Basis Point

August 31, 2024 Banking

One hundredth of one percentage point, used to state precise changes in rates, yields, spreads, and percentage-based fees.

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A basis point, abbreviated bp for one or bps for more than one, is one hundredth of one percentage point. Finance professionals use basis points to state small changes in interest rates, yields, spreads, and fees without confusing percentage-point changes with relative percentage changes.

$$ 1\text{ bp} = 0.01\% = 0.0001 $$

Key Takeaways

  • 100 basis points equal 1 percentage point.
  • Basis points describe an absolute difference between percentage rates.
  • A move from 4% to 5% is 100 basis points but a 25% relative increase.
  • Direction still matters: rates can rise, fall, widen, or narrow by a stated number of basis points.
  • The dollar effect depends on the balance, time period, cash-flow structure, and rate convention.
  • A basis-point move is not itself a prediction of profit, loss, or price change.

Basis-Point Conversions

Basis pointsPercentage pointsDecimal rate
1 bp0.01%0.0001
10 bps0.10%0.0010
25 bps0.25%0.0025
50 bps0.50%0.0050
100 bps1.00%0.0100
125 bps1.25%0.0125

When rates are written as percentages:

$$ \Delta bps = (r_{new,\%} - r_{old,\%})\times 100 $$

When rates are written as decimals:

$$ \Delta bps = (r_{new} - r_{old})\times 10{,}000 $$

To convert basis points to decimal form for a calculation:

$$ \Delta r = \frac{bps}{10{,}000} $$

Worked Example: Yield Change

Suppose a bond yield rises from 3.82% to 4.07%:

$$ 4.07\% - 3.82\% = 0.25\text{ percentage points} $$
$$ 0.25\times 100 = 25\text{ bps} $$

Market commentary would say the yield rose 25 basis points. It would not say the yield rose 25%, because the relative increase is approximately 6.54%:

$$ \frac{4.07 - 3.82}{3.82} \approx 6.54\% $$

Dollar Impact of a Basis-Point Change

For a constant USD 2,000,000 balance over one year under simple interest, a 25-bp increase adds:

$$ 2{,}000{,}000\left(\frac{25}{10{,}000}\right)(1) = 5{,}000 $$

This USD 5,000 estimate assumes the full balance remains outstanding for the year. An amortizing loan, changing deposit balance, partial-year period, compounding method, or fee structure produces a different result.

Where Basis Points Are Used

UseExample statementMeaning
Policy rateTarget range increased 25 bpsIncrease of 0.25 percentage points
Bond yieldTen-year yield fell 8 bpsDecrease of 0.08 percentage points
Credit spreadSpread widened from 140 to 175 bpsRisk premium increased 35 bps
Loan pricingBenchmark plus 225 bpsBenchmark plus 2.25 percentage points
Fund feeExpense ratio reduced 5 bpsFee rate decreased 0.05 percentage points
Derivative spreadFixed rate moved 12 bpsContract rate changed 0.12 percentage points

Terms such as widened and narrowed usually describe spreads. Increased and decreased describe rates more generally. Always identify the starting and ending measure.

Percentage Points vs. Percent Change

This distinction prevents a common error.

If a rate rises from 4% to 5%:

  • absolute change: 1 percentage point;
  • basis-point change: 100 bps; and
  • relative change: ((5-4)/4 = 25%).

All three statements are mathematically valid, but they answer different questions. Basis points make the absolute rate move unambiguous.

Basis Points and Bond Prices

A yield change stated in basis points does not translate into the same price change for every bond. Approximate price sensitivity depends on duration and convexity, while actual price movement also reflects cash flows and market conditions.

A 10-bp rise in yield generally has a larger price effect on a long-duration bond than on a short-duration bond. Therefore, “the bond lost 10 basis points” is ambiguous unless the speaker identifies whether 10 bps refers to yield, spread, or price quotation.

Common Mistakes

  • Saying a rate rose 1% when the intended meaning is 1 percentage point.
  • Converting 25 bps to 0.25 in decimal calculations instead of 0.0025.
  • Reporting a spread moved without stating whether it widened or narrowed.
  • Treating 100 bps as a 100% relative increase.
  • Multiplying a basis-point change by original principal when the balance amortizes.
  • Assuming equal basis-point moves create equal bond-price changes.
  • Confusing basis points of yield with cents or percentage points of price.
  • Using “bps” for a single basis point in formal writing.

Scenario-Based Sample Question

A lender increases a floating-rate business loan from 6.15% to 6.90%.

Question: By how many basis points did the rate increase?

Answer: 75 basis points.

Explanation: The rate increased by 0.75 percentage points, and each percentage point contains 100 basis points.

Quiz

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Authoritative Sources

  • Interest Rate: Percentage price of borrowing or return associated with lending and saving.
  • Bank Interest: Deposit or credit interest whose rate can change by basis points.
  • Coupon Rate: Bond interest rate stated as a percentage of face value.
  • Yield to Maturity: Discount rate linking a bond’s price with its promised cash flows.
  • Bond Yield: Return measure often quoted and compared in basis points.

FAQs

How many basis points equal one percentage point?

One percentage point equals 100 basis points. Therefore, 0.25 percentage points equals 25 basis points.

Is a 100-bp increase the same as a 100% increase?

No. A 100-bp increase is an absolute rise of 1 percentage point. The relative percentage increase depends on the starting rate.

Can basis points describe fees as well as interest rates?

Yes. Basis points can express small changes in management fees, expense ratios, spreads, yields, and other percentage measures.

Does a 25-bp rate increase show how much more I will pay?

No. The dollar effect also depends on balance, time, amortization, compounding, payment timing, and fees.

This page provides general financial education, not legal, lending, deposit, accounting, tax, investment, or personalized financial advice.

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