Single instrument
The loss of a single instrument can be decomposed into three components: the default probability of the obligor (PD), the loss given default (LGD), and the exposure at default (EAD). For the sake of simplicity, EAD is assumed to be non-random in the subsequent discussion.
LGD is the portion of EAD that gives negative impact in case of default. LGD is usually less than one because many default obligors are originally backed by securities.
The magnitude of the recovery rate is tied to the collateral properties during or after default. The recovery rate depends on the nature of the instrument: only the loss on principal can be claimed, not the loss on coupon interest.
PD and LGD are positively correlated, meaning PD and the recovery rate are negatively correlated.