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Risk & Reward
Research and investment strategies
#01
1st issue 2022
Multi-period portfolio selection:
4 a practical simulation-based
framework
Interview: “Simulation has
13 been a focus for me over
much of my career.”
Managing climate risk –
15 a 21st century approach for
commercial real estate
investors
Optimized sampling: ESG
21 integration the smart way
An innovative approach to
26 performance attribution in
fixed income factor portfolios
Earnings conference call
33 tone and stock returns:
evidence across the globe
This magazine is not intended for members of the public or retail investors. Full audience information is available inside the front cover.
Risk & Reward #01/2022
Multi-period portfolio selection: a practical simulation-based
4
framework
Kenneth Blay, Anish Ghosh, Harry Markowitz, Nicholas Savoulides and Qi Zheng
Our simulation-based portfolio selection approach addresses three requirements
for practical multi-period portfolio selection solutions: (1) effective duration
management, (2) incorporation of real-world asset dynamics and (3) consideration
of investment frictions and illiquidity.
“Simulation has been a focus for me over much of my career.”
13
Interview with Harry Markowitz
In this exclusive interview, founding father of modern portfolio theory, 1990
Nobel Laureate and co-author of our feature article, Harry Markowitz, discusses
his work with Invesco on multi-period portfolio selection.
Managing climate risk – a 21st century approach for commercial
15
real estate investors
Louis Wright and Zachary Marschik
With climate risk accelerating around the world, real estate investors need to
consider it’s impacts on their strategies. Learn how we approach these growing
challenges at Invesco Real Estate.
Optimized sampling: ESG integration the smart way
21
Georg Elsaesser, Dr. Martin Kolrep and Michael Rosentritt
Optimized sampling helps preserve the intended portfolio characteristics after
ESG integration, reduces tracking error and limits transaction costs.
An innovative approach to performance attribution in fixed
26
income factor portfolios
Jay Raol, Ph.D., Benton Chambers, Amritpal Sidhu and Bin Yang
Attribution analysis can be adapted for single-factor, multi-factor and factor
target portfolio strategies – three examples that correspond to the three stages
of our factor investment process for fixed income.
Earnings conference call tone and stock returns: evidence
33
across the globe
Tarun Gupta, Ph.D., and Yifei Shea, Ph.D.
Based on evidence from five investment regions, we show how the tone on
display during earnings calls can help predict stock returns.
Important information: The publication is intended only for Professional Clients, Qualified Clients/ Sophisticated investors and Qualified Investors
(as defined in the important information at the end); for Institutional Investors in Australia; for Professional Investors in Hong Kong; for Institutional
Investors and/or Accredited Investors in Singapore; for certain specific sovereign wealth funds and/or Qualified Domestic Institutional Investors
approved by local regulators only in the People’s Republic of China; for certain specific Qualified Institutions and/or Sophisticated Investors only in
Taiwan; for Qualified Professional Investors in Korea; for certain specific institutional investors in Brunei; for Qualified Institutional Investors and/or
certain specific institutional investors in Thailand; for certain specific institutional investors in Indonesia; for qualified buyers in Philippines for
informational purposes only; for Qualified Institutional Investors, pension funds and distributing companies in Japan; and for Institutional Investors in
the USA. The document is intended only for accredited investors as defined under National Instrument 45-106 in Canada. It is not intended for and
should not be distributed to, or relied upon by, the public or retail investors.
Global editorial committee: Chair: Kevin Lyman and Stephanie Valentine. Jutta Becker, Kenneth Blay, Bailey Buckner, Amanda Clegg, Jessica Cole,
John Feyerer, Ann Ginsburg, Tim Herzig, Kristina Hooper, Paul Jackson, Dr. Martin Kolrep, Damian May, Lisa Nell, Jodi L. Phillips, Dr. Henning Stein,
Scott Wolle.
In this edition of Risk & Reward we provide
you broad insight into Invesco’s research
capabilities. From multi-period portfolio
selection to ESG return optimization, new
applications for attribution analysis to
AI-assisted coverage of earnings calls –
our problem-solving approach is as
comprehensive as it is innovative. And there’s
Marty Flanagan one element that ties it all together: effective
President and CEO quantitative investment management.
of Invesco Ltd.
Our lead article addresses common portfolio construction
issues that a conventional one-period approach cannot solve.
