Are any of these false? For a given coupon rate, the sensitivity of bond prices

Question

1. Are any of these false?

1. For a given coupon rate, the sensitivity of      bond prices to changes in interest rates increases at an increasing rate      as maturity increases.  
2. For a given absolute change in interest rates      from the same base level, the proportionate increase in bond prices when      rates fall is larger than the proportionate decrease in bond prices when      rates rise
3. For identical coupon rates and a given absolute      change in interest rates from the same base level, long-term bonds change      proportionately more in price than short-term bonds.
4. For identical maturities and a given absolute change in interest rates from the same base level, low-coupon bonds change proportionately less in price than high-coupon bonds.

Explanation / Answer

For a given absolute change in interest rates from the same base level, the proportionate increase in bond prices when rates fall is larger than the proportionate decrease in bond prices when rates rise For identical coupon rates and a given absolute change in interest rates from the same base level, long-term bonds change proportionately more in price than short-term bonds. both are false

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