Betting Against Beta on Euronext Large Caps

Betting against beta, Frazzini and Pedersen (2014), is the claim that leverage-constrained investors bid up high-beta names, so a book that is long low beta and short high beta, with the two legs scaled to a similar market exposure, earns a premium. A minimum-variance optimiser often lands near low-beta names as a side effect. This page forces the comparison: the sort key is beta, and the leverage is explicit.

The names are the Euronext large-cap panel: Paris (*.PA), Amsterdam (*.AS), Brussels (*.BR), and Milan (*.MI). Beta is measured against the EURO STOXX 50. The same download feeds the factor-momentum page and the variance-premium page.

Beta uses 252 daily simple returns ending the day before the rebalance:

$${\hat{\beta }}_i=\frac{\mathrm{Cov}(r_i,r_m)}{\mathrm{Var}(r_m)}$$

The low third and the high third are the two legs. Let ${\bar{\beta }}_L$ and ${\bar{\beta }}_H$ be the average betas inside those legs, floored at 0.15 so a near-zero beta cannot demand infinite leverage. The leg multipliers are

$${\lambda }_L=\min \left(2.5,1/{\bar{\beta }}_L\right),{\lambda }_H=\min \left(2.5,1/{\bar{\beta }}_H\right)$$

Names inside a leg are equal-weighted and then multiplied by $\lambda$. The low-beta leg is positive. The high-beta leg is negative. One-way cost is 15 bps on L1 turnover, which matters because a 2.5 leverage cap makes the gross book larger than a unit long-short.

The reported mean is the Newey–West test on this net monthly return. The EURO STOXX 50 wealth path is the scale reference. The book is not constrained to a beta of zero after the fact; the cap at 2.5 leaves a residual market exposure whenever the raw betas are far from one.

Cards include the latest low-beta and high-beta sleeve averages so the leverage applied at the last rebalance is visible. The wealth chart compounds the net book against the EURO STOXX 50. Because the book is levered and short, a drawdown can exceed the index drawdown even when the average beta gap is small.

Frazzini–Pedersen betas are shrunk toward one and estimated with overlapping logs on a correlation-weighted window. The beta here is an ordinary 252-day OLS beta. The rank order is similar. The leverage is not identical.

A short leg in Milan or Brussels names is not the same operational object as a short leg in S&P 500 names. Borrow, tax, and the euro funding rate are outside the 15 bp haircut.

Yahoo Finance adjusted closes are not a point-in-time index membership file. The constituent lists are a liquid large-cap panel, fixed in the repository, not the official index as it stood on each rebalance date.

The risk-free rate is set to zero in every Sharpe ratio. A local bill rate would lower the ratios and would not, by itself, change a long-short spread.

Costs are a flat one-way haircut on weight turnover. They do not include borrow fees, lot-size rules, auction imbalance, stamp duty, or the Shanghai and Hong Kong short-sale bans that bind a live short book.

This is a research record. It is not a recommendation to trade the sleeve.