Burmeister, Roll, and Ross model

Burmeister, Roll, and Ross model definition

As we discussed in the introduction, the BIRR model uses five factors. Let’s discuss the factors in more detail:

• confidence risk: unanticipated changes in investors’ willingness to undertake risk investments. It is the difference between the yield on government bonds and risk corporate bonds
• time horizon risk: unanticipated changes in investors’ desired time to payouts. It is measured as the difference in the interest rate between 20-year long-term bonds and an 30-day T-bills.
• inflation risk: unexpected components of short-term and long-term inflation rates. It is measured as the difference between unexpected and actual inflation at the end of the month
• business cycle risk: the unexpected change in the level or real business activity. It is measured as the difference between expected and actual business activity.
• market timing risk: the part of the S&P 500 return that is not explained by the four first macroeconomic factors.

To get the model, we first perform a regression using historical data on the above factors. That way, we obtain parameter estimates that we can combine with forecasts on the five factors. The result is the required return based on the BIRR model.

Burmeister, Roll, and Ross model example

Let’s illustrate the model with an example. Suppose we used historical data to estimate the parameters of the model. Thus, we have the sensitivities of a stock to the macroeconomic factors. Next, we produce forecasts on the five macroeconomic factors and calculate the required rate of return as follows.