What aspects decide the correlation between US corporate bonds and US treasury ? I was told that some corporate bonds are more sensitive to treasury than others. Sectors or maturity?
The yield of a corporate bond can be split into the risk-free part, which is by constuction highly correlated to treasury yields; and the extra spread that the bond holders demand to compensate for credit, liquidity, and other risks.
For an investment grade bond, the risk-free part is a relatively larger part of the bond yield, so the yield is more correlated to risk-free rates in the same tenor bucket as the bond's maturity. Conversely, for a higher-yield (junk) bond, the risky spread is relatively larger, so their yields are less correlated to risk-free rates than IGs'. Further, bond paying relatively high coupons, are affected a little by the risk-free rates before their maturity. Distressed bonds on the verge of default are driven much more by their recovery assumption than by risk-free rates.
In general, there's no material correlation ($\rho$) between the risky spread and small movements of interest rates. Large unexpected movements do sometimes affect ($\tau$) some industries' credit spreads , similar to how they afect equity, and similarly hard to quantify or predict.
Edit: I've decided to mention the results (unpublished, of course) obtained by some former collegues who had access to lots of great historical data on risky bonds. A bond's extra speead can be further split into two spreads:
a "generic" spread that depends on the country of risk and on credit quality, is correlated to similar credit spreads (e.g. France B to Gemany BB), and of course between tenors (e.g. France B 5Y to France B 10Y) and is not materially correlated to interest rates. Surprisingly, trying to separate these spreads by sector/industry was not useful. Trying to separate by currency (e.g. Brazil USD v Brazil EUR v Brazil BRL), and looking at correlations to equities, equities implied vol, and commodities was of little use.
the issuer's "idiosyncratic" spread not correlated to anything except between its own tenors (e.g. IBM 5Y to IBM 10Y)). (It is handy for specific risk add-on.)