NN Investment Partners provide an in-depth look at the use of convertible bonds in the asset allocation process, from December 2015.

1. MindScope
December 2015For Professional Use Only
www.nnip.com
In-depth insights on important issues affecting the global economy and financial markets
NN Investment Partners explores the use of convertible bonds in the asset allocation process.
Convertible bond allocations in a
low-yielding investment world

2. MindScope
2
December 2015
Convertible bond allocations in a
low-yielding investment world
Convertible bonds occupy a unique niche in the breadth of asset
classes available to institutional investors in the execution of
Strategic or Tactical Asset Allocation (SAA or TAA) strategies.
Based on the premise that investors’ decisions for asset allocation
are primarily based on the search for optimal risk-adjusted
returns, we use the Capital Asset Pricing Model (CAPM) frame-
work to assess returns. Other allocation considerations include
liquidity, duration and alternate regulatory measures of risk, such
as Solvency Capital Requirements (SCRs) in the case of insurers.
Introduction
This Mindscope examines the benefits of convertible bonds in the
asset allocation process.
Investors have access to a wide range of asset classes, each with
specific benefits and drawbacks, in formulating their investment
strategies. In our analysis, we will reduce this universe to the most
liquid and relevant components, for which we have fair and relia-
ble historic measurements. We will then assess the historic contri-
butions of the selected asset classes and measure the relative
benefits of adding convertibles to the asset-allocation toolkit.
This analysis will allow us to draw initial conclusions with regard
to the various styles of convertible bond management and select
the style that leads to the best risk-adjusted contribution.
Our current low-yielding world has created a completely new
environment. The upside of all fixed income investments is more
limited than in the past, and decisions concerning equity alloca-
tions deserve, at the very least, to be revisited. In this context,
convertible bonds are worth considering. They may be viewed as
a derivative instrument, and their future returns can be estimated
using the outcome of the stochastic diffusion of the yield curve,
credit markets and equity markets. We have designed a model
that tries to capture the essence of the drivers of returns for a
portfolio of global balanced convertibles, our preferred style
and universe. This Mindscope provides the results of our model
calculations, as well as the rationale for our assumptions.
The model itself will be briefly described as well.
The following topics are covered in this Mindscope:
• Assessment of historical observations of relative risk-adjusted
returns of convertible bonds
• Considerations relative to the potential consequences of the now
low-yielding environment: The case of Japan
• Analysis of the specific features and performance
drivers of convertibles, and design of a predictive
convertible simulation model
• Calibration of the simulation model, market anticipations and
tail equity risk considerations
• Outcome of the simulation and assessment of the
relative future benefits of convertible allocation
• Performance of convertible bonds in rising treasury yield
environment
• Consideration of alternate measurement of risk in
the Solvency II environment for insurers
Appendices 1 through 4 provide supplementary data documenting
and supporting the studies and analyses conducted in the prepa-
ration of the Mindscope.
Assessment of historical observations of relative
risk-adjusted returns of convertible bonds
Convertibles are designed to advance alongside equities in rising
markets, while being protected from the inevitable sharp declines
because the value of the underlying bond kicks in to provide a
“floor” value for convertible bonds, which keeps prices from falling
with equities past a certain level.
Empirical evidence shows that the convertible indices have out-
performed equity, high yield and investment grade bond indices
over long periods of time. The most widely used family of indices
for global convertibles is the Thomson Reuters Convertible Index
suite (formerly UBS Convertible Indices). These indices measure
convertible performance since 1993. Figure 1 illustrates the
relative performances of global equities and global bonds,
both of which are surpassed by global convertibles.
Figure 1: Global asset classes total return (1993 = 100)
0
100
200
300
400
500
94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14
Convertible Bonds Global Equities Global Bonds Global
Source: Bloomberg, Thomson Reuters Global Focus Index, MSCI World Index,
J.P. Morgan Aggregate Bond Index (1993-2015)
For more insight and longer history, we turn to the US market.
The most widely used data to highlight this phenomenon are returns
on each asset class from 1973 through 2015. As shown in Figure 2,
convertibles in the US market have consistently outperformed high
yield and investment grade bonds over the last 40 years.
From 1973 to 1999, equities drove growth in asset prices, far ahead
of all fixed income. Still, convertibles managed to follow closely,
capturing 75% of equity performance.

