Question

Explain the relationship between bond’s volatility and a bond's coupon and bond’s maturity.

How do volatility and risk change for a zero coupon bond?

What is bond price volatility and how can it be calculated?

Answer 1

1.
Higher the maturity higher the volatility
Higher the coupon lower the volatility

2.
Volatility for zero coupon bond is highest

3.
Bond price volatility is duration and can be calculated as % change in price of bond with 1% change in yield

Answer 2

Bond Volatility :-

1. Coupon & Maturity Impact on Volatility

• Lower Coupon = Higher Volatility (Prices swing more because most value                                 comes from the faraway principal payment).

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• Longer Maturity = Higher Volatility (More time means more uncertainty                                      about future rates).

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Example:-

• A 5% coupon bond drops ~7.4% when rates rise 1%.

• A 10% coupon bond drops less because its coupons cushion the blow.

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2. Zero-Coupon Bonds = Maximum Volatility

• No coupons → all value depends on maturity payment.

• A 10-year zero-coupon bond drops ~9% when rates rise 1% (vs. ~7% for coupon bonds).

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3. Measuring Volatility: Modified Duration

• "How much will price drop if rates rise 1%?"

• Formula: Price Change ≈ -Duration × Rate Change

• Example: A bond with Duration = 4.4 falls ~4.4% if rates rise 1%.

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Bottom Line:

• Want stability? Pick high-coupon, short-term bonds.

• Higher risk/reward? Zero-coupon or long-term bonds swing more.