Convertible bond: Limited downside risk associated with a convertible bond

• "Because the straight bond value will provide a floor for the value of the convertible bond, downside risk is limited to the difference between the market price of the bond and the straight value."
• If interest rates are NOT expected to change:
• then the straight value of the bond will NOT change (ignoring the change in value resulting from the passage of time).
• If the straight bond value does NOT change, then downside risk is indeed limited to the difference between the price paid for the conversion bond and the straight bond value.
• If interest rates rise as the price of the common stock falls,
• the conversion value will fall and the straight bond value will fall, exposing the holder of the convertible bond to more downside risk.