3. December 2015
3
The story was very different in the period from 1999 through to
2015, when equity markets suffered through two severe down-
turns and recoveries, in what was overall a much more volatile
environment. Fixed income actually performed very well during
this time span, driven by the declines in corporate credit spreads
and interest rates and by a contained default rate. Convertibles,
whose bond element enabled them to benefit from these factors,
significantly outperformed equities as well.
Figure 2: US asset classes total return (1972 = 100)
72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12 14
0
1.000
2.000
3.000
4.000
5.000
6.000
7.000
Convertibles S&P 500 IG Govt/Corp Bonds HY Bonds
Source: Bloomberg, BofA Merrill Lynch Indices (1972-2014)
In addition to their ability to piggyback on the bull markets of both
asset classes during different periods, global convertibles have
shown a volatility that has on average been about 45% of that of
equities.
Recent analysis showed that some of the drivers of this relative
performance of convertible bonds are tied to the credit character-
istics of underlying issuers and the returns of underlying stocks
-- specifically, a fair compensation for credit risk associated with
a lower historical default rate of issuers displaying a moderate
leverage, as well as a better performance of underlying equities
and a steady flow of superior performance from newly issued
convertibles.
While we cannot assume that these factors will be repeated in the
future, other inherent elements to the convertible asset class may
support the case for solid future relative risk-adjusted returns in the
low-yielding environment. Introducing convertibles into the asset
allocation process adds the risk-reward characteristics of the asset
class on one end. It also adds convertibles’ diversification benefits
and the benefits of the asymmetrical nature of their returns.
Figure 3 plots the risk adjusted returns of the various asset
classes considered over the 2005-2015 period.
As the market went through a historic decline in rates over this
period, all bond asset classes delivered solid risk-adjusted returns,
and were more efficient than convertible bonds and equities.
Convertibles, on the other hand, delivered returns comparable to
equities with half the volatility.
We observe that despite having been less efficient than bond
asset classes over the period, convertible bonds have contributed
to the diversification of portfolios, as illustrated by the large num-
ber of portfolios including convertible bond allocations on, or
close to, the efficient frontier. This is a consequence of the unique
observed correlation characteristics of convertible bonds with the
other asset classes considered as listed on Appendix 4:
• Very high correlation to less efficient equities,
• Negligible or negative correlation to sovereign bonds and IG
• Medium correlation to high yield (c. 60%)
Given the prevailing low-yield environment, there is little doubt
that the returns of all bond asset classes will be significantly lower
in the coming five years.
Considerations relative to the potential consequences of
the now low-yielding environment: The case of Japan
Going forward, the general consensus is that the global macro
economy will be characterized by low growth, coupled with low
interest rates and compressed credit spreads. The question then
arises as to how convertibles are likely to act compared with other
asset classes in such an environment.
The global investment community is now facing the issue of
delivering returns in this low-yield environment (or even negatively
yielding, as is currently the case with some US$4 trillion of govern-
ment securities).
The situation is very similar to the one experienced in the past 10
years by Japanese institutional investors with constraints to invest
in JPY-denominated assets. Figure 4 shows that as expected, JPY
bond market returns were mediocre while Japanese equity returns
had a wide dispersion. Figure 5 plots the relative performances of
three-year investments in JPY asset classes – Japanese equities
(TOPIX), government bonds (JGBs) and convertibles.
Figure 3: Efficient Frontier Analysis (2005-2015)
AnnualizedReturns
Average 52W ann. Volatility
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
0% 5% 10% 15% 20%
Global
Sovereign
Global
Aggregate
Global High Yield
Global Equities
Global
Balanced
Convertibles
Source : Bloomberg, NN IP Analysis

4. MindScope
4
December 2015
Figure 4: JPY asset classes total return (2001-2014)
75
125
175
225
03 04 05 06 07 08 09 10 11 12 13 14
Thomson Reuters Japan Focus CB Index (JPY) TOPIX Total Return (JPY)
JGB Total Return Index (JPY)
Source: Bloomberg, NN IP
Figure 5: Annualized returns of three-year investments
in JPY asset classes (2002-2011)
-30,0%
-20,0%
-10,0%
0,0%
10,0%
20,0%
30,0%
40,0%
03 04 05 06 07 08 09 10 11
3YAnnualizedReturn
Investment Date with 3Y holding period
Thomson Reuters Japan Focus CB Index (JPY) TOPIX Total Return (JPY)
JGB Total Return Index (JPY)
Source: Bloomberg, NN IP
Table 1 summarizes the outcome in terms of annualized total
return resulting from investment decisions in the various
available asset classes: Japanese equities, government bonds
and convertibles.
Overall, Japanese convertibles delivered the best returns. They
were the best available choice of investment in 28% of the 108
cases and ranked second in 72% of the cases. In no cases were
convertibles the worst choice. This outcome is statistically
relevant in demonstrating the quality and stability of relative
convertible returns in a context where bonds have low carry
and where equity returns are volatile and uncertain.
Table 1: Observations of investments in JPY asset classes
with three-year horizon
Topix JPN CBs 10Y JGB
Average Annualized 3Y return 2.3% 5.6% 2.1%
Average 36M Volatility 18.5% 8.6% 2.7%
# Obs. % Obs.
CB Best Asset Class 30 28%
CB Second-Best Asset Class 78 72%
CB Worst Asset Class 0 0%
Total # 3Y Investment Observations 108
Source: Bloomberg, NN IP (2002-2011)
Based on these observations, the case for convertible bonds in
this context of low prevailing yields appears as strong as – and
even more robust than – in our previous global analysis.
This validates the traditional wisdom: “There is always a reason
for someone to invest in convertible bonds”, whether it be a bond
investor seeking higher returns or an equity investor seeking
protection.
Our case is that “We are all Japanese now”. We are a little older,
we expect less growth, both in demographic and in economic
terms, and we are very concerned with the returns of our financial
assets in this low-yielding world. As a result, we may want to look
a little further into convertibles as one of the solutions to our issue.
Analysis of the specific features and performance drivers
of convertibles, and design of a predictive convertible
simulation model
Convertible bond return prediction model
Focus convertible strategies concentrate the investments in
balanced convertibles, the modified duration of this Focus uni-
verse is about 3.8 and its equity sensitivity changes over time, but
remains in a 30%-50% bracket most of the time. “Busted” and
equity-like convertibles are excluded as rises or declines of their
underlying equities push them in these categories, and the market
gets regenerated with newly issued convertibles that on average
have an equity sensitivity of 40%.
The credit profile of the convertible market comprises roughly
one-third investment grade and two-thirds high yield credits.
The average credit spread on the convertible universe is compa-
rable to the weighted average the investment grade universe
and high yield universe.
We measured the aggregate time value of the convertible bond
universe as the weighted average across the universe of the mini-
mum of distance to investment value and distance to equity parity
of all components. This option value averages over time 10% for
an average volatility level of 30 for the convertible universe.

