Intro to Bond Portfolio Construction

9 February 2022
“Portfolio Management” course at Kyiv School of Economics
Guest lecture by Konstantin Yakunenko, PhD, CFA, CAIA at Adamant Capital
Intro to Bond Portfolio
Construction

Kyiv School of Economics ► Portfolio Management Course ► Intro to Bond Portfolio Construction, a guest lecture by Konstantin Yakunenko, PhD, CFA, CAIA at Adamant Capital, 9 Feb 2022
Statement of Purpose, Disclaimer 2
1. This course contribution aims to demonstrate the process of portfolio construction
from Ukrainian bonds and highlight some of its challenging steps
2. The lecture assumes that students are already familiar with the basics of straight
bonds (with no embedded options) and bond investing from the previous topics of this
course — but NOT with the concepts of duration and convexity management
3. This presentation is incomplete without its live delivery and demonstration of Excel
examples
4. The presentation is designed mainly for a desktop review after the lecture —
sorry not sorry for the busy slides
5. Mistakes/inaccuracies, if any, belong solely to the author Konstantin Yakunenko

Bonds in the syllabus of this course 3
• Constructing the yield
curve
• Forward pricing and
forward rate models
• Bootstrapping
• Forward rates and
forward rate agreements
• The swap rate curve
• Interpreting the term
structure
• The expectations theory
of interest rates
• Segmented market
theory
• The liquidity theory
• Overview of contracts
and their basic features
(coupon structures,
cross-border issuance,
bond indentures etc.)
• Investment grades and
grading agencies
• Contingency provisions
• Government
(supranational,
sovereign, non-
sovereign) and corporate
debt (bonds, commercial
papers)
• Bond pricing and yields
• Reinvestment risk vs.
price risk
• Default risk
• Bonds vs equities: a
portfolio perspective
• Yield curve:
Interpretation from macro
and micro perspectives,
basics of construction,
Nelson-Siegel
(-Svensson) model
• Bond portfolio horizon
analysis model
• Strategies of bond
portfolio positioning on
the yield curve
• Portfolio strategies
applications: Ukrainian
bonds cases
• Overview of modern term
structure models and
yield curve factor models
• Arbitrage-free valuation
of a fixed- income
instrument
• Binomial interest rate
tree valuation framework
• The risk structure of
interest rates
• Overview of modern term
structure models and
yield curve factor models
• Arbitrage-free valuation
of a fixed- income
instrument
• Binomial interest rate
tree valuation framework
Topic 5: The Term
Structure and Term
Structure Theories
Topic 6: Credit Market
Instruments I
Topic 7: Intro to Bond
Portfolio Construction
Topic 8: The risk structure
of interest rates
Topic 9: The Risk
Structure and Term
Structure Models
Previous topics Next topics
This topic

Lecture in a nutshell 4
Bond portfolio management is largely about positioning the expected cash flows on the expected yield curve over the
investment horizon: A wide variety of investment outcomes depends on (1) how we position our bond portfolio along the yield
curve at the beginning of the investment horizon, and (2) how the yield curve changes in level, slope and curvature by the end of the
horizon. The calculations below are not about forecasting the holding period return. Rather, they are about a What-If analysis that
helps select an optimal/reasonable allocation to the duration buckets that would reflect our capital market expectations, formulated
as the expected yield curve. Key takeaway: Bonds are complicated and risky instruments that do not automatically "lock-in"
any level of expected return. ⇒ Managing a bond portfolio requires that proper duration management is in place, along
with other portfolio construction techniques.

Contents 5
1. Bonds vs equities: a portfolio perspective
2. Yield curve: micro and macro view
3. Bond portfolio horizon analysis model
4. Strategies of bond portfolio positioning on the yield curve
5. Portfolio strategies applications: Ukrainian bonds case studies
Recommended literature
Appendix. Bonds-related functions in Bloomberg terminal
7
16
34
38
47
63
65

Contents — Cases 6
5. Portfolio strategies applications: Ukrainian bonds case studies 45
Case #1. Strategy 1 — B&H till maturity: example of a premium bond
Case #2. Strategy 2 — Riding down a stable upward-sloping yield curve
Case #3. Strategy 3 — Portfolio positioning in anticipation of a specific change in the yield curve
Case #4. What was the best recent year for Ukrainian bonds? Year 2019!
Case #5. How did Ukrainian bonds respond to Covid-19 outbreak?
Case #6. How did Ukrainian bonds respond to the early-2022 military escalation by RF?
Case #7. What is my expected return on the portfolio if I buy the dip now, during the military escalation,
and things get back to normal in 2 years?
Case #8. How to balance interest rate risk vs reinvestment risk?
Case #9. How do I stress-test my bond portfolio?
Case #10. How does modified duration help me understand the sensitivity of my portfolio allocations to YC (parallel) shifts?
Case #11. How does convexity complement modified duration in approximating
a bond (portfolio) price change in response to a YC shift?
Case #12. How volatile are Ukrainian bonds?
Case #13. How do Ukrainian bonds correlate with asset classes?
48
49
51
52
53
54
55
56
58
59
60
61
62

Section 1
Bonds vs Equities: a Portfolio Perspective
7

Bonds vs Equities: a Portfolio Perspective 8
Cash flow
certainty
Bonds Equities
‐ Known/assumed timing and size of cash flows
(for straight investment‐grade bonds)
‐ Legal obligation («облігація») of a borrower
‐ Bedrock of real economy, and essential capital market
mechanism through which tectonic amounts of capital flow
on an agreed‐upon schedule between institutional investors
and large borrowers
‐ It is not legally binding for a company to provide cash flows to
their shareholders through dividends or share buybacks
Asset class size
‐ Bonds are the second‐largest asset class, with a global value of
circa 124 trillion in 2020 (Source: SIFMA)
‐ Equities are the third‐largest asset class (circa $108 trillion)
after real estate (circa $300 trillion) and bonds
Liquidity
(except US
treasuries)
‐ Bonds are typically tailor‐issued for a cohort of large
accredited, or institutional, buyers who hold the issue till
maturity — and not for the general public
‐ Issuers often use offshore jurisdictions to escape regulation
aimed to protect a less knowledgeable retail public
‐ Varies from extremely liquid to illiquid
Turnover in
portfolio
‐ Bonds are typically a buy‐and‐hold investment till maturity
‐ Trading is usu. incidental, rebalancing‐driven, not speculative
‐ Low liquidity  (often prohibitively) high trading costs, e.g.,
up to 2% bid‐ask spread for Ukrainian issues
‐ Varies depending on portfolio needs and liquidity of equities in
the portfolio
Role in
portfolio
‐ Defensive: lower risk compared to equities of the same issuer
‐ Source of liquidity: thanks to scheduled cash flows; esp. useful
for pension funds, banks, and liability‐driven mandates overall
‐ Diversification: usually negative correlation with equities
‐ Growth role due to higher expected risk (shareholders absorb
losses while bondholders get paid) and return (retain profits)
‐ Protection of purchasing power from inflation if a company can
“pass” inflation onto their customers
Transaction
counterparty
‐ Bonds are usually traded in OTC markets through dealers, who
keep the bonds as an “inventory” on their books and, so, need
to hedge out the exposure  Charge higher commissions than
brokers
‐ Equities are usually traded on exchanges (organized venues)
through brokers
‐ Brokers match buyers and sellers and, so, do not take any
exposure to (directional risk in) the traded asset

Bonds Equities
Valuation
‐ The main challenge is in the denominator of a present value
equation — estimation of interest rates at which to discount
the bond’s expected coupons and principal repayment(s)
‐ The main challenge is in the numerator of a present value
equation — estimation of expected free cash flows to equity
holders
Definition of risk
‐ For investment‐grade bonds:
‐ Time to maturity
‐ Effective duration, or bond price sensitivity to a small
instantaneous parallel shift of the yield curve
‐ For non‐investment‐grade (junk, or high‐yield) bonds
‐ Expected loss = Probability of default x Loss given default
‐ In terms of volatility:
‐ Standard deviation, semi‐deviation, mean absolute
deviation, zero‐mean deviation etc.
‐ In terms of loss:
‐ CVaR, (conditional value at risk, or expected average loss)
‐ DD (drawdown) etc.
Definition of return
‐ YTM, or yield to maturity
‐ Math is the same as that of IRR, just a different name
‐ IRR, or internal rate of return
‐ Math is the same as that of YTM, just a different name
Risk‐return
perspective
0.1%0.1%
0.2%
0.4%
0.6%
1.0%
1.3%
1.5%
1.7%1.8%
2.1%2.1%
-
0.5%
1.0%
1.5%
2.0%
2.5%
1 mo2 mo3 mo6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr20 yr30 yr
Yield
to
Maturity
Time to Maturity
IVV
IJHIJR
EFA
SCZ
EEM
AGG
SHY
IEF
TLT
TIP
LQD
VNQ
GLD
-
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
- 5.0% 10.0% 15.0% 20.0% 25.0%
Annualized
Return
Annualized STD

Asset
class
definition
Investment‐grade (IG) bonds ≈ “Bonds” High‐yield (HY) bonds ≈ Equities
Investment‐grade bonds
‐ Behave like “traditional” bonds
‐ Low risk
‐ E.g.: US treasuries or AAA corporate bonds
High‐yield bonds
‐ Behave like equities
‐ High risk
‐ E.g.: junk (low‐grade) corporate or emerging market bonds
Certainty of
cash flows
‐ High ‐ Low
Price driver
Dominant component in the discount rate, or price driver:
‐ Spot rate from the benchmark yield curve
Dominant component in the discount rate, or price driver:
‐ Credit spread above the spot rate from the benchmark YC
Credit spread narrows during economic growth and explodes
before and during recession
Business
cycle exposure
‐ Counter‐cyclical
‐ Price ↓ during expansion (low‐yield investments are out
favor) and ↑ during recession (safe harbor)
‐ Pro‐cyclical
‐ Price ↑ during economic growth (risks get muted by growth)
and ↓ during recession (CF uncertainty rises)
 Source: O. Deniz Basar and E. Guneren
Genc, “Comparison of Country Ratings of
Credit Rating Agencies with MOORA
Method,” berj, vol. 10, no. 2, pp. 391–404,
Apr. 2019, doi: 10.20409/berj.2019.175.
IG
bonds
HY
bonds
Portfolio
management focus
‐ Duration (interest rate risk) management,
or portfolio positioning on the yield curve
‐ Credit quality management
Investable assets do not fall into “risky equities”
and “safe bonds” simple categories  There are
risky issuers, and there are investment‐grade
issuers  In real life, a line between bonds and
equities is blurred in terms of risk exposure.
It is critical to distinguish high‐yield bonds, which
behave like equities due to the high credit spread
associated with them. Ukrainian bonds belong to
this category

