# Duration gap - futures and interest rate expectation

``````   Liabilities                Assets
``````

|Value| EUR47.3 million| EUR49.8 million|
|Modified Duration| 12.6 years| 18.4 years|
|Basis Point Value (BPV) EUR59,598| EUR91,632|

Ruelas explains that he uses futures contracts on euro-denominated German government bonds to reduce the duration gap between assets and liabilities. However, because the pension fund has only a small surplus and he would like to increase this surplus through active management of the portfolio, he employs a contingent immunization strategy. The fund is currently short 254 contracts based on a 10-year bond with a par value of EUR100,000 and a basis point value (BPV) of EUR97.40 per contract.

Given the futures position entered into by the pension fund, Ruelas most likely believes interest rates will:

A. fall.
B. rise.
C. remain the same.

Answer: A is correct. The number of futures contracts needed to fully remove the duration gap between the asset and liability portfolios is given by Nf = (BPVL − BPVA )/BPVf , where BPV is basis point value (of the liability portfolio, asset portfolio, and futures contract, respectively). In this case, Nf = (59,598 − 91,632)/97.4 = −328.891, where the minus sign indicates a short position or selling of 329 futures contracts (328,891/1,000). In this case, the duration of assets is higher than the duration of liabilities so the pension fund will be hurt by rising interest rates and helped by falling interest rates. The short futures position of 329 contracts will hedge this exposure. Ruelas has under-hedged with a short position of less than 329 contracts, leaving the pension fund to be hurt by rising interest rates and helped by falling interest rates; therefore, he must believe interest rates will fall.

Can someone please expand? Am I missing smth here? I do not really understand the solution…
In the text, it says he is “short 254 contracts”. You are short when you want to reduce duration because the rates are rising…

It appears so.

He needed to be short 329 contracts to be net zero (money) duration.

He’s short only 254 contracts (underhedged), so he’s net long (money) duration.

When you’re long duration, you benefit when rates decrease; presumably he’s hoping to benefit.

Because if rates decrease, then your value goes up…
So, for interest rates falling, and with assets having a higher duration, whichever has higher duration will rise more… I see. Thank you!!!

Higher money duration. Finance people in general are, and the curriculum in particular is, very sloppy in their language on that.

My pleasure.