels inelegant to setup a problem using variables A and B in the first paragraph and solve for X and Y in the second (compounded with the implicit X==B, and Y==A).
There are lots of good books on writing mathematics:
1. How to Write Mathematics — Paul Halmos
2. Mathematical Writing — Donald Knuth, Tracy Larrabee, and Paul Roberts
3. Handbook of Writing for the Mathematical Sciences — Nicholas J. Higham
4. Writing Mathematics Well — Steven Gill Williamson
You can also trade bias against variance to minimize the mean squared error, which is the squared bias plus variance. This applies generally.
This is just the observed variance. Which means that you assume that this will be the variance in the future.
Don’t make decisions for evolving systems based on statistics.
Insider info on the other hand works much better.
This is why Markowitz isn't used much in the industry, at least not in a plug-and-play fashion. Empirical volatility, and the variance -covariance matrix more generally speaking, is a useful descriptive statistic, but the matrix has high sampling variance, which means Markowitz is garbage in garbage out. Unlike in other fields, you can't just make/collect more data to reduce the sampling variance of the inputs. So you want to regularize the inputs or have some kind of hybrid approach that has a discretionary overlay.
Upvoting b/c this comment is true, obviously I disapprove of insider trading.