As opposed to equities, bond valuation is largely a discounting exercise 11
Equity valuation model Bond valuation model
Discounting and interest
rates process for the
DENOMINATOR
Cash flows are known/
assumed from the onset for
investment‐grade bonds 
Cash flows estimation process for the
NUMERATOR
 Forecasting the cash
flows is required for equities
𝑃𝑉
𝑪𝒂𝒔𝒉𝑭𝒍𝒐𝒘𝒕
𝟏 𝒓 𝒕
Valuation:

Bonds’ negative cross‐asset correlations carry diversification benefit 12
Source: Portfolio Visualizer (https://www.portfoliovisualizer.com/asset‐class‐correlations)
Asset class correlations for time period 01/01/2008 - 12/31/2021 based on monthly returns
Name Ticker
iShares Core S&P 500 ETF IVV 1
iShares Core S&P Mid-Cap ETF IJH .94 1
iShares Core S&P Small-Cap ETF IJR .89 .96 1
iShares MSCI EAFE ETF EFA .89 .85 .80 1
iShares MSCI EAFE Small-Cap ETF SCZ .88 .86 .80 .97 1
iShares MSCI Emerging Markets ETF EEM .79 .79 .73 .88 .87 1
iShares Core US Aggregate Bond ETF AGG .04 .02 -.04 .15 .13 .16 1
iShares 1-3 Year Treasury Bond ETF SHY -.40 -.43 -.43 -.32 -.36 -.28 .54 1
iShares 7-10 Year Treasury Bond ETF IEF -.31 -.35 -.39 -.24 -.26 -.21 .83 .73 1
iShares 20+ Year Treasury Bond ETF TLT -.30 -.35 -.38 -.25 -.28 -.24 .79 .55 .91 1
iShares TIPS Bond ETF TIP .24 .23 .14 .30 .32 .37 .76 .32 .60 .51 1
iShares iBoxx $ Invmt Grade Corp Bd ETF LQD .34 .33 .26 .42 .41 .42 .83 .20 .48 .48 .66 1
Vanguard Real Estate ETF VNQ .74 .76 .74 .71 .69 .64 .33 -.18 -.03 -.01 .39 .47 1
SPDR Gold Shares GLD .05 .06 -.02 .12 .14 .25 .41 .32 .36 .25 .52 .30 .10 1
Invesco DB Commodity Tracking DBC .57 .59 .55 .62 .63 .63 -.07 -.29 -.32 -.37 .27 .15 .38 .31 1
IVV IJH IJR EFA SCZ EEM AGG SHY IEF TLT TIP LQD VNQ GLD DBC
• Over the long term, bonds have a negative correlation with equities and commodities
• In the realm of modern portfolio theory, when combined with other asset classes, negative correlation means lower risk all else being equal
• Bonds are a favourable investment in a risk‐off environment (e.g., overheated economy, recession, or macroeconomic shock) due to the
relative certainty of cash flows
• See slides 26‐27 on how the yield curve evolves during a business cycle

Use MIRR (modified IRR) Excel
function to account for a realistic
reinvestment rate
YTM for bonds = IRR for equities 13
• Making analogy with equities and corporate finance,
you can think of a straight bond as of an investment
project with a conventional cash flow pattern, where
an initial cash outlay is followed by positive cash flows
• Recall that IRR is a key metric to value a project. A
bond’s IRR is called yield to maturity, or YTM. YTM
implies a zero‐NPV valuation of a bond: the price you
pay for a bond today is equal to the sum of the bond’s
future cash flows discounted at the YTM
• YTM is the rate you EXPECT to “lock‐in” if you:
1. Hold the bond till maturity,
2. The borrower pays all cash flows according to
the schedule, and you
3. Reinvest the cash flows at YTM.
In practice, assumption 3 on reinvestment is
unrealistic:
4.3%
4.8%
5.4%
6.0%
6.6%
7.3%
7.9%
8.6%
9.3%
9.9%
0.0% 5.0% 10.0%
MIRR
Reinvestment rate
MIRR IRR

For comparability, YTM is a price proxy for investment‐grade bonds 14
Example of drastically different bonds with the same yield to maturity
31Jan2022 ($917.40) 31Jan2022 ($1,011.16) 31Jan2022 ($932.09) 31Jan2022 ($1,027.74)
31Jan2023 $1,000.00 31Jul2022 $50.00 31May2022 $12.50 31Jan2023 $100.00
31Jan2023 $1,050.00 31Aug2022 $12.50 31Jan2024 $100.00
30Nov2022 $12.50 31Jan2025 $100.00
31Jan2023 $12.50 31Jan2026 $200.00
31May2023 $12.50 31Jan2027 $200.00
31Aug2023 $12.50 31Jan2028 $200.00
30Nov2023 $12.50 31Jan2029 $200.00
31Jan2024 $1,012.50 31Jan2030 $200.00
31Jan2031 $200.00
31Jan2032 $200.00
YTM = XIRR 9.0% 9.0% 9.0% 9.0%
$price today ($917.40) ($1,011.16) ($932.09) ($1,027.74)
10Yr amortizing bond
2Yr straight bond
1Yr straight bond
1Yr
paid annually from Yr3
paid quarterly
paid semi-annually
bond
with fixed $100 coupon
with 5%coupon
with 10%coupon
zero-coupon
• Consider several bonds with a
face value of $1k. Notice how
different cash flows,
maturities and dollar prices as
of 31 January 2022 (today; in
red) equate to the same YTM
across all four bonds
• For comparability, bonds are
quoted in YTM because a
dollar price alone is a poor
descriptor of a bond
Always understand the cash
flows structure behind the
bond quote (YTM)!

Example of quotes on a YTM and %‐of‐face‐value basis 15
Source: Універ Облігації Telegram channel
Simply put, YTM («дохідність») is a synonym for price.
See «Дохідність купівлі» and «Дохідність продажу»
below
Notice the wide spreads between buy and sell quotes —
they speak to comparatively low liquidity of the asset
class itself and the dealer’s hedging costs
Source: Adamant Capital — Ukraine fixed income research, Weekly Digest January 12 – 18, 2022
It is common to quote junk (non‐investment‐grade) bonds — that usually have
high YTMs and, equivalently, deep discounts to face value — in % of the face
value
E.g., DTEK Energy 2027 is currently priced at 46% of face value, which
corresponds to 25.5% YTM

Section 2
Yield Curve:
Micro and Macro View
16

Likely a most basic yield curve you could imagine 17
5.5%
6.5%
7.0%
5.0%
5.5%
6.0%
6.5%
7.0%
7.5%
‐ 0.20 0.40 0.60 0.80 1.00 1.20
Yield to maturity
Time to maturity, years

100.00
70.00
Jan2022 Jul2022 Jan2023 Jul2023 Jan2024 Jul2024 Jan2025
Bond Repayment at Maturity = Future Value = Face Value
Bond Price Today = Present Value
Bond Appreciation = Amortization of discount = "The Power of Compounding"
Think of every individual cash flow as of a Zero‐Coupon Bond, or Zero 18
• Yield curves represent zero‐coupon yields
• A zero‐coupon bond is a bond with a single cash flow, principal
repayment. The interest income is implicitly embedded in form of
amortizing discount/premium: the bond price converges to its face
value (“pulled to par”) as the time approaches the maturity date
• You can find many economic equivalents of a zero:
• You are due to pay for a $5 lunch tomorrow
• You expect the construction of your pre‐paid property to
be finished in 1Yr and have a future value of $XX,000 by
that time
• You plan to accumulate a $5 mln portfolio in 20Yrs — you
“owe to yourself” a $5 mln 20Yrs zero‐coupon bond
• You expect to have a $1,000/month pension annuity to
start in 40Yrs — treat the future value of the annuity as
holding a zero‐coupon bond today maturing in 40 years
 The concept of Zero is essential to financial planning =>
Thinking in terms of zeroes is useful not only in bond
portfolio management but in financial planning overall.
Esp., when you develop an investment plan to meet legal
liabilities or life goals, each represented by an economic
equivalent of a zero‐coupon bond
A zero-coupon bond price trajectory

Bond portfolio = a portfolio of zeroes 19
• A critical concept, a zero is a basic building block, a Lego
part of a bond portfolio. Whenever you work with
bonds, think of every single cash flow as a zero‐coupon
bond
• Portfolio positioning on the yield curve = positioning of
zeroes on the yield curve, the maturity spectrum
‐
20,000
40,000
60,000
80,000
100,000
120,000
2022
Календарний графік купонів і погашень, UAH
‐
20,000
40,000
60,000
80,000
100,000
120,000
140,000
2022 2023 2024 2025 2026 2027 2028 2029 2030 2031
‐
2,000
4,000
6,000
8,000
10,000
12,000
14,000
2022 2023 2024 2025 2026 2027 2028 2029 2030 2031
A coupon bond
is a portfolio of zero‐coupon bonds where
each coupon and the last payment (last
coupon + principal repayment) are zero‐
coupon bonds
A portfolio of bonds
is a portfolio of… zero‐coupon bonds, where
each zero has its rate corresponding to the
maturity and risk
A zero‐coupon bond

Yield Curve: a microeconomic view 20
Yield curve is a term structure of interest rates. Making an analogy
with equities, the yield curve is an advanced, continuous version of a
discount rate
Why do we need a yield curve?
• Generally, observable benchmark zero‐coupon bonds are absent
for the same maturities of the cash flows we are tasked to value

