103282 v1
The absence of sovereign bond issuances with It should be noted that World Bank guarantees can
World Bank guarantee support for almost 15 years be structured in a number of ways depending on the
and the customized application of the WB guarantee issuer’s objectives as well as country and market
instrument led potential investors in the Ghana bond circumstances. For instance, guarantees could cover
to ponder the best way to value the instrument. This interest and/or principal payments of bonds.
paper provides guidance on this subject by Coverage could be on a first loss or back-ended
presenting four ways to assess the value of a World basis. Therefore, the most appropriate valuation
Bank guarantee for debt capital market issues. The method would depend on the specific features of the
methodologies presented are: nominal weighted guarantee being considered.
average yield; rolling nominal weighted average
yield; discounted cash flow; and recovery analysis. The World Bank is comprised of two entities, the
International Development Association (IDA) and the
The paper presents the methodologies by applying
International Bank for Reconstruction and
them to a fictional bond issuance by the government
of Emergistan, a fictional low income country. Development (IBRD) for low and middle income
countries respectively. Since IDA does not have any
Background information on the country and bond
outstanding bonds, it has been assumed that IBRD
issuance have been kept to the minimum as the sole
purpose of this example is to illustrate the results of would be used as a proxy for the risk of both IDA and
IBRD.
each of the methodologies.
1
Figure 1
World Bank Guarantee available from Day 1
Emergistan is an emerging country rated in the B/BB
category by credit rating agencies with several USD
denominated Eurobonds already outstanding. Table
1 illustrates the fictional yield curves of US
Unused portion of
Treasuries, IBRD and Emergistan. guarantee rolls over
Table 1
Spread vs
US IBRD Emergistan
US
1 year 0.20% 0.50% 7.00% 680bps
3 years 1.00% 1.20% 7.82% 682bps 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
5 years 1.29% 1.49% 8.44% 716bps Years
7 years 1.57% 1.77% 9.07% 750bps Guaranteed Coupon Coupon
Guaranteed Principal Principal
10 years 2.00% 2.20% 10.00% 800bps
15 years 2.50% 2.70% 11.00% 850bps One important feature of this guarantee structure is
Fictional yield curves
that the guarantee amount does not reduce as the
Emergistan intends to raise a 15-year, US$1 billion
bond amortizes, i.e. the full balance of the guarantee
bond in the debt capital markets with the support of
(US$400 million less any prior payments) remains
a US$400 million World Bank guarantee. To
available as long as the bond is outstanding.
smoothen out the repayment profile of Emergistan’s
Therefore, if Emergistan does not default on its
debt, it has been decided that the bond would have
payment obligations, over time an increasingly larger
a soft-bullet feature, amortizing in three equal
share of the remaining debt service is guaranteed by
installments in the last three years of its life. The
the World Bank. In the current case, the soft-bullet
World Bank guarantee has been structured as a first
amortization feature allows the World Bank to cover
loss arrangement until its maturity date.
the last three installments sequentially in full. Figures
2 and 3 show these increased shares of the debt
service covered in Years 8 and 14 when there is no
payment default.
The first loss feature means that, from the first day of Figure 2
the bond’s issuance, US$400 million of cover is
World Bank Guarantee after 8 years
made available by the World Bank for any missed without any payment default
payment by Emergistan. If Emergistan fails to make
any debt service payment under this particular bond,
the World Bank is obliged to pay instead of
Emergistan. After each coupon/principal payment Unused portion of
guarantee rolls over
date, the remaining balance of the guarantee
(US$400 million less any previous guarantee
payments) is then made available for the next
scheduled payment of interest and/or principal.
Figure 1 illustrates the profile of first loss coverage 1 2 3 4 5 6 8 9 10 11 12 13 14 15
7
over the life of the bond. Years
Guaranteed Coupon Coupon
Guaranteed Principal Principal
2
Figure 3
World Bank Guarantee after 14 years
without any payment default
The first methodology consists of calculating a
weighted average yield based on the weights of the
total guaranteed cash flows and the total uncovered
Last installment fully cash flows. For the purpose of this paper, it has been
guaranteed by the
World Bank assumed that the reference 14-year (average life of
the bond) IBRD and Emergistan yields are 2.60%
and 10.80% respectively.