5. December 2015
5
Our predictive model is based on the Arbitrage Pricing Theory
(APT) and measures the variations in price of all the instruments
that would constitute a perfect hypothetical hedge for the con-
vertibles underlying our convertible index.
The risks of holding a convertible bond would in theory be per-
fectly hedged by simultaneously selling a corporate bond issued
by the same issuer with the same maturity, and selling the call
option on the underlying stock with the same strike and maturity
as the conversion price and maturity of the convertible.
Our simulation model will process a multivariate stochastic
diffusion of the Government bond index (BBG Global Sovereign
Developed Index), the investment bond index (BBG Global Corp
Index), the High Yield Bond index (BBG Global High Yield Index),
the underlying equities of a virtual Global Equity index and the
underlying equities of a virtual Focus Convertible bond index.
Our virtual Convertible index follows all the rules of the Focus
Index and will retain the same stable characteristics (duration,
gamma, aggregate time value and composition of one-third
investment grade and two-thirds HY).
The diffusion is done with weekly steps, and tests for exclusion
of non-balanced convertibles are performed on a weekly basis.
We assume that excluded convertibles are replaced with new
issues with our average equity sensitivity of 40%, and that the
number of components of the convertible index remains constant.
The delta of each component is recalculated on a weekly basis,
and convertibles with less than 20% equity sensitivity are
excluded as well as convertibles with more than 80% equity
sensitivity.
We claim that the information contained in the price diffusion of
all these variables are sufficient to assess the change in value of
each index component, and recalculate the index every week.
• The price change the corporate bond can be estimated by the
duration-adjusted weighted price changes of the investment
grade corporate bond index and high yield index.
• The change in time value of our option can be estimated as the
time-value change of our index, which follows the rule of being
proportional to the square root of the duration.
• The change in value of our option resulting from the price
change in the underlying stock of the convertible can be
estimated with the current equity sensitivity of the convertible
bond, and the gamma that we assume constant over time and
across convertibles.
This way of splitting the sources of cost and returns of convertible
investments highlights the essence of the value of convertible
investments: by accepting a credit risk, the investor is compen-
sated by the accretion of the credit spread (the returns of the
above mentioned corporate bond), which provides the currency for
paying the cost of the option (the above-mentioned time value of
the option). The option paid for by this accepted credit risk pro-
vides the promise of equity upside participation. As it turns out,
convertibles have on average a duration that is long by option
market standards, and the time value cost is less than the credit
spread compensation for credit risk, when measured on average
on the convertible universe. Of course it is crucial that the investor
carefully analyse the credit of the companies he selects.
Asset Allocation Universe
Institutional investors have diversified their set of investable
assets as the result of both a globalisation of financial markets
and a search for yield in the declining yield environment, as
evidenced by the pre-euro era and post-2010 asset maps of
Dutch Institutional Investors in Figure 6.
In the Netherlands, convertibles have so far not really been
considered as an asset diversification option, whereas they
may represent a fair allocation of institutional portfolios in other
countries such as France.
Figure 6: Asset allocation Dutch institutional investors
Investment
Grade
BelowInvestment
Grade
Investment
Grade
BelowInvestment
Grade
Government Bonds
GE, NE Private Placements
Corporate Loans
Government Bonds
FR, IT, SP, POR
Securities
Liquidity
Loans Securities
Liquidity
Loans
CreditQuality
Corporate Bonds
Project Finance
CreditQuality
Euro Credit
EMD HC
AAA/AA
ABS
Core Euro
Government Bonds
EMD LC
ABS
High Yield
Senior Loans
Euro Government
Bonds Periphery
Covered bonds
Government
related Loans
Infrastructure
Loans
SME Loans
Corporate Loans
Export Credit
Agency Loans
CRE Loans
Dutch
Mortgages
Emerging
loans
Classes to 1999 Classes since 2010
* The size of the circles reflect the potential for investors
Source: NN IP (March 2015)

