1. LECTURE SIX
a. Portfolio performance measurement
b. Hedge fund risk management
c. Credit risk management
d. Probability of default
1
2. Part 1
PORTFOLIO
PERFORMANCE
MEASUREMENT
a. Intro. Performance measurement
b. Surplus at Risk
c. The Market Line (ML) and CAPM
d. Several ratios to measure market performance
2
3. Part 1. Portfolio Performance Measurement 1. Intro. Performance measurement
Portfolio management
Risk Return
Do profits reflect my risk exposure?
HOW?
• Looking at process/strategies in place, and
• Whether outcomes are in line with what was intended
or should have been achieved.
Lecture 6
• Pure luck?
• Good strategy
• Separate effect of the market and active management
4. 1. Intro. Performance measurement
Some definitions
Sell side Buy side
Part 1. Portfolio Performance Measurement
Creation, promotion, analysis and Final buyers of financial assets
sale of securities. (Large portions of securities)
Leverage and speculative Tend to me more conservative
No leverage
Examples? Examples?
Lecture 6
5. 1. Intro. Performance measurement
Some definitions
Sell side Buy side
Part 1. Portfolio Performance Measurement
Creation, promotion, analysis and Final buyers of financial assets
sale of securities. (Large portions of securities)
Leverage and speculative Tend to me more conservative
No leverage
Institutions such as Investing institutions such as
• Investment bankers • mutual funds,
(intermediaries between issuers • pension funds and
and public), • insurance firms
• Research companies that
perform stock research and
Lecture 6
make ratings. Ig. Roubini
• Market makers who provide
liquidity in the market.
6. 1. Intro. Performance measurement
Absolute and Relative risk
Absolute risk Relative Risk
Part 1. Portfolio Performance Measurement
With respect to the portfolio With respect to a benchmark
itself
• Tracking error : e = R P - RB
• Risk factor: σ • In dollar terms: exP
• P: Initial portfolio value
• In dollar terms
𝜎 (𝑅 𝑃 − 𝑅 𝐵 ) 𝑃
𝜎 ∆𝑃
∆𝑃 ∆𝐵
∆𝑃 𝜎( − ) 𝑃
𝑃 𝐵
𝜎 ∗ 𝑃
𝑃
𝜔 ∗ 𝑃
𝜎 𝑅𝑃 ∗ 𝑃 Tracking Error Volatility
Note that there is only Where
Lecture 6
the asset or portfolio
2 2 P 2 P B 2 P
7. 1. Intro. Performance measurement
Absolute and Relative risk
Part 1. Portfolio Performance Measurement
Example
SPX: 10% return -10% return
My trade: 6% return -4% return
Absolute risk Relative Risk
What would be the difference between absolute
and relative risk?
Lecture 6
8. What is my risk in the long term?
2. Surplus at Risk Focused on net profits
Performance Measurement
Sort of relative risk measurement
Part 1. Portfolio Performance Measurement
Two assets, long pension assets and short pension liabilities.
Assets $ 120,00 Liabilities $ 100,00
Surplus $ 20,00
Volatility 12% Volatility 3%
Expected R 8% Expected R 5%
Correlation 0,3
Change of assets Change of assets
$ 9,60 $ 5,00
(per period) 12% of $120 (per period) 5% of $100
Expected growth of surplus
$ 4,60 Change assets - liabilities
Expected surplus $ 24,60 Considering the surplus
Variance of surplus $ 190,44 variance(a – b) = variance (a) + variance(b) - (2)cov(a,b)
Volatility of surplus $ 13,80
Lecture 6
Confidence level 95%
Normal deviate 1,64
Surplus at Risk $VaR 18,03 –(expected surplus) + (volatility of surplus)*(normal deviate)
The complete variance formula is: σ12P12+ σ22P12-2 σ1σ2P1P2ρ
9. 3.The Market Line (ML) and CAPM
Small recap
Decompose total return into a component due to market risk premia and
Part 1. Portfolio Performance Measurement
other factors.
