Can Stock Prices Withstand a 6% Interest Rate? – An Analysis Based on the Relationship Between Interest Rates and P/E Ratios –

The recent 10-year U.S. Treasury yield has risen by 1% from 4.2% at the start of the year to 5.2%, and the impact on stock prices is a cause for concern.

The background includes inflation concerns such as rising oil prices due to escalating tensions in the Middle East, increased demand for capital due to AI investment, and an increase in the supply of government bonds due to massive fiscal deficits and debt expansion, making it an environment where interest rates may be difficult to lower.

If interest rates continue to rise to 5.5%, 6%, and so on, can stock prices withstand it?.
It is often said that “when interest rates rise, stock prices fall,” but in this article, I have explored “theoretically why and by how much stock prices fall,” including the relationship between P/E ratios and interest rates, expected EPS (earnings per share) growth rates, and the impact of AI, to provide a realistic look at the impact on stock prices.

1. Why does the “theoretical formula for P/E ratio” look like this in the first place?

The relationship that “when interest rates rise, the P/E ratio falls” can be derived algebraically from the “Gordon Growth Model,” which is a fundamental concept in finance.

[1: Stock Price Discount Model]
The current stock price (P), calculated by discounting a company’s future earnings (E) by the investor’s required return (r) and growth rate (g), is expressed as follows using the formula for the sum of a geometric progression.

[2: Decomposition of Required Return (r)]
The return (r) required by investors is the risk-free rate (Rf) plus the equity risk premium (ERP).

[3: Transforming into the P/E Ratio Form]
By substituting r into the above formula and dividing both sides by earnings E, the formula for the theoretical P/E ratio is completed.

Rf (Risk-free rate): Interest rates such as U.S. Treasuries
ERP (Equity Risk Premium): The additional yield sought as compensation for equity investment
g (Expected growth rate): The company’s long-term earnings growth rate

When the interest rate (Rf) in the denominator rises, the entire denominator increases, so theoretically, the P/E ratio is pushed down (since Stock Price P = Earnings E × P/E ratio, this becomes a factor for a decline in stock prices).

2. 2026 Real Data Verification: Why did stock prices rise by 13% even though interest rates rose from “4.2% to 5.2%”?

Now, let’s apply this theory to actual 2026 market data.

・2026 Beginning of year 10-year U.S. Treasury yield (Rf): 4.20%・2026 Beginning of year fwd P/E ratio 22x・Current (recent) interest rate (Rf): 5.20%・Current fwd P/E ratio 19x (down about 13.6% from the start of the year)・2026 S&P 500 expected EPS growth rate: approx. 32% (1.32x)・2026 Year-to-date stock price increase rate: approx. 13.3% (1.133x)

The basic formula for stock price fluctuation is “1 + Stock Price Increase Rate = (1 + EPS Growth Rate) × (1 + P/E Ratio Change Rate).”
Let’s substitute the numbers to calculate the stock price change rate.

Stock price fluctuation rate = EPS growth rate 1.32 × (1 + P/E ratio change rate (-13.6%)) = 1.14 → approx. 14% increase

, which is a figure roughly close to the actual S&P 500 year-to-date return of 13.3%.
It can be seen that the 13% stock price increase in 2026 is a market where the “32% growth in EPS” is straightforwardly pushing up stock prices, overcoming the gravity of rising interest rates.

3. [Simulation] What happens if interest rates rise further to 5.5%, 6.0%, and 6.5% in the future?

Using the current interest rate of 5.2% and a Forward P/E of 19.0x as a baseline, I will calculate the theoretical P/E ratio if interest rates rise further.

Current Forward P/E: 19.0x (Earnings Yield = 1 ÷ P/E = 1 ÷ 19 = 5.26%)
Current US 10-Year Treasury Yield (Rf): 5.20%
Difference between Equity Risk Premium and Growth (ERP – g):
Earnings Yield 1 ÷ P/E = Rf + (ERP – g)
→ (ERP – g) = Earnings Yield (1 ÷ P/E) – Rf
= 5.26% – 5.20% = 0.06%

To make it easier to understand, I will simulate what happens if this “difference between Equity Risk Premium and Growth (ERP – g = +0.06%)” remains constant and only the interest rate (Rf) rises.

