The Structure of Macroeconomic Factor Models

Stock returns are dependent on both the environment from business and shocks that occur in the economy from time to time. So perhaps they should be included in your multifactor return model.

__Macroeconomic factor models__ do exactly that. The factors used in a macroeconomic factor model are any differences from forecasts in variables such as inflation or real GDP growth. So when expected inflation of 4.5% becomes 4.8%, which value do you think becomes the factor value?

Not quite. That's the value, which was a surprise, but not the value of the true "surprise" itself.

No. That's just the expectation. There's nothing of use there.

That's right. It's not the value; it's the surprise.

Since there's usually an inverse relationship between inflation and stock prices, and assuming that this would be the case here, what would you predict about how this information enters a multifactor model?

You got it!

No. The sensitivity measure would be negative, actually.

The factor is the surprise inflation change, and the value of that factor is currently a positive 0.3%. But the negative relationship between inflation surprises and stock prices would be reflected in the sensitivity measure for that factor, so that sensitivity measure (the _b_ term, or beta) would be negative.

Here's what the model might look like. $$\displaystyle R_i = a_i + b_{i1}F_1 + b_{i2}F_2 + ... + b_{iK}F_K + \epsilon_i $$ The returns of the asset (stay with the idea that it's a stock for now) are predicted by some constant intercept, the factors (_F_), and the sensitivity measures (_b_). Maybe you just have that inflation surprise of 0.3%, and the other factors are all zero. What do you think would be the largest component of your predicted stock returns?

Exactly! If the inflation surprise were the main value, the model would predict negative returns.

No. That wouldn't really make sense. Remember that this influence is negative. If that were the main value, then the model would predict negative returns. Instead, the intercept is the largest component.

What does that mean the intercept should represent?

No. That would mean that the stock would return nothing without any macroeconomic shocks.

That's right!

No. That would mean that the stock would most likely return just the risk-free rate without any macroeconomic shocks.

Without any surprises, the stock should return what you expect it will return. That expected return will only be affected by surprises, like higher inflation that tends to be bad news.

And if the other factor is unexpected changes in GDP growth, what would you expect this sensitivity measure to be?

No. The factor would be zero in expectation, but not the sensitivity measure. Consider how surprise GDP growth would affect stocks.

Absolutely! Growth is good, especially for stocks. A positive surprise here is positive indeed. So expected growth of 2.0% might compare to actual growth of 2.1%. Then you would need a sensitivity measure for this factor, like maybe 5. Then the surprise factor of +0.001 translates into a change in the stock's expected return of five times that amount, or +0.005, which is +0.5%. These sensitivities are found with regression analysis, and of course you'll need to be careful and consistent with the figures. Maybe it's an annualized figure you're using each month to estimated annual stock returns. Just make sure it's clear how the values were estimated so that you can use them in the same way.

Probably not. This would suggest that higher GDP growth would cause stock prices to decline.

To summarize: [[summary]]

0.3%

4.5%

4.8%

The factor would be negative

The sensitivity measure would be negative

The intercept

The inflation influence

The risk-free rate

Zero in expectation

The asset's expected return

Zero

Something positive

Something negative

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