E(Ri)
Overvalued ML
M
E(RM)
RF
Undervalued
Lecture 6
RiskM Riski
Note: Risk is either b or
10. 3.The Market Line (ML) and CAPM
Small recap
E ( Ri ) rf b [ E ( RM ) rf ] Ri i b i RM ei
Part 1. Portfolio Performance Measurement
E ( Ri ) rf b [ E ( RM ) rf ] This is the CAPM model
E ( Ri ) rf i b i [ E ( RM ) rf ]
E(Ri)
B
ML
A
M
E(RM) C
E
RFR D
Lecture 6
RiskM Riski
Note: Risk is either b or
11. 3.The Market Line (ML) and CAPM
Small recap
Capital Market Line (CML)
obtained by combining the market portfolio and the riskless asset
Part 1. Portfolio Performance Measurement
• CML specifies the expected return for a given level of risk
• All possible combined portfolios lie on the CML, and all are Mean-Variance
efficient portfolios
• Here we have a clear relation between the risk of my portfolio and the risk
Lecture 6
of the market. This is reflected by beta
Cov( Ri , RM ) It measures how much an asset’s return
bi is driven by the market return
2M
12. 3.The Market Line (ML) and CAPM
Small recap
Capital Market Line (CML)
Part 1. Portfolio Performance Measurement
If the stock has a high positive β:
• It will have large price swings driven by the market
• It will increase the risk of the investor’s portfolio(in fact, will make the
entire market more risky …)
• The investor will demand a high Er in compensation.
If the stock has a negative β :
• It moves “against” the market.
• It will decrease the risk of the market portfolio
• The investor will accept a lower Er
Then the SML depicts the relation between β and the Expected Return (Er)
Lecture 6
For the risk-free security, b = 0
For the market itself, b=1.
13. 3.The Market Line (ML) and CAPM
Small recap
Capital Market Line (CML)
Part 1. Portfolio Performance Measurement
E ( Ri ) rf b [ E ( RM ) rf ]
E ( Ri ) rf b [ E ( RM ) rf ]
Excess of return of a portfolio is a function of the excess of return of the market
W.R. a risk free rate
Lecture 6
14. 4.Treynor Ratio
The Treynor measure calculates the risk premium per unit of risk (bi)
Part 1. Portfolio Performance Measurement
[ E ( RP ) RF ]
TR
b ( RP )
Beta measures the investment volatility relative to the market volatility
(systematic risk)
The Treynor Ratio is negative if
• RF > E[RP] AND β > 0 .
Manager has performed badly: failing to get performance better than
the risk free rate AND manager made a not good election of
portfolio
• RF < E[RP] AND β > 0
Manger has performed well, managing to reduce risk but getting a
Lecture 6
return better than the risk free rate
Higher Ti generally indicates better performance
15. 4.Treynor Ratio
ADVANTAGE: It indicates the volatility a ASSET brings to an entire portfolio.
The Treynor Ratio should be used only as a ranking mechanism for
Part 1. Portfolio Performance Measurement
investments within the same sector.
.
When presented with investments that have the same return, investments
with higher Treynor Ratios are less risky and better managed
Cov( Ri , RM )
bi
2M
Lecture 6
16. 5. Sharpe Ratio
Describes how much excess return you are receiving for the
extra volatility that you endure for holding a riskier asset.
Part 1. Portfolio Performance Measurement
[ E ( RP ) RF ]
SR
( RP )
The Sharpe measure is exactly the same as the Treynor measure, except
that the risk measure is the standard deviation:
• Tells us whether a portfolio's returns are due to smart investment
decisions or a result of excess risk.
• The greater a portfolio's Sharpe ratio, the better its risk-adjusted
performance has been.
• A negative Sharpe ratio indicates that a risk-less asset would perform
Lecture 6
better than the security being analysed.
