Risk free rate

[1495_sc]

Hello,

Why is risk free rate based on swap rates? Core Reading suggests that government bond yield is used only if a sufficiently deep and liquid market for swap doesn't exist.

Why would we not directly use government government bond yield as a reference point instead?

Thank you

 

[CapitalActuary]

This piece of core reading smells like it was taken from regulation: https://www.eiopa.europa.eu/rulebook/solvency-ii/article-2457_en

So the short answer is: “the regulation says so”.

To be honest just saying “swap rate” doesn’t tell us which swap rate either. Although the liquid swaps for most currencies are now the OIS instruments rather than LIBOR based, so using the OIS swaps to build a risk free curve would make the most sense to me. I vaguely remember life actuaries arguing about this kind of thing when I worked in consulting, but I worked in GI at the time so wasn’t close to the issue.

I can think of several reasons to use a swap curve instead of a bond curve. Bond prices might have weird effects distorting the curve.

For example Japan is currently controlling their yield curve by buying (or selling, but mainly buying) lots of government bonds to keep the 10y point of the yield curve within certain bounds. Meanwhile the swaps are trading in a more normal fashion.

A bond issue might trade at a discount or premium (so decrease the rate) if it becomes the cheapest-to-deliver against a bond future. (Google cheapest to deliver if you’re interested, I don’t know if the syllabus mentions this.)

A bond issue might trade at a premium if there is exceptional demand for it in the repo market. (Again, can Google if interested.)

The bond market is just a bit more idiosyncratic, you might say. So when you build a risk free curve using bonds you tend to need to smooth it out a bit as well. This makes it more subjective - different people might smooth it differently.

Using swaps is a bit more objective in the sense people tend to end up with a more similar curve to one another.

Some of this might be why the regulation says to use the swap curve if you can.

I guess it could give some weird effects if you hold government bonds as “risk free” assets though, because changes in the spread of swaps to bonds will cause assets (bonds) and liabilities (discounted at swap rates) to fluctuate by different amounts.

 

[Em Francis]

Hello,

Why is risk free rate based on swap rates? Core Reading suggests that government bond yield is used only if a sufficiently deep and liquid market for swap doesn't exist.

Why would we not directly use government government bond yield as a reference point instead?

Thank you

Hi

Yes, I agree with the above in the fact that the bond market can be distorted and not necessarily comparable amongst jurisdictions.

The swap market can be very deep and liquid in most jurisdictions (even more so than government bonds).

It is also virtually risk free because if the investor of the variable rate defaults the counterparty who pays the fixed rate will default and vice versa.

There is a credit risk deduction to allow for the fact that (for example) a UK investor who is swapping the variable rate has to deposit their cash for 6 months (in order to obtain the 6 month LIBOR rate) so is exposed to the bank defaulting. However, after this deduction the rates are risk free and because they are ‘over the counter’, they are not bound by specific rules of the jurisdiction as exchange-traded instruments are, they are comparable between jurisdictions.

Other involved in the swap market may also like to contribute to this discussion. However, for SA2 purposes it is enough to appreciate that they can be used to derive a comparable risk-free discount rate.


Hope this helps

 

[1495_sc]

Thank you, this was food for thought!

 

[CapitalActuary]

It is also virtually risk free because if the investor of the variable rate defaults the counterparty who pays the fixed rate will default and vice versa.

I’ve read this before, but not sure it’s correct.

If you enter into a swap agreement then the curve changes massively in your favour, it’s not just the next payment you lose out on - you’ve made PnL here from the curve move and the expected NPV of future payments is higher than you initially expected. If your counterparty defaults you could lose that PnL.

That’s the case for bilaterally traded swaps at least, i.e. just you and the bank are involved. People don’t really do that anymore though, exactly because of the credit risk. Instead people trade swaps with banks and they are cleared by a CCP (central counterparty clearing house) which eliminates almost all the credit risk. Both counterparties effectively face the clearing house, who sets the margin rules and so on based on the risk of the contract. E.g. most currencies have most of their swap volumes cleared by LCH.

This has been a significant change post financial crisis, and now it seems insane that a lot of this trading used to be done bilaterally.

 

[CapitalActuary]

All of which is to say yes in practice swap trading is now very low on credit risk (there is probably close to zero), but that’s because the swaps are cleared via LCH or CME (two CCPs). I wouldn’t say they are low on credit risk by definition of them being swaps. The idea that you can just enter into a new arrangement with someone else if your counterparty defaults in a bilateral swap arrangement only holds if you assume interest rates haven't changed. If the at-the-money rate changes you won't be able to enter into an equivalent swap with a new counterparty.

Perhaps the insurance perspective on this is a bit different though - I should reiterate again that I never worked in life insurance! But I have risk managed a portfolio trading interest rate swaps for a money manager.

Also, if you are interested, you can see the cleared volumes of swaps (both OIS swaps and LIBOR based which they call 'IRS') on the LCH website here: https://www.lch.com/services/swapclear/volumes . People trade a lot of swaps I think some currencies like Chilean Peso and Japanese Yen might also have quite a bit of volume clearing through CME, perhaps more than LCH, and you can see those volumes here: https://www.cmegroup.com/trading/interest-rates/cleared-otc.html

None of this is important for the actuarial syllabus, just adding some extra info for anyone interested.