• So, such zero‐coupon rates are estimated from the
observable prices of available government coupon bonds
• One of the most robust models to estimate a yield curve
from prices is a Nelson‐Siegel(‐Svensson) parametric
model
The estimated yield curve provides a continuous spectrum of rates
for discounting cash flows of specific maturities to estimate their
intrinsic value
Nelson and Siegel 1985
+ Svensson 1994
• There are two approaches to yield curve estimation:
parametric (e.g., Nelson‐Siegel 1985, Nelson‐Siegel‐
Svensson 1994) and spline‐based (e.g., Mcullogh 1971)
• Today, the NSS model is used by a vast majority
of Europe’s central banks
• Lars Svensson, researcher and ex‐deputy
governor of the central bank of Sweden, adds a
slope and a hump to a far end of the NS yield
curve estimate, thus “upgrading” NS to NSS
• In Ukraine, the parametric approach is used:
• NS, a simpler model, is used by NBU for USD‐
and EUR‐denominated domestic bonds
(«ОВДП»). The latter are few (just 13 issues
outstanding) and have short maturities (up to 2
Yrs)
• NSS model is used for UAH‐denominated
domestic bonds that are large in number (167
issues outstanding) and have maturities up to
2047, hence require a more complex estimation
model

Yield Curve: Definitions by the National Bank of Ukraine 21
Definitions by the National Bank of Ukraine:
• Крива безкупонної дохідності — графічна інтерпретація
дохідності однорідних безкупонних боргових цінних паперів з
різними періодами до погашення. Базова крива безкупонної
дохідності будується за державними облігаціями. Метою
побудови кривої безкупонної дохідності є отримання простого
інструменту для оцінки боргових цінних паперів.
• Спот‐ставка — теоретична дохідність однорідних безкупонних
облігацій на поточну дату, виражена у вигляді відсоткової
ставки.
• Основою для оцінки справедливої вартості боргових цінних
паперів є базові криві безкупонної дохідності, які будуються
окремо за такими групами державних облігацій: гривневі,
валютні.
Source: Постанова №732 про «Порядок оцінки за справедливою
вартістю цінних паперів резидентів, що перебувають у власності
Національного банку України або приймаються ним як забезпечення
виконання зобов’язань»

Putting together Nelson‐Siegel yield curve model and bond valuation 22
Beta 0 Beta 1 Beta 2 Tau
5.0% ‐4.0% 6.0% 5.00

0Y 3Y 6Y 9Y 12Y
Risky bond's cash flows
0Y 3Y 6Y 9Y 12Y
Zero coupon yield (spot rate)
Maturity
Long‐term rates level
0Y 3Y 6Y 9Y 12Y
Short‐term rates adjustment
0Y 3Y 6Y 9Y 12Y
Mid‐term rates adjustment
1.14%
0Y 3Y 6Y 9Y 12Y
Bond‐specific credit spread
0Y 3Y 6Y 9Y 12Y
Risky bond's YTM
Spot,
1.08%
Spot,
5.28%
YTM,
5.80%
YTM,
4.66%
102Y
Benchmark yield curve
(Nelson‐Siegel parametric
model of spot rates)
Risky bond
Govt bonds
Govt bond
❸ Among the three determinants of a
yield curve — level, slope, and curvature
— level generally has the strongest
impact on bond prices.
Beta0 is the 1st parameter to plug in the
NS function. It is responsible for the level
to which a spot rate on the "long" end of
the yield curve (at the most distant
maturity) asymptotically approaches. Such
a level shows the market long‐term
expectations of a real interest rate plus
expected inflation.
Beta0 must be a positive number.
Long rates tend to be more stable than
short ones due to investors' more homo‐
genous expectations regarding the LT.
❹ Beta1 (along with extent Tau) is an
adjustment to the long‐term rate made to
arrive at a short‐term, or policy rate on
the "short" end of the curve. For example,
a short‐term rate of 1% is set by (Beta0 +
Beta1) = (5% ‐ 4%) = 1%.
Beta1 largely defines the slope of the yield
curve, the 2nd most important
characteristic after the level and a marker
of a business cycle phase.
"Time decay", "time preference", and
"term structure of interest rates" are
other interpretations of Beta1.
(Beta0 + Beta1) must be a positive
number.
❺ Beta2 regulates curvature. It alters
mid‐term rates to make the middle of the
curve more nuanced: either monotonous,
S‐shaped, or humped/dumped. A +ve (‐ve)
Beta2 makes the curve more concave
(convex) and humped (dumped). Beta2
can be thought of as a weight (rather than
the value of interest rates as with Beta0
and Beta1) that a long end receives in
relation to the short end.
An auxiliary parameter to Beta1 and
Beta2, Tau can be thought of a year
(maturity) in which we observe a hump or
dump in the middle of the curve. It is esp.
useful to account for supply/demand
imbalances in a particular duration bucket,
or market expectations about a specific
year in the future.
❷ ... We need an *estimation* of the
rates, a yield curve.
 A yield curve is a *continuous*
maturity‐YTM spectrum estimated
from a limited number of actual and
observable maturity‐YTM *points*
represented by liquid government
bonds.
 Yield curve is a snapshot in time (it is
similar to a balance sheet item or
price).  It evolves with price
changes of the benchmark bonds the
YC is estimated from.
 Mathematically, the yield curve is a
fitted line that minimizes squared
differences between model YTMs and
actual YTMs. It is a graphic
representation of a function, a
parametric model, developed by
Charles Nelson and Andrew Siegel
back in 1985 (NS).
❻ See the next slide on how to derive
government, or benchmark YTM from
continuous zero‐coupon spot rates
The credit spread of an individual risky
bond (e.g., corporate or municipal) is the
return premium (price discount) that a
bondholder gets for taking the additional
risks above that of the benchmark
(government) bonds of the same maturity.
‐> Credit spread is equal to the bonds'
current YTM minus the current "model
yield", or spot return.
❶ To value a bond, we need a discount
rate that corresponds to its maturity. The
problem is benchmark bonds maturing on
the date in question almost never exist.
For example, when discounting cash flows
of a 1.5‐year bond, we might very well
have only 1‐year and 2‐years benchmark
(government) bonds as the closest peers
on the timeline at our disposal . ...
❼ Finally, we do a discrete discounting of
the risky bond's cash flows at its YTM.
The parameters` impact on the resultant YC do overlap  Consider interplay b/w them, esp. when applying different signs to Beta2 and Tau
When building a YC, start with Beta0 = Beta1 = Beta2 = 1% and Tau = 1
∑ of squares x 10^6
minimized: 172

Bond value (∑ of disco‐
unted CFs) 134.02

Credit spread over
govt YTM: 1.14%

Example 23
❶ Bond’s cash flows and their timing are available on the website of
the Ministry of Finance of Ukraine, “Outstanding domestic bonds”
page: https://mof.gov.ua/en/ovdp‐shho‐perebuvajut‐v‐obigu. This is an
example of a straight coupon bond maturing in 2026, ISIN
UA4000218531, from a list of outstanding issues as of 1 Jan 2022:
https://mof.gov.ua/en/download/page/3713
❷ National Bank of Ukraine regularly publishes their estimates of the
NSS model coefficients for the valuation of domestic UAH‐
denominated bonds (and NS for USD‐ and EUR‐denominated bonds),
typically every Tuesday or Wednesday, on the “Fair value of domestic
government bonds” page (Ukr: «коефіцієнти кривої спот‐ставок
безкупонної дохідності з безперервним нарахуванням відсотків»,
(https://bank.gov.ua/ua/markets/ovdp/fair‐value). These are
parameter coefficients as of 5 Jan 2022 for UAH bonds,
https://bank.gov.ua/files/Fair_value/NSS_parameters_LC.xlsx). The
coefficients enter into force on the next working day following their
publication, 6 Jan 2022 in our example.
❸ On the very same page (although only in the Ukrainian‐language
version), estimates of bonds’ fair value are available for every
outstanding domestic bond for every working day. This is an example of
estimates for the bond UA4000218531 as of 6 January 2022
(https://bank.gov.ua/files/Fair_value/202201/20220106_fv.xlsx).
Let’s reconcile the following numbers on the next slide and see how they
interact for the UA4000218531 bond as of 6 Jan 2022:
• Bond cash flows
• Nelson‐Siegel‐Svensson model coefficient values
• Fair value = “Cash”, or “dirty” price = UAH 1,013.61
• Yield to maturity = 13.053884%
• Quote, or “clean” price = 99.641% of face value

Math Behind: Use Spot Rate When Trading, Use YTM for Buy‐and‐Hold 24
❶ NSS coeﬃcients as of 5Jan2022 ,        effective next day 6Jan2022
Use cases:
Beta0 Beta1 Beta2 Tau Beta3 Tau1 ● Use YTM rate   ‐‐‐> for buy‐and‐hold ll maturity
0.85% 9.01% 4.37% 0.740
           31.85% 3.180
           ● Use Spot rates ‐‐‐> for trading  or selling before maturity
❹ Bond fair value calcs via discrete
❷ Bond fair value calcs via NSS (coun nuous compounding zero‐coupon) spot rates ❸ Bond YTM calcs compounding of a single rate, YTM
Date Remaining
cash flows
as of
6Jan2022
Term to
maturity,
years
NSS conti‐
nuous zero‐
coupon spot
rate
Continuous
discount
factor @
spot rates
Discounted
cash flows
@ spot rates
Date Cash flows YTM Discrete
discount
factor @
YTM
Discounted
cash flows
@ YTM
[1] [2] [3] [4] [5] [6] 6Jan2022 (1,013.61)
   [7] [8] [9]
18May2022 62.60
           0.362
           10.43% 0.963x
         60.28
           18May2022 62.60
           13.0539% 0.957x
         59.88

16Nov2022 62.60
           0.860
           11.00% 0.910x
         56.95
           16Nov2022 62.60
           13.0539% 0.900x
         56.33

17May2023 62.60
           1.359
           11.42% 0.856x
         53.60
           17May2023 62.60
           13.0539% 0.846x
         52.99

15Nov2023 62.60
           1.858
           11.76% 0.804x
         50.32
           15Nov2023 62.60
           13.0539% 0.796x
         49.84

