Required long-term return on Equity and Yield Curve shape

Hey guys,

Im confused by the following answer from EOCQ - Corporate Finance, Cost of Equity - Advanced Topics:

“The required return reflects the magnitude of the historical ERP,
which is generally higher when based on a short-term interest rate (as a result of
the normal upward-sloping yield curve), and the current value of the rate being
used to represent the risk-free rate. The short-term rate is currently higher than
the long-term rate, which will also increase the required return estimate. Th
short-term interest rate, however, overstates the long-term expected inflatio
rate. Using the short-term interest rate, estimates of the long-term required re
turn on equity will be biased upward.”

In this case, what is the relationship between the short-term interest rate and the long-term expected inflation? How does the use of short-term interest rate affects the estimate of long-term required return on equity?

Also, with a downward-sloping yield curve, the requiret rate of return is higher because of this equation?

re = rf + ERP, and, in this case we are increasing the risk-free rate, is that why required return increases? But at the same time, isn’t the ERP decreasing? I’m confused here…

I would appreciate if anyone can solve this doubt, exams are close and I’m worried I still have basic doubts.

Thank you so much!

Understanding the relationship between short-term interest rates, long-term expected inflation, and the required return on equity is complex. A higher short-term interest rate generally increases the required return due to its impact on the risk-free rate component of the CAPM model. However, this doesn’t necessarily mean the equity risk premium will also rise. The shape of the yield curve, either upward or downward sloping, influences the choice of the risk-free rate and subsequently affects the required return. It’s crucial to consider both the risk-free rate and the equity risk premium when estimating the required return on equity, as they are influenced by various factors beyond short-term interest rates.