[Theoretical P/E Simulation During Interest Rate Hikes (19x Baseline)]
■ Interest Rate Rf = 5.2% (Current)
・Earnings Yield (1 ÷ P/E): 5.26%
・Theoretical P/E: 19.0x (Baseline)
■ ① Interest Rate Rf rises to 5.5%
・Earnings Yield: 5.56% (5.50% + 0.06%)
・Theoretical P/E: 18.0x
・P/E Change Rate: Approx. -5.4% decline from current
■ ② Interest Rate Rf rises to 6.0%
・Earnings Yield: 6.06% (6.00% + 0.06%)
・Theoretical P/E: 16.5x
・P/E Change Rate: Approx. -13.2% decline from current
■ ③ Interest Rate Rf rises to 6.5%
・Earnings Yield: 6.56% (6.50% + 0.06%)
・Theoretical P/E: 15.2x
・P/E Change Rate: Approx. -19.8% decline from current

Even though the starting fwd P/E is relatively stable at 19x, if interest rates rise to 6% or 6.5%, without earnings growth, the P/E will drop to 16.5x or 15.2x, and stock prices will fall by up to 20%…

4. Simulation applying the 2027/2028 projected EPS growth rate of “11%”

Next, I will perform a simulation factoring in earnings growth. The future S&P 500 projected EPS growth rates based on major analyst consensus are as follows.

2027 Projected EPS Growth Rate: Approx. 11% – 15%
2028 Projected EPS Growth Rate: Approx. 11%

As a baseline, I will apply a “projected EPS growth rate of 11% (1.11x)” to calculate future stock price fluctuations (EPS change × P/E change).

[Stock Price Fluctuation Simulation Assuming 11% EPS Growth]
■ Scenario ①: Interest Rate Rf = 5.2% (No P/E change)
・Stock price fluctuation: 1.11 × 1 = 1.11 (11% increase)

■ Scenario ②: Interest Rate Rf = 5.5% (P/E drops to 0.946x)
・Stock price fluctuation: 1.11 × 0.946 = 1.04 (approx. 4% increase)

■ Scenario ③: Interest Rate Rf = 6.0% (P/E drops to 0.868x)
・Stock price fluctuation: 1.11 × 0.868 = 0.963 (approx. -3.7% decline)

■ Scenario ④: Interest Rate Rf = 6.5% (P/E drops to 0.802x)
・Stock price fluctuation: 1.11 × 0.802 = 0.89 (approx. 11% decline)

Even if the entire S&P 500 reports strong earnings with “11% EPS growth,” if interest rates rise to 6% or 6.5%, it will not be enough to offset the valuation compression, resulting in a calculation where the index as a whole leans slightly toward a decline… It seems necessary to be prepared for an adjustment of this magnitude… (though I don’t want to).

5. [Counterattack Trump Card] What happens if the growth rate (g) increases due to AI?

If you ask, “So, if interest rates rise to 6%, are stocks definitely going to be negative?” there is a counterattack trump card.

That is the improvement in expected growth rate (g) due to the AI revolution.
As you can see from the P/E formula, when the growth rate (g) increases, the denominator becomes smaller, which acts as a power to raise the P/E ratio.

Let’s calculate what would happen if the full-scale adoption of AI improves productivity and increases the long-term growth rate (g) priced into the market by 1.0%.

[Simulation of AI Growth Rate (g) Improvement at Interest Rate Rf = 6.0%]
■ Baseline (No AI effect: no change in g)
・Theoretical P/E: 16.5x (approx. -13.2% decline from the current 19x)

■ AI Revolution Scenario (g increases by +1.0% due to AI)
・Earnings Yield (1÷P/E): 5.06% (6.00% + 0.06%-1%）
・Theoretical P/E: 1÷5.06% = 19.8x (approx. +4.0% increase from the current 19x)

・Stock price fluctuation: 1.11 × 1.04 = 1.154 (a significant 15.4% increase)

Even if interest rates rise to 6.0%, a mere 1% improvement in the future growth rate (g) due to AI could potentially prevent a P/E drop and lead to a significant 15.4% increase in stock prices.

Summary

In a phase where interest rates jump further, there may come a time when market average growth (approx. 11%) alone is not enough to push stock prices higher.

However, rather than looking only at interest rates, I want to continue investing calmly by keeping a close eye on the numbers for the other factor that determines stock prices: earnings performance, such as business expansion due to AI-driven productivity gains and increases in expected growth rates.

I am writing this article these days as a reminder to myself to avoid panic selling without looking at earnings performance, just because I am surprised by news of “sharp interest rate hikes!”
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※ This article is for educational and informational purposes only and does not recommend any specific stocks or investment products. Please make investment decisions at your own risk.