6. MindScope
6
December 2015
For the purpose of our analysis, we will limit ourselves to five liquid
asset classes, and assume that investors will make allocation
decisions across these five asset classes: global equities, high
yield bonds, investment grade bonds, sovereign bonds and
convertible bonds.
This is obviously limited as many more investment choices are
available, as it was illustrated in the second asset map in Table 2.
Still, this selection includes the most liquid assets, and accounts
for US$80 trillion, which makes it relevant.
Calibration of the simulation model, market anticipations
and tail equity risk considerations
Calibration
The most complex part is the calibration of our diffusion model.
We assume that volatilities and correlations are stable over time.
Appendix 1 shows our calibrated volatility and correlation matrix.
The calibration process is designed to make sure our five asset classes
are correlated in a way that is consistent with historical obser­vations.
The only way to achieve this was to design the underlying universe
of our equity index distinct from a large part from the underlying
universe of our convertible index. This is consistent with reality.
Still, we kept the same risk/returns characteristics for the compo-
nents even though the convertible underlying universe has always
displayed higher return and volatility in the past.
Introducing this feature would have further enhanced the relative
performance of our simulated convertible index. But in the absence
of evidence supporting the case that these characteristics would
stand in the future, we opted for a more conservative route.
Simulation Scenarios
As of 30 January 2015, the “yield to worst” and 52-week volatility
measures of our bond indices were as follows:
• Bloomberg Global Sovereign Developed Bonds:
0.9% and 3.5%
• Bloomberg Global Investment Grade Bonds:
2.25% and 4%
• Bloomberg Global High Yield: 5.5% and 6%.
From there we considered various scenario and “guesstimated”
the expected five-year annualized returns of these indices under
these scenarios. We assumed that volatilities would remain con-
stant. Figure 10 shows our expected return estimates with their
economic rationale.
We then looked at the full history of the MSCI World Index. Graphs
plotting the distribution and cumulative distribution of five-year
rolling periods can be seen in Appendix 2. We discarded both tails
of the distribution, and defined our distribution of scenarios for
equity returns. The average expected equity return of our scenario
distribution stands at 6%, which is consistent with current market
estimates. We assumed that the distribution of equity returns over
five years would be independent from our various yield scenarios,
which leads to 16 different and equally likely simulations.
From current equity valuation levels, we considered the upper tail
of the historical equity return distribution as highly unlikely, but
added four equity tail risk scenarios consistent with the recorded
history of the MSCI World, and associated these equity scenarios
to a deflationary hypothesis for yields. Altogether, this leads us to
20 simulations for our model.
Outcome of the simulation and assessment of the relative
future benefits of convertible allocation
We have defined our four basic asset classes, and the resulting
model-calculated convertible asset class defined by our 21
stochastic variables (government bond returns, investment
grade returns, high yield returns, equity index components,
and convertible index underlying components).
We ran our “Monte Carlo” simulations of these asset classes with a
multivariate normal diffusion satisfying our calibrated covariance
matrix. These simulations involve making a number of projections of
the stochastic variables following our selected statistic distribution
and averaging the results in order to assess the expected result.
We applied these simulations to periodically rebalanced compos-
ite portfolios representing all combinations of allocations in
our five asset classes with a five-year investment horizon.
We performed these simulations with the data for expected
returns and volatilities as defined in our 20 economic scenarios.
Table 2: Expected market return scenarios for convertible model
Monte-Carlo Simulation Hypothesis Yield Scenario 1 Yield Scenario 2 Yield Scenario 3 Yield Scenario 4 Equity Tail risk
Economic Scenario Deflation
Yield Decline
Low defaults
Continuation
Flat Yield
Low defaults
Continuation
Mild yield rise
Moderate Defaults
Recovery
Yield rise
Moderate defaults
Deflation
Yield decline
Moderate Defaults
Volatility Ann. Ret. Ann. Ret. Ann. Ret. Ann. Ret. Ann. Ret.
Global Developed Government Bond 3.5% 1.50% 0.90% 0.50% 0.00% 1.50%
Global Investment Grade Bonds 4.0% 3.00% 2.25% 1.50% 1.00% 2.00%
Global High Yield 6.0% 6.50% 5.50% 4.25% 3.50% 4.00%
Equity Scenario 1 12.0% 0.00% 0.00% 0.00% 0.00% 0.00%
Equity Scenario 2 12.0% 4.00% 4.00% 4.00% 4.00% -2.00%
Equity Scenario 3 12.0% 8.00% 8.00% 8.00% 8.00% -4.00%
Equity Scenario 4 12.0% 12.00% 12.00% 12.00% 12.00% -6.00%
Source: NN IP (March 2015)