17. 4-5. Sharpe V Treynor Ratio
The Sharpe and Treynor measures are similar, but different:
• Sharpe uses the standard deviation, Treynor uses beta
Part 1. Portfolio Performance Measurement
X
• Sharpe is more appropriate for well diversified portfolios, Treynor for
Portfolio Return
15%
RFR
5%
Beta Std. Dev. Trenor Sharpe
2.50 20% 0.0400 0.5000
Y 8% individual assets14% 0.0600 0.2143
5% 0.50
Z
Market
6%
• Sharpe and Treynor: The ranking, not the number itself, is what is most
10%
5%
5%
0.35
1.00
9%
11%
0.0286 0.1111
0.0500 0.4545
important
Risk vs Return
15%
Portfolio Return RFR Beta Std. Dev. Trenor Sharpe
X
M
X Y 15% 5% 2.50 20% 0.0400 0.5000
Return
10%
Portfolio Return RFR Beta
Y 8% 5% 0.50 14% 0.0600 Dev.
Std. Trenor Sharpe
0.2143
5% X 15% 5% 2.50 20% 0.0400 0.5000
Z Z 6% 5% 0.35
Y 8% 9%5% 0.0286
0.50 14% 0.11110.2143
0.0600
Market
0% 10% 5% 1.00
Z 6% 11% 5% 0.0500
0.35 9% 0.45450.1111
0.0286
0.00 0.50 1.00 1.50 2.00 2.50 Market 10% 5% 1.00 11% 0.0500 0.4545
Beta
Risk vs Return Risk vs Return
X Risk vs Return
15% 15%
15% M X
M X
Return
10%
Return
M 10% Y
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Return
10% Y Y
5% Z 5%
Z
0% 5% 0%
Z
0% 5% 10% 15% 20% 0.00 0.50 1.00 1.50 2.00 2.50
Std. Dev. Beta
0%
18. 6. Sortino Ratio
The Sortino ratio generalizes (focus on the downside) from the Sharpe by
using:
Part 1. Portfolio Performance Measurement
• In the numerator, instead of excess return (above riskfree), Sortino uses
excess above hurdle (MAR, minimum acceptable return)
• In the denominator, instead of volatility (annualized standard deviation),
Sortino uses downside deviation.
[ E ( RP ) MAR]
SR
L ( RP )
• Appears to resolve several of the issues inherent in the Sharpe ratio:
• It incorporates a relevant return target, in both the numerator and the
denominator;
• It quantifies downside volatility without penalizing upside volatility; and
because of its focus on downside risk,
• It is more applicable to distributions that are negatively skewed than
Lecture 6
measures based on standard deviation.
19. 5-6. Sortino Ratio and Sharpe Ratio
Example
Only consider the
returns below the Square difference WR
hurdle rate Sq. Difference WR the
Part 1. Portfolio Performance Measurement
the hurdle rate
average of returns
Sumation of returns
Excess over Hurdle
We take a minimun Averag montly return of P 1,821%
acceptable return
Squared difference Average yearly return 21,851% Times 12
Month Price Returns Hurdle rate R - HUR Hurdle>R (R-Hur)^2 (R-Av)^2 Hurdle rate yield return Y 18,000% 1.5% * 12
1 663,03 -2,539% 1,50% -4,04% -4,04% 0,1631% 0,1901%
2 680,3 -9,834% 1,50% -11,33% -11,33% 1,2847% 1,3585% Rf month 1,80%
3 754,5 10,132% 1,50% 8,63% 0,6907% RF Y 21,60% Times 12
4 685,09 8,234% 1,50% 6,73% 0,4113% Use the formula
5 632,97 9,120% 1,50% 7,62% 0,5327%
6 580,07 -0,136% 1,50% -1,64% -1,64% 0,0268% 0,0383% Volatility 29,06%
7 580,86 -3,966% 1,50% -5,47% -5,47% 0,2988% 0,3349% Sharpe ratio 0,865%
8 604,85 -5,675% 1,50% -7,17% -7,17% 0,5148% 0,5619%
9 641,24 3,719% 1,50% 2,22% 0,0360% Sortino 19,54%
10 618,25 6,575% 1,50% 5,07% 0,2260% Excess return 3,851% P-Hurdle
11 580,11 -10,186% 1,50% -11,69% -11,69% 1,3656% 1,4416% Montly downside VaRianc 19,71%
12 645,9 7,760% 1,50% 6,26% 0,3527%
13 599,39 1,139% 1,50% -0,36% -0,36% 0,0013% 0,0047%
14 592,64 15,067% 1,50% 13,57% 1,7545%
15 515,04 -4,791% 1,50% -6,29% -6,29% 0,3958% 0,4372%
16 540,96 -10,391% 1,50% -11,89% -11,89% 1,4140% 1,4913%
17 603,69 19,217% 1,50% 17,72% 3,0262%
18 506,38 -4,280% 1,50% -5,78% -5,78% 0,3340% 0,3722%
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19 529,02 -2,772% 1,50% -4,27% -4,27% 0,1825% 0,2109%
20 544,1 -7,270% 1,50% -8,77% -8,77% 0,7692% 0,8265%
20. 7. Jensen alpha
Shows by much the returns of an
actively managed portfolio are
Part 1. Portfolio Performance Measurement
above or below market returns.
