# Basis points vs percentage change

When we say "rates have increased from 2% to 3%," we are really saying that rates have increased 1%, or 100 basis points. However, this is different from percent change, as that would be (.03-.02)/.02 = 50% = 50 basis points.

So, when someone says "X changed 50 basis points" I should think in absolute terms and literally add .50% to whatever changed. If I am told that "X changed by Y percent," then I should carry out the (.03-.02)/.02 = 50% = 50 basis points calculation above.

Is this correct?

1% = 100bps
so 50% = ?

not 50 bps.

#### shzhang

my understanding is that if x is a rate which has units in percentage already, the "change by certain percentage " is supposed to be additive.
if x is in units of other stuff like price, number, then the "change by certain percentage " is supposed to be multiplicative.

do note that I'm not expert in finace and not even native in english speaking so I could very well be wrong here...

#### LochWulf

More often than not I see a general preference for expressing rate changes in terms of their absolute change, and further, expressing that absolute change in terms of either basis points or points (100 bps). A rate that went from 7.00% to 7.25% would thus be unambiguously described as increasing by 25 bps or one-quarter point.

Saying that a 10% rate "increased by 3% " leaves open the possibility that it went to 13% or that it went to 10.3%, and so I tend to see people deliberately avoiding this language, and using the "points / basis points" lingo instead. Still, it's not a universal agreement by any stretch, so get clarification whenever there's doubt.

#### Rasmus

Lets use 50% as an example:

Saying "an increase of 10%" equals 50% x 1.1 = 55%
Saying "an increase of 10 percentage points / pp / % points" equals 50% + 10% = 60%
Saying "an increase of 100 basis points / bps" equals 50% + 1% = 51%

If in doubt, better to give too much information than to give too little.

#### Ken Abbott

##### Managing Director
Movements in yields and yield spreads are usually (but not always) measured in basis points. That, however, is not necessarily indicative of any stationarity assumption. Rates can be normal (absolute changes gaussian) or log-normal (relative changes gaussian) or anything in-between.

where alpha can be between zero and unity.

Some firms measure total credit spread risk not as spread PV01, but rather as PV10%, which represents a 10% increase in overall spread levels across the board.

Replies
0
Views
2K
Replies
2
Views
11K
Replies
2
Views
2K
Replies
0
Views
12K
Replies
2
Views
79K