7. December 2015
7
We will first analyse the results of our 16 basic scenarios, and then
consider our tail equity risk scenarios described in the previous
section. Figure 7 plots the average risk-return for each composite
portfolio, assuming all 16 scenarios are equally likely to occur.
Figure 7: Simulation output: average across 16 market
scenarios
y = 1.0495x + 0.0025
0%
1%
2%
3%
4%
5%
6%
7%
8%
0% 2% 4% 6% 8% 10% 12%
Expected3YReturn(Annualized)
Volatility
Portfolios withoout CBs Portfolios with CBs Efficiency line
Govt Corp HY
Equities CBs
CBs Equities Corp Govt
Portfolio without CBs Portfolios with CBs Efficiency line
Source: NN IP (Feb 2015)
Given the lower expectations on bond returns, equities have the
highest expected return, but owing to their higher risk (volatility),
high yield and convertible bonds compete close to the efficient
frontier. We observe that the efficient frontier is highly populated
with portfolios that contain a convertible bond allocation.
We conclude that it appears wise to consider allocating to
convertible bonds in search for the most efficient risk-return.
Of course, in the scenarios where equities perform poorly, con-
vertibles are further away from the efficient frontier. Still, in most
cases, they deliver absolute returns that compare favourably to
sovereign and investment grade bonds. Even in these cases, owing
to the low to marginally negative correlation of convertible bonds
to fixed income asset classes, the efficient frontier is heavily pop-
ulated with portfolios containing a convertible bond allocation.
Appendix 3 shows the results for each scenario, with average
expected returns for each yield scenario, as well as the outcomes
of our tail equity risk scenarios. Only in the worst of these equity
tail risk scenarios – in which equities returned a -6% annualized
return over five years – did convertible bonds’ expected annual-
ized return turn marginally negative.
We observe that even in these extreme cases convertible contrib-
ute positively to the process of portfolio diversification, with a
material number of portfolios containing convertibles on the
efficient frontier.
The results delivered by our model are consistent with historical
behaviours of convertibles in severe equity downturns when
measured over a five-year period.
Performance of convertible bonds in rising Treasury yield
environment
As bond investments, convertibles might be expected to be
negatively impacted by a rise in yields. Empirical evidence shows
a negative correlation between Treasury yields and convertibles.
In fact, we observe the exact opposite: periods of rising Treasury
yields have consistently been periods of very strong equity return
over the past 30 years. Figure 8 plots the eight periods since 1983
during which Treasury yields attempted to break their declining
trend. All these periods, which together accounted for 48 quar-
ters, demonstrated solid equity returns. The average annualized
return of equities over these chained 48 quarters has been 18%.
As a result convertibles have performed very strongly as well.
During the six periods, or 33 quarters, of rising Treasury yields
that took place within the recorded history of the Thomson Reuter
Global Convertible Index, the annualized return of this convertible
index has been 20%.
Figure 8: Asset class behaviour comparison in a rising Treasury yield environment
Period 1 : Dec'86 - Mar'89
9 Quarters
+205Bps
Period 2 : Sep'93 - Dec'94
5 Quarters
+244Bps
Period 5 : Jun'03 - Jun'06
12 Quarters
+166Bps
Period 8: Sep'12-Dec'13
5 Quarters +139Bps
0%
2%
4%
6%
8%
10%
12%
14%
16%
-20%
-10%
0%
10%
20%
30%
40%
50%
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
10YTreasuryrate
AnnualisedReturn
MSCI World (NDDLWI) (LHS) CB (UBS Global Hedged USD) (LHS) Treasury 10Y (MLT1US10) (LHS) US IG (LHS) 10Y Treasury Rate (RHS)
Period 4 : Sep'98 - Dec'99
5 Quarters
+202Bps
MSCI World (NDDLWI) (LHS) CB (UBS Global Hedged USD) (LHS) Treasury 10Y (MLT1US10) (LHS) US IG (LHS) 10Y Treasury Rate (RHS)
Source: Bloomberg, NN IP (1984-2014)

