Economics · Debt Market Mathematics

Evaluate the following statements regarding the technicalities of bond pricing, the behavior of yields, and the impact of market volatility on debt portfolios. Statement 1. The market price of a coupon-paying bond is calculated by taking the sum of the present values of all future periodic interest payments and the present value of the face value to be received at maturity. When the market interest rate or required yield is exactly equal to the coupon rate, the bond will trade at its par value. However, if the market yield rises above the coupon rate, the present value of these fixed cash flows decreases, causing the bond to trade at a discount. Conversely, if market yields fall below the coupon rate, the bond becomes more attractive, and its price rises to a premium above the par value. Statement 2. The relationship between bond price and interest rates is characterized by a property known as convexity, which implies that the price-yield curve is not a straight line but is bowed toward the origin. Because of this curvature, the percentage increase in a bond price when interest rates fall by a certain amount is actually greater than the percentage decrease in price when rates rise by the same amount. For a standard bond without any embedded options, this positive convexity is a highly desirable feature for an investor as it provides a better risk-reward profile during periods of high volatility. In contrast, certain bonds like callable bonds may exhibit negative convexity at low yield levels where the price increase is capped by the likelihood of the issuer calling the bond. Statement 3. Macaulay Duration represents the weighted average time an investor must wait to receive the cash flows from a bond, and it is expressed in units of years. For any bond that pays intermediate coupons, the Macaulay Duration will always be strictly less than the actual time to maturity because some value is returned to the investor before the final date. In the specific case of a zero-coupon bond, since there is only a single cash flow at the end of the term, the Macaulay Duration is mathematically identical to the bond's term to maturity. As the coupon rate of a bond increases, the duration decreases because a larger proportion of the bond's total value is recovered earlier in its life. Statement 4. Modified Duration is a derived measure that quantifies the price sensitivity of a bond to a 1 percent change in its yield to maturity, and it is the primary tool used by bank treasurers to manage interest rate risk. It is calculated by taking the Macaulay Duration and dividing it by the quantity of one plus the yield per compounding period, which is usually semi-annual for most Indian Government Securities. While Modified Duration provides an excellent linear approximation for small shifts in interest rates, it tends to underestimate the actual price of the bond for large changes in yield due to the omission of the convexity effect. Most sophisticated risk management systems in banks now use a combination of both duration and convexity to calculate the total potential impact on the bank's capital. Based on banking principles and debt market mathematics, which of the following is correct?