Core Bond Theorems in JAIIB
The JAIIB Syllabus covers core bond theorems (often referred to as Malkiel’s bond theorems) under the Indian Economy & Financial System (IE & IFS) and Accounting and Financial Management for Bankers (AFM) modules. These rules explain how bond prices react when market interest rates or yields change.
Core Bond Theorems in JAIIB
- Theorem 1 (Inverse Relationship): Bond prices and market interest rates move in opposite directions. When yields (market interest rates) rise, bond prices fall. When yields drop, bond prices go up. If the required rate of return equals the coupon rate, the bond trades exactly at its par (face) value.
- Theorem 2 (Asymmetric Price Volatility): The percentage increase in a bond’s price when interest rates fall is greater than the percentage decrease in price when interest rates rise by the same amount. This asymmetry happens because bond prices are bounded below by zero but can rise infinitely.
- Theorem 3 (Maturity and Price Sensitivity): Bonds with longer terms to maturity have higher price sensitivity than bonds with shorter terms, assuming the change in yield is the same. Longer duration exposes cash flows to rate shifts over a wider timeline.
- Theorem 4 (Coupon Rate and Sensitivity): Between two bonds with identical maturity, the bond with the lower coupon rate is more sensitive to interest rate changes than the high-coupon bond. Reason is that Lower coupon bonds receive a larger portion of their total cash flow (the principal repayment) further out in the future, increasing their effective duration.
- Diminishing Marginal Sensitivity (Theorem 5): Price volatility increases as maturity increases, but it does so at a decreasing (diminishing) rate. In other words, the increase in price sensitivity from a 10-year to a 20-year bond is much larger than the increase from a 20-year to a 30-year bond.
Key Exam Concepts
- Bond Value: Calculated as the present value of all future periodic coupon payments plus the present value of the face (redemption) value, discounted at the required Yield to Maturity (YTM).
- Duration & Convexity: Duration measures the linear price sensitivity of a bond to interest rate changes, while Convexity accounts for the curvature of the price-yield relationship (explaining Theorem 2).
Par, Discount, and Premium
- If Coupon Rate = YTM, the bond trades at Par (Face Value).
- If Coupon Rate < YTM, the bond trades at a Discount.
- If Coupon Rate > YTM, the bond trades at a Premium.
Quick Revision Table
Concept Formula/Logic Exam Tip Bond Value PV of coupons + PV of redemption Always discount at market rate Price vs. Rate Inverse relationship Expect MCQs on this Duration Longer maturity → more volatile Case study questions Coupon Impact Higher coupon → less volatile Compare bonds in MCQs YTM Rate equating PV inflows to price Numerical problems
Read more… Bonds & Debentures: Meaning, Types & Differences
Frequently Asked Questions (FAQs)
What happens to a bond’s price if the market yield equals the coupon rate?
The bond sells at par value (face value). If the yield is higher than the coupon, it trades at a discount. If the yield is lower, it trades at a premium.
Which bond is more sensitive to a 1% change in interest rates: a 5-year bond or a 10-year bond?
According to Theorem 3, price volatility climbs as the maturity period lengthens. Hence, the 10-year bond is more sensitive.
Do these theorems apply to corporate bonds and government securities alike?
Yes. The fundamental mathematical relationship between price, yield, maturity, and coupon applies to any fixed-income fixed-coupon security.
MCQs on Bond Theorem & YTM
Q1. If market interest rates rise, the price of an existing bond will:
a) Increase b) Decrease c) Remain unchanged d) Double
Answer: b) Decrease (Bond price and interest rate have an inverse relationship.)
Q2. A bond with longer maturity is:
a) Less sensitive to interest rate changes b) More sensitive to interest rate changes c) Not affected by interest rate changes d) Always priced at par
Answer: b) More sensitive (Duration effect: longer maturity → higher volatility.)
Q3. Higher coupon bonds are:
a) More sensitive to interest rate changes b) Less sensitive to interest rate changes c) Always priced below par d) Always priced above par
Answer: b) Less sensitive (Because frequent coupon inflows reduce risk of rate changes.)
Q4. Yield to Maturity (YTM) is: a) Coupon rate of the bond b) Current market price of the bond c) Discount rate equating PV of inflows to bond price d) Redemption value of the bond
Answer: c) Discount rate equating PV of inflows to bond price
Q5. A bond of ₹1,000 face value, 10% coupon, 5 years maturity, market rate = 12%. The bond will be valued:
a) Above par b) At par c) Below par d) Equal to coupon rate
Answer: c) Below par (Market rate > coupon rate → bond trades at discount.)