For the first iteration, Emergistan’s uncovered bond
1 2 3 4 5 6 78 9 10 11 12 13 14 15 yield is used to simulate a series of bond cash flows.
Years The total nominal debt service over the life of such a
Guaranteed Coupon Coupon
Guaranteed Principal Principal bond is US$2,512 million. The weight of the
guaranteed cash flows is therefore 400/2,512 =
The World Bank guarantee supporting Emergistan’s 15.9%. Using this number, the weighted average
bond issuance is non-accelerable. This means that yield is:
even if bondholders decide to accelerate the partially
15.9% x 2.60% + 84.1% x 10.80% = 9.49%
guaranteed bond following an event of default, the
World Bank guarantee does not accelerate and the Using 9.49% as the yield of the guaranteed bond for
World Bank pays out according to the original a second iteration, the new total debt service is
payment schedule. As a general rule, World Bank US$2,329 million and the new weight of the
guarantees are non-accelerable but IBRD may guaranteed cash flows is 400/2,329 = 17.2%.
provide accelerable guarantees in exceptional Through this second iteration, the weighted average
circumstances. yield can be refined to:
17.2% x 2.60% + 82.8% x 10.80% = 9.39%
Before embarking on a deeper assessment of the Figure 4
methodologies presented in this paper, please note: Total nominal cash flows
The calculations do not take into account any
World Bank
premiums the market may demand (such as for guaranteed
new issue); and cash flows
17%
The calculations used to develop this note are
contained in a financial model that can be
downloaded from the World Bank Guarantees Remaining
website. This model could help readers assess debt service
83%
other planned bond issues that could benefit from
a World Bank partial guarantee.
As the impact of additional iterations is limited to 1 or
2bps, two iterations are usually sufficient to provide
an estimate of the blended yield of a bond partially
guaranteed by the World Bank.
This methodology is the most basic one. However, it
has two major drawbacks. First, it does not capture
3
the rolling feature of the guarantee (i.e. as long as The first series of cash flows is simulated using the
Emergistan does not default on its payment yield of an uncovered Emergistan bond in a similar
obligation the share of remaining debt service fashion to Methodology #1. The weights of the
guaranteed by the World Bank increases). Second, it remaining guaranteed cash flows and the uncovered
does not account for the time value of money. As a guaranteed cash flows are then calculated 15 times
result, it produces the lowest estimate of the value of (once every year until bond maturity). The
the World Bank guarantee support. corresponding nominal weighted average yields for
each year are then calculated and then used to
Table 2
subsequently calculate the average of all these
Features captured by methodology #1
yields. This number is used to run additional
Blending of WB and EM yields
iterations until the yield converges. In the present
Rolling feature
Time value of money example, the average percentage of cash flows
Bond Yield 9.4% guaranteed by the World Bank over the life of the
Implied value of World Bank guarantee 142bps bond is 32% and the resulting rolling nominal
weighted average yield is 8.18%.
While this methodology still does not account for the
time value of money, it captures the rolling feature of
the guarantee as it accounts for the fact that, over
time, an increasingly larger share of the remaining
cash flows are guaranteed by the World Bank.
Table 3
One of the key features of a first loss World Bank Features captured by methodology #2
Guarantee is that after each interest/principal Blending of WB and EM yields
payment date, the unused portion of the guarantee Rolling feature
rolls over to the next scheduled payment of principal Time value of money
and interest. The previous methodology can thus be Bond Yield 8.2%
improved by calculating the percentage of the Implied value of World Bank guarantee 262bps
remaining cash flows guaranteed by the World Bank
at any point in time during the life of the bond (instead
of just once at the time of issuance).