8. MindScope
8
December 2015
This is another comfort for allocation to convertibles in this low-
yield environment: the ability to capture solid equity returns in
the event that traditional bond markets strongly underperform
because of rising yields.
But rising yields are not our current base-case scenario. Still,
from these levels we cannot discard this option. Figure 9 puts our
current situation in perspective when compared to the Japanese
Yield experience. Whatever the forthcoming outcome, we
conclude that convertibles are worth considering in an asset
allocation process.
Figure 9: Japanese 10-year government bond yield vs.
US Treasury 10-year yield (time scaled to fit)
US Treasury Jun '07
US Treasury Jun'09
US Treasury Jun '11
US Treasury Nov 2014
0%
1%
2%
3%
4%
5%
6%
'92
'93
'93
'94
'95
'95
'96
'96
'97
'97
'98
'99
'99
'00
'00
'01
'02
'02
'03
'03
'04
'04
'05
'06
'06
'07
'07
'08
'09
'09
'10
'10
'11
'11
'12
'13
'13
'14
'14
FED withdrawing QE &
Market Normalisation
Global Japanisation
US Treasury 10-Year Yields (Time scaled to fit) JPB 10-Year Yields (Historic)
Source: Bloomberg, NN IP (1992-2014)
Consideration of alternate measurement of risk in the
Solvency II environment for insurers
Our recent study of the treatment of convertibles in the Solvency
II framework showed that convertible bonds, despite being
stressed sequentially on rates, credit and equity under solvency
stress tests, still provide a solvency-friendly exposure to equities.
A typical portfolio of balanced convertibles with moderate
durations with 40% to 50% equity sensitivity suffers a SCR
Market penalty of 16% to 20% at the current level of equity
stress of 46.5%.
Two of the conclusions of our Solvency II study are as follows:
• Any composite portfolio with a content of 40% to 50% equities
will by definition have a SCR Market portfolio of at least:
SCR Market = (40% to 50%) X 46.5% = 18.6% to 23.25%.
The SCR Market of such a portfolio will be further increased
by the SCR contributions of the balance of 50% to 60% of
other investments contained in such a portfolio.
Hence, convertible bonds are a solvency-friendly way to gain
exposure to equity returns, not to mention the benefits of the
asymmetry of these returns with the promise of 60%-70%
participation to equity returns in rising markets. They also
offer a form of protection in declining equity markets as outlined
both by historical observations and the results of our model
stated earlier in this Mindscope.
• Historical observations and the results of our analysis under
various scenarios show that convertible bonds and high yield
compete as the most efficient asset classes, i.e. closest to the
efficient frontier. We measured the SCR of the Bloomberg
Global High Yield index that aggregates US$1.7 trillion of High
Yield bonds at 24%, assuming it is fully hedged in currency.
This figure is higher than our estimate of the SCR of a portfolio
of balanced convertibles. Our conclusion is that with a lower
SCR for comparable expected risk-adjusted returns, converti-
bles are more solvencyfriendly than high yield.
Solvency II defines a new measure of risk to be considered by
insurers as an alternate to volatility. We will plot the average
results of our simulations on the following chart and substitute
SCR Market for Volatility on the horizontal axis as a measure of
risk.
Except for sovereign bonds, all other asset classes are penalized
in this new framework, and are pushed to the right when compared
to our previous return/volatility chart, some more than others.
The outcome is that the most solvency-efficient asset classes are
sovereign bonds and convertible bonds, and to a lesser extent
investment grade bonds. Efficient portfolios have solid allocations
to both government bonds and convertible bonds as they are
uncorrelated.
Our conclusion is that SCR-constrained investors – a large part
of the insurers’ community – have new incentives to consider
convertibles as they deploy their asset investments. In many
countries, they already were active players in the segment,
but the asset class has been largely overlooked in others.
Under Solvency II, the case for convertible bonds is strengthened.
We expect further flows into the convertible segment on the back
of the actual implementation of Solvency II in 2016.
On the subject of Solvency II, and more generally insurers’
investment case for convertibles, other directions of analysis
could be considered.
Figure 10: SCR Market Risk approach: average across
16 market scenarios
Portfolios withoout CBs Portfolios with CBs Efficiency line
Govt Corp HY
Equities CBs
0%
1%
2%
3%
4%
5%
6%
7%
8%
0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Expected3YReturn(Annualized)
SCR Market
CBs HY Equities Corp Govt
Portfolio with CBs Portfolios without CBs Efficiency line
Source: NN IP (Feb 2015)

9. December 2015
9
One approach would be to allocate a cost of capital to this regula-
tory capital, and assess the contributions of the various portfolios
after this capital has been costed and volatility has been adjusted.
This is a much more complex exercise that may not be done on the
asset side of the equation without considering the liability side of it.
Another interesting direction to explore is that convertibles
provide access to the promised return of equities in a solven-
cy-capital-friendly way. And they do so with a non-zero duration
figure attached to the instrument as opposed to equities. Such
an assessment, while technically true, may require further investi-
gation in the insurance international and local regulations.
Conclusions
This Mindscope highlights the dual aspect of convertible bonds:
Convertible bonds are a defensive proxy for equities. Beyond their
three classical promises – equity-like expected returns with half
the expected volatility, unlimited equity upside with downside
protection, and convex asymmetrical returns linked to equities –
convertible bonds have a stable and competitive positioning in the
asset classes map.
• Convertible bonds compete with high yield, with similar
expected return/volatility characteristics. Both asset classes
rank highly in terms of expected efficiency, and they demon-
strate low correlation. As a result, they supplement each other
with diversification benefits. Composite allocations to both
asset classes reduce the risk and/or improve expected returns
of high yield investments. Investors who seek better yields
through high yield, but are concerned with the risk involved, may
increase the former and reduce the latter with a combined peri-
odically rebalanced exposure to both asset classes.
• Convertible bonds altogether are a unique and useful tool in the
asset allocator toolkit. In the low-yielding environment their rel-
ative return and diversification benefits are further enhanced
with regards to the lower expected returns of bonds and uncer-
tainty of equities.
There is more to convertibles than their traditional tactical
risk-on/risk-off use by either bond or equity investors. The value of
their asymmetrical returns accretes over time, and they should be
part of the strategic allocation arsenal of all institutional investors.
For more information about NN IP’s convertible bond
strategies, please contact Pierre Lepicard, Client Portfolio
Manager, at pierre.lepicard@nnip.com.

