The IRR in fixed income: Why many investors make mistakes when choosing bonds

When it comes to choosing between different bonds, many investors make the same mistake: focusing only on the coupon the security pays. However, there is a fundamental tool that reveals the actual return: the IRR formula, short for Internal Rate of Return.

Why is IRR more reliable than the coupon?

Imagine two bonds: one pays an 8% coupon, another only 5%. At first glance, you would choose the first. But here’s the trick: if you bought the 8% bond at a very high price (above its face value), you will lose money on the reversal as it approaches maturity. In contrast, the 5% bond bought at a good price could offer you a higher return.

This is precisely the function of the IRR: to capture not only the income from coupons but also the gain or loss you will get from the price differential.

Understanding how a fixed income security works

A regular bond works like this:

• You acquire the security at a determined price in the market
• You receive periodic payments (coupons) that are usually annual, semiannual, or quarterly
• At maturity, you recover the face value (100€ per 100€ face value) plus the last coupon

The bond’s price fluctuates constantly during its term. Depending on where you buy, you will be in one of three situations:

Buy below par: You acquire below the face value (e.g., 94.5€ instead of 100€). This amplifies your return.

Buy at par: You pay exactly the face value (100€). No additional gain or loss.

Buy above par: You buy above the face value (e.g., 107.5€). This reduces your final return.

The IRR formula: How to calculate it

The IRR formula relates the current price of the bond, the periodic coupons you will receive, and the time until maturity:

Price = Σ [Coupon / ((1 + IRR)^n] + [Nominal / )(1 + IRR)^n]

Where:

• Coupon = periodic payment
• n = time period
• Nominal = value at maturity

For those who do not wish to solve complex equations, there are specialized online calculators that do the work automatically.

Practical calculation example

Case 1 - Buy below par: A bond quotes at 94.5€, pays 6% annually, and matures in 4 years.

Applying the IRR formula = 7.62%

Note how the IRR (7.62%) exceeds the coupon (6%) thanks to the advantageous purchase price.

Case 2 - Buy above par: The same bond quotes at 107.5€ (high price).

Applying the IRR formula = 3.93%

Here, the IRR drops significantly, demonstrating that the overprice paid is a burden on the return.

Key differences between IRR, TIN, and TAE

It is crucial not to confuse these three metrics:

IRR (Internal Rate of Return): Actual profitability discounted cash flows. Specific for bonds and investment projects.

TIN (Nominal Interest Rate): The agreed rate without additional costs. The purest interest rate.

TAE (Annual Equivalent Rate): Includes commissions, insurance, and hidden expenses. The Bank of Spain recommends it for comparing financing offers.

For example, a mortgage could have a TIN of 2% but a TAE of 3.26% due to opening fees and insurance.

Factors that determine IRR

Several elements directly influence the result:

The coupon: The higher the coupon, the higher the IRR. Inversely proportional if the coupon decreases.

The purchase price: If below par, the IRR improves. If above par, it worsens.

Special features: Some bonds (convertible, inflation-linked) have additional variables that condition their IRR depending on the evolution of underlying assets.

What investors should know

IRR is your compass to identify real fixed income investment opportunities. Don’t be fooled by attractive coupons without checking the entry price.

However, remember a critical point: IRR does not guarantee profit if the bond issuer is at risk of insolvency. During the Greek crisis of 2012, Greek bonds traded with an IRR above 19%, reflecting market distress. Only the intervention of the Eurozone prevented default. Therefore, always validate the credit quality of the issuer before deciding on the asset with the highest IRR.