Learn how we make use of computing power to effectively
manage duration, account for illiquidities, and maximize
wealth over multi-period investment horizons. And you won’t
want to miss our interview with Nobel Laureate Harry
Markowitz, co-author of the study and pioneer of modern
portfolio theory.
We’ve also included two articles about ESG, the first of which
looks at commercial real estate, the considerable greenhouse
gas emissions associated with the asset class and the
rebounding impacts of global warming on real estate asset
performance. The second article examines how a well-known
technique from passive management – optimized sampling –
can be used to integrate ESG into a portfolio while matching
the tracking error to the original, non-ESG allocation.
And we explore the topic of attribution analysis for fixed
income. Much more than just a reporting tool, attribution
analysis can help investment professionals comprehend
the many complexities involved in translating theoretical
investment concepts into real-world trading strategies –
to ensure that factor portfolios behave as intended.
Finally, we break down the true relationship between the
tone on display in earnings calls and expected stock
performance. A data mining approach helps separate
the signal from the noise.
We hope you enjoy this latest edition of Risk & Reward!
Best regards,
Marty Flanagan
President and CEO of Invesco Ltd.
Multi-period portfolio
selection: a practical
simulation-based
framework1
By Kenneth Blay, Anish Ghosh, Harry Markowitz, Nicholas Savoulides and Qi Zheng
Since the advent of portfolio theory in 1952,
investment researchers have made notable
advances in optimal portfolio selection. However,
research on multi-period portfolio selection
has been limited in its practical application by
‘the curse of dimensionality’ – the exponential
increase in computational requirements with each
additional state variable. Real-world multi-period
problems include numerous state variables that
make the computation of solutions impractical if
not infeasible. And, while relevant computational,
theoretical and numerical methods have improved
significantly, many important aspects of multi-
period investing still remain unaddressed.
4 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework
We develop a simulation-based portfolio 1. Solutions must evolve allocations and
selection (SBPS) approach that addresses duration over time to align with expected
three requirements for practical multi- cash flows
period portfolio selection solutions: The long investment horizons and
expected cash inflows and outflows of
1. Effective duration management multi-period investing must be reflected in
the evolution of allocations and duration
2. Incorporation of real-world asset profiles across the investment horizon.
dynamics
For example, consider the risk-free asset,
3. Consideration of investment frictions which in a single-period context is usually
and illiquidity cash or US Treasury bills, due to their low
volatility. Over long investment horizons,
We start with an analytical model that these assets are not ‘risk free’ as they
provides intuition and offers some expose investors to meaningful
guiding principles on how allocations uncertainty.
and duration should evolve across a
multi-period investment horizon. We Figure 1 illustrates this, presenting 20
then unveil our SBPS approach and simulated paths for each of three duration
demonstrate how it provides solutions approaches. Of the three options, a 10-year
for common investor objectives that are zero-coupon US Treasury bond has the
intuitive and flexible, and which satisfy lowest risk if held until maturity, despite
our requirements for practical multi- exhibiting material volatility across the
period solutions. investment horizon.
Single-period versus multi-period This demonstrates how essential effective
portfolio selection duration management is to multi-period
A key distinction between single-period solutions. In cases like this, hold-to-
and multi-period portfolio selection is the maturity investments can be the most
consideration of intermediate actions efficient assets to employ. In more complex
within an investment horizon that extends cases, time-varying combinations of short
over many periods. In the single-period and long-duration bond funds may be used
setting, an investor decides how to invest to achieve the desired outcome.
at the beginning of the period and then
waits until the end of the period to assess 2. Solutions must consider real-world asset
the outcome. In practice, however, dynamics
investing is rarely so straightforward. Asset pricing dynamics may exhibit unique
Pension fund managers, retirement characteristics over long horizons, which
investors and other long-term investors can materially impact the performance of
Duration management should fund their portfolios over time and often theoretical solutions when implemented in
be a key consideration for long pursue many objectives across a multi- the real world. For example, equity
horizon optimizations in the stage investment horizon, necessitating a valuations exhibit mean-reverting
variety of intermediate steps. tendencies that result in negative
presence of inflows and outflows.
autocorrelation over longer horizons.
