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Default Probability, Credit Exposure & Recovery Rate:
Risk valuation which is involved in an credit can be calculatedafter obtaining the Default Probability, Credit Exposure and
Possible Recovery Rate.
Default ProbabilityWe can calculate degree of default
probability through counterpart credit assessment and credit
rating.
Default Probability is the possibility of non-payment of the
obligation. In other words, default probability is the amount of
risk which we have calculated from credit rating.
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Recovery Rate:
Recovery Rate is possible amount which we would like to recover
during the process of bankruptcy of the counterparty out of total
obligation.
Credit Exposure :
Credit Exposure is the amount of total credit with the borrower
or say total loan exist with the counterparty.
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Expected Risk or Default Loss :
Expected Risk or Default Loss in an Individual Credit is the product
of degree of default probability, credit exposure and recovery rate.
Expected Loss = Expected Probability of Default x Credit Exposure
x (1-Recovery Rate)
or
Default Loss = Default Probability x Credit Exposure x
(1-Recovery Rate)
Simple, Default Loss = Expected Probability of Default x
Credit Exposure
(when the credit exposure without any CDO).
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Credit Spread : Credit spread is a variable that incorporates both the
probability of default and recovery rate.
Credit Spread is the difference between a riskier bonds yield and a
risk free bonds yield.
The risk free bond may be
RBI Bond/Govt. Bond (e.g. Flood Relief Bond)
Risk Free Bond of a Corporate without Risk Premium.Risky bond with risk premium (all corporate bond).
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For Calculation of Credit Spread we require to find out1. Yield of Government Bond
2. Yield of Corporate Bond Without Risk Premium,
3. Yield of Corporate Bond With Risk Premium,
4. Find calculate and Compare between the Yield of 1 & 2,
between 1 & 3, and between 2 & 3.
For Example :
Yield of RBI treasury
Yield of RIL bond without any risk premium.Yield of RIL bond with risk premium.
Credit Spread between 1 & 2, between 1 & 3, and between 2 & 3.
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Risk Free Government Bond: Risk free Government bond has
100% payback of principal and interest on due date. In case of India
risk free government bond such as RBI treasury bill (independent oron behalf of central government) or RBI / SBI issues the treasury bill
on behalf of the state government/s. All these treasury bills are risk
free/default free bond, because they are backed by the full faith and
credit of a countrys government/provincial government.
Expected Return
Investment in Govt. Bond = ---------------------------------------------
1 + Rate of Interest on Treasury Bill
Suppose expected return = 100, and rate of interest = 5% p.a., then
Required Investment = 100 / 1+ (5%) = 100/1.05 = Rs. 95.24
or say for return of Rs. 100 @ interest 5% we require Rs. 95.24.
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Corporate Bond Without Risk Premium (CBWRP)
Corporate bond without risk premium or say Risk free corporate bond has
higher probability of payback of principal and interest on due date at lower
rate of return. The corporate bond has lower risk without any backing.
Properties of CBWRP -
1. There are inherent risk or say there are probability of default e.g.10%.
2. You are not looking for a risk premium e.g. 0% risk premium on 10%
risk probability i.e. inherent risk probability on CBWRP.
2. The recovery rate will be
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Now we can calculate the expected value of bond by combining the
assumed value which you will get in case of default and non-default of
bond.
(a) In case bond does not default, you will receive 100 with 90% chance,
(b) in case of bond default you will receive 70 with 10% chance from your
bond.
Combined Value will be as below -
(a) 100 x (100-Inherent Risk) --- in case of non-default.
(b) Recovery Amount x Inherent Risk --- in case of default.
For ExampleIn case RIL there are 10% inherent risk, 70% recovery
Amount if the firm default.
The Estimated Payment Value = 100 x (90/100) + 70 x (10/100)
= 100 x 0.90 + 70 x 0.10 = 97
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That means your maximum estimated amount will be Rs. 97 with 10%
inherent risk and 70% recovery rate at estimated amount Rs. 100.
Now we calculate the required amount of investment to obtain Rs. 97 @
5% fixed rate of return.
Expected Return
Investment in CBWRP = ---------------------------------------------
1 + Risk Free Rate of Return
Or 97 / 1 + (5/100) = 92.38
or say for return of Rs. 97 @ interest 5% we require Rs. 92.38.
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You have now calculated following
1. Projected maximum return Rs. 100.
2. After applying inherent risk @10% and recovery rate 70% at projectedReturn Rs. 100 the estimated payment from the firm will be Rs. 97.
3. Our final return will be Rs. 97 only instead of Rs. 100
Now we calculate the required amount of investment to obtain Rs. 97 @
5% fixed rate of return.
Expected Return
Investment in CBWRP = ---------------------------------------------
1 + Risk Free Rate of Return
Or 97 / 1 + (5/100) = 92.38
or say for return of Rs. 97 @ interest 5% we require Rs. 92.38.
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Corporate Bond With Risk Premium (CBRP)
From previous calculation we can obtain only Rs. 97 instead of Rs.
100 at investment of Rs. 92.38 with inherent risk 10% and recovery
rate 70% of default probability from CBWRP.
Investment @5% risk premium in CBRP
Discount Rate = 5% or 1/1+5% or 1/1+(5/100) = 0.9523
Expected Amount of Return = 97 (after DP & RR)
Expected Investment to obtain Rs. 97 = 92.38
Now Expected Investment in CBRP = Investment at CBWRPDR
= 92.380.9523 = 91.43
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Thus, to obtain Rs. 100; RBI investment = Rs 95.24 and impossible to get
return 100 from CBWRP & CBWRP.
To obtain Rs. 97 from CBWRP we require Rs. 92.38
To obtain Rs. 97 from CBRP we require Rs. 91.43 at 5% Risk Premium.
CREDIT SPREAD
100
Credit Spread = ------- = EPV EPV = expected payment value
1+r+s r = discount rate and s = spread
100
Credit Spread (CBWRP) = ------- = 92.38
1+5%+s
100 / (1+r+s) = 92.38
1+5/100+s = 100/92.38
1+0.05+s = 1.0824
therefore, s = 1.0824 - 1.05
s = 0.0324 or 0.0324*100 = 3.24
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100
Credit Spread (CBRP) = ----------- = 91.43
1+5%+s
100 / (1+r+s) = 91.43
1+5/100+s = 100/91.43
1+0.05+s = 1.0937
therefore, s = 1.0937 - 1.05
s = 0.0437 or 0.0437*100 = 4.37
Now, Credit Spread at basis point
CSbp = (s2s1) * 100 = 4.37329 - 3.24853
= 1.12475
= 1.12475 * 100
= 112.475 basis point or 113 CSbp.
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We know that (when other things remain constant) -Higher risk = Higher return
Higher risk = Higher premium
Higher risk = Higher spread
Higher risk = Lower quality of securityor conversely
Lower risk = Lower return
Lower risk = Lower premium
Lower risk = Lower spread
Lower risk = Higher quality of security.