So under-diversified portfolios will under perform...
If I can invest in either of two portfolios, where one is LogNorm(1.25, 0.5), and the other is LogNorm(1,1), which should I prefer? They have the same mean, but my expected return over time still is dominated by one that has a lower standard deviation. (Try it in excel.)
If you’re looking at long-term results, you don’t really want the (arithmetic) mean of short-term results, you want the geometric mean (or, equivalently, the arithmetic mean of logarithmic short-term results). So the first of those portfolios is unambiguously better if what you care about is typical long-term performance.
We’re not arguing about what’s a good idea. We’re arguing about what could cause actively managed funds to do worse on average. I suppose it’s possible that the statistic I saw was calculated using a geometric mean, or even a median.
If you look at the single period mean, it will not represent the portfolio return. That’s why the expectation of an RV in a single period is insufficient information for looking at the return, and why we want to reduce volatility, and preserve expected.
So under-diversified portfolios will under perform...
If I can invest in either of two portfolios, where one is LogNorm(1.25, 0.5), and the other is LogNorm(1,1), which should I prefer? They have the same mean, but my expected return over time still is dominated by one that has a lower standard deviation. (Try it in excel.)
If you’re looking at long-term results, you don’t really want the (arithmetic) mean of short-term results, you want the geometric mean (or, equivalently, the arithmetic mean of logarithmic short-term results). So the first of those portfolios is unambiguously better if what you care about is typical long-term performance.
We’re not arguing about what’s a good idea. We’re arguing about what could cause actively managed funds to do worse on average. I suppose it’s possible that the statistic I saw was calculated using a geometric mean, or even a median.
Exactly.
If you look at the single period mean, it will not represent the portfolio return. That’s why the expectation of an RV in a single period is insufficient information for looking at the return, and why we want to reduce volatility, and preserve expected.