In this workout, we're told that you are working as head of trading for old field LLPA long short equity hedge fund.

This means they're gonna have long positions and short equity positions as well.

Your fund has assets under management or a UM of 1.8 billion euros, and an equity analyst at the fund is bullish of Adidas shares and bearish of Puma.

The old field, CEO, likes the idea and suggests a long position in Adidas, equivalent to 3% of the fund assets under management.

So here's now question.

How many shares do you need to trade to create a beta adjusted market neutral trade? So let's introduce the issue here.

We're definitely going to have a long position in Adidas.

In order to have a market neutral trade, we're going to sell shorts, Puma shares.

So that's great. That's what we've got a highlighted in bold here.

Adida shares to buy and Puma shares to sell short.

The only slight issue is that they've got completely different beaters.

0.88 for Adidas, 1.24 puma.

So to get to our market neutral trade, we'll have to do some calculations.

Let's start with the Aidas.

Long market value, we were told by the CEO 3% of assets under management was fine.

So let's do that. That gives us our notional position in Euros and it's 54 million.

However, how many actual shares do I need to buy? Well, I'll divide by the added as share price, and that gives us the number of shares we can buy.

Now, unfortunately, it's very difficult to buy 0.7 of a share. So I'm gonna choose the round down function it asks for the number of digits.

I'm gonna go with zero to make sure it goes to a whole number.

Great. There's our final number of Adida shares we need to buy, but I still need to get down to my PMA shares to sell short, and they've got these different beat of figures.

So how do we deal with this? I need to work out, instead of this 54 million value for Adidas that we want to buy, I need to work out a beta adjusted long market value.

So I'll take that 54 million that we had, and I'm going to multiply it by the beta figure.

And this gives me a market neutral position.

Now I can take that exact same figure and make that my beta adjusted short market value.

So if Puma had a beta of one, this would be the value of Puma that would be selling short.

But Puma don't have a beta of one. They've got a beta of 1.2.

So I'm gonna take that 47 million and Divide it by the 1.2.

And now I've got the notional position in Euros of PMA that I actually want to sell short.

I'll take that figure and divide it by the share price.

I'll use the round down function again this time, 39 divided by the 41 to zero decimal places.

And we've now got our final answer.

We want to buy 267,591 ADIDA shares, and to have a market neutral trade, we'll sell short 957,678 PMA shares.