Basics of Government Bonds and the Mechanism for Calculating and Evaluating 'Long-Term Interest Rates (10-Year Bond Yields)'

Following our previous discussion on the ‘basics of interest rates,’ this time we will delve deeper into ‘government bonds (long-term interest rates),’ which are the stars of the stock market and currency news!

Let’s clearly organize the mechanism of the strange inverse correlation where ‘when bond prices fall, yields rise,’ as well as the actual calculation process.

1. What is a government bond? It is a ‘promissory note issued by the government’

A government bond (treasury bond) is a debt (bond) issued by the government for the purpose of raising funds (for public works, social security, etc.).

• Extremely high safety: Backed by the government’s credit (principal is guaranteed unless the country defaults)

• Has a maturity date: The duration is fixed, such as 1 year, 5 years, or 10 years

• Interest (coupon) is received: Interest is paid periodically during the holding period

2. Why do ‘price’ and ‘yield’ move in opposite directions?

The ‘interest rate’ of a bond is fixed at the time of issuance, but the ‘market price’ fluctuates daily due to trading.market price fluctuates daily due to trading.

The point is that the overall rate of return (yield) on the invested money changes depending on ‘how much you bought it for (purchase price)’ when you want to buy it.

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【例：額面100円 / 利息：年1円（固定）の1年物国債】

◆ パターン A：債券が人気で買われ「値上がり」したとき

  購入価格：101円（高値で購入）
  手に入るお金：利息 1円 － 満期での損 1円（101円→100円） ＝ 0円
  ──► 利回りは【低下】する（0%）

◆ パターン B：債券が不人気で売られ「値下がり」したとき

  購入価格：99円（安値で購入）
  手に入るお金：利息 1円 ＋ 満期での得 1円（99円→100円） ＝ 2円
  ──► 利回りは【上昇】する（約 2.02%）
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Tips for remembering

‘If you can buy it cheap, it’s a bargain (yield rises)’
‘If you buy it high, the benefit decreases (yield falls)’

Bond prices and yields are always in aseesaw relationship.

3. Simple calculation formula for yield (simple interest)

The ‘final yield (annual rate %)’ that investors check when buying government bonds can be calculated using the following formula.

$$
text{Yield (%)} = frac{text{Annual interest} + frac{text{Face value (100 yen)} – text{Purchase price}}{text{Remaining years}}}{text{Purchase price}} times 100
$$

Calculation example: Remaining period 10 years / Interest rate 1.0% / Purchase price 98 yen

1. Annual interest = 1.0 yen

2. Capital gain per year = $${(100 – 98) div 10 = mathbf{0.2text{yen}}}$$

3. Total annual return = $${1.0 + 0.2 = mathbf{1.2text{yen}}}$$

4. Yield = $${(1.2 div 98) times 100 approx mathbf{1.22%}}$$

4. Why is the ’10-year bond yield’ considered so important?

There are government bonds with various maturities in the world, but the ’10-year government bond yield’ is treated specially in the financial markets.

1. Representative indicator of long-term interest rates: Serves as the benchmark (floor) for fixed-rate mortgages and corporate long-term borrowing rates

2. Rival to the stock market: When bond yields rise, funds shift to safer government bonds, making stocks (especially growth stocks) more prone to being sold

3. Determinant of exchange rates (such as Dollar-Yen): As the gap (interest rate differential) between US and Japanese 10-year bond yields widens, the currency with the higher interest rate becomes easier to buy

Summary: Key Points Check

• Bond prices and yields move in opposite directions (price decline = yield rise)

• The coupon rate (interest) is fixed, but the yield changes daily based on the purchase price

• The 10-year bond yield is the ‘market benchmark axis’ that directly impacts stocks, exchange rates, and mortgages

If you remember this along with the previous ‘Basics of Interest Rates,’ you will be able to intuitively understand what kind of capital movements are happening behind the daily economic news!