Macaulay duration – the weighted average time to receipt of cash flows – is positive.
Modified duration – the negative of the percentage price change in a bond divided by the change in its yield to maturity – is equal to the Macaulay duration divided by (1 + YTM) (where YTM is for a single payment period), so it’s positive.
Effective duration and spread duration are usually positive, though effective duration may be negative in some situations (as I mentioned above). Key rate durations for par and premium bonds are generally positive, but key rate durations for key rates for less than the maturity on discount bonds are usually negative.
And, if you read the curriculum, it says just what I mentioned, above: when the underlying risk-free rate changes, a high-yield bond’s spread generally changes in the opposite direction and by more. Therefore, when risk-free rates increase, the bond’s YTM decreases and vice-versa.
Duration measures the change of interest rate relative to the change in bond price and the relationship is negative, right? The bond price-interet rate curve is a downward sloping curve and the tangent line which is duration is downward sloping.
Modified duration, effective duration, spread duration, key rate duration (and so on, but not Macaulay duration) measure the _ negative _ of the percentage price change given a small incremental change in the bond’s yield. When duration is positive, the price change for a positive yield change is negative.
By the way, (modified or effective) duration is _ not _ the slope of the line tangent to the price/yield curve. That slope gives the (absolute) price change, not the percentage price change.
This a “general” statement. Because generally the reserve bank raises rates when the economy is doing good and in that case the high yield may do better because the credit risk decreases. This leads to spread reducing, the overall the yield reducing and bond prices rising. So rates go up and bond prices go up -> negative duration.
“In practice, however, credit spreads tend to be negatively correlated with risk-free interest rates. One important reason for this phenomenon is that key macro factors, such as economic growth, default rates, and monetary policy, usually have opposite effects on risk-free rates and spreads. For example, a better economic environment generally leads to higher risk-free rates and narrower credit spreads, whereas a weaker economic environment generally results in lower risk-free rates and wider credit spreads. As a result of the typically negative correlation between risk-free rates and credit spreads, changes in risk-free rates tend to generate smaller changes in corporate bond yields than theoretical measures of duration suggest.”
I just cant get the idea of the sentence in bold. Why do they mention abt " changes in risk-free rates tend to generate smaller changes in corporate bond yields than theoretical measures of duration suggest".
I only understand that: bond yield change = change in Rf + change in spread
=> Change in price of bond = (- change in Rf * Bond duration) + (-change in spread * spread duration)
Not sure if this will help, but I’ll try to explain this way. Different types of bonds (e.g. US Treasuries, investment grade credit, high yield) are impacted differently by interest rate movements. US Treasuries are most sensitive to interest rate movements (hence having higher empirical duration) while high yields are less sensitive (has lower empirical duration) as credit risk primarily drives their returns. Further, high yields are more highly correlated to equities so when interest rates rise (assuming a strong growth environment), then credit spreads are likely to tighten/narrow (I.e. HY valuations are richening) whereas Government bonds (US Treasuries) will underperform in a rising rate environment (government bonds will perform well in a low growth low inflationary environment). So to tie it all together, you can have one US treasury with a 5 year effective duration and a high yield credit with 5 year effective duration, but the high yield credit will have a much lower “empirical duration” than what it’s effective duration would indicate because of its lower interest rate sensitivity due to its embedded credit risk (HY has a higher OAS as they are usually callable).