You hold a $10 million bond portfolio with a modified duration of 8 years.How would you,using T-bond futures,hedge this portfolio? Assume that the bond to be delivered has a modified duration of 9 years and that the futures price is currently $92 for $100 par value.

Question

Quizplus · Accepted Answer

To hedge a $10 million bond portfolio with a modified duration of 8 years, we need to find the number of T-bond futures contracts required.

The formula for calculating the number of futures contracts required is: 
No. of contracts = (portfolio value x portfolio modified duration)/ (futures price x futures modified duration x conversion factor)

Using the given values: 
- Portfolio value = $10 million 
- Portfolio modified duration = 8 years 
- Futures price = $92 for $100 par value, so $92 x 100 = $9,200
- Futures modified duration = 9 years 
- Conversion factor = 0.8 (for T-bond futures)

Substituting these values in the formula: 
No. of contracts = ($10,000,000 x 8) / ($9,200 x 9 x 0.8) = 96.74

Rounding it off, we get approximately 97 contracts.

Therefore, the best choice is option A) Sell approximately 97 contracts to hedge the bond portfolio.

You Hold a $10 Million Bond Portfolio with a Modified