Figure 5
Remaining nominal debt service
guaranteed by the World Bank This methodology consists in breaking down the
100% bond cash flows into two separate streams and using
two different discount rates (IBRD’s and
80%
Emergistan’s) to calculate their present value. The
60% resulting bond yield is subsequently adjusted so that
the sum of the two present values is equal to the face
40% Average: 32% value of the bond.
20% One limitation of this methodology is that it does not
capture the rolling feature of the guarantee. This is
0% because a predetermined US$400 million cash flow
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Years stream needs to be isolated and discounted at
IBRD’s discount rate, while the rest of the debt
4
service is discounted at Emergistan’s yield. This methodology results in yields ranging from
A pessimistic scenario is to assume that Emergistan 8.16% to 9.89%.
defaults in Year 1 by discounting the first US$400 Even though this methodology captures the time
million at IBRD’s discount rate and the rest of the value of money component that was missing from the
cash flows at Emergistan’s yield. Another scenario is previous methodologies, it still does not capture the
to assume that the guarantee rolls over until maturity full value of the guarantee as the rolling feature is not
of the bond and the last US$400 million due by taken into account. The ability to call on the
Emergistan are therefore guaranteed by the World guarantee for any missed payment during the life of
Bank. the bond is indeed not captured by this methodology.
The yield derived from equalizing the cash flows’ Table 4
present value to the face value of the bond is driven Features captured by methodology #3
by whether the cash flows guaranteed by the World Blending of WB and EM yields
Bank are assumed to occur at the beginning, the Rolling feature
middle or the end of the bond’s life. The more distant Time value of money
in time the guaranteed cash flows, the lower the Bond Yield 8.2% - 9.9%
yield. Figures 6 and 7 illustrate how cash flows are Implied value of World Bank guarantee 91 - 264bps
discounted using different discount rates.
Figure 6
First $400 million discounted at IBRD’s yield
Discounted at Emergistan’s yield
A more rigorous way to capture the value of the
World Bank guarantee, and especially its rolling
Discounted at
IBRD’s yield feature, is to run a detailed recovery analysis.
The first step of this methodology consists in
extracting the implied annual probability of default
1 2 3 4 5 6 8 9 10 11 12 13 14 15
7 from the current trading levels of Emergistan’s
Years
Guaranteed Coupon Coupon bonds. To do so, the World Bank model assumes
Guaranteed Principal Principal that, once adjusted for the probability of default and
Figure 7 proceeds received from recovery, an Emergistan
bond should have a yield to maturity similar to that of
Last $400 million discounted at IBRD’s yield
a similar maturity, risk-free bond (the risk-adjusted
Discounted at Emergistan’s yield
yields of the two bonds being equal) adjusted by any
liquidity premium currently priced by the market.
The probability of default is calculated such that:
Discounted at
IBRD’s yield
(1 + YTMEM) x (1 - PdEM) + REM x PdEM = 1 + Rf + L,
where YTMEM is the Yield of Emergistan, PdEM is the
annual probability of default of Emergistan, REM is the
recovery rate from Emergistan, Rf is the risk free rate
1 2 3 4 5 6 8 9 10 11 12 13 14 15
7 and L the implied liquidity premium embedded in
Years Emergistan’s spread over UST.
Guaranteed Coupon Coupon
Guaranteed Principal Principal The following scenario analysis assumes that if
Emergistan were to default on its bonds, investors
5
would recover 25% of the outstanding principal at the default of 8.6%, in Year 2 this probability is 7.9%
time of default, following exhaustion of the World (8.6% x (1-8.6%)) and for any subsequent years, the
Bank guarantee. It has also been assumed that the probability of Emergistan defaulting in a particular
probability of Emergistan defaulting on a partially Year Y is Pdi=8.6% x (1-8.6%)Y-1 (this methodology
guaranteed bond and non-guaranteed bonds are assumes that if Emergistan has not defaulted in the
equal, that the US Treasury has a probability of first N-1 years of the life of the bond, the probability
default of 0% and that the implied liquidity premium of default in Year N is 8.6%).
for Emergistan bonds is 100bps. Once the implied annual probability of default for
Figures 8 and 9 illustrate the mechanics of the World Emergistan bonds has been calculated, the next step
Bank guarantee in the cases of events of default in is to simulate the behavior of the World Bank
Year 6 and in Year 14. guarantee and recoveries from Emergistan for each
Figure 8 year as per the assumptions described previously.
