m2a default prob spread and expo

8/3/2019 M2A Default Prob Spread and Expo

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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



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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



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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.

m2a default prob spread and expo

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