15May2024 62.60
           2.356
           12.01% 0.753x
         47.17
           15May2024 62.60
           13.0539% 0.749x
         46.88

13Nov2024 62.60
           2.855
           12.20% 0.706x
         44.19
           13Nov2024 62.60
           13.0539% 0.704x
         44.10

14May2025 62.60
           3.353
           12.31% 0.662x
         41.43
           14May2025 62.60
           13.0539% 0.663x
         41.48

12Nov2025 62.60
           3.852
           12.36% 0.621x
         38.88
           12Nov2025 62.60
           13.0539% 0.623x
         39.02

13May2026 1,062.60
      4.351
           12.35% 0.584x
         620.79
         13May2026 1,062.60
      13.0539% 0.586x
         623.08

Bond Fair Value = "Dirty" price = ∑DCFs = 1,013.61
      YTM = XIRR = 13.053884% Bond Fair Value = ∑DCFs = 1,013.61

   └  vs value reported by NBU 1,013.61
         └  NBU 13.053884%
❺ Bond clean (quote) price calcs
where: Days b/w prev. cpn & val‐n date = 6Jan2022 minus 17Nov2021 50

[3]  =  YEARFRAC(  6Jan2022,  [1]  ,3  ), where 3 is for "Actual/365" daycount basis Days between coupons = 18May2022 minus 17Nov2021 182

[4] Fraction of coupon period passed =  50 / 182 0.27x

Next coupon = as of 18May2022 62.60

Accrued interest =  0.27x * 62.60 17.20

where "Maturity" is "Term to maturity, years" [3]
[5]  =  EXP(  ‐1  *  [3]  *  [4]  ) [6]  =  [2]  *  [5] Clean, or quote price = Dirty price ‐ Accrued interest = 996.41

[8]  =  1  /  (  (  1  +  YTM  )  ^  [3]  ) [9]  =  [2]  *  [8] Pct of face value 99.641

Note: bond valuation as of 6Jan2022    └  vs value reported by NBU 99.641

=  LET(  Beta0,  $C$32,  Beta1,  $D$32,  Beta2,  $E$32,   Beta3,  $G$32,  Tau,  $F$32,  Tau1,  $H$32,  Maturity,  $E40,
Beta0  +
Beta1  *  (  (     1  ‐  EXP(  ‐1 * Maturity / Tau  )  )  )  /  (  Maturity / Tau  )  +
Beta2  *  (  (  (  1  ‐  EXP(  ‐1 * Maturity / Tau     )  )  /  (  Maturity / Hump1  )  )  ‐  EXP(  ‐1 * Maturity / Tau    )  )  +
Beta3  *  (  (      1  ‐  EXP(  ‐1 * Maturity / Tau1  )  )  /  (  Maturity / Tau1  )   ‐  EXP(  ‐1 * Maturity / Tau1  )  )    )
Fair value of the
bond set at its price
Here, we
discount CFs at a
single rate (YTM)
across the entire
maturity
spectrum
Each of the bond's cash flows is discounted at an individual, maturity(time)‐
specific rate from the yield curve. The latter is described by coefficients of the
Nelson‐Siegel‐Svennson parametric model of continuous zero‐coupon spot rates

Math behind: How bond price depends on yield curve shape 25
Continuing our UA4000218531 example, let’s
value this bond under different historical yield
curve scenarios. In Table 1, we draw the
historical yield curves for some pronounced risk-
on/off situations over 2015-2022. The more risk,
the higher the level of the spot rates. These
rates provide discount factors for the bond’s
cash flows from Table 2. Summing up the DCFs
in Table 3, we arrive at the bond price under a
particular yield curve scenario. In Table 3, notice
how differently each cash flow is priced
(discounted) in each macroeconomic
environment. …
… Combining the price estimate with the
scheduled cash flows, we calculate YTM using
the Excel function ‘XIRR’ in Table 4. This YTM is
basically a discount at which you buy a bond:
Higher risk  Higher discount Lower
price  the higher the difference between the
face value and coupons you’ll receive (should
the issuer honor their obligations) and the
current price. Pay attention to (1) low prices and
the corresponding high YTMs under risky macro
environments reflected in elevated yield curves,
(2) inverse relation between YTM and price.
Historical yield curves as described by Nelson-Siegel-Svensson model
Historical yield
curves
Кінець
«військового»
2015 р.
Деескалація
2016 р.
Стабілізація
2017 р.
Військовий
стан 2018/9 р.
Пік до
Коронакризи
Дно під час
28Jul2020 6Jan2022
Beta0 12.00% 20.00% 1.61% 1.58% 1.01% 8.50% 1.19% 0.85%
Beta1 10.00% -2.00% 14.63% 17.80% 10.32% 5.50% 6.46% 9.01%
Beta2 30.00% -10.00% 3.54% -99.87% 20.27% 45.00% 11.84% 4.37%
Tau 0.80x 8.00x 0.38x 1.09x 5.58x 0.80x 7.21x 0.74x
Beta3 -5.00% -15.00% 38.44% 130.72% -10.53% -5.00% 10.98% 31.85%
Tau1 20.00x 11.00x 2.18x 1.34x 2.98x 20.00x 0.87x 3.18x
Yield Curve
Bond cash flows as of valuation date, 6Jan2022 Bond price calcs
6Jan2022 Coupon Principal Total CFs Mty, yrs
Discounted
cash flows
Кінець
2015 р.
2016 р.
2017 р.
стан 2018/9 р.
Пік до
28Jul2020 6Jan2022
18May2022 62.60 62.60 0.362 18May2022 57.18 58.74 59.33 58.62 60.15 58.14 60.48 60.28
16Nov2022 62.60 62.60 0.860 16Nov2022 49.98 54.06 55.35 53.69 57.08 50.93 57.03 56.95
17May2023 62.60 62.60 1.359 17May2023 44.21 49.99 51.43 48.95 54.29 44.94 53.67 53.60
15Nov2023 62.60 62.60 1.858 15Nov2023 39.80 46.43 47.59 44.48 51.69 40.47 50.64 50.32
15May2024 62.60 62.60 2.356 15May2024 36.40 43.28 43.97 40.49 49.26 37.19 47.95 47.17
13Nov2024 62.60 62.60 2.855 13Nov2024 33.67 40.49 40.69 37.07 46.97 34.71 45.54 44.19
14May2025 62.60 62.60 3.353 14May2025 31.41 37.98 37.80 34.22 44.79 32.76 43.36 41.43
12Nov2025 62.60 62.60 3.852 12Nov2025 29.45 35.72 35.29 31.91 42.72 31.16 41.37 38.88
13May2026 62.60 1,000 1,062.60 4.351 13May2026 470.57 571.38 562.54 510.06 691.84 505.44 671.01 620.79
Price = ∑DCF 792.68 938.08 934.00 859.49 1,098.80 835.72 1,071.05 1,013.61
Bond YTM calcs
Cash flows
Кінець
2015 р.
2016 р.
2017 р.
стан 2018/9 р.
Пік до
28Jul2020 6Jan2022
Price ---> 6Jan2022 (792.68) (938.08) (934.00) (859.49) (1,098.80) (835.72) (1,071.05) (1,013.61)
18May2022 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
16Nov2022 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
17May2023 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
15Nov2023 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
15May2024 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
13Nov2024 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
14May2025 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
12Nov2025 62.60 62.60 62.60 62.60 62.60 62.60 62.60 62.60
13May2026 1,062.60 1,062.60 1,062.60 1,062.60 1,062.60 1,062.60 1,062.60 1,062.60
YTM = XIRR 21.7% 15.7% 15.8% 18.7% 10.4% 19.7% 11.3% 13.1%
1
2 3
4

Macro interpretation of YC for IG bonds — barometer of the economy 26
1. Initial recovery 2. Early upswing 3. Late upswing 4. Slowdown 5. Recession
Biz cycle
phase
YC shape for
IG bonds
Steep Moderately steep Flat Inverted Flat & bottomed
CB policy Loose/dovish/accomodating Loose/dovish/accomodating Tight/hawkish/restrictive Tight/hawkish/restrictive Loose/dovish/accomodating
Challenge Weak growth Stagflation risk Post‐recession debt Inflation Unemployment
Macro
environ‐
ment
• YC is upward sloping =
normal YC: LT investments
are riskier than those ST
• Economy is expected to
recover after enough
stimulation
• First rate hikes by CB
increase short rates, while
long rates remain stable =>
YC steepness ↓ => YC
flattens
• Uncertainty about future
monetary policy =>
laddered / diversified
allocation to all duration
buckets
• Or: expectation that high
rates today will neutralize
inflation in the mid‐term
• A sign of a possible
recession looming
• Short end is high after CB
rate hikes to curb strong
inflation at the cycle peak
• Long end is lower as
investors rotate into LT
bonds in anticipation of a
recession (safe harbor) and
rate cuts (seek long
duration = strong price↑)
• Growth and inflation
growth prospects fade
• Recession = 2 successive
quarterly declines in GDP
• Monetary and fiscal stimuli
kick in
• Rates bottom out across all
maturities:
• Short end: CB cuts policy
rate
• Long end: remains low as
monetary and stimulation
efforts have not worked
out yet
Capital
market
dynamics
Cheap money rush from
expensive bonds (being at risk
of CB rate ↑) into undervalue‐
ed risky assets after the
market crash => Stocks and
HY bonds rally, and IG bonds
decline
As the business cycle unfolds:
• Level of interest rates goes up = IG bonds prices decline = bond yields grow
• Credit spread (discount for extra risk) narrows amid growing investor, consumer and
producer confidence
• Risky assets (HY bonds, emerging market equities and bonds) grow
• IG bond prices top
• Risky assets' prices crash
(although benchmark interest
rates bottom, credit spread
explodes — see next slide)

