Definition — what a basis point (bp or bps) is
– A basis point is a unit for expressing changes or differences in percentages in finance.
– One basis point = 1/100th of 1% = 0.01% = 0.0001 in decimal form.
Why traders, risk managers, and investors use basis points
– They remove ambiguity when describing percentage moves. Saying “a 100 bp rise” clearly means +1 percentage point; saying “a 10% rise” could be interpreted as relative (multiplicative) or absolute.
– Basis points are a convenient, precise way to quote small changes in interest rates, bond yields, credit spreads, fees (expense ratios), and other rates.
Quick conversions and rules (step-by-step)
1. To convert basis points to percentage points: divide by 100.
– Example: 50 bps → 50 / 100 = 0.50% (or 0.005 in decimal).
2. To convert percentage points to basis points: multiply by 100.
– Example: 0.25% → 0.25 × 100 = 25 bps.
3. To convert from a decimal rate to bps: multiply the decimal by 10,000.
– Example: 0.035 (3.5%) → 0.035 × 10,000 = 350 bps.
Worked numeric examples
– Interest-rate example: If the Fed rate drops from 4.00% to 3.50%, the change is 0.50 percentage points = 50 basis points.
– Yield difference example: A bond yielding 4.0% vs. another yielding 4.3% — the difference is 0.3 percentage points = 30 bps.
– Small price move example: A stock at $200 falling to $199 is a $1 drop = 0.5% = 50 basis points.
Price Value of a Basis Point (PVBP / DV01)
– What it measures: the approximate dollar change in a bond’s price for a one-basis-point move in yield. It’s used to quantify interest-rate sensitivity in absolute dollars.
– Relationship to duration: PVBP is a special-case of dollar duration (DV01). Modified duration measures the percent price change for a 1% (100 bp) change in yield; PVBP uses a 1 bp change instead.
– Formula (linear approximation): PVBP ≈ Modified Duration × Price × 0.0001
– Assumption: small yield changes and linear approximation; accuracy falls off for large moves because of convexity.
– PVBP worked example:
– Suppose a bond’s price = $1,000 and its modified duration = 7.5.
– PVBP ≈ 7.5 × 1,000 × 0.0001 = $0.75.
– Interpretation: a 1 bp increase in yield would reduce the bond’s price by about $0.75; a 1 bp decline would raise it by about $0.75.
Where basis points appear in practice
– Central-bank rates and policy announcements (Fed rate changes often quoted in bps).
– Bond yields and changes in yield curves.
– Credit spreads (difference between corporate bond yields and benchmark government yields), typically quoted in bps.
– Investment fees and expense ratios (e.g., a 25 bps fund fee = 0.25%).
– Risk reports, stress tests, and scenario analysis that model portfolio sensitivity to interest-rate moves (e.g., “assess impact of a 200 bp shock”).
Why use basis points rather than plain percentages
– Precision and clarity when describing absolute changes in rates.
– Avoids confusion between relative (percent change of a percent) and absolute (percentage-point) moves.
– Easier to read and compare small differences (e.g., 7 bps instead of 0.07%).
Short checklist — when writing or interpreting basis-point moves
– Identify the starting rate (percentage or decimal).
– Confirm whether the move is absolute (bps or percentage points) or relative (% change).
– Convert units if needed (bps ↔ % ↔ decimal).
– For bond PVBP calculations: use modified duration, current price, and remember the linear approximation assumption.
– Note direction (increase vs decrease) and scale (1 bp vs 100+ bps) to judge materiality.
How basis-point moves affect everyday finances (brief)
– Borrowing costs: variable-rate loans and some mortgages often change with benchmark rates; a rise measured in bps increases monthly payments.
– Savings rates: larger benchmark rates typically translate into higher deposit yields (measured in bps).
– Investments: bond prices move inversely to yield changes measured in bps; equity and currency markets react to rate shifts and credit-sp