Multi-period portfolio selection must Additionally, fixed income returns may be
therefore consider these intermediate skewed in a low rate environment where
events while seeking to determine rates have limitations as to how low they
efficient, time-varying portfolio allocations can go. For these and other reasons, a
across the investment horizon. log-normal model of asset price dynamics
may produce unrealistic – if not utterly
Requirements for multi-period portfolio implausible – results.
selection
In practice, three requirements must be
fulfilled for practical multi-period portfolio
selection solutions:
Figure 1
Twenty simulated paths of USD 1 invested in three different ways
Portfolio balance (LHS) Asset duration (RHS)
Money market fund Duration targeted (10-year): US Treasury bond index fund 10-year zero coupon: US Treasury bond
USD Years USD Years USD Years
1.6 10 1.6 10 1.6 10
8 8 8
1.4 1.4 1.4
6 6 6
1.2 1.2 1.2
4 4 4
1.0 1.0 1.0
2 2 2
0.8 0 0.8 0 0.8 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
Time (years) Time (years) Time (years)
Source: Invesco.
5 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework
3. Solutions must consider investment 1. Optimal asset allocation through time
frictions and illiquidity Making some simplifying assumptions, we
Real-world portfolios implemented across derive an analytical solution for optimal
multiple periods may be updated for a asset allocation.2 The analytical solution is
variety of reasons. These updates can best understood in a standard accumulation-
include cash inflows, cash outflows, decumulation problem depicted in figure
the purchase, sale or replacement of 2(a); it shows inflows and outflows, and
investments, and portfolio rebalancing. All how the portfolio balance increases and
such intermediate portfolio management decreases over time.
activities can have transaction cost and/or
tax implications. The optimal analytical solution suggests
that, the dollar risk should stay constant
Over the short term, these real-world through time. In a two-asset context, it
elements may only result in negligible implies that the portfolio dollar allocated to
differences in expected outcomes. Over the high risk asset (equity) stays roughly
the long term, however, significant constant through time. This is depicted in
differences between actual and expected figure 2(b) for three different solutions,
outcomes can arise from not adequately depending on the investor’s risk preference.
accounting for their impact. This constant dollar equity allocation gives
rise to a U-shaped glidepath in the
Analytical framework accumulation-decumulation problem.
To provide intuition for the multi-period
portfolio selection problem in the presence 2. Optimal duration management through
of cash flows, we address two central ideas time
analytically: Similarly, we obtained an analytical solution
for optimal duration. It is driven by four
1) Optimal asset allocation through time components, as shown in figure 3: expected
2) Optimal duration management through cash flows, bonds-equity correlation,
time expected yield curve changes, and yield
curve slope.
To this end, we develop an analytical
solution to the mean-variance problem in Analytically driven guiding principles
the multi-period context with intermediate To better understand the first order impact
cash flows. Our findings are best understood of cash flows and various other parameters
in a two-asset world in which, at any given on allocation and duration decisions,
time, the investor has access to an equity we introduce an example: a standard
asset and a government bond with accumulation-decumulation problem on a
arbitrary duration. shorter timescale. We assume an investor
with a 10-year investment horizon starting
Figure 2
Stylized accumulation-decumulation problem
a) Cash flows and portfolio b) Allocation of portfolio balance for low, medium and high risk solutions
balance
Inflows Portfolio balance Bond Equity
Outflows
Low-risk Medium-risk High-risk
Portfolio balance Portfolio balance Portfolio balance Portfolio balance
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
Time (years) Time (years) Time (years) Time (years)
Source: Invesco.
Figure 3
Components driving optimal duration and their directional impact
Duration = Magnitude and timing + Correlation with equity + Yield curve drift + Yield curve slope
of cash flows
Inflows (+) Positive (–) Increasing yields (–) Positive (+)
Outflows (–) Negative (+) Decreasing yields (+) Negative (–)
Source: Invesco.
