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Introduction

The following explains what credit spreads are and why they are important. How credit risk occurs in Treasury and what we need to do to manage this risk. The links between credit spreads, bond prices, default probabilities and recovery rates.

What They Are

When a bank lends, or invests it earns interest. That interest reflects the term structure (yield curve) and credit risk (credit spread). In the lending business credit spreads are driven by what the competition charge and what the bank can get away with. In this respect the bank (within reason) has the flexibility to adjust the loan price as it thinks fit. This is not the case in the traded market. For bonds the market price reflects supply and demand. This means the buyer either decides to accept the price or walks away without dealing.

Whilst we recognise that government debt is not “risk free”. The “risk free rate” is used as a benchmark comparator. It relates to the yield curve that represents the return on government debt. Another benchmark that can be used is the swap yield curve, this loosely reflects the credit risk of the banking system.

Two simplified examples may help:

1. A fixed rate bond trades with a yield of 3.00%. The swap rate for the same maturity is 2.50%. The spread is (3.00%-2.50%) = 0.50%. This is the additional return you get, over and above, the swap rate if you invest in the bond.

2. A floating rate note trades at 99%, it has 5 years to maturity, redeems at par and pays a coupon of Libor. The return is Libor + (100%-99%) / 5 = Libor + 0.20%. The 0.20% is the additional return you get over Libor if you invest in the bond.

In example (1) if the yield increased (bond price falls) to 4.00% and the swap rate was unchanged the return above the swap rate is now 1.50%.

Similarly, if the FRN price fell to 98% the return would increase to Libor + 0.40%.

So as the price of the bond falls, provided the benchmark yield curve is unchanged, the spread increases.

Why could the bond price fall?

Probably because the credit risk of the issuer has deteriorated and investors want a greater return for putting their money at risk. In this way, the return over Libor or swaps is a credit spread. It widens as the risk of loss increases.

The spread may also reflect liquidity. That is the ease of buying and selling. Bonds that are liquid are more expensive than ones that aren’t. In our example, it means that some of what we are calling credit spread is also a “liquidity premium”.

The credit spread has a lot of uses. Here are some:

1. Investment decisions: Deciding whether the credit spread adequately rewards you for the risk you are taking with your capital.

2. Comparison: Compare similar bonds, (similar maturity and credit standing), which pays you the biggest spread? Is there an explanation (like liquidity) or is one bond simply just a better investment than the other?

3. Pricing and valuation: You want to check the price of a bond. Use the spread to make the calculation. It’s what dealers do and it’s also a simple method to check valuations that are being used.

4. Trading: Buy bonds with wide spreads and sell similar bonds with narrow spreads hoping that spreads will converge. Typically, this trade is put on with bonds issued by the same issuer. It’s risky and can lead to large losses if the market doesn’t do what you expect.

5. Cost of funds: New issue pricing will be closely related to the credit spread on the outstanding debt you have already issued.

6. Key indicator: Monitoring credit spreads tells us about market sentiment. Spreads on bank debt tell us what the market thinks about specific banks. Comparing swap rates with government bond yields or overnight index rates with Libor give a picture of systemic risk.

Credit Derivatives – An Alternative

This market is where dealers buy or sell protection on a given entity or basket of entities. The price of the credit derivative representing the market’s assessment of the credit risk involved. For example, selling credit protection on a specific entity may bag you 0.50% per annum.

This is paid to you provided the Reference Entity doesn’t default. If it does you will end up paying a sum of money that represents the credit loss incurred. In this way, the Credit Default Swap (CDS) pays you to take risk. Unlike lending this is an unfunded risk. It’s a sort of “bet” on creditworthiness.

From a credit standpoint if the entity you have chosen weakens, the CDS price will widen (move from 0.50% to 1.00%). In this sense the CDS is a barometer of single name credit risk.

Similarly, credit default swap indices tell us about the market’s perception of credit risk associated with the basket of entities from which they are constructed.

It therefore makes sense to consider using CDS or credit index prices to monitor and evaluate how the market sees credit risk.

Treasury & Credit Risk

Treasury is an area where it’s easy to incur credit exposure. This can be through any of the following:

• Investment: money market deposits, commercial paper, certificates of deposit and bonds;

• Derivatives: Positive mark-to-market values (where you are reliant on the performance of the counterparty;

• Settlements: ideally when you pay money away you receive the counter payment simultaneously. This is not always the case. Sometimes there is a timing difference. This creates a credit exposure to the counterparty that can last minutes or hours.

Because the sums involved are large there needs to be a proper set of credit risk limits and a reporting system that shows the exposures (preferably in in real time).

The credit limits input into such a system are normally approved by credit committee after an appropriate amount of due diligence by a credit team has been undertaken. This credit team being segregated from the dealers who transact.

Credit limits are “time banded” with larger credit exposures being permitted for short term exposures and smaller limits for longer dates reflecting the increased uncertainty.

The system also needs to be flexible incorporating regular credit reviews and where appropriate limits need to be cut and exposures reduced or assets sold.

Some firms use credit ratings to decide whether a credit exposure is appropriate. This approach means the credit analysis is outsourced. There are both pros and cons. A balanced approach would be to use credit ratings in addition to doing your own analysis.

Firms can go further.

Counterparty credit exposures comprise current exposures plus potential future exposures (future positive values on derivatives) offset with any collateral held. These three inputs can be used to provide an Expected Loss.

Example:

Exposure:                     \$10,000,000

Probability of default:   1%

Loss given default:       40%

Expected loss:              \$10,000,000 x 1% x 40% = \$40,000

This is much lower than the initial exposure. However, if default occurs the expected loss jumps to \$10,000,000 x 40% = \$4,000,000

Applied to a portfolio of credit exposures it gives a measure of the capital that is at risk. Caution must be applied. PDs and LGDs vary over time.

The cyclical nature of credit risk therefore means that lax credit standards in Treasury can lead to large credit losses in economic downturns.

Default probabilities & recovery rates

Data for the probability of default (PD) and the loss given default (LGD) is commercially available. This is time series data collected from all types of different entities (sovereigns, municipalities, banks, corporates). It also covers the span of seniority (senior secured, senior unsecured, subordinated). The data will reflect the economic cycle. Defaults increasing in recession and decreasing during growth. Similarly, LGDs vary. They range from 100% (complete capital recovery) to 0% (complete capital loss). The entity and seniority of the debt involved largely influencing the outcome.

When you invest, whether you are a lending bank or bond investor, the credit spread you anticipate receiving compensates you for the credit risk you take.

Credit spreads, probability of default and recovery rates are linked. If you know two of the variables you can calculate the third. Examples follow together with a cautionary note.

If you know the probability of default and the recovery rate the price of the bond can be calculated:

Example:

Probability of default          =    0.50%

Libor                                   =     3.00%

Recovery rate (1-LGD)        =     40%

Value of survival                 =    100 x 99.50% x 1/1.03

=     96.6019

Value of default                  =     100 x 0.50% x 40% x 1/1.03

=     0.19417

Bond Price                          =     96.6019 + 0.19417 = 96.7961

If you know the default probability and the recovery the credit spread can be calculated:

Example:

Bond return       100 – 96.7961 = 3.2039

3.2039/96.7961 = 3.30% or 0.30% over Libor

If you know the credit spread and recovery rate the default probability can be calculated:

Example:

Return / Loss given default = 0.30/ (100-40) = 0.005 or 0.50%

Caution

Whilst it may be attractive to calculate the bond price, credit spread or default probability your calculations include historic data or best estimates for default probabilities and loss given default. This is a serious weakness as the future may not be like the past.