>0
A positive Alpha means that a
portfolio has beaten the market, =0
while a negative value indicates
underperformance <0
Risk Premium
A fund manager with a negative
alpha and a beta greater than one
has added risk to the portfolio but
has poorer performance than the
0
market
Market Risk Premium
R i RFR i b i R M RFR i
Lecture 6
Alpha = Excess of return – (Beta * (Excess of return))
21. Part 1. Portfolio Performance Measurement 7. Jensen alpha
R i RFR i b i R M RFR i
Alpha = Excess of return – (Beta * (Excess of return))
Lecture 6
22. 7. Jensen alpha
Portfolio Portfolio Market
P Q
Part 1. Portfolio Performance Measurement
Beta 0.90 1.6 1.0
RM-Rf 11% 19% 10%
Alpha 2.0% 3.0% 0%
R i RFR i b i R M RFR i
Portfolio P
Expected Return
Portfolio Q
19%
SML
16%
M
11% M2
P
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9%
0.9 1.6 Beta
23. 8. Information Ratio
Measure of the risk-adjusted return of a portfolio.
Part 1. Portfolio Performance Measurement
Defined as expected active return divided by tracking error
• Active return : difference between the return of portfolio and
the return of a benchmark
• Tracking error is the standard deviation of the active return
E[ R P RB ] Component attributable to the manager’s skill
IR
VAR( R P RB ) While Sharpe consider the σ of total
returns, IF consider σ of alpha
• Measures the active return of the manager's (abnormal return)
portfolio per unit of risk that the manager takes relative to the
benchmark.
• The higher the information ratio, the higher the active return of
the portfolio, given the amount of risk taken, and the better the
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manager.
24. 8. Information Ratio
Returns
Date Portfolio Market Excess
Part 1. Portfolio Performance Measurement
01/01/2010 2% 2,06% -0,49%
01/02/2010 1% -5,62% 6,64%
01/03/2010 0,61% -3,42% 4,03%
01/04/2010 0,76% 2,84% -2,08%
01/05/2010 9,69% -5,00% 14,69%
01/06/2010 1,39% 5,30% -3,91%
01/07/2010 3,10% -2,33% 5,44%
01/08/2010 0,46% 8,57% -8,12%
01/09/2010 6,11% 4,77% 1,34%
01/10/2010 9,37% 14,69% -5,32%
01/11/2010 3,88% -6,68% 10,56%
01/12/2010 9,54% 1,38% 8,16%
Mean 3,96% 1,38% 2,58% Expected excess of return (Benchmark)
Standard Dev 3,73% 6,40% 6,88%
Lecture 6
Information Ratio 0,3750 E[ R P RB ]
IR
VAR( R P RB )
25. 9. Modigliani´s Risk Adjustment Performance
• Also known as M2
• Closely related to the Sharpe Ratio
Part 1. Portfolio Performance Measurement
• Focuses on total volatility as a measure of risk, but its risk adjusted
measure of performance has the interpretation of a differential return
relative to the benchmark index
• The idea is to lever or de-lever a portfolio (i.e., shift it up or down the
capital market line) so that its standard deviation is identical to that
of the market portfolio.