6 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework
with USD 1,000 of initial capital, yearly that the instantaneous yield for the bond
inflows (contributions) of USD 500 for the asset starts at 2% with no drift and exhibits
first five years and outflows (withdrawals) an annualized volatility of 1%.
of USD 500 for the last five years. The
investor seeks to maximize mean terminal Based on the analysis and the example
wealth, subject to a given level of risk as presented, we make the following key
measured by its variance. observations:
Figure 4 presents the optimal equity-bond 1. Allocations should shift to safer (riskier)
allocation and optimal duration profile over allocations as inflows (outflows) occur
time. Specifically, we consider the sensitivity As we have shown, the lowest-risk solution
of the solution to different levels of yield has 100% allocation to bonds and exhibits
curve slope and bond-equity correlation. zero risk. For higher-risk solutions, the
analytical solution suggests an approximately
For this example, we will assume the equity constant dollar allocation to equity through
asset has an average 6% annual return and time. To maintain such a constant dollar
annualized volatility of 15%. We also assume allocation, the investor will allocate
Figure 4
Maximizing mean terminal wealth in the analytical model
Inflows, outflows, and terminal wealth
Inflows Outflows Terminal wealth
Cash flow (USD)
1,500
1,000
500
0
-500
?
-1,000
-1,500
0 1 2 3 4 5 6 7 8 9 10
Time (years)
Asset allocation and duration for nine combinations of asset class correlation (ρ) and yield curve slope
Bond (LHS) Equity (LHS) Bond duration (RHS) Portfolio duration (RHS)
ρ = -0.25 ρ=0 ρ = 0.25
% Years % Years % Years
100 30 100 30 100 30
75 75 75
20 20 20
Slope = 2%
50 50 50
10 10 10
25 25 25
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time (years) Time (years) Time (years)
% Years % Years % Years
100 30 100 30 100 30
75 75 75
20 20 20
Slope = 0%
50 50 50
10 10 10
25 25 25
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time (years) Time (years) Time (years)
% Years % Years % Years
100 30 100 30 100 30
75 75 75
20 20 20
Slope = -2%
50 50 50
10 10 10
25 25 25
0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time (years) Time (years) Time (years)
Source: Invesco.
7 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework
conservatively when the portfolio balance is asset returns may offer guidance on
high and aggressively when it is low. This adjusting portfolio durations.
results in a U-shaped allocation to risk assets
across the investment horizon. As the Simulation-based portfolio selection
probability of running out of money (SBPS)
increases because of extended or higher Traditional approaches to solving multi-
withdrawals, allocations shift back to safer period problems employ dynamic
assets. programing. SPBS builds on much of the
traditional thinking to date on long-horizon
2. Asset duration should match the multi-period investing but diverges in that
investment horizon when there are no it does not employ this technique. Instead,
cash flows we propose a much more flexible
In the case with no yield curve slope and framework that decomposes the multi-
no correlation between bond and equity period problem into three distinct parts:
assets, the duration of the bond mirrors the
remaining investment horizon. This follows 1. The objective function (the investment
from the cash flow contribution of the objective)
duration equation. 2. Simulation
3. Optimization
In this simple example, the desired duration
profile could be implemented with a This provides substantial flexibility in
buy-and-hold strategy using a duration- addressing the central challenges of
matched zero-coupon US Treasury bond. implementing and managing portfolios
Notice the contrast with liability-driven across a multi-period investment horizon.
investing (LDI), which focuses on managing The approach allows us to consider any
funding ratio volatility, seeking to match objective function and incorporate
the portfolio’s overall duration to the real-world asset dynamics and investment
investment horizon and leading to longer frictions through advanced simulation
duration targets than are suggested here. methods. At the core of SBPS is the
While the LDI approach makes sense for a optimization algorithm that incorporates
plan fiduciary, it may be overly restrictive simulated investment outcomes (based
and suboptimal for an investor seeking to on the objective function selected and the
maximize terminal wealth. simulation engine used) and optimizes
all the asset weight vectors through time
3. Duration should be extended (shortened) all at once. This stands in contrast to
with expected inflows (outflows) dynamic programming approaches
When inflows and outflows are introduced, where consideration of many real-world
we see a very dramatic change to the aspects of multi-period portfolio
duration profile. By extending (or shortening) management would likely require a
duration, the investor can effectively lock non-trivial reformulation of the solution
in buying (selling) bonds with future to be used.
inflows (outflows) at today’s rate.