1 4 7 1013161922252831343740434649 1 4 7 1013161922252831343740434649 1 4 7 1013161922252831343740434649 1 4 7 1013161922252831343740434649 1 4 7 1013161922252831343740434649
 Benchmark YC =
Expected real growth
+ Expected inflation
Credit risk
premium =
Credit spread
Driven by a credit spread, high‐yield bonds behave like risky equities 27
1. Initial recovery 2. Early upswing 3. Late upswing 4. Slowdown 5. Recession
Steep YC Moderately steep YC Flat YC Inverted YC Flat & bottomed YC
Credit spread above
the benchmark yield
curve (required return
for extra risk)
dominates in the
interest structure of
HY bonds =>
HY bonds are pro‐
cyclical:
uncertainty of cash
flows increases
(decreases) =>
=> credit spread
widens (narrows)
 they go down
(up) in price
High Moderate Low Moderate‐High Extremely high
While rates on IG
bonds bottom out,
credit spreads on risky
assets skyrocket during
a recession, volatility,
and FUD (fear,
uncertainty, doubt).
The investors rush into
the quality and value
factors out from
overpriced, small‐cap
and junk securities
As economy shows first
signs of recovery,
investors start seeing
less risk in risky assets
=> Credit spreads
tighten as investors
flock into undervalued
assets => Risky assets
rally out from the
bottom and the “risk‐
on” regime begins
Although inflation and rates
peak in tune with the
economic cycle, credit
spreads contract by a
larger absolute extent =>
The net effect is the lowest
discount rate for risky
assets during the entire
cycle => Risky assets reach
their maximum price and
even junk securities are
overvalued (high‐yield
bonds, emerging markets
bonds and stocks)
Credit spreads further
decline as:
‐ economic growth
softens many risks
‐ investors get more
confident and
‐ capital market gains
momentum
Credit spreads start rising
as investors start
recognizing the weakness
of the economy => The
market loses momentum
as some of its sectors
stop growing or even
start a decline. Investors
start cashing out from
the riskiest / overvalued
assets

Historical yield curves for Ukrainian Eurobonds 28
Кінець «військового» 2015 р.
Деескалація 2016 р.
Стабілізація 2017 р.
Військовий стан 2018/9 р.
Пік до «Коронакризи»
Дно під час «Коронакризи»
Нормалізація кін. 2021 р.
Ескалація поч. 2022 р.
-
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Спотова ставка
Років до погашення
Суверенні євробонди Укр.
• Ukrainian Eurobonds (denominated mostly in USD) is
the main pillar of the country’s external debt
• The Eurobonds YC went up dramatically in turbulent
times — military escalations (2018/2019, 2022) and
the first major Covid‐19 lockdown (2020). Inverted
shape signalled higher risks in the short‐term
compared to the long‐term
• The YC exhibited moderate levels and the normal
upward slope during de‐escalations
• The YC posted the lowest levels in late 2019 and
2021, when major risks seemed to have been behind
• A humped or flat YC also can be interpreted as a
transition from a healthy economy (marked by an
upward‐sloping YC) into a risk of recession (inverted
YC). A permanent hump/inversion can indicate that
economic growth is fragile and the YC can dip in any
direction

Кінець «військового» 2015 р.
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ОВДП ₴
Historical yield curves for Ukrainian UAH‐denominated domestic bonds 29
• Domestic bonds YC is typically humped around 3Yrs‐
5Yrs maturities as investors price in more risks in that
horizon compared to short and long ends of the
curve
• A long‐term decline in level can indicate that the
country is on the right macroeconomic and
institutional trajectory
• Interestingly, UAH domestic bonds did not respond
as sharply to the early‐2022 Ukraine‐Russia‐NATO
political standoff as they did in 2018 amid another
period escalation of a similar nature

2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
1 2 3
ОВДП $, €
Historical yield curves for Ukrainian USD‐denominated domestic bonds 30
• Domestic USD‐ and EUR‐denominated bonds are few
and typically of short maturities, up to two years
• Similar to Eurobonds, domestic foreign currency
bonds exhibit a pronounced response to a risk‐on/off
episodes

Useful resources on Ukr. yield curve: Fair value of domestic bonds by NBU 31
URL: https://bank.gov.ua/ua/markets/ovdp/fair‐value
NSS model is used for UAH‐denominated domestic bonds that
are large in number (167 issues) and have maturities up to
2047, hence require a more complex estimation model
NS, a simpler model, is used by NBU for USD‐ and EUR‐
denominated domestic bonds: they are few (just 13 issues as of
lecture date) and have short maturities (up to 2 Yrs)
Extrapolated

Useful resources on US yield curve: Dynamic Yield Curve on StockCharts 32
StockCharts home page  Charts & Tools  Charting Tools  Dynamic Yield Curve URL: https://stockcharts.com/freecharts/yieldcurve.php
When scrolling the “Trail”, notice how the US yield curve decreased in level in March 2020 amid policy rate cut, rollout of monetary stimulus
package and lockdowns unfolding worldwide. At the same time, Ukrainian yield curve increased in level due to widening country credit spread
over the US benchmark.

Useful resources on US yield curve: CME TreasuryWatch Tool 33
CME Group Home page  Markets 
QuickStrike Tools  Single‐Asset Class
Tools  TreasuryWatch Tool
URL: https://www.cmegroup.com/tools‐
information/quikstrike/treasury‐
watch.html?itm_source=quikstrike_singl
e_asset_page&itm_medium=tool_tile_
&itm_campaign=treasury_watch_tool
There is an 89%
probability (implied
from Fed Fund futures)
that Fed will raise the
policy rate from the
current 0%‐0.25% to
0.25%‐0.50% on March
16
Current yield curve

Section 3
Bond Portfolio Horizon Analysis Model
34

Concept:
Holding period return model for an investment asset 35
Holding
period
return
Income earned
during the
holding period
Price change
of the asset
itself
Asset price at
the beginning of
holding period
Holding period = 1 Yr
Buy 1 AAPL
stock at
$130
Sell or revalue
1 AAPL stock at
$150
Receive 4x quarterly dividends, total $0.86 HPR =
($0.86+$20)/$130 – 1
= 16%
Buy a
4Yr
bond at one yield
curve (price)
Sell or revalue a
3Yr
bond at another yield
curve (price)
Receive coupons
Holding period = 1 Yr
HPR =
(Coupons + Chg in
price) / Investment
See next slide 
Stock:
Bond:

Change in bond portfolio price comes from (1) a “roll” and (2) YC change 36
Consider investing into a 5Yr bond
(portfolio) when 5Yr and 2Yr rates are
9% and 7%, respectively. You expect
that a 2Yr bond will be priced at 5% in
three years and have a modified
duration of 1.8. Your approximate
expected total holding period return
the 3 years will be the sum of:
1) Roll‐down return on a stable
upward‐looking YC ≈
≈ 3 x 9% ≈ 27%
2) Return due to change in the YC (a
so‐called “last‐minute rally”
according to Hanke&Henderson,
when an old YC instantaneously
evolves into a new one):
≈ ‐1 x (5% ‐ 7%) x 1.8 ≈ 3.6%
The total value change is ≈30.6%, or ≈
10.2% p.a. Notice this is a higher return
than you could have expected to “lock‐
in” when investing at 9% YTM because
you earn an extra 1.2% p.a. from the
favorable decline of the yield curve over
your 3‐years horizon. YTM is an
imperfect descriptor of expected return.
Note: If the YC is downward‐sloping, the
portfolio will be repriced at higher rates
and, so, experience a price decline.
Expected YC at
horizon
Current YC
A. Current
portfolio
B. Rolled portfolio
as if YC were
stable
C. Portfolio at
horizon
‐ 1 2 3 4 5 6
Maturity
Total Price Change of the Portfolio (AC) =
= Price Change due to roll (AB) + Price Change due to YC change (BC)
A 5Yr portfolio "rolls down" the YC (at a
rate equal to YTM) over 3 years to
become a 2Yr portfolio. The remaining
cash flows are repriced at lower
rates, hence roll yield
A
change
in YC at the
congruent
maturity brings
additional change
in price of the
remaining cash
flows
Horizon = holding period = 3 years
Approximate price chg
due to YC chg =
‐1 x (YTM of a 5Yr bond
@ current YC
MINUS
expected YTM of a 2Yr
bond @ horizon YC)
x Modified duration of
a 2Yr bond @ horizon
Source: adaptation of material from CFA Program Curriculum for Level III: (1) "Overview of Fixed-Income Portfolio Management" by Bernd Hanke, PhD, CFA,
and Brian J. Henderson, PhD, CFA; (2) "Yield Curve Strategies" by Robert W. Kopprasch, PhD, CFA, and Steven V. Mann, PhD

Our horizon model is a full repricing model for a bond portfolio 37
= Coupons / Bond purchase price
= Bond price change under stable YC
= Approximated by duration and convexity;
or do a full repricing for accuracy
= A realistic rate, as opposed to assuming
reinvestments at YTM
= Due to currency exchange fluctuations
= Based on credit analysis, which is esp. important for high-yield bonds.
In the model presented hereinafter, expected loss — if any — is
reflected in the cash flows inputs for the specific bond
Rolling
yield
Source: adaptation of material from CFA Program Curriculum for Level III: (1)
"Overview of Fixed-Income Portfolio Management" by Bernd Hanke, PhD,
CFA, and Brian J. Henderson, PhD, CFA; (2) "Yield Curve Strategies" by
Robert W. Kopprasch, PhD, CFA, and Steven V. Mann, PhD
Income
return
Return due to credit spread change
Income yield
Rolldown return
Return due to yield curve change
Return from cash flows reinvestment
FX effect on received coupons and principals
Expected loss of face value at horizon
TOTAL PORTFOLIO RETURN
Amortization of discount (premium)
= For risky bonds only, expected change in credit spread

Section 4
Strategies of Portfolio Positioning
on the Yield Curve
38

Strategies are built around the expected yield curve and time horizon 39
A full repricing model of a bond portfolio:
- Macroeconomic analysis is summarized in the expected shape of the YC by the
end of the holding period, or investment horizon
- The YC describes how investors will price the risk at the date of our exit = what
discounts they will command to offtake the risk from our portfolio onto their own
books
- The model does not rely directly on duration (which is a linear approximation of a
convex yield-price relationship) management
- The model boils down to a What-If analysis of holding-period returns under different
- Investment horizons
- Expected yield curves by horizon end
- Portfolio structures, or allocations to duration buckets: 1 bond issue per bucket

