In this workout, we're looking at an investor that has a Time Horizon of one year and considers the following two stocks and some macroeconomic projections.

We are asked what is the expected return for each stock derived from an Arbitrage pricing Theory or apt model based on unexpected changes and inflation and GDP.

So we've got two different stocks ABC Corp and XYZ Corp, and we've got back to beaters in relation to each of our two factors inflation and GDP growth.

The way that we can identify the expected return on each stock is to look at the surprise factor that we have.

From inflation and GDP growth rates being different from what was expected.

The underlying assumption here is that the expected inflation and expected GDP growth are somehow baked into the risk-free rate of return that we're given of 2% So to help us with this calculation the first thing we're going to have a look at is our formula for our expected return.

And that formula is going to be that our expected return is going to be the risk free rate of return plus the inflation beta for each company.

as our sensitivity to the inflation shock multiplied by that inflation shock or inflation surprise We're then going to add to this.

The GDP beta the sensitivity of each stock to a change in GDP away from the expected level multiplied by that GDP.

shock or surprise So this is the formula that we're going to be using to identify the expected return of each of our two companies.

If we just have a look at the beaters for a second though, we can see that for the inflation beta.

ABC Corp has a negative beta what this tells us is that there is an inverse relationship between the inflation shock and the performance of this company.

If inflation ends up higher than expected this company is going to do badly as a result.

Whereas if inflation is below it's expected level. That will be a good thing for this Company's stock price performance.

XYZ on the other hand as a positive inflation beta so if there's a positive shock inflation is higher than expected. This will add to the return of XYZ Corp.

So let's go down and put the numbers together for this. We're gonna build this up in turn. So we're going to take the risk free rate for both.

They both start off with that expected return of 2% And then for ABC Corp the impact of the inflation differential we need to look at.

What inflation actually was? The 1.5% and subtract from that the expected value.

What this tells us is that inflation is half a percent below what we expected it to be.

But then we need to multiply this by the beta.

And the beta for this Factor? For ABC Corp, is this negative factor of four times? So as a result? Inflation being half a percent below. It's expected level is adding 2% to the return of ABC Corp.

If I then look on to the expected and actual inflation levels, we can then copy this to the right and get the inflation impact for XYZ Corp.

Which is a negative 1.2% the beta but XYZ Corp has of 2.4% indicates that the return on the stock will move in the same direction as the difference between the actual level of inflation and the expected level since we are half a percent below the expected level for the actual level of inflation with multiply through by the beta to give us minus 1.2.

As the implication of inflation being half a percent below its expected level for XYZ Corpus stock performance.

If we then look at the GDP growth effects again same outcome. We need to look at the actual GDP level.

3.5% and subtract from that the expected level of 3% So here we have inflation that is half a percent above its expected level. I'm going to lock onto both of these two factors.

and then for ABC Corp within its pick up the beta Factor here for GDP growth.

GDP growth being above its expected level is a good thing.

For ABC Corp, and it adds an extra 4% return. So overall the expected return for ABC Corp is 8% because inflation is below it's expected level and GDP growth rates are above their expected level. Both of these two factors add to the expected return of ABC Corp.

If I copy this across for XYZ Corp, then we can see that inflation being below its expected level is a bad thing for XYZ Corps to return but they still have a positive impact from GDP growth rates being above their expected level just to a lower degree than ABC Corp because they have a lower beta.

Overall XYZ Corps. Therefore is generating that much lower level of Return of 2.6% because of their positive correlation to the inflation shop level.