CM-02 Basics of Real Interest Rates, Long-term Interest Rates, and the Yield Curve
Basics of Interest Rates
In the previous article, we looked at the mechanism by which money flows from those who have a surplus to those who are in need. The “price” of borrowing money is the interest rate. In this article, we will organize the concepts of “real interest rates,” “long-term interest rates,” and the “yield curve” using materials from the Bank of Japan and the Ministry of Finance.
Prerequisite for this article: The flow of money and the role of financial institutions
Conclusion
The real interest rate is the interest rate obtained by subtracting the expected inflation rate from the nominal interest rate, and it influences the motivation to borrow and spend money. The Bank of Japan guides the uncollateralized overnight call rate (also called the next-day rate) among short-term interest rates as its policy interest rate. The policy interest rate is the interest rate that a central bank guides as a target for monetary policy. Long-term interest rates are fundamentally formed in the financial market. The yield curve is a curve representing the relationship between residual maturity and interest rates, reflecting expectations for future short-term interest rates and the term premium.
First, the overall picture
An interest rate is the percentage that indicates how much interest is added to the principal when lending or borrowing money. Interest is the consideration that arises when lending, depositing, or borrowing money, and it occurs in deposits, bond investments, and loans.
In this article, we will look at interest rates by dividing them along two axes. One is whether or not to subtract changes in prices (nominal and real), and the other is the length of the lending/borrowing period (short-term and long-term). The yield curve is a line connecting the interest rates for each period.
【Figure 1: Overall picture of how interest rates are determined (Overnight rates by the Bank of Japan, long-term rates by the market)
Breaking down the mechanism
Nominal interest rates and real interest rates
The real interest rate is the interest rate obtained by subtracting the expected inflation rate from the nominal interest rate. The nominal interest rate is the interest rate itself displayed on deposits or government bonds. The expected inflation rate is how much people expect prices to rise in the future.
The Bank of Japan states that it is important to look at real interest rates when making decisions on consumption and investment. The reason is that a low nominal interest rate does not necessarily mean that the motivation to borrow and spend money is strong. Japan’s short-term interest rates have remained near 0% since the late 1990s. Even so, the inflation rate from 2000 to the first half of the 2010s averaged below 0%. If prices are expected to fall, the motivation to borrow money for consumption or investment becomes weak.
The expected inflation rate cannot be observed directly, and it is necessary to look at it with a range depending on the indicator. In the Bank of Japan’s estimates, the expected inflation rate estimated by staff is subtracted from the government bond yields of each maturity.
The Bank of Japan organizes that the degree of easing is higher as the real interest rate falls below the “natural rate of interest” (the level of the real interest rate that is neutral to the economy and prices). However, the natural rate of interest also cannot be observed directly and varies greatly depending on the estimation method.
【Figure 2: Breakdown of nominal policy interest rates (Created based on materials from the Bank of Japan Deputy Governor’s lecture in January 2025)
Even with the same nominal interest rate, if the expected inflation rate is high, the real interest rate will be low.
Short-term interest rates and long-term interest rates
The difference between short-term interest rates and long-term interest rates is whether the lending/borrowing period is within one year or exceeds one year.
Short-term interest rates are mainly interest rates in markets where financial institutions participate, and a representative example is the call rate. The call market is a market where financial institutions adjust their daily surplus or shortage of funds. Banks, securities companies, insurance companies, etc., participate, and money market brokers play the role of mediating transactions. The center of trading is the uncollateralized overnight call rate, which is a transaction where money is borrowed today and returned on the next business day.
The representative long-term interest rate is the 10-year Japanese Government Bond (JGB) yield, which is used as a benchmark in various financial transactions.
How short-term interest rates are determined
The Bank of Japan directly guides the uncollateralized overnight call rate, which is a short-term interest rate. Since March 2024, this rate has been used as the policy interest rate. The target level for this guidance is decided and announced at the Monetary Policy Meeting (the meeting where the Bank of Japan determines its monetary policy stance).