Strategies are build based on expected YC, spreads chg, and time horizon 40
Macroeconomic forecast Credit analysis of the issuers
Expected yield curve + credit spread adjustments for each bond in the portfolio
Concluded in terms of YC
Expected yield curve is STABLE Yield curve is expected to CHANGE
Buy and hold
till maturity
Riding the
upward‐sloping YC
Duration management,
Portfolio positioning on the yield curve
• Avoid YC segments that are expected to go up over the horizon
• Allocate to YC segments that are expected to go down
• For convenience, operate with general portfolio structures:
Seek maximum expected
rolling yield, a sum of
expected income yield and
expected rolldown return
Allocate all capital to the
desired maturity and “lock‐
in” the corresponding
return by holding the
bonds till maturity
Expected yield curve Expected credit spreads of individual bonds
Bullet
Concentrated
in/around specific
maturity years;
least diversified
strategy
Ladder
Even distribution
among duration
buckets; a most
diversified
portfolio
Barbell
Concentrated in
short and long
ends, with empty
buckets in the
middle
Concluded in terms of bond’s credit spreads
Yield cur- Rolldown Bond tra- Amortization
ve slope return ding @ of prem/disc
Discount Positive
Premium Negative
Discount Positive
Premium Negative
Discount bond: Coupon rate < YTM
Premium bond: Coupon rate > YTM
Upward
Downward Negative
Positive

Pre‐set yield curve scenarios: historical and expected 41
25
26
27
28
29
30
31
32
33
34
2020 2022 2024 2026 2028 2030
Валютний курс
UAHUSD UAHEUR

Pre‐set portfolio structures 42
Duration buckets
For example:
• Allocation #6, an extreme bullet, is a
portfolio 100% invested in 3Yrs bonds
• Allocation #20 is an extreme barbell, with
1Yr and 10Yrs bonds comprising a 50/50
weight
• Allocation #15, a ladder, provides an even
distribution of portfolio weights across the
buckets, 10% per each maturity year
• The rest of the allocations are variations of
the three above

Bullet portfolio structure: Most concentrated and risky 43
‐
20,000
40,000
60,000
80,000
100,000
120,000
140,000
2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031
Інвестиційний горизонт = 2.0 роки (29 Вер 2021 – 29 Вер 2023) Дюрація Маколея = 4.5 роки
Notice how all the three portfolio cash flows structures (bullet,
barbell, ladder), however different they are, have portfolio
Macaulay durations in a narrow range of 4.1 ‐ 4.5 years

Barbell portfolio structure 44
‐
10,000
20,000
30,000
40,000
50,000
60,000
70,000
2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031

Ladder portfolio structure: most diversified; often a baseline portfolio 45
‐
2,000
4,000
6,000
8,000
10,000
12,000
14,000
2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031

Key output: A portfolio/allocation of choice is the one with the highest
expected return given the anticipated yield curve and investment horizon 46
Прогнозні Holding Period Returns, річних у UAH, за період з 9 Лют 2022 (T0) по 9 Лют 2024 (T1) залежно від позиціноування портфеля на кривій доходності на 9 Лют 2022 та самої К/Д на 9 Лют 2024
Портфель на 9 Лют 2022 (T0) Крива доходності на кінець інвестгоризонту, 9 Лют 2022 (T0)
Історичні сценарії кривої доходності Наші прогнози кривої доходності на 9 Лют 2024 (T1)
Валюта обчислення доходності = UAH
Кінець
«військовог
о» 2015 р.
2016 р.
2017 р.
стан 2018/9
р.
Пік до
«Коронакри
зи»
зи»
5 Січ 2022 Сценарій 1 Сценарій 2 Сценарій 3 Сценарій 4 Сценарій 5
Позиціонування портфеля на кривій
доходності на 9 Лют 2022 (T0)
Дюрація
Маколея,
років
Конвексія
(розкид ГК у
часі навко‐
ло дюрації)
Доход‐
ність до
погашення
(YTM) 15Y
1Y
     1Y    2Y   3Y   4Y   5Y   6Y   7Y  8Y  9Y  10Y
1 0.8
               1.3
                11.2% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33% 3.33%
2 1.2
               2.7
                11.7% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03% 6.03%
3 6.5
               52.4
              10.0% ‐7.46% ‐0.56% 0.39% ‐1.95% 8.61% ‐3.27% 3.35% 8.07% 10.90% 16.68% 20.45% 26.23%
4 5.8
               42.5
              10.2% ‐6.60% 0.19% 0.62% ‐2.17% 8.62% ‐3.33% 3.88% 7.83% 10.74% 15.64% 19.09% 23.99%
5 1.7
               4.9
                11.7% 5.53% 6.88% 7.31% 6.76% 7.89% 5.86% 7.85% 7.90% 8.48% 8.67% 8.95% 9.28%
6 2.5
               8.3
                11.7% 4.74% 8.23% 9.35% 7.92% 10.84% 5.60% 10.74% 10.88% 12.36% 12.84% 13.58% 14.44%
7 3.5
               14.9
              11.3% ‐2.03% 4.93% 6.17% 2.90% 10.48% ‐1.30% 9.06% 9.49% 12.77% 14.46% 16.33% 18.43%
8 4.3
               21.7
              10.9% ‐4.84% 2.68% 3.01% ‐0.95% 9.76% ‐3.68% 6.83% 8.32% 11.95% 14.77% 17.42% 20.43%
9 4.5
               25.5
              10.7% ‐5.53% 0.92% 0.78% ‐2.63% 7.74% ‐3.93% 4.31% 6.56% 9.57% 12.74% 15.44% 18.64%
10 5.0
               32.4
              10.4% ‐5.07% 1.65% 1.41% ‐1.89% 9.48% ‐2.67% 5.07% 8.43% 11.42% 15.58% 18.81% 22.91%
11 6.2
               46.1
              10.2% ‐7.51% ‐0.32% ‐0.31% ‐3.31% 8.92% ‐3.87% 3.31% 8.10% 11.08% 16.66% 20.56% 26.00%
12 4.4
               23.7
              10.8% ‐5.19% 1.77% 1.86% ‐1.81% 8.72% ‐3.81% 5.53% 7.41% 10.72% 13.72% 16.40% 19.51%
13 4.3
               23.7
              10.8% ‐4.37% 2.53% 2.83% ‐0.65% 9.36% ‐2.89% 6.30% 8.20% 11.41% 14.38% 17.00% 20.11%
14 4.3
               24.4
              10.7% ‐3.50% 2.93% 3.29% 0.18% 9.46% ‐1.82% 6.49% 8.51% 11.44% 14.39% 16.91% 19.99%
15 4.1
               25.8
              10.6% ‐2.15% 2.95% 3.43% 1.21% 8.59% ‐0.28% 5.83% 7.97% 10.22% 13.12% 15.33% 18.32%
16 4.0
               26.6
              10.5% ‐1.37% 3.00% 3.55% 1.82% 8.15% 0.63% 5.51% 7.72% 9.60% 12.47% 14.51% 17.45%
17 3.8
               27.5
              10.3% ‐0.86% 2.78% 3.43% 2.21% 7.45% 1.28% 4.94% 7.22% 8.72% 11.56% 13.43% 16.33%
18 3.8
               27.7
              10.3% ‐0.48% 2.79% 3.40% 2.39% 7.20% 1.64% 4.71% 7.00% 8.33% 11.16% 12.95% 15.80%
19 4.0
               27.6
              10.4% 0.96% 4.19% 4.60% 3.53% 8.58% 3.01% 5.98% 8.35% 9.65% 12.47% 14.30% 17.10%
20 3.6
               27.9
              10.1% ‐1.79% 1.50% 2.31% 1.34% 5.94% 0.38% 3.55% 5.75% 7.11% 9.95% 11.72% 14.61%
     1Y    2Y   3Y   4Y   5Y   6Y   7Y  8Y  9Y  10Y
Позиціонування портфеля на кривій доходності: 1) Власна 1; 2) Власна 2; 3) Власна 3; 4) Власна 4; 5) Власна 5; 6) Exreme Bullet, 3Y; 7) Extreme Bullet, 4Y; 8) Extreme Bullet, 5Y; 9) Extreme Bullet, 6Y; 10) Extreme Bullet, 7Y
11) Extreme Bullet, 8Y; 12) Bullet; 13) Bulleted; 14) Bulleted; 15) Ladder; 16) Barbelled; 17) Barbelled; 18) Barbell; 19) Extreme Barbell; 20) Extreme Barbell

Section 5
Case Studies
47

Case #1. Strategy 1 — B&H till maturity: example of a premium bond 48
Portfolio construction:
• Consider a historical yield curve for UAH OVDP for 29 September 2021
• We invest in a premium short‐term bond and set a horizon at 31
October 2022 so that both bonds mature by this date
• The bond is UKR 2022‐10‐12 UAH 14.91% 199210
• Bond YTM at entry is 10.4%, and the coupon rate is 14.91%
• => This is a premium bond (coupon > YTM)
• Assume that by 31 October 2023 a yield curve will evolve into the
same we observed immediately after an announcement of the first
Covid‐19 lockdown back in March 2020 — a “disaster” yield curve
Investment outcome:
• As the premium bond was pulled to par approaching its maturity, its premium was
amortizing. In other words, amortization was contributing a negative price change
over the horizon
• Notice how premium decay was more than offset by coupons and reinvestments
• Notice the zero effect of the yield curve change as the bond matured by this date
(on October 12) — no need to resell it at an unfavorable curve (prices)
• Be prepared to explain the price decline of a premium bond to your client!
Прогнозний портфель на 31 Жов 2022 (T1) у UAH
Дюрація‐‐‐>
Складові очікуваної зміни вартості (% від
початкової вартості) та доходність
(holding period return, річних)
ПОРТФЕЛЬ
Кількість облігацій у портфелі x 100

