Hello Forum, Bank A has a given loan with fixed interest rates and hedges the interest risk by entering a corresponding swap (A pays fixed gets floating) with another bank B. The receiver of the loan, bank A and bank B have all different creit ratings etc., and the loan, the fixed side of the swap and the floating side of the swap have different margins. My problem is to show to a regulator / auditor that still the interest rate risk in the loan position is hedged. A quantitative measure is needed!

You can compare the net duration of the whole transaction (Duration Bank A Perspective = Duration Fixed Loan to Company - Duration Fixed Leg of Swap + Duration Floating Leg of Swap). You can show that duration of the swapped out transaction is smaller than duration if Bank A does not do the swap. Resutling duration here is not Zero. It just shortened the duration of the asset side of the balance sheet.Considering funding of theLoan to Company... it is usually done using floating rate.Total Duration Bank A Perspective = Duration Bank A Perspective - Duration Floating Rate Funding... Ideally this will be near zero.If the bank funded the loan using fixed rate, going into the swap actually increases the mismatch risk.

Thanks for your reply. Indeed there is this duration mismatch (due to the different margins) and the resulting duration of the swapped transaction is not zero. In some cases the effect of the mismatch is very large, i.e. the ratio between the duration of the swapped transaction and the transaction without swap goes above (beyond) some predefined bounds. Are there any alternative methods to isolate the impact of the interest rate risk?

The regulators are typically most concerned with the economic value of the banking book, and managers and shareholder's are typically most worried about net interest income. I'd have a look at the BIS documents that cover interest rate risk in the banking book. You can download them from the BIS website.It is my understanding that regulators use a value at risk measure to quantify the interest rate risk in financial institutions balance sheets. If you hedge the interest rate risk of fixed loans with a swap, this will significatly decrease the VaR of the combined loan and derivative portfolio, as opposed to the loan book in isolation. This should show in a quantitative way, that by entering the swap you have decreased the interest rate risk in the book.Hope this helps

You say "that the interest rate risk in the loan position is hedged". You need to be very careful in defining things. By this, do you mean that there is no outstanding interest rate risk? (hasn't happened) Or that there is less interest rate risk than before (slightly easier). Also, allocating risk between various components is always arbitrary - you can probably choose a way of splitting it that suits your purposes. Often for accounting purposes when you do this, you consider a hypothetical loan, which has all the characteristics of the actual loan except has a swap credit rating, and then show the impact of any sort of rate shock on the swap value and the hypothetical loan value.But I'd stress, if they have given a definition, you have to follow that.

Since we're talking about the two types of IR risk perspectives (Cash flow and economic value <macca's earlier post>)...I'd say that you have to make a distiction in your documentation and state your puprose of hedging.And you should realize that hedging one type of IR risk does not mean you hedge the other type as well.As you might have probably observed, hedging economic value through (by neutralizing Duration ang VaR) results into cash flow mismatches.On the other hand, matching cashflows and earning from spreads (as pointed out in krk's example) will result into some Duration / VaR risk.You can actually split duration into two measures...Discount rate duration (sensitivity to changes in your benchmark rates used for discounting)Spread duration (sensitivity to changes in spreads)Again this will still show residual duration risk since the purpose of your swap is to hedge cash flows in the first place.

krk, are you trying to satisfy the auditor (i.e. in relation to IAS39 - hedge effectiveness testing), or are you trying to satisfy the regulator?If you are trying to satisfy the auditor in relation to IAS39, than what I've said below does not apply. There are several approaches to proving hedge effectiveness (e.g. regression analysis, cumulative dollar offset, etc).

Thanks for all your comments, very helpfull. It's about IAS39. The regression methods and also the dollar offset method work in my case very well. The problem is that the IAS39 has also the requirement for 'prospective test', and the above methods work only 'retrospectively'. In addition to that, IAS39 has actually set up tighter bounds for the prospective tests then for the retrospective. On the other hand, there are a lot of degrees of freedom how to make the prospective test -- I have tried durations and scenario-analysis. As pointed out by jomni, the cashflows in the example match, so I get duration mismatch, which is large anough to get above the stricter bounds for prospective tests. I though that there could be some other method (for example comming from Basel II / regulators / risk management) which would be more suited in my case. I would try the suggestion of gjlipman.

have sent you a pm.

Thanks!

....also remember that the business of banks is to (try to)make money by taking two types of risk - interest rate risk and credit risk.... most banks do not hold a loan/swap portfolio which is completely DV01-neutral because they are intentionally expressing rate risk in the market (this can be outright directional rate risk or curve slope/shape risk).... so neither regulators nor internal controllers should have a fundamental issue with a non-zero net rate duration, as long as this duration falls within the pre-established risk limits.... also, i would suggest that the slight rate mismatch in the original example below is negligible when compared to the likely credit risk assumed by making the loans.....

This is an accoutning question not a Quant Finance question I think. very simply, per IAS 39 and FAS 133 require that the hedge is "effective" enough to stay on the books as a hedge and not straight mark-to-market. In order to do that you need a regression analysis, both retro and prospective. Retro you can get regressions easy based upon your market indicies, and you answered your own question about prospective, which is your dollar offsett calcuation in which you just compare the value of your underlying transaction and the paper transaction. The unwritten rule is if you are showing anywhere outside of 80%-120% variance in you dollar offsett the auditor MAY question that it is not a hedge unless you can provide support otherwise.

You can do prospective tests through sensitivity analysis or monte carlo.