Jerry X. answered • 02/23/22
Tutor
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(40)
10+ years financial valuation & accounting experiences on Wall Street
Question 1: Under what condition(s) Bond price = Face value ?
Answer: when the bond YTM equals its coupon rate
Question 2: When yield to maturity (YTM) increases, everything else equal, how does bond price change ?
Answer: bond price decreases
Question 3: Is the interest rate risk higher or lower as the time to maturity increases ?
Answer: higher
Jerry X.
Ok, Added reasons: Question 1: Under what condition(s) Bond price = Face value ? Answer: when the bond YTM equals its coupon rate Reason: intuitive way: Face value is defined in the bond indenture, whereas the bond price is the market view/sentiment/response to the bond value. when bond price = face value, which usually happens when the bond is initially issued, the market view and bond indenture matches. YTM is the return demanded from investors, whereas coupon rate is defined in the bond indenture. so when market view matches with the bond indenture ( bond price = face value ), then YTM = coupon rate. Reason: based on bond math: F -- Face Value; P -- Bond price, C -- coupon rate; n -- number of year P/F = C / YTM + ( 1- C / YTM ) / ( 1 + YTM )^n So, when bond price = face value, then P = F, the above formula leads to ( 1 - C / YTM ) * ( 1 - 1/(1+YTM)^n ) = 0 But 1 - 1/(1+YTM)^n > 0 So, we have ( 1 - C / YTM ) = 0, which leads to YTM = C Question 2: When yield to maturity (YTM) increases, everything else equal, how does bond price change ? Answer: bond price decreases Reason: From the above bond price formula, we can tell that the bond price is inversely related to YTM ( because YTM is the discount rate, in the denominator ). So as YTM increases, the bond price decreases. Question 3: Is the interest rate risk higher or lower as the time to maturity increases ? Answer: higher Reason: As maturity increases, the bond duration increases, leads to higher price sensitivity to interest rate changes, means higher interest rate risk I can show you with more detailed theory / bond math if you can schedule a session with me to walk through. Thanks
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02/26/22
PJ S.
Can you explain the reason for the above answers. Thank you.02/23/22