when does current yield equals yield to maturity

Current yield equals yield to maturity (YTM) under very specific and rare circumstances in the world of bonds. This happens when a bond is priced exactly at par value, meaning the bond’s market price is the same as its face value. 

To unpack this, let’s consider what these terms mean. Current yield is a measure of the annual income (interest or dividends) from an investment relative to its current price. Yield to maturity, on the other hand, accounts for all future coupon payments and the difference between the bond’s current price and its face value, held until it matures. Essentially, YTM is a comprehensive measure of a bond’s return, factoring in its current market price, its coupon interest payments, and the gain or loss if held to maturity.

When a bond sells at par, the annual interest payments (coupons) are effectively aligned with the bond’s price. Therefore, the income you receive relative to the bond’s price (current yield) coincides with the bond’s overall yield if you hold it until it matures (YTM). This alignment is a delicate balance, reflecting a market perception that the bond’s interest rate is fair compensation for its risk, neither overpriced nor underpriced.

This equilibrium is delicate because any shift in interest rates or changes in the bond's market price due to credit risk, inflation expectations, or other economic factors disrupts this balance. Therefore, while conceptually straightforward, in practice, bonds at par where current yield equals YTM are like rare gems in the vast landscape of fixed income securities.