Examples and key insights
The implications are profound, particularly We present unconstrained SBPS solutions
in situations with prolonged inflows, for the investor problem introduced in the
where optimal solutions could require analytical section. Instead of optimizing
dramatic duration extensions. While this the mean versus variance objective, here
might seem counterintuitive, in the we are interested in the median versus
absence of directional views on interest median -5% value at risk objective. The
rates, this will lead to more efficient investment opportunity set includes
long-term results. US equity, international developed equity,
emerging market equity, and 1-year to
4. Duration should be adjusted based on 30-year maturity STRIPS indexes (separate
the slope of the yield curve, expected trading of interest and principal securities).
correlation of bond and equity assets Figure 5 shows cash flows, the efficient
and expected yield curve changes frontier, and the optimal allocations
If the yield curve is positively sloped, and durations for three selected solutions
duration should be extended. This allows on the frontier: low, medium, and high
investors to earn higher returns by risk.
investing in higher-yielding parts of the
yield curve. And it provides the opportunity The SBPS-based optimization results,
to potentially earn additional roll-down coupled with our analytical intuition from
returns. If yields are positively correlated the previous section, leads us to the
with equity returns (that is, if bond returns following observations:
are negatively correlated with equity
returns), duration should be extended, 1. SBPS generates allocations and
in line with standard diversification seeking duration profiles aligned with analytical
to exploit negative correlations. If yields expectations
are expected to increase, duration should All the key principles derived from our
be shortened so that assets can be analytical examples still hold true.
reinvested at increasingly higher rates. Specifically, allocations shift to safer
(riskier) assets as inflows (outflows)
Although it is difficult to develop occur and duration is extended
expectations about future yields, the (shortened) in the presence of future
general shape of the yield curve and the inflows (outflows).
correlation of its movements with equity
8 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework
2. SBPS allows for long-term real-world slightly positive correlation over the past
asset dynamics decade. Details such as these can
We can model assets more flexibly and meaningfully affect our solutions.
realistically than with the more simplistic
analytical model. For example, SBPS prices 3. SBPS allows for the consideration of
fixed income instruments based on investment frictions and illiquidity
simulated interest rate curves. This results Simulation also lets us consider real-world
in more consistent pricing while better investment challenges, including assumed
reflecting current market realities. For transaction costs (we assume 50 bps per
example, in a low rate environment, when transaction). This not only incorporates
bond returns are materially skewed, the the impact of transaction costs on
simulator is better aligned with market expected outcomes but also encourages
realities. Additionally, correlations between the optimization process to produce
rates and equities in SBPS are assumed to solutions with lower turnover.
be slightly negative, as opposed to their
Figure 5
Maximizing median terminal wealth with SBPS
Inflows, outflows and terminal wealth
Inflows Outflows Terminal wealth
Cash flow (USD)
1,500
1,000
500
0
-500
-1,000 ?
-1,500
0 1 2 3 4 5 6 7 8 9 10
Time (years)
Efficient frontier
Median terminal wealth (USD)
2,750
2,500
Medium risk High risk
2,250
2,000
Low risk
1,750
1,500
0 500 1000 1500 2000 2500 3000
Median terminal wealth with 5% VaR (USD)
Optimal allocations and durations
Bonds (STRIPS): 1yr 2yrs 3yrs 4yrs 5yrs 6-10yrs 10+yrs
Equities: Emerging markets Developed markets US
Low risk Medium risk High risk
Allocation (%) Allocation (%) Allocation (%)
100 100 100
75 75 75
50 50 50
25 25 25
0 0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time (years) Time (years) Time (years)
Optimal bond duration (years) Optimal bond duration (years) Optimal bond duration (years)
30 30 30
20 20 20
n/a
10 10 10
0 0 0
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
Time (years) Time (years) Time (years)
Source: Invesco.
9 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework
SBPS for the income investor As before, the investment opportunity set
To demonstrate the flexibility of our SBPS includes US equities, non-US developed
approach, we now consider the retirement market equities, emerging market equities
The goal of income maximization income problem. We consider a 40-year- and 1-year to 30-year maturity STRIPS
is to identify the solution that old investor who plans to retire at age 60, indexes. In addition, 1 to 30-year TIPS
leads to the highest probability at which time he expects to withdraw a indexes (Treasury inflation protected
fixed annual income for 20 years. We securities) are also available. Note that we
of success for a given level of
assume: can work with both nominal cash flows
income. (contributions) and real cash flows (income
• An initial investment of USD 100,000 withdrawals). In real dollar terms, nominal
• Annual inflows of USD 50,000 (nominal) contributions have less value as we go out
for 20 years towards retirement into the future. The ability to convert
• Annual outflows (real) beginning in nominal dollars into real dollars and vice
year 20 and continuing to year 40 versa allows us to work in one single unit.