From the moment Emergistan misses one coupon
Event of default in Year 6 and/or principal payment, the World Bank guarantee
is assumed to be drawn on each payment date until
the full US$400 million has been exhausted.
Subsequently, investors accelerate the bond and
Event of recover 25% of the outstanding principal of the bond.
default Figure 8 illustrates the steps of the recovery analysis.
This methodology leads to the simulation of 16
probabilistic scenarios (one event of default for each
of the 15 years and one scenario assuming no
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 default).
Years
Recovery proceeds Figure 10
World Bank guarantee payout
Payments made by Emergistan Year 0 Bond issuance
Figure 9
Payment made by
Event of default in Year 14 Year 1 Emergistan
Event of
proba.
proba.
91.4%
8.6%
default
World Bank pays Investors receive
Yes No out until guarantee 25% of outstanding
is exhausted principal
Payment made by
Year 2 Emergistan
proba.
proba.
91.4%
8.6%
World Bank pays Investors receive
Yes No out until guarantee 25% of outstanding
is exhausted principal
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Payment made by
Years Year 3 Emergistan
Recovery proceeds
World Bank guarantee payout …
Payments made by Emergistan Payment made by
Year 15
Emergistan
proba.
proba.
91.4%
8.6%
On the basis of above, the implied annual probability
World Bank pays
of default of Emergistan is calculated at 8.6%. Yes No out last installment
in full
Therefore, in Year 1 Emergistan has a probability of
6
The last step of this methodology consists in finding This methodology adequately captures all the
the yield of the bond such that once adjusted for the features of a World Bank guarantee and thus results
probability of default and the payments received from in lower yields, and higher implied value of the World
the World Bank guarantee, the risk-adjusted yield of Bank guarantee.
the bond is equal to that of a US Treasury bond (plus
Table 6
the implied liquidity premium) with a similar maturity.
Features captured by methodology #4
In the present example, this methodology results in a
partially guaranteed bond yield of 7.59% and an
Blending of WB and EM yields
Rolling feature
implied guarantee value of 321bps. Time value of money
A sensitivity analysis assuming different levels of Bond Yield 7.0% - 8.1%
liquidity premium embedded in the current spread of Implied value of World Bank guarantee 270 - 383bps
Emergistan vs US Treasuries shows the potential
dispersion of results.
Table 5
Liquidity premium 0bps 100bps 200bps
Partially guaranteed bond yield 6.97% 7.59% 8.10%
Yield reduction vs naked bond 383bps 321bps 270bps
The World Bank recently guaranteed a Sovereign bond issue that was difficult for some investors to value. This
paper will help future investors in World Bank guaranteed bonds by explaining four ways to value ways to value
these types of instruments. A hypothetical US$1 billion, 15-year, soft-bullet maturity bond issued by the
government of fictional Emergistan, all supported by a US$400 million World Bank non-accelerable first loss
guarantee, was used to analyze each method.
The first technique considered was the nominal weighted average yield method, which is a simple approach
but does not capture the rolling aspect of a guarantee or account for the time value of money. The rolling
nominal weighted average yield method, as the second method, is more acc urate, accounts for a guarantee’s
rolling nature but does not account for the time value of money. The discounted cash flow approach, as a third
method, assesses time value but does not include the rolling feature of the guarantee. None of these methods
therefore fully values a World Bank guarantee.
