FRM Fun 3

[Suzanne Evans]

FRM Fun 3.

In recent days, a scandal has roiled around LIBOR (e.g., yesterday from @moorehn at http://www.marketplace.org/topics/world/easy-street/libor-mortals-easy-explainer), the interest rate used to signify the risk-free rate in many financial texts. Assuming the scandal taints LIBOR, the question is: do we need a risk-free rate in financial analysis (e.g., modeling, valuation, risk measurement) and, if we do need to assume a risk-free interest rate, what is the best alternative to LIBOR?

(no multiple choice here, just a star for the best given answer!)

 

[Aleksander Hansen]

Overnight Index Swaps (OIS) is currently being used by most banks, hedge funds and investment companies as a risk-free rate.
That is, whereas the, e.g. 3m LIBOR is still used to project the forward rate [if stipulated by the contract that 3m LIBOR is the index]. Thus, we end up with an interesting phenomena, called dual-curve stripping. That is, given, e.g. a Fixed-Floating swap, the floating rate used to price the future cash-flow is the LIBOR curve, however, the curve used to discount this to PV is the OIS, hence the name, dual-curve stripping. The interesting part about this is that it leads to a non-zero value for the swap at inception! It will generally be close, but not zero: if you want to force it to zero you need to explicitly solve for a zero premium using, e.g., a spread over/under LIBOR on one of the legs.

Now, as to the question do we need a risk-free rate, I think the answer is no. Let me rephrase, I know the answer is no, because we have never had a truly risk-free interest rate. Would it be nice to have - sure! What is immensely useful though, is a rate that we can consider to be close to risk-free. It should have certain properties, such that, e.g. there is no re-investment risk and so forth.

The OIS satisfies this and many other desirable properties, and has thus, become the de-facto risk-free rate used. Importantly, unlike the LIBOR and LIBID, there is no submission of rates you 'think' you can borrow or lend at. It is governed by the market, that is, the price-system, and thus ensures efficient allocation of resources.

Can we find a better rate? Most certainly, and a lot of bright minds are currently working on this.

 

[PL]

Hello Alex,

The use of OIS as discount factor - i think - comes from the fact that most of the OTC transactions are fully covered under the CSA (daily exchange of collateral). From my point of view we should use different discount factor in cases of no collaterilized transactions versus transactions under CSA.
What is your opinion?

PS
Congrats to your success in the exams and i wish you the best in the future plans (wedding - company etc)

 

[Aleksander Hansen]

Hello Alex,

The use of OIS as discount factor - i think - comes from the fact that most of the OTC transactions are fully covered under the CSA (daily exchange of collateral). From my point of view we should use different discount factor in cases of no collaterilized transactions versus transactions under CSA.
What is your opinion?

Actually, in my experience, a typical OTC is not necessarily covered by a CSA, indeed, they are often shunned, so no exchange of collateral actually takes place, but there is an ISDA and credit support annex, with agreed upon collateral [but not exchanged less deault on contact].

Now, comparing a CSA vs a non-CSA (with no loss of generality), the appropriate discount curve would still be the risk-free OIS in my opinion. Any 'excess' risk should be built into the payments in form of a higher rate or a spread over a floating index.

Thanks, and congrats to you too on passing!

 

[David Harper CFA FRM]

Aleks, thank you, that is a winning and HELPFUL reply (i.e., you are entered in the weekly drawing)! From my notes (this didn't have a correct answer but my prep happens to comport with your view and frankly you have a better realistic perspective) :

• John Hull section 4.1. (emphasis mine): "The credit crisis that started in 2007 caused many derivatives dealers to critically review their practices. This is because banks became very reluctant to lend to each other during the crisis and LIBOR rates soared. Many dealers have now switched to using the overnight indexed swap (OIS) rate as a proxy for the risk-free rate. This rate will be explained in Section 7.8. It is closer to the risk-free rate than LIBOR"
• A short article by CFA Institute that concludes "there is no such thing as a risk-free rate of return" at http://blogs.cfainstitute.org/investor/2012/03/20/rethinking-the-risk-free-rate/
• More technical presentation on OIS at the expert blog xenomorph: http://www.xenomorph.com/news/events/2012/wilmott/; e.g., "The credit crisis of 2007 brought the usage of LIBOR and LIBOR swap rates for discounting purposes into acute focus, as LIBOR spreads to US Treasury rates dramatically increased from the then typical levels of around 50bp to a peak of 450bp in October 2007. This has led many practitioners to now use Overnight Indexed Swap (OIS) rates as a proxy for risk-free rates in derivatives valuation.

