# Quick Question

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?

A. Sell 18 contracts

B. Sell 9 contracts

Choose an appropriate answer ?

A I think .

Since DD is given to be 5000

The # Of contracts = 100,000/5000 * 0.9 = 18

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.

I should stop browsing these specific question threads… it makes me realize how much I’ve forgotten

Just so you know.

dollar duration means that if the ptf moves by 100bps it will move by the dollar duration.

so in this case, a movments of 100 bps is 100 000\$ on the portfolio.

on the CTD the movments for the CTD adjusted with the conversion factor for a 100 bps is 5000\$/0.9 = 5555.5\$

a perfect hedge would be 100 000 / 5555.5 = 18 contrats.

50 bps movements would be this :

portfolio : 0.5 * -100 000 = -50 000\$ ( int. rise, so lose money )

CTD portfolio : 0.5 * 18 * -5555.5 = -50 000\$

so you are hedged. The bps size doesn’t count on small increase. but be aware. IF convexity is not match, bigger movments can create differences.

ohh yes…thankyou thankyou so much summerside. I am not even a good nerd ! Your concepts are crystal clear !! thanks everyone guys for your inputs