Let's see how equity beta hedging works in practice.

Suppose your long 500,000 shares of Alpha Bank trading at 32.15 euros per share with a historical beta of 1.4 to hedge that exposure.

In other words, to remove market risk, you could sell short B Financial Co, a peer company in the same sector with a beta of 1.1, or you could short the National Equity Index if you hedge with B Financial Co.

Your long market value is 500,000 shares times 32.15.

That's 16,000,070 5,000 euros to beta adjust this multiply by 1.4, giving a beta adjusted long market value of about 22.5 million euros.

To neutralize that exposure, the short position must also have a beta adjusted value of 22.5 million euros.

So with B Financial COS beta of 1.1 and price of 3.2, you'd need to short roughly 6.39 million shares to balance the trade 22.5 million divided by 1.1 divided by 3.2.

But please note that this only neutralizes market risk.

You still carry the spread risk between Alpha Bank and B Financial Co.

They don't move perfectly in line with each other, so some tracking error will remain.

Alternatively, if you hedge using the index, you again target a short notional of about 22.5 million euros.

In practice, you need to convert that notional into futures contracts.

Using a contract multiplier then round to a whole number of contracts and a small residual exposure is normal.

As a reminder, as the index has a beta of one, and we are using the beta adjusted long value already, no further beta adjustment will be required.

When putting together a hedge like the one above, there are two main practicalities to budget for borrow or short costs and dividends owed while short, if you hedge with stock and roll or slippage, if you use futures currency or time zone mismatches between legs can also introduce noise.