Why Do Yields Rise When Bond Prices Fall?

Asked on January 15, 2025

Tags: #bond-yields #bond-prices #rising-yields #fixed-income #investment-basics

If you’ve been learning about bonds, you might have noticed something seemingly paradoxical: when bond prices fall, yields rise, and when bond prices rise, yields fall. This inverse relationship is one of the most important - and confusing - concepts in bond investing. But once you understand why this happens, it will all make perfect sense.

The Short Answer

Yields rise when bond prices fall because yields are calculated as a ratio of the bond’s fixed payments to its current price. When the price goes down, the ratio (yield) goes up - and vice versa.

This is actually very simple math. Let me show you exactly why.

At its heart, the relationship between bond prices and yields is mathematical. The yield of a bond is essentially:

Yield = Annual Payment ÷ Current Price

This is the fundamental formula. And math tells us that when you divide by a smaller number, you get a larger result. When you divide by a larger number, you get a smaller result.

So:

When price falls (smaller divisor), yield rises
When price rises (larger divisor), yield falls

It’s really that simple. The rest is just understanding why this mathematical relationship exists in the bond market.

A Simple Example

Let’s say you have a bond that pays $50 per year in interest.

Scenario 1: Price is $1,000

Yield = $50 ÷ $1,000 = 5%

Scenario 2: Price falls to $900

Yield = $50 ÷ $900 = 5.56%

Scenario 3: Price falls further to $800

Yield = $50 ÷ $800 = 6.25%

Notice what happened: as the price went down, the yield went up. The bond is still paying the same $50, but because you can buy it for less, your percentage return is higher.

Why Does the Price Fall in the First Place?

Now you understand that lower prices mean higher yields. But why do bond prices fall? There are several reasons:

Reason 1: Rising Interest Rates

This is the most common reason bond prices fall. When market interest rates rise:

New bonds are issued with higher coupon rates
Existing bonds with lower coupon rates become less attractive
To sell these existing bonds, prices must fall
As prices fall, yields rise to match the new market rates

Reason 2: Credit Concerns

If investors worry about a bond issuer’s ability to repay:

They demand a higher return for taking on more risk
This pushes the price down
The lower price creates a higher yield

For example, if a company’s financial situation deteriorates, its bond price might fall from $1,000 to$ 900. The yield rises from 5% to 5.56% to compensate investors for the increased risk.

Reason 3: Inflation Expectations

When investors expect higher inflation:

They demand higher yields to compensate for lost purchasing power
Bond prices fall to push yields up
This is why yields often rise before the Federal Reserve raises rates

Reason 4: Supply and Demand

Like any market, bond prices are affected by supply and demand:

If many investors want to sell but few want to buy, prices fall
If many investors want to buy but few want to sell, prices rise

The Mathematical Proof: Present Value and Yields

To truly understand why yields rise when prices fall, let’s look at the underlying mathematics.

Present Value Calculation

The price of a bond is determined by calculating the present value of all its future cash flows. The formula is:

Price = C/(1+r)¹ + C/(1+r)² + ... + C/(1+r)^n + F/(1+r)^n

Where:

C = coupon payment
r = market interest rate (discount rate)
n = number of periods
F = face value

What Happens When Rates Rise?

When market interest rates (r) rise:

The discount factor (1+r) increases
Each future payment is discounted more heavily
The total present value (price) falls
As price falls, the yield (calculated as C/Price) rises

What Happens When Rates Fall?

When market interest rates (r) fall:

The discount factor (1+r) decreases
Each future payment is discounted less heavily
The total present value (price) rises
As price rises, the yield (calculated as C/Price) falls

The Yield to Maturity Perspective

While the simple “payment ÷ price” formula gives you the current yield, professional bond investors use Yield to Maturity (YTM), which is more comprehensive.

YTM considers:

All coupon payments until maturity
The difference between purchase price and face value
The time value of money

Example of YTM Calculation

Imagine a bond with:

Face value: $1,000
Coupon rate: 5%
Years to maturity: 10
Current price: $900

Simple calculation: Current yield = $50 ÷$ 900 = 5.56%

YTM calculation: This considers that:

You’ll receive $50/year for 10 years =$ 500
You’ll receive $1,000 at maturity, but you paid$ 900, so you gain $100
But money received in the future is worth less than money today

The YTM for this bond would be approximately 6.6% - higher than the 5.56% current yield because you’re getting your $100 principal gain over time.

