Which of the following equations assume a linear relationship between price and yield?
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A. B. C. D.B
The answer to the question is A. Yield to maturity equation.
Explanation:
Yield and price have an inverse relationship; as yield increases, price decreases and vice versa. This relationship can be either linear or nonlinear. When the relationship between yield and price is linear, a change in yield results in an equal and opposite change in price.
The yield to maturity (YTM) equation assumes a linear relationship between yield and price. The YTM is the interest rate that equates the present value of a bond's cash flows to its current market price. It is the yield an investor would receive if they held the bond until maturity and reinvested all interest payments at the same rate. The equation is as follows:
P = (C/ (1 + YTM)^1) + (C/ (1 + YTM)^2) + ... + (C + Par/ (1 + YTM)^n)
Where: P = market price of the bond C = coupon payment YTM = yield to maturity Par = face value of the bond n = number of years to maturity
The YTM equation assumes a linear relationship between price and yield, which is appropriate for bonds that have a small change in yield. However, for bonds with a large change in yield, the relationship becomes nonlinear, and the use of duration and convexity is more appropriate.
Duration measures the bond's sensitivity to changes in interest rates and assumes a linear relationship between bond prices and yields. Convexity is a measure of the curvature of the relationship between bond prices and yields and takes into account the nonlinear relationship between price and yield. The immunization equation is used to construct a portfolio that will immunize the investor from interest rate risk. It assumes a linear relationship between price and yield, similar to the YTM equation.