10. MindScope
10
December 2015
Appendices
Appendix 1. Model Calibrated Volatility/Correlation Matrix
Appendix 2. MSCI World Index returns compared with model hypothesis
Appendix 3. Simulation output scenarios
Appendix 4. Model Calibration and correlation considerations

11. December 2015
11
Appendix 1: Model calibrated volatility/
correlation matrix
Simulation Convertible Index Components
Simulation Equity Index Components CB1 CB2 CB3 CB4 CB5 CB6 CB7 CB8 CB9 CB10
Govt IG HY EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7 EQ8 EQ9 EQ10
Govt 4% 0.80 0.35 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10 -0.10
IG 0.80 4% 0.50 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20
HY 0.35 0.40 6% 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30
EQ1 -0.10 0.20 0.30 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ2 -0.10 0.20 0.30 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ3 -0.10 0.20 0.30 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ4 -0.10 0.20 0.30 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ5 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ6 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ7 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
EQ8 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
CB1 EQ9 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
CB2 EQ10 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
CB3 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33 0.33
CB4 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33 0.33
CB5 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33 0.33
CB6 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33 0.33
CB7 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33 0.33
CB8 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33 0.33
CB9 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18% 0.33
CB10 -0.10 0.20 0.30 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 18%
Source: NN IP (Feb 2015)

12. MindScope
12
December 2015
Appendix 2: MSCI World Index returns
compared with model hypothesis
Historic MSCI World five-year total return distribution
(1970-2015) vs. model hypothesis
0%
5%
10%
15%
20%
25%
30%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Historic Global Equity 5Y Annualized Distribution
Equity scenario Distribution
0%
20%
40%
60%
80%
100%
120%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Cumilative Historic Global Equity 5Y Annualized Distribution
Cumulative Equity scenario Distribution
0%
5%
10%
15%
20%
25%
30%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Historic Global Equity 5Y Annualized Distribution
Tail Equity Risk Scenarios Distribution
Historic Global Equity 5Y Annualized Distribution
Equity Scenario Distribution
Source: MSCI, Bloomberg, NN IP
Historic MSCI World five-year total return cumulative
distribution (1970-2015) vs. model hypothesis
0%
5%
10%
15%
20%
25%
30%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Historic Global Equity 5Y Annualized Distribution
Equity scenario Distribution
0%
20%
40%
60%
80%
100%
120%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Cumilative Historic Global Equity 5Y Annualized Distribution
Cumulative Equity scenario Distribution
0%
5%
10%
15%
20%
25%
30%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Historic Global Equity 5Y Annualized Distribution
Tail Equity Risk Scenarios Distribution
Cumilative Historic Global Equity 5Y Annualized Distribution
Cumulative Equity Scenario Distribution
Source: Bloomberg, NN IP
Historic MSCI World five-year total return distribution
(1970-2015) vs. equity tail risk scenarios
0%
20%
40%
60%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Cumilative Historic Global Equity 5Y Annualized Distribution
Cumulative Equity scenario Distribution
0%
5%
10%
15%
20%
25%
30%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
Historic Global Equity 5Y Annualized Distribution
Tail Equity Risk Scenarios Distribution
Tail Equity Risk Scenarios Distribution
Historic Global Equity 5Y Annualized Distribution
Source: NN IP

13. December 2015
13
Appendix 3: Simulation output scenarios
Simulation output: Yield Scenario 1
y = 1.35x + 0.0025
0%
2%
4%
6%
8%
10%
0% 2% 4% 6% 8% 10% 12%
y = 1.0768x + 0.0025
0%
1%
2%
3%
4%
5%
6%
7%
0% 2% 4% 6% 8% 10% 12%
y = 1.0973x + 0.0025
0%
1%
2%
3%
4%
5%
6%
7%
0% 2% 4% 6% 8% 10% 12%
y = 1.5307x + 0.0025
0%
2%
4%
6%
8%
10%
12%
14%
0% 2% 4% 6% 8% 10% 12%
y = 1.2305x + 0.0025
0%
2%
4%
6%
8%
0% 2% 4% 6% 8% 10% 12%AnnualizedTotalReturnAnnualizedTotalReturn
CBs
Equities
HY
Corp
Govt
Portfolio without CBs
Portfolios with CBs
Efficiency line
AnnualizedTotalReturnAnnualizedTotalReturnAnnualizedTotalReturn
Volatility Volatility
Volatility
Volatility
Volatility
Source: NN IP (Feb 2015)

14. MindScope
14
December 2015
Simulation output: Yield Scenario 2
0%
2%
4%
6%
8%
10%
12%
14%
0% 2% 4% 6% 8% 10% 12%
0%
1%
2%
3%
4%
5%
6%
0% 2% 4% 6% 8% 10% 12%
0%
1%
2%
3%
4%
5%
6%
0% 2% 4% 6% 8% 10% 12%
0%
2%
4%
6%
8%
10%
0% 2% 4% 6% 8% 10% 12%
0%
2%
4%
6%
8%
0% 2% 4% 6% 8% 10% 12%
AnnualizedTotalReturnAnnualizedTotalReturn
CBs
Equities
HY
Corp
Govt
Portfolio without CBs
Portfolios with CBs
Efficiency line
AnnualizedTotalReturnAnnualizedTotalReturnAnnualizedTotalReturn
Volatility Volatility
Volatility
Volatility
Volatility
y = 1.4172x + 0.0025 y = 1.1445x + 0.0025
y = 0.9289x + 0.0025 y = 0.8858x + 0.0025
y = 1.0537x + 0.0025
Source: NN IP (Feb 2015)

