The current dollar duration of a portofolio is $100,000 an investor fears a 50-basis-point rise in interest rates and he wants to completely hedge the portfolio. The dollar duration of the cheapest-to-deliver (CTD) issue is $5,000, and its conversion factor is 0.9. How will he hedge this position?

Your answer is right, and schweser has also explained the same way… My confusion is that since the investor is concerned about movement on only 50 bps, should not he be done by hedging through 9 contracts.

i think the rate change issue doesnt matter if its 50bps or 500bps, its irrelevant data in the question, the point is the investor wants to completely hedge the portfolio. Therefore you would use the formula above to completely hedge.