Figure 6
SBPS for the income investor
Inflows and outflows
Inflows (nominal expressed as real) Outflows (real)
Cash flow (real USD 1,000)
100
Accumulation
50
Consumption
0
-50
-100
40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
Age (years)
Efficient frontier
Distribution (real USD 1,000)
300
200
High risk
Medium risk
Low risk
100
0
0 10 20 30 40 50 60 70 80 90 100
1 – probability of success (%)
Optimal allocations and durations
Bonds (STRIPS): 1-30yrs
Bonds (TIPS): 1-2yrs 3-5yrs 6-10yrs 11-20yrs 20+yrs
Equities: Emerging markets Developed markets US
Low risk Medium risk High risk
Allocation (%) Allocation (%) Allocation (%)
100 100 100
75 75 75
50 50 50
25 25 25
0 0 0
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Time (years) Time (years) Time (years)
Real bond duration (years) Real bond duration (years) Real bond duration (years)
30 30 30
20 20 20
10 10 10
0 0 0
0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35
Time (years) Time (years) Time (years)
Source: Invesco.
10 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based frameworkThe goal of income maximization is to Conclusion: SBPS is more intuitive,
identify the solution that leads to the flexible, and adaptable
highest probability of success for a given We first presented the results of an
level of income. Figure 6 shows the cash analytical framework we developed that
flows in real dollar terms, the income provides a theoretical foundation for
investor’s efficient frontier, and the optimal multi-period portfolio selection and lends
allocations and real durations for three intuition for how portfolio allocations and
selected solutions on the frontier: low, duration should evolve over time. We then
medium, and high risk. present SBPS and demonstrate how it
addresses the three key requirements we
From our results, we can see the following: laid out for multi-period portfolio selection
solutions: (1) It produces solutions that
1. Low-risk solutions seek duration early align portfolio durations with expected
on and diversify with growth assets in cash flows, (2) it incorporates real-world
later years asset dynamics, and (3) it considers
In the low-risk allocation, the solution investment frictions and illiquidities. It
focuses on duration assets with extended also allows for the inclusion of individual
durations early in the investment horizon. hold-to-maturity and defined-maturity
At this stage, it is most important to investments.
eliminate the interest rate risk associated
with future purchases (and dispositions) SBPS provides substantial flexibility in
SBPS provides substantial of bonds that may be required from (for) addressing the major challenges of
flexibility in addressing the major upcoming inflows (outflows). As the implementing and managing portfolios
challenges of implementing and portfolio progresses through the investment across multi-period horizons. Decomposing
horizon and expected outflows increasingly the multi-period problem into three
managing portfolios across multi-
outweigh expected inflows, allocations distinct parts (the objective function,
period horizons. gradually shift to shorter duration bonds simulation, and optimization) also
and introduce equity exposures for facilitates further research into multi-
diversification. period portfolio selection, as innovations
in any of these three areas can easily be
2. High-risk solutions focus early on incorporated into our framework.
growth assets, with duration added
in later years Finally, SBPS readily accommodates new
In the high-risk solution, instead of methods of leveraging advances in
maintaining a 100% allocation to equity computing and optimization algorithms
assets through time, the solution moves to to solve multi-period portfolio selection
safer assets as outflows begin. Intuitively, problems using a simulation-based
during inflows, the solution seeks maximum approach.
return and, consequently, maximum risk.
Once outflows begin, they are assumed to
be constant. There is also no utility to any
remaining portfolio balance following
outflows. The result is that, for a given
outflow amount, the successful paths
will have no remaining upside and will
be exposed only to the risk of becoming
insolvent. To mitigate this effect, once
the outflows begin, the portfolio gradually
moves to some duration assets.
Notes
1 The full version of this article was published in the fourth quarter 2020 issue of The Journal of Investment Management.
Charts and content used with permission from the Journal of Investment Management.
2 For more details and the analytical solutions, please refer to the full version of this article.
References
K. Blay, A. Ghosh, S. Kusiak, H. Markowitz,
N. Savoulides and Q. Zheng (2020): Multi-
Period Portfolio Selection: A Practical
Simulation-Based Framework”, Journal of
Investment Management 18(4), pp. 94-129.
