Fixed Income - Return assumptions

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unemployed1

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New to the forum and looking for some help. Could anyone provide a simple explanation to why these assumptions hold:
1. “If the market YTM for the bond, our assumed reinvestnment rate, increases after the bond is purchased but before the first coupon date, a buy and hold investors realized return will be higher than the YTM of the bond when purchased.”
2. “If the market YTM for the bond, our assumed reinvestment rate, increases after the bond is purchased but before the first coupon date, a bond investor will earn a rate of return that is lower than the YTM at bond purchase if the bond is held for a short period”
3. “If the market YTM for the bond, our assumed reinvestment rate, decreases after the bond is purchased but before the first coupon date, a bond investor will earn a rate of return that is lower than the YTM at bond purchase if the bond is held for a long period.”
Please and thank you!
 
Three components of bond return: coupons received, interest earned from reinvesting coupons received, price received if sell bond prior to maturity.
Actual return equals YTM if: 1. bond held until maturity 2. all coupons received as promised 3. all coupons reinvested at YTM when received
1. Buy and hold investor reinvests coupon at a higher rate. The interest earned on that coupon interest is higher it would’ve been if reinvested at YTM, making overall return higher. ASSUMING bond is not sold.
2. Selling bond at a higher yield (lower price) without getting benefit of higher interest earned on reinvested coupons.
3. Selling bond at lower yield (higher price) without having to take the hit of lower interest earned on reinvested coupons.
 
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