Recovery analysis is a more comprehensive and more complex way to value a World Bank guarantee. This
involves calculating the implied annual probability of default, simulating the behavior of the World Bank
guarantee and recoveries from Emergistan and then calculating the yield of the bond after the probability of
default and payments received under the World Bank guarantee are included. The implied value of the
guarantee in the study case is 270 – 383 basis points, which is greater than the other methods because it fully
captures time value and the value of a rolling guarantee.
The structure considered in this note is only one of many possibilities as the guarantee instrument offered by
the World Bank is highly flexible. Investors should therefore carry out their own analysis to determine the
methodology they believe to be the most relevant to price a particular security.
The Financial Solutions team is available to help guide its clients, their advisors and investors in developing
new financing solutions.
7
Table 7 and figures 11 and 12 summarize the results of the four methodologies in the case of Emergistan.
Table 7
Methodologies
Features captured by methodology #1 #2 #3 #4
Blending of WB and EM yields
Rolling feature
Time value of money
Bond Yield 9.4% 8.2% 8.2% - 9.9% 7.0% - 8.1%
Implied value of World Bank guarantee 142bps 262bps 91 - 264bps 270 - 383bps
Figures 11 & 12
Summary of valuation methodologies Implied World Bank guarantee value
6.0% 7.0% 8.0% 9.0% 10.0% 11.0% 0 bps 100 bps 200 bps 300 bps 400 bps 500 bps
#1 - Nominal
#1 - Nominal weighted
weighted
average yield
9.4% average yield 142 bps
#2 - Rolling nominal
#2 - Rolling nominal
weighted average
weighted average yield
8.2% yield 262 bps
#3 - Discounted #3 - Discounted
Cash Flows Cash Flows
8.2% - 9.9% 91 - 264bps
#4 - Recovery #4 - Recovery
analysis analysis
7.0% - 8.1% 270 - 383bps
8
Nominal weighted average yield
∑ ∑
= × + (1 − ) ×
∑ ℎ ∑ ℎ
Rolling nominal weighted average yield
Through several iterations, the yield is calculated as follows:
∑ ∑
∑
=1 × + (1 − ) ×
∑ ℎ ∑ ℎ
=
Discounted Cash Flows
Yield to Maturity of a partially guaranteed is bond determined such that:
∑
+∑ =
(1 + ) (1 + )
Where:
YTMWB = World Bank (IBRD) Yield to Maturity
YTMEM = Emergistan estimated Yield to Maturity
FV = Face Value of the bond1
GCF = Guaranteed Cash Flows (equal to guarantee amount)
NGCF = Non-Guaranteed Cash Flows (total bond cash flows less GCF)
N = Number of installments covered by the World Bank Guarantee
T= Number of payment periods
1 assuming the bond has not been issued yet and that the face value is equal to the present value of the bond cash flows
9
Recovery analysis
First step: extract the annual implied probability of default from outstanding bonds (annual probability of default
found such that the risk-adjusted YTM is equal to the risk free rate, in this case the US Treasury yield, plus any
liquidity premium currently priced by the market)
The formula used to calculate the implied annual probability of default is the following:
(1 + ) × (1 − ) + × = 1 + +
⇔ ( − 1 − ) × = + −
− −
⇔ =
1 + −
Where:
YTMEM is the Yield of Emergistan
PdEM is the probability of default of Emergistan
REM is the estimated recovery rate following an event of default of Emergistan
Rf is the risk free rate (US Treasury)
L is the liquidity premium embedded in Emergistan’s yield (accounts for the fact that Emergistan’s spread over UST
is not credit risk only)
First step: check that the risk-adjusted YTM of the Emergistan bond is equal to the risk free rate + liquidity premium
Scenario Cumulative Default Years
probability probability year 1 2 3 4 5 6 7 8 9 10 11 12 13 14
