How is the effectiveness of a hedge affected by inaccurate yield beta, projected basis values?

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Anyone?

Stàte Q’s. In simple English please0

Your hedge will act poorly if you made an erroneous yield beta calculation, have a wrong number of contracts or have wrongly projected the basis.

you will end up buy more / less then required hedge position that will expose your portfolio to uncertainity in change in interest rates.

Yield beta is used to calculate the number of contracts you need long / short to hedge your position (think this like equity beta hedging). Generally, if not given, the yield beta is assumed to be, but if given you should use this to calculate the value of position / contracts you need to take.

Example: if your portfolio’s current modified duration is 4, target is to reduce it to 3, futures durations is 4, and yield beta is 1.5 or .5, you will calculate the value of short position as {[(3-4)/4]* [(value of portfolio / future multiplier)]} * yield beta. if yield beta is captured incorrectly or ommitted it will give you a number that is not optimum to hedge your position.

Hope this helps.

If nor mistaken, OP asked abt. “Projected basis change” as well. If basia as well.

Would love some discussion on projected basis change as well.

Any physical and futures will have basis. A defined basis and followed trajectory has a basis with 0 basis risk. Not so, when the physical s And futures are responding to different risk factors. The yield beta will now be challenged with every instance of basis change.

I was under the impression that basis is just the difference between spot rate and forward rate…here i am guessing you are saying that basis risk is between the price ofunderlying and price of futures…in which case the underlying might perform differently than futures so that is why we are not properly hedged…

The hedge asset and the hedge instruments r 2 different animals, more so when belong to 2 different countries. The risk would systematically corrupt the yield beta.

The hedge asset and the hedge instruments r 2 different animals, more so when belong to 2 different countries. The risk would systematically corrupt the yield beta.

Basis risk is caused due to imperfect correlation between two assets - in this case, asset under portfolio and the hedge instrument (futures on probably another bond). There would be basis risk if you simply short the futures on the same stock / index / bond you are long, however that just neutralises your position your position and you earn RfR, assuming futures are priced correctly.

However in a case where we are using futures to reduce bond duration, the underlying for future is likely a different asset than that you want to hedge and thus, there is a possibililty (for all practical reasons) that it would turn out to be a sub-optimal hedge.

Yield beta attempts to capture the linear relationship between interest rates, likely when these instruments are in different countries (example: if interest rate for US AAA rated bond increases by 1%, what would be the likely change in EUR AAA bond, or so), I think.

@mrawat Did you mean to say ‘No basis risk’ here- " There would be basis risk if you simply short the futures on the same stock / index / bond you are long, however that just neutralises your position your position and you earn RfR, assuming futures are priced correctly. "

Also how is the hedge ratio different from yield beta, then?

if you only hedge (or better say make neutral position) by selling the Future for the same stock / bond (that means all factors affecting the price movement are same and assuming the there is no mispricing in the futures, you will earn risk free rate as future price will converge to spot price as you near expiration.

However, since we are hedging using different durations, it is safe to assume the ‘asset in portfolio’ that you want to hedge and the underlying asset for the future will have different sensitivity to change in rates, which could be due to duration, convexity, or quality / spread or general market mispricing (not all investment grade bonds have exactly same spread). Given this, it is good to assume imperfect correlation between the asset and the future, which is the reason for basis risk.

To summarize, if you can hedge your position with a perfectly correlated future or underlying, there is no basis risk.

for yield beta - it is a measure of the sensitivity of a bond’s yield to a general measure of bond yields in the market that is used to refine the hedge ratio (source: likeforex.com)