Hi

@akrushn2 No, I'm including T-bonds which are an investment asset commodity, so they

*should *fit the logic along with all the consumption commodities. Basis risk is firstly a mark-to-market risk. Basis strengthening/weakening is a dynamic over time, from today until maturity. I'm saying: say you are the bond manager who is long $10.0 million (e.g., similar to Hull's EOC Q 6.17) and, for convenience's sake, the T-bond future contract happens to be exactly $100.00. At the hedge horizon, your portfolio's duration is estimated (will be) to be 9.0 years. Your hedge will estimate the cheapest-to-deliver bond (by definition, it isn't known with certainty when you put on the hedge) will have duration of 10.0 years. Per the duration-based hedge, you will short $10,000,000/100,000 * (9 yrs/10 yrs) = 90.0 T-bond contracts. You have a value on the underlying exposure and a (dynamic) price on the T-bond that hedges. What happens if:

- Interest rates increase (the risk to the exposure): value of portfolio and
*price *of *futures contract *decreases, but you are short the futures contract so your T-bond *short position *increases in value, thereby hedging.
- Interest rates decrease: value of long portfolio and
*price *of *futures contract* both increase, but you are short the futures contract so the value of your *short position *decreases. As far as I can see, B = S - F still applies. In this rate decrease scenario, an unexpected basis strengthening would include when (for whatever reason) the futures T-bond contract price dropped less than anticipated, so you lost less on the hedging contract here.

Indeed there is another "basis risk" with respect to the cheapest-to-deliver "option" in the futures contract but I think that's second order (e.g., if the anticipated CTD bond were to change along the way, we could expect this to create strengthening/weakening) and i don't see how it can be analyzed if we aren't clear firstly on the ordinary basis risk between the exposure (in this example, long a bond portfolio) and the hedge (in this case, short T-bond futures contracts). I hope that helps,

## Stay connected