• The formula for M2 is:
M 2 M R i R f R f
i
Lecture 6
• The M2 of a portfolio is the return that this adjusted portfolio earned.
This return can then be compared directly to the market return for the
period.
26. 9. Modigliani´s Risk Adjustment Performance
• Suppose that
• Return Ri: 35% RM: 28%
• Volatility σi: 42% σM: 30%
Part 1. Portfolio Performance Measurement
• Find a portfolio combination with the same level of risk than the
benchmark (market)
M 30 0.714
• Portion of the portfolio i
42
• Portion of risk free asset 1 M 0.286
i
• The return of this portfolio will be [0.286 * 0.06] [0.714 * 0.35] 0.267
• This portfolio is -1.3% than the market return.
This is the M2
Expected Return
Market
M Portfolio
M2
P
P*
Lecture 6
• Reduce the return of the P
• Obtain leSs volatility
Volatility
27. 9. Modigliani´s Risk Adjustment Performance
M 2 M R i R f R f
i
SR
[ ( RP ) RF ]
Part 1. Portfolio Performance Measurement
( RP )
Portfolio Return RFR Beta Std. Dev. Trenor Sharpe
X 15% 5% 2.50 20% 0.0400 0.5000
Y 8% 5% 0.50 14% 0.0600 0.2143
Z 6% 5% 0.35 9% 0.0286 0.1111
Market 10% 5% 1.00 11% 0.0500 0.4545
X 0.200.15 0.05 0.05 0.105
M 2 0.11 Risk vs Return
0.11 0.08 0.05 0.05 0.074
15%
M2 M
X
Y 0.14
0.11 0.06 0.05 0.05 0.062
Return
10% Y
2
M
5%
Z 0.09
Z
• Recall that the market return 0.50 0.10,1.00 only X outperformed. This is the
was so
0%
0.00 1.50 2.00 2.50
same result as with the Sharpe Ratio. Beta
Risk vs Return X
• The M2 of a portfolio is the return that this adjusted portfolio earned. This
15%
return can then be compared directly to M market return for the
the
Lecture 6
Return
10%
period. Y
5% Z
0%
0% 5% 10% 15% 20%
Std. Dev.
28. 10. Marginal Risk
• Represents the change in risk due to a small increase in one of the
allocations. It is essentially a derivative that measures the rate of change in
some measure of interest given a small change in a variable.
Part 1. Portfolio Performance Measurement
P Cov( Ri , RP )
M arg Risk b i , P P
wi P
• Beta represents the marginal contribution to the risk of the total portfolio
• Large values of beta indicates that a small addition will have a relatively large
effect on the portfolio
• Positions with large betas should be cut first to reduce risk
The portfolio risk/standard deviation is the sum of the risk contributions from
each asset.
ContributionToRisk wi b i , P P
Lecture 6
29. 10. Marginal Risk M arg Risk
P Cov( Ri , RP )
b i , P P
wi P
I am running a hedge fund
Part 1. Portfolio Performance Measurement
Bank of America 25% . Beta=3
σp =10%,
Contribution to Risk =.25 x 3 x 10%= 7.5%
• 7,5% of my portfolio risk is going to be dictated by what happens to
Bank of America
• The risk is too concentrated in one stock. In practice, it is
desirable to spread out total risk contributions across as many stocks
or assets as you can in the most equivalent manner.
Lecture 6
31. 1. Introduction
What is a H.F.?
Part 2. Hedge Funds
Lecture 6
32. 1. Introduction
What is a H.F.?
Part 2. Hedge Funds
Lecture 6
33. 1. Introduction
What is a H.F.?
Part 2. Hedge Funds
Lecture 6
34. Instruments whose prices
2. H.F. Strategies Achieve a beta as close to zero to
fluctuate based on the changes
in economic policies along
protect against systematic risk
An heterogeneous group with the flow of capital
Long positions in stocks
expected to increase.