The target level has been raised several times from the range of around 0 to 0.1% in March 2024. On September 18, 2026, it was decided to set it at around 1.25% (effective from September 24). The trends and the mechanism for adjusting the policy interest rate will be covered in CM-04.
How long-term interest rates are determined
Since March 2024, long-term interest rates have fundamentally been determined in the financial market.
However, the large amount of government bonds held by the Bank of Japan reduces the amount of interest rate risk remaining in the market, which pushes down long-term interest rates (stock effect). The April 2024 Outlook Report (a report summarizing the Bank of Japan’s outlook for the economy and prices) estimates this effect. The result is that government bond purchases have pushed down long-term interest rates by an average of approximately 1%, though it notes that this should be viewed with a considerable margin of error.
Bond prices and yields move in opposite directions
The face value is the amount stated on a bond, which is paid at redemption (when the principal is returned at maturity). The coupon rate is the ratio of the annual interest to the face value, which is determined at the time of issuance and remains unchanged until redemption. The yield is the rate of return that includes not only the interest but also the difference between the redemption amount and the purchase price, converted to an annual basis. Therefore, the yield changes depending on the purchase price.
The Ministry of Finance presents the yield to maturity (the yield if held until redemption) using the following formula:
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Yield to Maturity (pre-tax, simple interest, %) = {Coupon Rate + (100 yen – Purchase Price) ÷ Years to Maturity} ÷ Purchase Price × 100
In this formula, the coupon rate and years to maturity are fixed at the time of purchase, and only the purchase price changes in the market. As the purchase price rises, the numerator (100 yen – purchase price) decreases, and the denominator increases. Since both work to lower the yield, the yield falls when the price rises, and the yield rises when the price falls. Government bonds are traded daily in the bond market, and because prices change daily, long-term interest rates also fluctuate daily.
What the yield curve represents
The yield curve is a curve that connects interest rates of different maturities, with the horizontal axis representing the remaining maturity and the vertical axis representing the interest rate. The remaining maturity is the time remaining until the bond is redeemed.
A paper in the Ministry of Finance’s “Finance” (October 2019 issue) lists three theories to explain the shape of the curve: the pure expectations hypothesis, the liquidity premium hypothesis, and the market segmentation hypothesis. Here, we look at the first two.
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Pure Expectations Hypothesis: Long-term interest rates can be viewed as the average of expected future short-term interest rates. An upward-sloping curve is interpreted as representing expectations of rising future short-term interest rates.
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Liquidity Premium Hypothesis: A compensation for the interest rate risk of holding long-term bonds (liquidity premium) is added to long-term interest rates. The same paper notes that this is often academically referred to as a term premium.
Under the latter approach, the long-term bond yield can be expressed as “average of expected short-term interest rates + risk premium.” Because long-term bonds have fixed interest rates, the longer they are held, the more susceptible they are to changes in the market environment, and the greater the price volatility. The logic is that an additional premium is required for this. The paper states that it is a widely held view in both the business and academic communities that the expectations hypothesis alone cannot fully explain the relationship between interest rates across different periods.
A situation where long-term interest rates fall below short-term interest rates is called an inverted yield curve. In a speech in June 2022, the Deputy Governor of the Bank of Japan (at the time) introduced the rule of thumb that an inverted yield curve is often followed by an economic recession. On the other hand, the Governor (at the time) expressed the view in a press conference in June 2018 that it does not necessarily lead to an economic recession.
Thinking with a concrete example
The figures in Example 1 and Example 2 are hypothetical numbers for illustrative purposes.
Example 1: Calculation of Real Interest Rate
Suppose Person B borrows money at an interest rate of 1% per year. If people expect prices to rise by 2% over the next year, the real interest rate is approximately 1% – 2% = -1%. Even though interest is being paid in nominal terms, the burden in terms of purchasing power is light. If prices were expected to fall, the same 1% interest rate would result in a heavier real burden.
