How does risk-free interest rate and interest rate differ on their impact on stock price?

Question

According to investopedia: how interest rates affect stock market,

"Higher interest rates tend to negatively affect earnings and stock prices (with the exception of the financial sector)."

However, according to analystprep: The value of an option:

If you know the risk-free interest rate is a known 5%, you would expect the stock price to increase by more than 5% on average.

In other words, if risk-free interest rate is higher, the stock price would be higher.

Do these two statements contradict each other? Does "risk-free interest rate" differ from "interest rate" in these two contexts?

Answer 1

Do these two statements contradict each other?

No - the first is saying that higher interest rates reduce expected earnings for companies that borrow money to operate (which is why financial companies are excluded), lowering current stock prices.

The second is talking about future stock prices. It is talking about prices from a derivatives (options) standpoint, calculating the expected future price of a stock just using interest rates. So they are somewhat orthogonal.

Although, higher interest rates also tend to lower stock prices because the expected return for stocks will be higher. With a (relatively) constant expected future value, a higher return means that current stock prices would be lower - meaning you'd want to pay less for the stock now to increase your expected return.

Answer 2

Unexpected rises in interest rates increase current stock prices (according the EMH, expected rises have already been priced in). Higher interest rates also tend to mean higher increases in stock prices. In calculus terms, the interest rate is negatively correlated with the stock price, but positively correlated with the derivative of the stock price.

With bonds, this can be explained a bit simpler: the bond is expected to reach face value at maturation. The higher the interest rate, the faster the bond is reaching face value. Since the face value is fixed, and the current value is calculated backwards from the maturation date, increasing in value faster means that its current value must be lower. Stocks are more complicated (there's no fixed "maturation date", for one thing), but the same general trends also apply to them.