# Credit Triangle

This is way of connecting the market prices with the credit risk variables
There are 3 credit risk variables

Default Probability
Recovery Rate

This triangle displays the connection between these 3. If you have 2 of the values then you can calculate the other one.

Lets assume that the return from a riskless asset and that of a risky asset (after adjusting for default probability and recovery rate) are the same.
Then it is possible to calculate the third element of the triangle if two of the elements are known.

### Lets estimate the default probability

Lets assume the rate of return on a riskless government bond is ert
Lets assume we have a risky asset with 0% recovery rate
Lets assume the investor wants a premium Y so that his return is e(r+y)t
If the returns are the same and we include the default probability then we have

(1-P)e(r+y)t = ert

P = 1 - e-yt

not forgetting PV = FV(e-rt) and FV = PV(ert)

### Reverse Engineering / Credit Analysis

The concept of reverse engineering various components is relatively straightforward, but in practice extremely difficult.
As portfolios and instruments have become more complicated there have been attempts to be more objective in determing values for default probabilities through development of sophisticated credit pricing models.
1) Creditmetrics (underpins Riskmetrics)
2) Moodys KMV model (used in CreditEdge Plus)

These models attempt to give structure to the various individual components of credit risk.

1) Lack of available data (defaults are fairly infrequent)
2) Complexity of inputs
3) Small variations in input may lead to large variations in output
4) Often need to calibrate models so they are consistent with market data
5) Lack of prrecision means thay are unlikely to affect the day-to-day pricing of individual bonds

In foreign exchange the overall theory of "Fair prices" (such as purchasing power parity) also doesn't affect the day-to-day prices shown by foreign exchange trades.

### Liquidity

Another problem when you are attempting to generate components of credit risk from market prices is the fact that they are not solely determined by credit issues.
Bondholders will pay a premium for securities that are more liquid
The most recently issued bonds are called "on the run" as opposed to bonds that are "off the run"
These bonds obviously have the same default risk but their yields are slightly different.
On the run bonds are more liquid than "off the run" and will therefore trade at a higher price (ie lower yield)
This effect can be amplified in risky bond markets
It is therefore difficult to reverse-engineer credit components (such as default probabilities) from market prices since theprice is a function of liquidity as well as credit.

### Credit Analytics

Name Recognition - there is an implicit assumption that a well known borrower/issuer is more creditworthy than an unknown.
As markets have grown agents nowadays tend to focus on credit ratings, where credit rating agencies perform their own risk analysis on the borrowers.