Treasury yields explained: what does the yield curve tell us?

Interested in something specific? Skip ahead using these links:

• What is the treasury yield?
• What affects treasury yields?
• Treasury yield durations
• How to calculate treasury yields
• How to calculate treasury bill yields
• How to calculate treasury bond and note yields
  • What is yield to maturity?
• What is the yield curve?
• Why does the yield curve invert?

What is the treasury yield?

The treasury yield is the return on investment for government debt obligations, expressed as a percentage. It considers both the initial value of the treasury security and any interest payments – also known as coupons – paid to the investor.

All governments issue debt instruments to raise capital for projects, such as building infrastructure. When we talk about treasuries, it’s most commonly those filed by the US government via the Treasury department. They’re considered low-risk assets because they’re backed by one of the largest economies in the world.

The US government offers three types of instruments:

• Treasury bills (T-bills) are short-term debts that mature within a year and pay no interest
• Treasury notes (T-notes) are fixed-income assets that mature within ten years
• Treasury bonds (T-bonds) - are fixed-income securities that mature within 20-30 years

When they’re issued, Treasuries have a face value (the cost of the security) and – if relevant – a fixed interest rate (or coupon rate). But when they’re sold on the secondary debt market – from investor to investor – the highest bidder gets the security, which means they can pay more or less than the face value.

The higher the purchase price, the lower the yield, as the investor will only ever receive the face value upon maturity.

 

What affects treasury yields?

Like all financial markets, treasury yields are impacted by the supply and demand of the underlying security.

Yields move in the opposite direction of the value of the bond. If there’s a lot of demand, the price of the treasury will rise, and the yield value will be lowered because less incentive is needed to buy the debt obligation. If there’s little demand, the security will fall in value and the yield will rise to remain competitive and bring in investors.

Treasury yields are a good indicator of how investors are feeling about the economy. Demand tends to rise during economic crises when investors have a risk-off attitude and want to put their capital into more secure investments. So, although bond prices rise, yields fall in periods of economic uncertainty.

When investors have a more bullish outlook on the economy, and are willing to move their capital back to riskier asset classes like stocks, commodities and currencies, yields rise in price. Typically, this coincides with the Federal Reserve rising interest rates, which causes bond prices to fall – this is known as interest rate risk.

Treasury yields can also have a ripple effect on the cost of borrowing money, which can impact the value of other markets – such as stocks.

 

Treasury yield durations

Treasury yield duration, more commonly known as maturity, is the date on which the face value of the debt will be repaid to the investor.

The maturity depends on the type of debt instrument.

• T-bills mature within a year
• T-notes mature within ten years
• T-bonds mature within 20-30 years

Longer-term debt instruments have a higher yield, due to the increased risk from holding the security for a longer period, as its value could be impacted by changing interest rates.

So, your decision about which yield duration to select will depend on whether you intend to hold your bond to maturity. If you do, the fluctuations in price won’t matter so much, as you’ll be paid the interest rate and the full-face value. Alternatively, you could sell your treasury on the secondary debt market – this would mean changing prices would influence your strategy.

 

How to calculate treasury yields

At a very basic level, to calculate treasury yields, you’ll need to divide its face value by the amount of interest it pays. But the real calculation varies depending on what type of treasury you’ve bought.

 

How to calculate treasury bill yields

Treasury bills pay no interest, which is why they’re also known as zero-coupon debt instruments. They’re usually auctioned at below face value to ensure investors get a return.

The Federal Reserve Bank of New York describes two different methods to calculate yield on T-bills: the discount yield method and the investment yield method.

 

The discount yield formula looks like this:

[(FV – PP)/FV] * [360/M]

Where:

• FV = face value of the T-bill
• PP = purchase price of the T-bill
• M = maturity of the T-bill in days

The 360 is just the number of days used by banks to determine short-term interest rates.

 

So, say you had a 182-day treasury bill, auctioned at an average price of $9,500 per $10,000 face value, the discount yield would be:

[(10,000 – 9,500)/10,000] * [360/182] = 1.97%

 

Alternatively, you could use the investment yield, which is the same calculation but is based on the calendar year, so you’d just replace 360 days, with 365 days – or 366 in leap years. Using the same treasury bill from the example above, the treasury yield would be:

[(10,000 – 9,500)/10,000] * [365/182] = 2.01%

How to calculate treasury bond and note yields

As bonds and notes pay coupons or interest, the formula to calculate their yield is more complex. Unlike T-bills, they’re usually purchased at or near their face value, as income can be generated from the coupon.

 

The formula looks like this:

[C + ((FV – PP) / M)] ÷ [(FV + PP)/2]

• C = coupon rate
• FV = face value of the T-bill
• PP = purchase price of the T-bill
• M = maturity of the T-bill in days

 

Let’s say the Treasury issued a 5-year note with a $100 face value and a 5% coupon rate that sold at an average of $99.5. The treasury yield would be calculated as follows:

[5 + ((100 – 99.5) / 1825)] ÷ [(100 – 99.5)/2] = 20%

 

There are also other means of assessing a bond’s value, which account for the time value of money and compounding interest payments, the most common being yield to maturity (YTM).

What is yield to maturity?

Yield to maturity (YTM) shows how much an investor will earn if the bond is held until it matures.

For example, let’s say that you buy a T-bond with a 2.25% coupon rate. After a year of holding the treasury, interest rates fall to 1.50%. Your bond would still pay you a 2.25% rate, making it more valuable than newly-issued bonds that would only have a 1.50% interest rate.

You could choose to hold the bond until it matures, or you could sell it. The bond’s price will have risen, due to its increased value. The new buyer would have a lower yield to maturity, due to the higher price they invested at.

However, if the interest rate increased instead, up to 3%, your bond would be less valuable. New T-bonds would have a 3% coupon rate, which means the price of your bond would fall.

What is the treasury yield curve?

The yield curve is a graph that shows the returns of short-term T-bills compared to the returns of longer-term T-notes and T-bonds. It shows the relationship between the term of bonds and interest rates.

The curve is based on the closing market prices of the most recently auctioned Treasury securities in the over-the-counter (OTC) market.

Typically, the yield curve slopes upward, as securities with longer durations have higher yields due to the increased risk associated with them.

But as treasuries are constantly resold on the secondary market, the yield curve fluctuates regularly. So, the curve can become flatter or steeper depending on the health of the economy and Federal Reserve decisions about monetary supply.

Traders and investors can use the yield curve to predict where the economy might be heading and make decisions about their open positions.

Why does the yield curve invert?

The yield curve inverts when short-term bonds pay more than long-term bonds. This creates a yield curve that slopes downward instead of up. It’s seen as a sign that interest rates are declining and may even have fallen below-short term rates.

It’s an unusual situation, in that long-term investors become willing to settle for lower yields as they believe the economic outlook is so terrible that it’s still worth investing in the safer instruments. This is normally the case in a recession.