Відхилення від оціночної вартості на T0 ‐
(+) Амортизація премії (дисконту) ‐9.5%
(+) Роллдаун ‐0.8%
(+) Зміна ціни за незмінної кривої дох‐ті ‐10.3%
Зміна рівня кривої доходності ‐
Зміна нахилу ‐
Зміна вигину ‐
(+) Зміна форми кривої доходності ‐
(+) Зміна індивідуального cпреду ‐
Зміцнення (девальвація) ₴ до $ ‐
Зміцнення (девальвація) $ до € ‐
(+) Зміна валютного курсу ‐
Зміна вартості облігацій на 31 Жов 2022 ‐10.3%
Отримані купони 20.1%
Зміцнення (девальвація) ₴ до $ ‐
Зміцнення (девальвація) $ до € ‐
Накопичені купони ‐
(+) Купонний доход з урах. валютного курс 20.1%
(+) Прибуток від реінвестування 5.8%
Зміна варт. портфеля до комісійних витрат 15.5%
Торгові комісії на вході, 29 Вер 2021 ‐0.5%
Торгові комісії на виході, 31 Жов 2022 ‐0.5%
Active Management Fee, 31 Жов 2022 ‐
(‐) Комісійні ‐1.0%
Зміна вартості портфеля після комісійних 14.5%
∑(+): Доходність (HPR) до коміс., річних 14.20%
∑(+): Доходність (HPR) після коміс., річних 13.29%

Case #2. Strategy 2 — Riding down a stable upward‐sloping yield curve 49
• Consider an OVDP UAH yield curve as of 16 March 2021
• The then‐curve had an inflection point around 5Y
bucket, with shorter maturities sloping upward and
longer ones sloping downward
• Our 1Y horizon starts on 29 September 2021
• We expect the YC to remain stable over the horizon
• We construct a portfolio of four bonds:
1. A premium short‐term bond on the short
upward‐sloping segment
2. A discount short‐term bond on the short
3. A premium long‐term bond on the long
downward‐sloping segment
4. A discount long‐term bond on the long
Let’s examine the expected amortization of premiums
(discounts) and rolldown return, and their combined
effect on the expected total portfolio return
‐
2,000
4,000
6,000
8,000
10,000
12,000
14,000
2021 2022 2023 2024 2025 2026 2027 2028 2029 2030
7%
8%
8%
9%
9%
10%
10%
11%
11%
12%
12%
‐ 2 4 6 8 10
Крива доходності для ОВДП у UAH
29 Вер 2021 (T0)
29 Вер 2022 (T1)
Roll Roll

Case #2. Strategy 2 — Riding down a stable upward‐sloping yield curve 50
• Bonds’ 207682 and 186555 maturities are both on the upward‐sloping segment => Expected to
deliver a positive rolldown return as they are expected to be discounted at LOWER rates in 1 year
from today (+71 and +67, respectively)
• Bonds’ 196224 and 187348 maturities are both on the downward‐sloping segment => Expected to
deliver negative rolldown returns as they are expected to be discounted at HIGHER rates in 1 year from
today (‐154 and ‐146, respectively)
• Discount bonds 207682 and 196224 will see a “time decay” of their discounts by +72 and +36,
respectively => Smaller discount means a higher price and a positive contribution of amortization to the
price change as the bond is being “pulled to par”
• By the same logic, 186555 and 187348 bonds will see their premiums shrinking over our holding period
by ‐243 and ‐64, respectively => Negative contribution of such a shrinkage/amortization to the price
change
7%
8%
8%
9%
9%
10%
10%
11%
11%
12%
12%
‐ 2 4 6 8 10
Крива доходності для ОВДП у UAH
29 Вер 2021 (T0)
29 Вер 2022 (T1)
Roll Roll
YTM @ T0 10.9% 10.9% 11.1% 11.3%
Coupon 9.8% 13.3% 10.0% 12.5%
Discount or premium bond? Discount Premium Discount Premium
Очікувана вартість портфеля на 29 Вер 2022 (T1) у UAH
Складові очікуваної зміни вартості
портфеля
ПОРТФЕЛЬ
UKR 2023‐02‐
15 UAH 9.84%
207682
UKR 2023‐02‐
01 UAH
13.30%
186555
UKR 2030‐05‐
08 UAH 9.95%
196224
UKR 2029‐10‐
12 UAH
12.50%
187348
             x  10
                x  10
                x  10
                x  10

Фактично сплачені кошти 29 Вер 2021 41,829
10,013
            10,538
            9,922
              11,356

(+) Відхилення від оціночної вартості ‐
‐
                       ‐
                       ‐
                       ‐

Вартість за поточним курсом на 29 Вер 202 41,829
10,013
            10,538
            9,922
              11,356

(+) Амортизація премії (дисконту) (198)
72
                    (243)
                36
                    (64)

(+) Роллдаун (162)
71
                    67
                    (154)
                (146)

(+) Зміна ціни за незмінної кривої дох‐ті (360)
143
                  (176)
                (118)
                (209)

Yield cur- Rolldown Bond tra- Amortization
ve slope return ding @ of prem/disc
Discount Positive
Premium Negative
Discount Positive
Premium Negative
Upward
Downward Negative
Positive
=> Notice how amortization of
premium (discount) and
rolldown can offset each other
and, combined, lead to
UNINTUITIVELY DIFFERENT bond
price changes on the SAME
stable yield curve for different
bonds

Case #3. Strategy 3 — Portfolio positioning
in anticipation of a specific change in the yield curve 51
Portfolio construction:
• Assume a very favorable yield curve for Ukrainian Eurobonds, as
of 14 September 2021: a calm market, normal shape, low yields
• Assume we expect the curve to evolve into a similar one we
observed immediately before Covid‐19
• How shall we allocate among the duration buckets if our
investment horizon is 1 year?
Answer:
• A 100% allocation to a 10Y promises the highest holding‐period
return, 14%. However, this is an ultimately concentrated position,
where risk is aggravated by the high duration of the bond itself
• A reasonable baseline is a LADDER portfolio with 8% expected
return, 6% less than the maximum possible — a tradeoff for higher
diversification and liquidity. Use barbell or bullet structures to
target mid‐range expected returns
Прогнозні Holding Period Returns, річних у USD, за період з 14 Вер 2021 (T0) по 14 Вер 2022 (T1) залежно від позиціноування портфеля на кривій доходності на 14 Вер 2021 та самої К/Д на 14 Вер 2022
Портфель на 14 Вер 2021 (T0) Крива доходності на кінець інвестгоризонту, 14 Вер 2021 (T0)
Історичні сценарії кривої доходності Наші прогнози к/д на 14 Вер 2022 (T1)
Валюта обчислення доходності = USD Статистика портфеля
Кінець
«військовог
о» 2015 р.
2016 р.
2017 р.
стан 2018/9
р.
Пік до
зи»
зи»
Нормалізаці
я кін. 2021 р.
Ескалація
поч. 2022 р.
Вибрати дату:
2021‐09‐14
Стрес‐тест:
Beta0 +300
bps
Історична
середина:
легкий
Історична
середина:
інверсія
Позиціонування портфеля на кривій
доходності на 14 Вер 2021 (T0)
Дюрація
Маколея,
років
Конвексія
(розкид ГК
у часі навко‐
ло дюрації)
Доход‐
ність до
погашення
(YTM T0) 15Y
1Y
     1Y    2Y   3Y   4Y   5Y   6Y   7Y  8Y  9Y  10Y
1 0.9
               1.8
                2.4% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51% 1.51%
2 1.4
               3.6
                3.0% ‐1.72% 0.48% 1.87% ‐0.78% 2.26% ‐2.99% 2.46% ‐7.02% 2.46% 1.08% 1.56% 0.83%
3 1.9
               5.3
                3.3% ‐4.86% ‐0.53% 2.22% ‐3.01% 2.99% ‐7.35% 3.38% ‐15.28% 3.38% 0.67% 1.60% 0.16%
4 2.7
               10.1
              4.1% ‐8.22% ‐2.22% 3.09% ‐6.96% 4.61% ‐12.50% 4.79% ‐18.65% 4.79% ‐0.55% 2.53% 0.17%
5 3.5
               16.0
              4.7% ‐9.92% ‐3.56% 3.87% ‐10.29% 6.18% ‐16.38% 5.57% ‐19.92% 5.57% ‐2.17% 4.67% 1.07%
6 4.3
               22.9
              5.2% ‐10.96% ‐4.72% 4.33% ‐13.18% 7.51% ‐19.52% 5.93% ‐21.03% 5.93% ‐3.97% 7.49% 2.40%
7 4.9
               30.7
              5.5% ‐11.79% ‐5.78% 4.43% ‐15.72% 8.56% ‐22.17% 6.09% ‐22.17% 6.09% ‐5.74% 10.59% 3.93%
8 5.4
               37.6
              5.7% ‐9.35% ‐3.72% 6.70% ‐14.39% 11.65% ‐20.62% 8.58% ‐19.68% 8.58% ‐4.34% 15.90% 8.03%
9 6.0
               45.8
              5.9% ‐11.42% ‐5.65% 5.69% ‐17.71% 11.68% ‐24.18% 7.94% ‐22.15% 7.94% ‐6.84% 18.01% 8.62%
10 6.9
               57.9
              6.1% ‐15.61% ‐9.96% 1.82% ‐23.17% 9.02% ‐29.55% 4.56% ‐26.23% 4.56% ‐11.90% 18.20% 7.15%
11 7.4
               70.5
              6.3% ‐12.72% ‐6.50% 5.00% ‐20.69% 13.90% ‐27.04% 8.93% ‐23.10% 8.93% ‐9.11% 26.85% 13.92%
12 4.6
               26.8
              5.4% ‐11.37% ‐5.25% 4.38% ‐14.45% 8.04% ‐20.84% 6.01% ‐21.60% 6.01% ‐4.86% 9.04% 3.17%
13 4.5
               27.2
              5.4% ‐10.47% ‐4.42% 4.89% ‐13.43% 8.58% ‐19.71% 6.61% ‐20.67% 6.61% ‐4.07% 9.88% 4.00%
14 4.5
               27.4
              5.4% ‐10.36% ‐4.36% 4.69% ‐13.20% 8.39% ‐19.41% 6.48% ‐20.68% 6.48% ‐4.03% 9.89% 4.02%
15 4.4
               30.1
              5.5% ‐9.36% ‐4.11% 3.94% ‐12.42% 7.87% ‐17.88% 5.81% ‐18.75% 5.81% ‐4.24% 10.87% 4.78%
16 4.4
               31.6
              5.6% ‐8.85% ‐3.99% 3.49% ‐12.01% 7.54% ‐17.07% 5.42% ‐17.78% 5.42% ‐4.37% 11.35% 5.15%
17 4.3
               33.8
              5.7% ‐7.92% ‐3.63% 3.16% ‐11.32% 7.41% ‐15.77% 5.16% ‐15.86% 5.16% ‐4.37% 12.35% 5.97%
18 4.3
               34.4
              5.7% ‐7.96% ‐3.86% 2.69% ‐11.42% 6.98% ‐15.72% 4.69% ‐15.87% 4.69% ‐4.72% 12.26% 5.82%
19 4.3
               30.9
              5.5% ‐10.08% ‐5.11% 2.02% ‐12.80% 5.92% ‐18.13% 3.95% ‐20.60% 3.95% ‐5.43% 9.66% 3.56%
20 4.3
               37.8
              5.9% ‐5.92% ‐2.67% 3.33% ‐10.09% 7.99% ‐13.41% 5.39% ‐11.35% 5.39% ‐4.04% 14.75% 7.99%
     1Y    2Y   3Y   4Y   5Y   6Y   7Y  8Y  9Y  10Y
Позиціонування портфеля на кривій доходності: 1) Власна 1; 2) Власна 2; 3) Exreme Bullet, 2Y; 4) Exreme Bullet, 3Y; 5) Extreme Bullet, 4Y; 6) Extreme Bullet, 5Y; 7) Extreme Bullet, 6Y; 8) Extreme Bullet, 7Y; 9) Extreme Bullet, 8Y; 10) Extreme Bullet, 9Y
11) Extreme Bullet, 10Y; 12) Bullet; 13) Bulleted; 14) Bulleted; 15) Ladder; 16) Barbelled; 17) Barbelled; 18) Barbell; 19) Extreme Barbell; 20) Extreme Barbell