Why This Matters for Investors

Understanding why yields rise when prices fall is crucial for making smart investment decisions:

For Buying Bonds

When you see yields rising (prices falling):

It might be a good time to buy (you’re getting more yield for your money)
But you need to understand why yields are rising (credit concerns? rising rates?)
Higher yields can be good, but not if the bond is risky

For Selling Bonds

When you need to sell a bond and prices have fallen:

You’ll receive less than you paid
But if yields have risen, you’re selling into a higher-rate environment
Consider whether waiting might be better

For Bond Funds

Bond funds experience this relationship constantly:

When rates rise, fund prices fall, yields rise
When rates fall, fund prices rise, yields fall
This is why bond fund returns fluctuate

The Role of Duration

Not all bonds react the same way to interest rate changes. This is measured by duration.

Duration Explained

Duration measures how sensitive a bond’s price is to interest rate changes:

High duration bonds (long-term) have large price swings
Low duration bonds (short-term) have small price swings

Example

10-year bond with duration of 8 years:

If rates rise 1%, price falls about 8%
Yield rises as price falls

2-year bond with duration of 2 years:

If rates rise 1%, price falls about 2%
Yield rises, but less dramatically

This is why duration management is crucial for bond fund managers.

Historical Examples

2022: The Rate Hike Cycle

When the Federal Reserve raised rates aggressively in 2022:

Bond prices fell across the board
Long-term Treasury prices dropped 15-20%
Yields rose correspondingly
Investors who sold during the decline realized losses
Investors who bought during the period got higher yields

2008: The Financial Crisis

When the Fed cut rates to near zero:

Bond prices rose dramatically
Long-term Treasury prices doubled from their lows
Yields fell as prices rose
Investors who bought during the crisis were rewarded

1980s: The Volcker Era

When Paul Volcker raised rates to fight inflation:

Bond prices fell initially
Yields on long-term bonds exceeded 15%
Later, when rates fell, prices rose substantially
Patient investors were well-rewarded

Common Misconceptions

”Rising yields are always good for bond investors”

Not necessarily! Rising yields mean falling prices. If you need to sell, you might realize a loss. Rising yields are good only if you’re buying or holding to maturity.

”A bond with higher yield is always better”

Not true! Higher yield often means higher risk. A junk bond yielding 8% is riskier than a Treasury yielding 4%. Always consider risk-adjusted returns.

”Yields will eventually go back up”

Not guaranteed! In a low-growth, low-inflation environment, yields can remain low for years. Japan has had near-zero rates for decades.

Practical Implications

For Individual Investors

Understand the relationship: When yields rise, prices fall - and vice versa
Consider your time horizon: If you’ll hold to maturity, price fluctuations matter less
Watch duration: Longer bonds have more price volatility
Don’t chase yield: Higher yields often mean higher risk

For Portfolio Construction

Diversify across maturities: Don’t put all your money in long-term bonds
Consider your view on rates: If you think rates will rise, shorten duration
Balance risk and return: Higher yields usually come with higher risk
Rebalance regularly: As rates change, your portfolio characteristics change

For Income Planning

Higher yields = more income: But higher prices might mean paying more
Consider the total picture: YTM gives you the complete picture
Think about reinvestment: What will you do when bonds mature?
Plan for changes: Your income needs might change over time

The Bottom Line

Yields rise when bond prices fall because of simple mathematics: yield is calculated as the bond’s fixed payment divided by its current price. When the price goes down, the yield goes up.

This relationship is fundamental to how bonds work and affects everything from individual bond prices to entire bond fund values. Understanding it helps you:

Make better decisions about when to buy and sell
Understand why your bond investments fluctuate
Build a portfolio that matches your goals and risk tolerance
Navigate changing interest rate environments

The next time you hear that “bond yields are rising,” you’ll understand that bond prices are falling - and you can use that knowledge to make smarter investment decisions.