I’m not sure how to calculate it precisely, I think you’d want to run a regression where the independent variable is the value factor and the dependent variable is the fund or strategy being considered. But roughly speaking, a Vanguard value fund holds the 50% cheapest stocks (according to the value factor), while QVAL and IVAL hold the 5% cheapest stocks, so they are 10x more concentrated, which loosely justifies a 10x higher expense ratio. Although 10x higher concentration doesn’t necessarily mean 10x more exposure to the value factor, it’s probably substantially less than that.
I just ran a couple of quick regressions using Ken French data, and it looks like if you buy the top half of value stocks (size-weighted) while shorting the market, that gives you 0.76 exposure to the value factor, and buying the top 10% (equal-weighted) while shorting the market gives you 1.3 exposure (so 1.3 is the slope of a regression between that strategy and the value factor). Not sure I’m doing this right, though.
To look at it another way, the top-half portfolio described above had a 5.4% annual return (gross), while the top-10% portfolio returned 12.8% (both had similar Sharpe ratios). Note that most of this difference comes from the fact that the first portfolio is size-weighted and the second is equal-weighted; I did it that way because most big value funds are size-weighted, while QVAL/IVAL are equal-weighted.
(These numbers are actually more similar than I expected—I would have predicted the top-10% portfolio to have something like 5x more value factor loading than the top-half portfolio, not 2x.)
I’m not sure how to calculate it precisely, I think you’d want to run a regression where the independent variable is the value factor and the dependent variable is the fund or strategy being considered. But roughly speaking, a Vanguard value fund holds the 50% cheapest stocks (according to the value factor), while QVAL and IVAL hold the 5% cheapest stocks, so they are 10x more concentrated, which loosely justifies a 10x higher expense ratio. Although 10x higher concentration doesn’t necessarily mean 10x more exposure to the value factor, it’s probably substantially less than that.
I just ran a couple of quick regressions using Ken French data, and it looks like if you buy the top half of value stocks (size-weighted) while shorting the market, that gives you 0.76 exposure to the value factor, and buying the top 10% (equal-weighted) while shorting the market gives you 1.3 exposure (so 1.3 is the slope of a regression between that strategy and the value factor). Not sure I’m doing this right, though.
To look at it another way, the top-half portfolio described above had a 5.4% annual return (gross), while the top-10% portfolio returned 12.8% (both had similar Sharpe ratios). Note that most of this difference comes from the fact that the first portfolio is size-weighted and the second is equal-weighted; I did it that way because most big value funds are size-weighted, while QVAL/IVAL are equal-weighted.
(These numbers are actually more similar than I expected—I would have predicted the top-10% portfolio to have something like 5x more value factor loading than the top-half portfolio, not 2x.)