Case #4. What was the best recent year for Ukrainian bonds? Year 2019! 52
Прогнозний портфель на 1 Бер 2020 (T1) у USD
Дюрація‐‐‐> ~1 рік
             ~2 роки
         ~3 роки
         ~4 роки
         ~5 років
        ~6 років
        ~7 років
        ~8 років
        ~9 років
        ~10+ років

ПОРТФЕЛЬ
UKR 2022‐12‐
14 UAH
11.50%
222145
UKR 2023‐11‐
22 UAH
11.67%
206460
UKR 2024‐12‐
11 UAH 9.50%
188593
UKR 2025‐12‐
24 UAH 6.00%
192686
UKR 2026‐12‐
23 UAH 6.00%
196745
UKR 2027‐12‐
08 UAH 9.70%
199798
UKR 2028‐12‐
06 UAH 9.70%
199814
UKR 2029‐11‐
28 UAH 6.00%
196380
UKR 2030‐12‐
11 UAH 6.00%
196448
UKR 2031‐12‐
10 UAH 9.99%
196521
             x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10

Відхилення від оціночної вартості на T0 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
(+) Амортизація премії (дисконту) ‐1.4% 11.5% 10.9% ‐1.3% ‐3.7% ‐4.7% ‐4.0% ‐4.5% ‐3.7% ‐4.2% ‐5.6%
(+) Роллдаун 2.6% 6.5% 4.8% 1.5% 0.4% 0.5% 1.8% 2.2% 2.5% 3.0% 3.4%
(+) Зміна ціни за незмінної кривої дох‐ті 1.2% 18.0% 15.7% 0.2% ‐3.2% ‐4.2% ‐2.2% ‐2.4% ‐1.2% ‐1.3% ‐2.3%
Зміна рівня кривої доходності 16.5% 14.2% 13.8% 13.4% 14.9% 15.8% 15.9% 16.7% 19.4% 20.5% 19.4%
Зміна нахилу ‐62.2% ‐66.6% ‐61.9% ‐58.0% ‐61.0% ‐61.4% ‐59.7% ‐60.5% ‐65.3% ‐66.2% ‐63.0%
Зміна вигину 66.0% 81.9% 77.7% 72.3% 73.1% 69.1% 64.2% 61.2% 59.1% 55.6% 53.8%
(+) Зміна форми кривої доходності 20.3% 29.4% 29.6% 27.8% 27.1% 23.6% 20.4% 17.5% 13.2% 9.9% 10.2%
(+) Зміна індивідуального cпреду ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
Зміцнення (девальвація) ₴ до $ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
Зміцнення (девальвація) $ до € ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
(+) Зміна валютного курсу ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
Зміна вартості облігацій на 1 Бер 2020 14.1% 40.1% 38.3% 21.5% 16.8% 12.1% 11.0% 7.8% 3.9% 0.4% 0.2%
Отримані купони 8.9% ‐ ‐ 12.4% 12.3% 12.2% 11.6% 11.2% 8.1% 7.9% 10.3%
Накопичені купони 1.5% ‐ ‐ 2.4% 1.3% 1.3% 2.3% 2.2% 1.7% 1.4% 1.8%
(+) Купонний доход з урах. валютного курс 10.4% ‐ ‐ 14.9% 13.6% 13.5% 13.8% 13.4% 9.8% 9.3% 12.2%
(+) Прибуток від реінвестування 0.2% ‐ ‐ 0.3% 0.4% 0.4% 0.3% 0.3% 0.2% 0.2% 0.2%
Зміна варт. портфеля до комісійних витрат 32.1% 40.1% 38.3% 36.6% 30.8% 26.0% 25.1% 21.4% 13.9% 9.8% 12.6%
Торгові комісії на вході, 1 Січ 2019 ‐0.5%
Торгові комісії на виході, 1 Бер 2020 ‐0.5%
Active Management Fee, 1 Бер 2020 ‐
(‐) Комісійні ‐1.0%
Зміна вартості портфеля після комісійних 31.1%
∑(+): Доходність (HPR) до коміс., річних 27.00%
∑(+): Доходність (HPR) після коміс., річних 26.18%
Довідково: YTM на вході 19.1% 18.0% 16.5% 14.8% 13.7% 13.3% 12.5% 11.2% 10.5% 10.8%
Investment outcome:
The year 2019 was an exceptional year for Ukrainian bonds. Consider an example of a UAH OVDP
ladder structure that enjoyed (1) rebounding from the «Військовий стан»‐driven sharp drawdown in
late 2018, (2) further decline in interest rates and (3) UAH appreciation

Case #5. How did Ukrainian bonds respond to Covid‐19 outbreak? 53
Investment outcome:
• Minus 21% in a matter of weeks. We do not show the
annualized numbers as they would imply an undue
extrapolation (the market rebounded quickly)
• This illustrates how risky high‐yield bonds are
Прогнозний портфель на 25 Бер 2020 (T1) у UAH
Дюрація‐‐‐> ~1 рік
             ~2 роки
         ~3 роки
         ~4 роки
         ~5 років
        ~6 років
        ~7 років
        ~8 років
        ~9 років
        ~10+ років

ПОРТФЕЛЬ
UKR 2022‐12‐
14 UAH
11.50%
222145
UKR 2023‐11‐
22 UAH
11.67%
206460
UKR 2024‐12‐
11 UAH 9.50%
188593
UKR 2025‐12‐
24 UAH 6.00%
192686
UKR 2026‐12‐
23 UAH 6.00%
196745
UKR 2027‐12‐
08 UAH 9.70%
199798
UKR 2028‐12‐
06 UAH 9.70%
199814
UKR 2029‐11‐
28 UAH 6.00%
196380
UKR 2030‐12‐
11 UAH 6.00%
196448
UKR 2031‐12‐
10 UAH 9.99%
196521
             x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10
                x  10

Відхилення від оціночної вартості на T0 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
(+) Амортизація премії (дисконту) 10.0% 10.2% 10.2% 10.2% 10.2% 10.2% 10.1% 10.0% 9.9% 9.7% 9.7%
(+) Роллдаун ‐8.1% ‐8.1% ‐8.2% ‐8.2% ‐8.2% ‐8.2% ‐8.2% ‐8.2% ‐8.1% ‐8.0% ‐7.9%
(+) Зміна ціни за незмінної кривої дох‐ті 1.9% 2.0% 2.0% 2.0% 2.0% 2.0% 1.9% 1.9% 1.8% 1.7% 1.7%
Зміна рівня кривої доходності ‐29.4% ‐14.8% ‐17.1% ‐22.0% ‐28.1% ‐31.7% ‐30.9% ‐33.1% ‐39.3% ‐41.4% ‐37.9%
Зміна нахилу ‐27.6% ‐25.0% ‐25.9% ‐28.9% ‐31.4% ‐30.8% ‐28.3% ‐27.5% ‐27.4% ‐26.3% ‐25.2%
Зміна вигину 33.7% 13.0% 18.3% 26.1% 34.8% 38.8% 36.7% 38.6% 45.3% 46.5% 41.8%
(+) Зміна форми кривої доходності ‐23.3% ‐26.8% ‐24.8% ‐24.9% ‐24.8% ‐23.7% ‐22.5% ‐21.9% ‐21.4% ‐21.2% ‐21.3%
(+) Зміна індивідуального cпреду ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
(+) Зміна валютного курсу ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
Зміна вартості облігацій на 25 Бер 2020 ‐21.4% ‐24.8% ‐22.7% ‐22.9% ‐22.8% ‐21.7% ‐20.6% ‐20.1% ‐19.6% ‐19.4% ‐19.6%
Отримані купони ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
Накопичені купони ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
(+) Купонний доход з урах. валютного курс ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
(+) Прибуток від реінвестування ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
Зміна варт. портфеля до комісійних витрат ‐21.4% ‐24.8% ‐22.7% ‐22.9% ‐22.8% ‐21.7% ‐20.6% ‐20.1% ‐19.6% ‐19.4% ‐19.6%

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