# Spread change wipes out yield income

CFAI Bk 4 Reading 30 EOC pg 149 problem 8. US and German bond spread of 300 bps. Gives German investors a quarterly income of 75 bps. German bonds duration is 8.3. The problem asks what change in German interest rates will wipe out their income. The answer , and I knew how to calculate this because there is a blue section with same numbers , is 75/8.3 = 9.04 bps My question is why do they use quarterly yield and calculate a change in rates based on quarterly numbers to calculate a spread change I’m sure my understanding is wrong , but something seems amiss to me

some time period needs to be specified, so for example 3 months.

I know that duration measures sensitivity of price for a 100 bps change in interest rates , but always thought that the said interest rate was an annual one . Now 9 bps change for one quarter will wipe out 75 bp of yield but the 9bps is not an annual number . On the same basis , it would be annualized at about 36 bps . But they never mention this. Am I wrong to assume ( or even write down in the answer in the exam ) that it is 9.04 bps per quarter or 36.16 bps per annum change?

My suggestion : Give them both (9.04 bps per quarter or 36.16 bps per annum change).

Thanks AMA , that is a practical suggestion, and I don’t hear anybody saying I have the completely wrong idea about this question!

As you said, something is never mentioned in the text.

this 9.04 yield change is YTM change (p.a.). the duration is calculated as number of years too. 9.04 x 8.3 = 75 bp Price change so what you earn on yield spread (75bp x principal) over 3 months period you would lose on price change. this yield change can repeat every quarter (for simplicity no convexity)