Example 2: Bond Prices and Yields
Consider a government bond with a coupon rate of 2% (2 yen of interest per 100 yen face value) and 5 years until maturity. Applying the Ministry of Finance’s formula, it looks like this:
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Buying at 100 yen: {2 + 0 ÷ 5} ÷ 100 × 100 = 2.00%
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Buying at 98 yen: {2 + 2 ÷ 5} ÷ 98 × 100 ≒ 2.45%
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Buying at 102 yen: {2 – 2 ÷ 5} ÷ 102 × 100 ≒ 1.57%
Even if the interest is the same 2 yen per year, the cheaper you buy it, the higher the yield becomes. When market interest rates rise and the yields on new bonds increase, previously issued bonds will not find buyers unless their prices fall. This is the mechanism behind ‘when interest rates rise, bond prices fall.’
Example 3: Current Yield Curve
The government bond interest rates published by the Ministry of Finance (as of October 15, 2026) are as follows:
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1 year: 1.652%
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2 years: 1.913%
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5 years: 2.331%
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10 years: 2.948%
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20 years: 3.786%
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25 years: 4.048%
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30 years: 4.024%
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40 years: 4.031%
From 1 year to 25 years, the longer the maturity, the higher the rate, while the 25-year, 30-year, and 40-year rates are mostly flat.
The 1.652% 1-year interest rate does not match the policy interest rate of approximately 1.25%. This is because the Bank of Japan uses the overnight interest rate as its target. Under the expectations hypothesis, the 1-year interest rate reflects expectations for the overnight interest rate over the next year.
Even after the interest rate hike in September 2026, the Bank of Japan maintains that real interest rates remain at a “still low level,” particularly in the short-to-medium term zone.
Note that the consumer price index (all items excluding fresh food) for August 2026 was +1.7% year-on-year. However, subtracting this figure from the nominal interest rate does not result in the real interest rate as defined by the Bank of Japan. This is because the figure to be subtracted is the expected inflation rate.
How it works in practice
Knowledge of interest rates is directly linked to both bond operations and cash management at securities firms.
In departments that hold bonds for proprietary trading, changes in interest rates directly affect the valuation of the bonds held. This is because prices and yields move in opposite directions. Since price volatility is greater for longer-term bonds, it is fundamental to track holdings by residual maturity.
When handling interest rate data, verify how the figures are calculated. Government bond interest rates from the Ministry of Finance are final yields based on semi-annual compounding derived from actual market prices. They are calculated using a method that assumes a constant residual maturity for each term. Since the calculation method differs from the simple interest formula used above, it is important not to mix figures from different sources.
Short-term interest rates are relevant for cash management. Securities firms are also participants in the call market, where they adjust daily funding surpluses and deficits. If the target level for the policy interest rate changes, the assumptions regarding the cost of borrowing funds in the call market also change. Therefore, it is necessary to check the statement released after the Monetary Policy Meeting and update these assumptions.
Common Misconceptions
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Misconception: If nominal interest rates are low, monetary policy is accommodative.
→ Reality: The Bank of Japan states that low nominal interest rates do not necessarily mean a high degree of accommodation. Real interest rates are used for this assessment. -
Misconception: The Bank of Japan also determines long-term interest rates.
→ Reality: Since March 2024, these are fundamentally formed in the financial markets. However, the stock effect of the government bonds held by the Bank continues to have an influence. -
Misconception: Coupon rates and yields are the same thing.
→ Reality: The coupon rate is fixed at the time of issuance, while the yield changes based on the purchase price. -
Misconception: An upward-sloping curve always indicates expectations of interest rate hikes.
→ Reality: Due to the term premium, the curve can be upward-sloping even if interest rates are not expected to rise.
Summary
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The real interest rate is the interest rate obtained by subtracting the expected inflation rate from the nominal interest rate.
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The Bank of Japan uses the uncollateralized overnight call rate as its policy interest rate. Long-term interest rates are fundamentally formed in the market.
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The yield curve represents the relationship between residual maturity and interest rates, reflecting expectations for future short-term interest rates and the term premium.