TIR: The Metric No Bond Investor Should Ignore

When talking about real yield in fixed income, most people only think about the coupon. Wrong. True profitability depends on something deeper: the IRR formula or Internal Rate of Return. This indicator is what really shows you how much you will (gain) or (lose) if you hold that bond until maturity.

Why is it so important? Because two bonds with the same coupon can offer completely different returns depending on the price at which you buy them. Let’s see why.

Understanding How a Plain Bond Works

Before discussing calculations, you need to understand what happens with a traditional fixed income bond. Imagine buying a bond at its face value. During its term, you will receive periodic interest payments (coupons), whether annual, semiannual, or quarterly. When the bond matures, the issuer returns the nominal value plus the last coupon.

But here’s the key: that bond does not maintain the same price throughout its life. It fluctuates constantly based on interest rate movements, the issuer’s credit quality, and other factors.

Suppose a five-year bond. As time passes, its value oscillates. If you buy it when its price is below the nominal value (buying below par), you harvest an additional gain when it matures. If you buy it above (buying over par), you assume a guaranteed loss upon reverting to the nominal.

Real Yield: Beyond the Coupon

This is where the IRR or Internal Rate of Return comes in. This percentage interest rate captures not only the coupons you receive but also the gain or loss you get from the price difference.

Let’s take a concrete example: you have two bonds to choose from.

Bond A: pays an 8% coupon, but you buy it at €105.
Bond B: pays a 5% coupon, but you buy it at €99.

If you only looked at the coupon, you would choose A. But the reality is different. Bond A suffers a penalty because you buy it above par. At maturity, you only receive €100, resulting in a €5 loss on the revert. Bond B, on the other hand, generates a €1 gain at maturity.

When you calculate the IRR of both, you find that B is more profitable. The IRR formula captures exactly this.

How It’s Calculated: The IRR Formula

The formula you need to know is:

Current Price = C/(1+IRR) + C/(1+IRR)² + C/(1+IRR)ⁿ + N/(1+IRR)ⁿ

Where:

• C = coupon
• N = face value
• n = periods until maturity
• IRR = the rate you are solving for

It sounds complicated, but let’s see with real numbers.

Scenario 1: Bond at €94.5, annual coupon of 6%, matures in 4 years.

Applying the formula, you get an IRR of 7.62%. Notice it’s higher than the 6% coupon because you bought below par. That extra margin up to the nominal adds to your returns.

Scenario 2: The same bond but trading at €107.5.

Now the IRR drops to 3.93%. The overprice paid penalizes you, diluting that 6% annual return.

To avoid complex math operations, there are online calculators that do the work. You just need to input the price, coupon, and time, and you get the IRR automatically.

Differentiating: IRR, TIN, TAE, and Technical Interest

It’s essential not to confuse these metrics:

IRR (Internal Rate of Return): Captures the full profitability by discounting all cash flows and the current purchase price. It’s the most accurate metric for bonds.

TIN (Nominal Interest Rate): The pure rate agreed upon with your counterparty, without considering additional costs. The most basic way to express interest.

TAE (Annual Equivalent Rate): Includes expenses not shown in TIN. For example, in a mortgage, you might see a TIN of 2% but a TAE of 3.26%, because the latter adds fees and insurance. It’s what the Bank of Spain recommends for comparing offers.

Technical Interest: Mainly used in savings insurance. Includes additional costs like life insurance embedded in the product.

Factors That Move Your IRR

Three main elements influence the outcome:

Coupon: The higher the coupon, the higher the IRR. It’s straightforward. The lower the coupon, the lower the potential return.

Purchase Price: If you buy below par, your IRR increases. If you buy over par, your IRR decreases. The revert to nominal always favors or harms you depending on the initial price.

Special Features: Some bonds have additional variables. A convertible’s IRR will be affected by the evolution of the underlying stock. An inflation-linked bond will fluctuate with economic changes.

Final Warning: Credit Quality Matters

IRR shows the potential return, but never ignore the issuer’s solvency. A Greek bond once traded with an IRR above 19% during the Grexit crisis. It seemed like an extraordinary opportunity. In reality, that astronomical yield reflected massive default risk.

Only the European rescue prevented Greece from defaulting on its payments. Moral: a high IRR without solid credit fundamentals is a trap.

The IRR formula is your ally to detect truly attractive bond investments, but always combine it with credit risk analysis. That way, you will choose bonds with genuine profitability, not numerical illusions.