11 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based frameworkAbout the authors
Kenneth Blay Anish Ghosh
Head of Research Senior Analyst, Research and Analytics
Invesco Global Thought Leadership Invesco Investment Solutions
Kenneth Blay works closely with investment Anish Ghosh is responsible for driving
teams and researchers to lead the quantitative research and analysis. This
development of original research, the involves carrying out and publishing
authorship of white papers and articles for innovative original research, providing
publication in practitioner journals, and the in-depth research presentations to internal
creation of innovative investment content and external teams, and building out new
focused on strengthening Invesco’s profile research and technological functionalities
as a global thought leader in asset in Invesco Vision.
allocation, risk management, systematic
and factor investing, and portfolio
implementation.
Dr. Harry Markowitz Nick Savoulides
Economist, Nobel Laureate, and Head of Research & Portfolio Analytics
Invesco Investment Solutions Research Invesco Investment Solutions
Partner Nicholas Savoulides leads the development
Harry Markowitz is a consultant in the of Invesco Vision – a cloud-based portfolio
area of finance. In 1990, he was awarded research and analytics platform that
the Sveriges Riksbank Prize in Economic encompasses analytical and optimization
Sciences in Memory of Alfred Nobel for capabilities that facilitate the identification
his groundbreaking work in portfolio of portfolio solutions that address client-
theory. In 1989, he received the Jon specific investment objectives. As part
von Neumann Theory Prize from the of this effort, Nicholas engages with both
Operations Research Society of America internal and external investors and sets
for his work on portfolio theory, sparse the direction for future research and
matrix techniques, and the SIMSCRIPT development.
simulation programming language.
Qi Zheng
Senior Analyst, Research and Analytics
Invesco Investment Solutions
Qi Zheng is responsible for conducting
quantitative research and analysis
within the multi-asset solution space,
as well as developing and enhancing
various investment frameworks and
tools for asset allocation and portfolio
construction in Invesco Vision.
12 Risk & Reward #01/2022 | Multi-period portfolio selection: a practical simulation-based framework“Simulation has been a focus for me
over much of my career.”
Interview with Harry Markowitz
Risk & Reward
Dr. Markowitz, your 1952 Portfolio Selection
paper has been called the big bang of
modern finance and presented a single
period portfolio selection framework. In
your 1959 Portfolio Selection book, you
build out the theory on the single-period
framework and briefly discuss multi-period
portfolio selection. What is the difference
between single-period and multi-period
portfolio selection?
Harry Markowitz
As the name implies, the single-period
framework considers optimal action over a
single, finite period. However, the investor
can take no intermediate action over that
period. Consider the problem of maximizing
a series of cash flows. This can’t be
accomplished over a single period. Now,
the length of the period could be 30 years,
one decade, one month – or anything you
In this edition of Risk & Reward, we are proud to present an exclusive like. And you might approach the problem
interview with Dr. Harry Markowitz, father of modern portfolio theory, by optimizing a sequence of single periods
and withdrawing cash flows in between
1990 Nobel Laureate and co-author of our feature article on multi-
each. But, for a number of reasons, this
period portfolio selection. wouldn’t be the optimal solution. That
requires a multi-period approach which
optimizes outcomes while considering the
entire length of the investment horizon,
portfolio inflows and outflows, transaction
costs and other frictions – as well as an
investor’s intermediate actions.
Risk & Reward
In your 1959 book, you point to dynamic
programming to solve multi-period
problems. But in your work with the Invesco
team, you use a simulation-based approach
instead. Why?
Harry Markowitz
Let me first point out that, while most
people know me for my portfolio selection
work and the Nobel Prize that resulted
from it, I was also awarded the John von
Neumann Theory Prize in 1989 for my work
on simulation, the development of the
SIMSCRIPT simulation programming
language, portfolio theory and sparse
matrix techniques. So, simulation has been
a focus for me over much of my career.
