What exactly is yield to maturity? How are bonds priced in? I am trying to understand the differences between coupon rate and yield to maturity?

Yield to maturity is just basically the average compounded return of the bond taking into account the Purchase price and its remaining term (Time).

Imagine all of us bought the exact same bond, but at different price and at different Time. The yield would be the same for all of us as it is the same bond. But YTM will be different. Those who bought cheaper will have a higher YTM. And the longer the remaining Term of the bond, the lower the YTM.

YTM is usually worked backwards. That means using the purchase price (or market price) as the present value. Then using trial and error to find the discount rate, that will discount all future cashflow to get the current present value (market price). This discount rate is the Yield to maturity.

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