 

[caramel]

http://www.rotman.utoronto.ca/~hull/DownloadablePublications/LIBORvsOIS.pdf

A little late at jumping on the bandwagon . But the above link provides some really useful insights.

 

[Aleksander Hansen]

http://www.rotman.utoronto.ca/~hull/DownloadablePublications/LIBORvsOIS.pdf

A little late at jumping on the bandwagon . But the above link provides some really useful insights.

Thanks for posting this, I had actually been looking for something more than just a few paragraphs on the topic by a respected authority to reference when using it in my work, so this was just what I needed for documentation purposes!

 

[PL]

Thanks a lot
Great addition

 

[David Harper CFA FRM]

@caramel: thank you for sharing this Hull paper, I just read and this is the best summary I've read on the LIBOR-OIS topic (I entered you into the weekly drawing, fwiw. Gold star share ).

Some helpful explain on the OIS (emphasis mine) in the pape:

Overnight index swaps are interest rate swaps in which a fixed rate of interest is exchanged for a floating rate that is the geometric mean of a daily overnight index rate. The calculation of the payment on the floating side is designed to replicate the aggregate interest that would be earned from rolling over a sequence daily loans at the overnight rate. In U.S. dollars, the index rate is the effective federal funds rate. In Euros, it is the Euro Overnight Index Average (EONIA) and, in sterling, it is the Sterling Overnight Index Average (SONIA). OIS swaps tend to have relatively short lives (often three months or less). However, transactions that last as long as five to ten years are becoming more common. For swaps of one-year or less there is only a single payment at the maturity of the swap equal to the difference between the fixed swap rate and the compounded floating rate multiplied by the notional and the accrual fraction. If the fixed rate is greater than the compounded floating rate, it is a payment from the fixed rate payer to the floating rate payer; otherwise it is a payment from the floating rate payer to the fixed rate payer. Similar to LIBOR swaps, longer term OIS swaps are divided into 3-month sub-periods and a payment is made at the end of each sub-period.

... There are two sources of credit risk in an OIS. The first is the credit risk in fed funds borrowing which we have argued is very small. The second is the credit risk arising from a possible default by one of the swap counterparties. This possibility of counterparty default is liable to lead to an adjustment to the fixed rate. The size of the adjustment depends on the slope of the term structure, the probability of default by a counterparty, the volatility of interest rates, the life of the swap, and whether the transaction is collateralized. The size of the adjustment is generally very small for at-the-money transactions where the two sides are equally creditworthy and the term structure is flat. It can also reasonably be assumed to be zero in collateralized transactions. Based on these arguments we conclude that the OIS swap rate is a good proxy for a longer term risk-free rate.

 

[David Harper CFA FRM]

FYI, blog today from soberlook on this:

But in the past few years practitioners have been asking the question: is LIBOR really relevant for discounting derivatives cash flows? In the age of bilateral master derivatives agreements (Credit Support Annex or "CSA") when each counterparty is expected to post margin, what is the true financing cost of derivatives cash flows? The answer for most cases turns out to be quite simple. Generally the interest on collateral posted by one party to another is Fed Funds or its equivalent in another currency. The cost of funds for a derivatives contract is basically the overnight effective rate. And for most currencies there is an active market to price overnight rates expectations years into the future. The chart below shows the term structure of JPY OIS for example ...
Converting this OIS term structure into a zero coupon curve provides a more appropriate set of discount factors that reflect the true cost of cash flow financing. To the extent there is another collateral arrangement, the discounting should be adjusted to reflect the appropriate costs. This is already the standard for discounting interest rates swaps and is becoming common in CDS as well. Using the LIBOR curve simply because it has always been done that way is no longer appropriate, as it does not reflect the actual cost of funds. Most academic derivatives pricing literature is yet to be adjusted to reflect this fact.

--link: soberlook 8/13

 

[Aleksander Hansen]

FYI, blog today from soberlook on this:

I agree with everything but the part about interest on collateral posted with another Counterparty is the fed funds rate. That is too general to hold true. A necessary and sufficient condition would be that the trade is entered into by investors on the margin. However that is not always the case for OTCs.
A sufficient condition would also be that the margin in the projection of rates that informs future CFs (not the discounting) reflects this.

 

[bhar]

Hi All. Just to add, there are poll results that indicate that the minds of investors and market players is to move from LIBOR to the Overnight Index Rate. So this could be the future Risk free rate while valuing Swaps. However, the concept of 'Risk free rate' will not be 'eradicated', if I may say so, from the minds of market players. IT would be simply replaced with a non-manipulative one.