Explain the relationship observed between ratings and yield to maturity.

The relationship observed between ratings and yield to maturity is that higher rated bonds tend to have lower yields, while lower rated bonds typically offer higher yields. This is due to the fact that investors are willing to accept a lower return for a smaller risk of default on higher rated bonds whereas they require a higher yield as compensation for taking on additional risk with lower quality debt instruments.

The coupon rate and the yield-to-maturity determine why the bonds would trade at a discount, premium or par because when the coupon rate is greater than the prevailing market interest rates, then it will be trading at a premium (higher than face value). Conversely, if the coupon rate is less than market interest rates then it will trade at a discount (lower than face value) since there is no incentive to purchase such an instrument relative to another offering with substantially similar characteristics but possessing better terms in regards of coupons paid out over time. Lastly, if both values are equal then it means they are trading at par which simply indicates zero difference between them so nothing more nothing less.

Regarding expectations if time-to maturity were increased or decreased by 5 years: If time span was expanded this could potentially result in very slight increase bond’s YTM due extra period added before principal payment made alongside other associated interest payments yet often not really noted upon unless significant gains derived namely whole sale bulk purchases otherwise minimally noticed changes hardly visible plain sight least noticeable aspect equation given traditionally fluctuations small increments occur generally non volatile environment speaking however amount differs based upon quality underlying security instance AA Rated class considered highest ranks spectrum A B ones step below respectively cause fall fluctuate accordingly industry standards markets participants dictates level movement experienced anything related particular field conditions applied subject case scenario example let us imagine decreasing NPER 5 year window decreases results lowering overall sale price quote reflecting demand supply dynamics play role domino effect occurs whereby decrease leads consequently downwards trend followed closely yields respective maturities cause reflected minor change indicated fluctuation predictably consistent movements patterns predictable nature continues after periods ended holding steady levels set commencement proceedings started again reset same positions earlier stasis equilibrium achieved sooner expected while powerful forces tugging tug opposite directions equals signs pointed straight ahead negotiating settlement deal somewhat analogous situation regarding maturity dates kept mind favor issuer investor compromise struck beneficial both sides transaction concluded successfully parties happy end result foreseeable future beneficial fast outcome want achieve grow business reaching specified goals objectives planned out full potential reached maximum capacity stretch limits aim reach stars touch skies process journey begins hard work dedication pays off patience virtue rewards sweeter success approaches near distance.