8.6% 8.6% 1 250.0 - - - - - - - - - - - - -
7.9% 16.5% 2 108.0 250.0 - - - - - - - - - - - -
7.2% 23.7% 3 108.0 108.0 250.0 - - - - - - - - - - -
6.6% 30.3% 4 108.0 108.0 108.0 250.0 - - - - - - - - - -
6.0% 36.3% 5 108.0 108.0 108.0 108.0 250.0 - - - - - - - - -
5.5% 41.8% 6 108.0 108.0 108.0 108.0 108.0 250.0 - - - - - - - -
5.0% 46.8% 7 108.0 108.0 108.0 108.0 108.0 108.0 250.0 - - - - - - -
4.6% 51.4% 8 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0 - - - - - -
4.2% 55.6% 9 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0 - - - - -
3.8% 59.4% 10 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0 - - - -
3.5% 62.9% 11 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0 - - -
3.2% 66.1% 12 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0 - -
2.9% 69.0% 13 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0 -
2.7% 71.7% 14 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 250.0
- 71.7% 15 - - - - - - - - - - - - - -
28.3% 100.0% No default 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 108.0 1,108.0
Probability weighted sc. #### 120.2 109.9 100.4 91.7 83.8 76.6 70.0 64.0 58.4 53.4 48.8 44.6 40.7 320.1
Probability weighted YTM 3.4%
Difference with UST + Liquidity premium 0 bps
10
Second step: Simulate bond cash flows received from Emergistan
Scenario Cumulative Default Years
probability probability year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8.6% 8.6% 1 - - - - - - - - - - - - - - -
7.9% 16.5% 2 75.9 - - - - - - - - - - - - - -
7.2% 23.7% 3 75.9 75.9 - - - - - - - - - - - - -
6.6% 30.3% 4 75.9 75.9 75.9 - - - - - - - - - - - -
6.0% 36.3% 5 75.9 75.9 75.9 75.9 - - - - - - - - - - -
5.5% 41.8% 6 75.9 75.9 75.9 75.9 75.9 - - - - - - - - - -
5.0% 46.8% 7 75.9 75.9 75.9 75.9 75.9 75.9 - - - - - - - - -
4.6% 51.4% 8 75.9 75.9 75.9 75.9 75.9 75.9 75.9 - - - - - - - -
4.2% 55.6% 9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 - - - - - - -
3.8% 59.4% 10 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 - - - - - -
3.5% 62.9% 11 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 - - - - -
3.2% 66.1% 12 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 - - - -
2.9% 69.0% 13 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 - - -
2.7% 71.7% 14 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 409.3 - -
2.4% 74.2% 15 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 409.3 384.0 -
25.8% 100.0% No default 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 409.3 384.0 358.6
Third step: Simulate the World Bank Guarantee payout
Scenario Cumulative Default Years
probability probability year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8.6% 8.6% 1 75.9 75.9 75.9 75.9 75.9 20.3 - - - - - - - - -
7.9% 16.5% 2 - 75.9 75.9 75.9 75.9 75.9 20.3 - - - - - - - -
7.2% 23.7% 3 - - 75.9 75.9 75.9 75.9 75.9 20.3 - - - - - - -
6.6% 30.3% 4 - - - 75.9 75.9 75.9 75.9 75.9 20.3 - - - - - -
6.0% 36.3% 5 - - - - 75.9 75.9 75.9 75.9 75.9 20.3 - - - - -
5.5% 41.8% 6 - - - - - 75.9 75.9 75.9 75.9 75.9 20.3 - - - -
5.0% 46.8% 7 - - - - - - 75.9 75.9 75.9 75.9 75.9 20.3 - - -
4.6% 51.4% 8 - - - - - - - 75.9 75.9 75.9 75.9 75.9 20.3 - -
4.2% 55.6% 9 - - - - - - - - 75.9 75.9 75.9 75.9 96.2 - -
3.8% 59.4% 10 - - - - - - - - - 75.9 75.9 75.9 172.2 - -
3.5% 62.9% 11 - - - - - - - - - - 75.9 75.9 248.1 - -
3.2% 66.1% 12 - - - - - - - - - - - 75.9 324.1 - -
2.9% 69.0% 13 - - - - - - - - - - - - 400.0 - -
2.7% 71.7% 14 - - - - - - - - - - - - - 384.0 16.0
2.4% 74.2% 15 - - - - - - - - - - - - - - 358.6
25.8% 100.0% No default - - - - - - - - - - - - - - -
Fourth step: Simulate recovery proceeds
Scenario Cumulative Default Years