Short positions in stocks
expected to decrease
Exploit pricing inefficiencies
before or after a corporate
event:
Bankruptcy, Merger, Acquisition
Find “bargains” and accept risk
Part 2. Hedge Funds
1000 basis points above the risk-
free rate of return
Exploits pricing differentials
between fixed-income
Lecture 6
securities. Long position in convertible securities.
AND Holds a portfolio of other investment
Short position in the same company’s funds instead of investing directly in
common stock. securities
36. 1. Introduction
Definition
The potential for loss due to failure of a borrower to meet its
contractual obligation to repay a debt in accordance with the agreed terms
• Its effect is measured by the cost of replacing cash flows if the other
party defaults
• Commonly also referred to as default risk
• Credit events include
Part 3. Credit Risk Management
• bankruptcy,
• failure to pay,
• loan restructuring
• loan moratorium
• Example: A homeowner stops making mortgage payments
Market Risk Credit Risk
Potential loss due to the non
Potential loss due to changes in
performance of a financial
Lecture 6
market prices or values
contract, or financial aspects of
non performance in any contract
37. 2. Drivers of Credit Risk
Default:
Discrete state for the counterparty (Default or not). It has associated the
Probability of Default (PD) defined as the likelihood that the
borrower will fail to make full and timely repayment of its financial
obligations
Exposure At Default (EAD)
Part 3. Credit Risk Management
The expected value of the loan at the time of default
Loss Given Default (LGD)
The amount of the loss if there is a default, expressed as a percentage of the
EAD
Recovery Rate (RR)
The proportion of the EAD the bank recovers
Lecture 6
38. 3. Settlement risk
In initial consideration
Settlement risk: The risk that one party will fail to deliver the terms of a
contract with another party at the time of settlement
Foreign exchange (FX) settlement risk is the risk of loss when a bank in a
foreign exchange transaction pays the currency it sold but does not receive
the currency it bought.
Part 3. Credit Risk Management
Settlement Risk management:
• Real time systems
• Bilateral netting agreements (two institutions)
• Multilateral netting agreements (two industries)
CLS Bank. In foreign exchange and operates the largest
multicurrency cash settlement system. It is owned by the
world's leading financial institutions
Lecture 6
39. 4. Credit losses (overview)
Set up:
The credit losses are defined by
CL i 1 bi * CEi * (1 f i )
N
Where
• Random Variable bi is a bernoulli trial that takes values of 1 (Def) or 0 (non Def)
• CEi is the Credit Exposure at time of default
• fi is the recovery rate (What means 1-fi )
Part 3. Credit Risk Management
The Expected Credit Loss for a portfolio is:
E[CL] i 1 E[bi ] * CEi * (1 f i )
N
Default is affected by
correlation among
i 1 pi * CEi * (1 f i )
N
assets:
Example Expected Credit Loss
Asset Exposure Prob. Def.
(5% * 25) (10% * 30) (20% * 45)
Lecture 6
A $25 5%
$13.5M
B $30 10%
C $45 20%
TT $100
40. 4. Credit losses (overview)
Description of the complete distribution
Issuer Exposure P. Def P. No Def.
A £ 25.00 5% 95%
B £ 30.00 10% 90%
C £ 45.00 20% 80%
Default Loss Probability Cumulative Exp. Loss Variance
None
Part 3. Credit Risk Management
A
B
C
A,B
A,C
B,C
A,B,C
Lecture 6
1. How can I find the loss
2. What is the prob. Associated to each scenario?
3. Easy
4. Expected loss of each scenario
What could be the VaR of this portfolio? 5. Variance
41. Part IV
PROBABILITY OF
DEFAULT
Likelihood that the borrower will fail to make full and timely
repayment of its financial obligations
a. Actuarial
b. Market prices methods
41
42. 1. Methodologies
Actuarial methods
• Measure default rates using historical data
• Provided by external rating agencies
Part 4. Probability of default
Market price methods
• Infer default risk from market prices of debt, equity
prices, credit derivatives
Lecture 6
43. 1. Actuarial Methods Corporate Default Probabilities Increase
Factor 1 exponentially across Credit Grades
Credit Ratings b.
a.
