Convertible Bond Arbitrage- Small Clarifcation

The idea of arbitrage is buy low and sell high.
According to the curriculum, we are setting up a convertible bond arbitrage by selling the overvalued stocks and buying the undervalued convertible bond. But my question is- does it this go the other way around meaning, can we sell the convertible bond and buy the shares if the shares are undervalued in the market?
The book only says that we can set up an arbitrage with buying the convertible bond and selling the overvalued shares.

No.

You need control of the conversion option. If you sell the convertible bond, you’re giving control of the conversion option to someone else.

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Theoretically speaking, if I believe the implied volatility of convertible is less than the current vol and shares in open market are undervalued, what s stopping me from such a trade?

Nothing.

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ok got it
thanks