15. December 2015
15
Simulation output: Yield Scenario 3
0%
2%
4%
6%
8%
10%
12%
14%
0% 2% 4% 6% 8% 10% 12%
0%
1%
2%
3%
4%
5%
6%
0% 2% 4% 6% 8% 10% 12%
0%
1%
2%
3%
4%
5%
0% 2% 4% 6% 8% 10% 14%12%
0%
2%
4%
6%
8%
10%
0% 2% 4% 6% 8% 10% 12%
0%
2%
4%
6%
8%
0% 2% 4% 6% 8% 10% 12%
AnnualizedTotalReturnAnnualizedTotalReturn
CBs
Equities
HY
Corp
Govt
Portfolio without CBs
Portfolios with CBs
Efficiency line
AnnualizedTotalReturnAnnualizedTotalReturnAnnualizedTotalReturn
Volatility Volatility
Volatility
Volatility
Volatility
y = 1.0089x + 0.0025
y = 0.8005x + 0.0025
y = 0.7048x + 0.0025
y = 1.2397x + 0.0025
y = 0.9019x + 0.0025
Source: NN IP (Feb 2015)

16. MindScope
16
December 2015
Simulation output: Yield Scenario 4
0%
2%
4%
6%
8%
10%
12%
14%
0% 2% 4% 6% 8% 10% 12%
-1%
1%
0%
2%
3%
4%
5%
6%
0%
1%
2%
3%
4%
0% 2% 4% 6% 8% 10% 14%12%
0%
2%
4%
6%
8%
10%
0% 2% 4% 6% 8% 10% 12%
0% 2% 4% 6% 8% 10% 12%
0%
2%
4%
6%
8%
0% 2% 4% 6% 8% 10% 12%
AnnualizedTotalReturnAnnualizedTotalReturn
CBs
Equities
HY
Corp
Govt
Portfolio without CBs
Portfolios with CBs
Efficiency line
AnnualizedTotalReturnAnnualizedTotalReturnAnnualizedTotalReturn
Volatility Volatility
Volatility
Volatility
Volatility
y = 0.8398x + 0.0025
y = 0.5268x + 0.0025
y = 1.2386x + 0.0025
y = 0.7884x + 0.0025
y = 0.6817x + 0.0025
Source: NN IP (Feb 2015)

17. December 2015
17
Simulation output: equity tail risk analysis
0%
1%
2%
3%
4%
5%
0% 2% 4% 6% 8% 10% 12%
-4%
-2%
0%
2%
4%
6%
-6%
0%
-2%
-4%
2%
4%
6%
2% 4% 6% 8% 10% 12%
-2%
-1%
0%
1%
2%
3%
5%
0% 2% 4% 6% 8% 10% 12%
0% 2% 4% 6% 8% 10% 12%
-4%
0%
-2%
2%
4%
6%
0% 2% 4% 6% 8% 10% 12%
0%
4%
y = 0.7182x + 0.0025
y = 0.6834x + 0.0025
y = 0.7641x + 0.0025
y = 0.7107x + 0.0025
y = 0.7316x + 0.0025
AnnualizedTotalReturnAnnualizedTotalReturn
CBs
Equities
HY
Corp
Govt
Portfolio without CBs
Portfolios with CBs
Efficiency line
AnnualizedTotalReturnAnnualizedTotalReturnAnnualizedTotalReturn
Volatility Volatility
Volatility
Volatility
Volatility
Source: NN IP (Feb 2015)

18. MindScope
18
December 2015
Appendix 4: Model calibration and
correlation considerations
Asset classes historic correlation and five-year average correlations
4/9/2015 Sovereign Bonds Investment
Grade
High Yield Equities Convertible
Bonds
Sovereign Bonds 1.00
Investment
Grade 0.89 1.00
High Yield 0.38 0.55 1.00
Equities 0.06 0.15 0.63 1.00
Convertible
Bonds -0.06 0.06 0.60 0.91 1.00
10 11 12 13 14
10 11 12 13 1410 11 12 13 14
10 11 12 13 1410 11 12 13 1410 11 12 13 14
10 11 12 13 1410 11 12 13 1410 11 12 13 14
0.8
0.9
1,0
10 11 12 13 14
0.0
0.5
1.0
-0.5
0.0
0.5
-0.5
0.0
0.5
0.0
0.5
1.0
-0.5
0.0
0.5
-0.5
0.0
0.5
0.0
0.5
1.0
0.0
0.5
1.0
0.85
0.90
0.95
1.00
Source Bloomberg, NN IP (260D Return Correlations)
The model intends to assess the convertible returns as the
estimated result of the diffusion outcome of the four other
asset classes, and we intend to capture the effect of dispersion
of convertible underlying equities which is a key element for
the ability of convertible bonds to deliver asymmetrical. As a
consequence, both equities and convertible underlyings could
not be considered as single stochastic variables, but as a
baskets of individual stocks (or a basket of sub-indices).
Our model is based on the assumption of stable volatilities and
correlations of asset classes returns.
The assumption of stable volatilities is historically valid for
averages over long periods.
Stable correlations are less so: The recent interest rate decline
towards zero rates has had a material impact on correlations of
government bonds and investment grade bonds with regards to
all riskier asset classes which declined significantly.
The riskier asset classes − high yield, equities and convertibles −
retained their correlation characteristics amongst each other.
We used the average 260D correlations over the 2010-2015 period
stated in the above table as both the input and the targets of our
calibration.

19. December 2015
19

20. MindScope
20
December 2015
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