In interest rate futures another futures contract is added that has a bond for an underlying. I didn’t understand that how does a bond futures add negative duration to the portfolio.

In stock index futures I didn’t understand the process of calculating number of contracts needed to enter to cover the notional amount.

I believe the negative duration has to do with hedging the current bond portfolio, which lows the duration. It’s the same answer as your other question regarding why swaps lower duration.

Options represent a number of shares. 1 options contract usually represents 100 shares unless you’re on the eMini contracts which if I recall is 10 shares. If you want to hedge 100 shares of a stock, you get 1 option. For futures, the futures will represent a value that is usually X amount of the index. For example, one S&P 500 index futures contract obligates the buyer to 250 units of the S&P 500 index. If the index is trading at $1,000 , then the single futures contract is similar to investing $250,000 (250 x $1,000 ). Therefore, $250,000 is the notional value underlying the futures contract. The problem will specify the size the futures represents, and you do the math.

Do futures lower duration? If you have interest rate exposure in a bond porfolio, the best way to hedge that risk is to enter a pay fixed receive floating swap. Futures have the same interest rate risk as the underlying bond.

^ His response was incorrect regarding the impact of futures on duration. Follow S2000’s answer. Going long on a futures contract in a bond portfolio does nothing to hedge interest rate risk. This means if interest rates goes up, both the bond prices and the futures prices fall. Adding the futures contract does nothing to reduce duration.

“Because most interest rate futures contracts are futures contracts in which the underlying is a bond, this type of contract would have a duration that is consistent with the forward behavior of the underlying deliverable bond. That is, the interest rate futures price will move as though it was the forward price of the bond on the expiration date. The price sensitivity of the futures will, therefore, reflect a type of forward duration that is based on the underlying bond. Thus, the futures price will move fairly consistently and proportionately with the yield that drives the underlying bond. Continuing with the example earlier in which the manager whose portfolio has a duration of five years wants to lower the duration to three years, the general principle is the same: By selling bond futures, a portfolio manager “adds negative duration” to the portfolio, and if done in the right quantity, the overall duration can be reduced to the target level.”

4 (Institute 435) Institute, CFA. 2018 CFA Program Level II Volume 5 Fixed Income and Derivatives. CFA Institute, 07/2017. VitalBook file. The citation provided is a guideline. Please check each citation for accuracy before use.

All that is saying is your bond futures have a similar duration than the bond portfolio, so you sell (short) the bond future to remove that exposure. Using #2 from above, you can calculate how much of the bond future contracts you need to hedge the amount of the bond portfolio you have to get you to the duration you want to be. And I think you can pick a future with an underlying with a higher or lower duration.

It’s the same thing as if you had an equity position of largecap stocks and you want to lower the volatility/exposure on that, you can sell some S&P index futures. THe amount of the futures you sell determines how much of the equity position you will hedge.