probability probability year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8.6% 8.6% 1 - - - - - 250.0 - - - - - - - - -
7.9% 16.5% 2 - - - - - - 250.0 - - - - - - - -
7.2% 23.7% 3 - - - - - - - 250.0 - - - - - - -
6.6% 30.3% 4 - - - - - - - - 250.0 - - - - - -
6.0% 36.3% 5 - - - - - - - - - 250.0 - - - - -
5.5% 41.8% 6 - - - - - - - - - - 250.0 - - - -
5.0% 46.8% 7 - - - - - - - - - - - 250.0 - - -
4.6% 51.4% 8 - - - - - - - - - - - - 250.0 - -
4.2% 55.6% 9 - - - - - - - - - - - - 244.9 - -
3.8% 59.4% 10 - - - - - - - - - - - - 225.9 - -
3.5% 62.9% 11 - - - - - - - - - - - - 207.0 - -
3.2% 66.1% 12 - - - - - - - - - - - - 188.0 - -
2.9% 69.0% 13 - - - - - - - - - - - - 169.0 - -
2.7% 71.7% 14 - - - - - - - - - - - - - - 83.3
2.4% 74.2% 15 - - - - - - - - - - - - - - -
25.8% 100.0% No default - - - - - - - - - - - - - - -
11
Final step: Combine all cash flows and solve coupon such that the risk adjusted YTM is equal to that of the US
Treasury yield plus any liquidity premium currently priced by the market
Scenario Cumulative Default Years
probability probability year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8.6% 8.6% 1 75.9 75.9 75.9 75.9 75.9 270.3 - - - - - - - - -
7.9% 16.5% 2 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - - - - - - - -
7.2% 23.7% 3 75.9 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - - - - - - -
6.6% 30.3% 4 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - - - - - -
6.0% 36.3% 5 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - - - - -
5.5% 41.8% 6 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - - - -
5.0% 46.8% 7 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - - -
4.6% 51.4% 8 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 270.3 - -
4.2% 55.6% 9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 341.1 - -
3.8% 59.4% 10 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 398.1 - -
3.5% 62.9% 11 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 455.1 - -
3.2% 66.1% 12 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 512.0 - -
2.9% 69.0% 13 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 569.0 - -
2.7% 71.7% 14 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 409.3 384.0 99.4
2.4% 74.2% 15 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 409.3 384.0 358.6
25.8% 100.0% No default 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 75.9 409.3 384.0 358.6
Probability weighted cash flow #### 75.9 75.9 75.9 75.9 75.9 92.7 84.7 77.4 70.7 64.6 59.1 54.0 217.6 118.9 104.1
Probability weighted YTM 3.4%
Difference with UST + Liquidity premium 0 bps
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Author
Vincent Launay, CFA
vlaunay@worldbank.org
+1 202 473 7501
Financial Solutions, Capital Markets team
Pankaj Gupta
Practice Manager - Financial Solutions
pgupta2@worldbank.org
+1 202 473 6188
Sebnem Erol Madan Jukka-Pekka Strand, CFA
serol@worldbank.org jstrand@worldbank.org
+1 202 458 8104 +1 202 458 8410
Vincent Launay, CFA
vlaunay@worldbank.org
+1 202 473 7501
Disclaimer
The World Bank does not endorse or recommend any particular valuation method presented in this paper, nor
does the World Bank represent that these are the only methods that may be used for valuing this type of
instrument.
This research paper should not be relied upon to assess the features of a particular security guaranteed by the
World Bank as some features of a particular guarantee may differ from the ones assumed in this paper.
Investors should read the prospectus of the security partially guaranteed or to be partially guaranteed by the
World Bank and make their own assessment of the value of the security.
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