Part 4. Probability of default
• Credit rating is a measure of the firm’s
credit risk
• External credit rating: Standard & Poor’s,
Moody’s, Fitch, etc.
Factor 2
Prob. Of default
• Probability of staying in the
same rating category is
given on the diagonal.
Lecture 6
• Off-diagonal probabilities
present the likelihood that
the rating will change
within a one-year period.
44. Part 4. Probability of default 1. Actuarial Methods Factor 3
Transition Matrix
• Credit migration or transition matrices use ratings migration
histories.
• One-year horizon.
• Measured using the cohort and the duration method.
Lecture 6
• Generally, the transition matrix is affected by the business cycle:
downgrades including defaults are higher during recessions
45. Part 4. Probability of default 1. Actuarial Methods Factor 4
Cumulative Default Rates
Lecture 6
• How many companies rated ( ) defaulted in each year
• This measure is cumulative. It necessarily increases with the horizon
46. 1. Actuarial Methods
d1 Default
Default
1 - d1 d2
No Default
1 – d2 d3 Default
Part 4. Probability of default
No Default
1 – d3
No Default
Cumulative d1 d1+ (1- d1)d2 (1- d1)(1- d2) d3
Lecture 6
Compute the cumulative probability of default:
• The probability of default in the first year is 5%
• The probability of default in the second year is 7%
47. 1. Actuarial Methods
Compute the cumulative probability of default:
• The probability of default in the first year is 5%
• The probability of default in the second year is 7%
d1=5% Default
Default in 2=
95%*7%=6.65% Default
Part 4. Probability of default
Survival rate = 95%
No Default
d3 Default
Survival rate 2=
95%*97% = 0.883
No Default
1 – d3
Lecture 6
No Default
Cumulative d1 d1+ (1- d1)d2 (1- d1)(1- d2) d3
48. Factor 5
1. Actuarial Methods Recovery Rates
Recovery Rates
Amount recovered through foreclosure or bankruptcy procedures in a credit
event (default), expressed as a percentage of face value
Are function of
• The state of the economy. Higher with expansion
• The obligor’s characteristics: Higher when the borrower’s assets are
tangible and when previous rating was high
• The credit event: distressed debt has higher recovery rate than plain
Part 4. Probability of default
default
• The status of the debtor: Higher seniority has higher recovery rates
Credit rating agencies have used two methods to calculate RECOVERY
RATES (Moody’s)
• Average issuer-weighted trading price on a sovereign's bonds 30 days
after its initial missed interest payment
Lecture 6
• Ratio of the value of the old securities to the value of the new
securities received in exchange,
49. 1. Actuarial Methods
Recovery Rates
Part 4. Probability of default
Lecture 6
• Average historical sovereign recovery rate: 53%
• 67% of recovery rate according to the ratio of value
50. 1. Actuarial Methods
Recovery Rates
Part 4. Probability of default
Senior debt has a higher recovery rate.
• According to S&P recovery rates have averaged 51% on a discounted basis and 60%
on a nominal basis, based on a sample from 1987 to 2011.
• If measured on a dollar-weighted basis, which is the sum of all defaulted debt in the
sample divided by the sum of the dollar amount of debt recovered, the averages are
slightly lower: 48%
• Loans and revolving credit facilities, that have seniority in the capital structure and are
Lecture 6
often secured: recovered 74% on a discounted basis and when measured on a dollar-
weighted basis, the average recovery for loans and facilities is 65%
• Bonds have lower average recoveries. The long-run discounted average recovery for
bonds is 38%
51. Next Lecture
2. Market price methods
Infer default risk from market prices of debt, equity prices, credit
Part 4. Probability of default
derivatives
• Infer default risk from bonds
• Merton's model (Structural Model)
Lecture 6