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If the rate of return is positive, can percentage price change be negative?

If the rate of return is positive, can percentage price change be negative?

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Answer: Yes, if the rate of return is positive, percentage price change can be negative. Bond price is nothing but the present value of future coupon payments and par value repayment at maturity. There is an inverse relation between interest rate and present value of future cash flows. When interest rate rate increases, present value decreases; when interest rate decreases, present value increases. Therefore, if interest rate rises, the present value of the payments to be received by the bondholders falls and bond prices fall; if interest rate falls, the present value of the payments to be received by the bondholders increases and bond prices increases as a result. Therefore, even if the interest rate is positive but increases subsequently, bond price tend to fall from its issue price. It results, negative percentage price change in bond. That is, percentage change in bond price is calculated by: (Bonds new price - Bonds old price) / Bonds old price. When bond price decreases due to increase in interest rate, numerator used in the percentage change in bond price formula will be negative, resulting negative price change percentage though the interest rate is postive. Rate of return is calculated by: (Change in bond priceCoupon interest received)/ Bonds initial price. If the coupon receipt is more than the dollar change in bond price, it is obvious that the rate of return is positive because numerator will be positive. Still, there is a nagative percentage price change in this case. In simple terms, If the rate of return is positive, percentage price change can be negative.

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