The general approach for implementing
dynamic programming is to work backwards
through time. You begin by determining
the best action for each of the possible
13 Risk & Reward #01/2022 | Interview with Harry Markowitz: “Simulation has been a focus for me over much of my career.”circumstances in the last period, then the multi-period investment horizons for
next to last, and so on until you work your different asset classes, investment types
way back to the first period. The problem (active and passive) and account types
is that the possible circumstances in each (taxable, tax-deferred and tax-exempt).
period increase exponentially as you We then optimized the net present value
consider additional variables. This is what (NPV) of those outcomes. That work
is known as the curse of dimensionality. addressed the taxation question – and it
And this is also the reason we have yet also considered multi-period investment
to see full-fledged implementations of horizons.
dynamic programming solutions to
practical multi-period problems. Dynamic The SBPS framework we developed with
programming methods are certainly used Invesco significantly evolved that work
to inform portfolio construction. But the and, more importantly, generalized it to
number of variables that have to be address a number of other practical realities
considered continues to be a key limiting of multi-period investing – like duration
factor. Moreover, customizing dynamic management over long investment horizons,
programming solutions is a non-trivial investment frictions and real-world asset
exercise that can require a complete dynamics. The Invesco framework also
reformulation of the problem being allows for the incorporation of individual
considered. bonds in developing solutions.
The simulation approach we’ve taken Risk & Reward
provides a way around the dimensionality Could you tell us a bit more about the
problem. By decomposing the problem collaboration with Invesco?
into three distinct parts – the objective
function, simulation and optimization – Harry Markowitz
we also gain a great deal of flexibility in The team at Invesco has done a tremendous
the types of problems that can be solved job. They’ve successfully developed the
and in the ability to develop solutions that analytical intuition for how portfolio
address specific investor needs. allocations should evolve over time given
different objectives and in developing the
Risk & Reward optimization algorithm for computing
How would you characterize Simulation- these types of problems. That isn’t easy
Based Portfolio Selection, or SBPS for work. And they not only made it work for
short, the latest iteration of your portfolio our research effort, but they’ve also made
selection work with Invesco? the capability accessible to their clients
through the Invesco Vision portfolio risk
Harry Markowitz and research platform. This is a great
Our SBPS research builds on previous work example of theory turned into practical
in both portfolio selection and simulation. application.
Specifically, it expands on an article I wrote
together with Kenneth Blay back in 2013.1 Risk & Reward
Based on the insight that the impact of Dr. Markowitz, thank you very much for
taxes is path-dependent, we simulated your time!
after-tax investment outcomes over
Note
1 Blay, K. and H. Markowitz. 2016. “Tax-Cognizant Portfolio Analysis: A Methodology for Maximizing After-Tax Wealth.”
Journal of Investment Management, Vol 14, no. 1, 26-64.
14 Risk & Reward #01/2022 | Interview with Harry Markowitz: “Simulation has been a focus for me over much of my career.”Managing climate risk -
a 21st century approach
for commercial real
estate investors
By Louis Wright and Zachary Marschik
Not only is real estate a major contributor to CO2
emissions, as an asset class it is also suffering
increasingly from the very natural disasters
global warming brings about. With climate risk
accelerating around the world, real estate investors
need to consider the impact on their strategies.
Read on to learn how we approach these growing
challenges at Invesco Real Estate (IRE).
15 Risk & Reward #01/2022 | Managing climate risk – a 21st century approach for commercial real estate investorsPopulations around the globe face As figure 2 shows, global temperature
heightening climate risk. In 2021 alone, anomalies have risen considerably over
the world witnessed severe flooding in the last 100 years, and there is consensus
Western Europe and China, ice storms that this is the main reason for the rise in
in Texas and wildfires in California – the frequency and severity of natural
all of which exacted enormous economic disasters. Though governments, not-for-
and human costs. profit organizations and the private sector
have joined the fight against climate
Re-insurance data highlights the increasing change, even the most drastic of
cost of such disasters: Global economic interventions will require many years to
Global economic losses losses from natural and man-made reverse the global warming trend, and
from natural and man-made catastrophes totaled USD 202 bn in 2020, the cost of extreme weather is expected
catastrophes totaled USD 202 bn up from USD 150 bn in 2019.1 Figure 1 to continue climbing into the foreseeable
shows global losses broken down in line future.
in 2020. with the industry standard categorization
of climate events into primary perils and Real estate and the climate challenge
secondary perils. Primary perils are natural Real estate is a major contributor to global
disasters with known severe loss potential CO2 emissions. In 2020, the built
for the insurance industry, such as environment was estimated to be
tropical cyclones or earthquakes, responsible for 75% of annual global
whereas secondary perils are smaller greenhouse gas emissions,3 with buildings
to moderate events or the secondary alone accounting for about half of this
effects of a primary peril. Examples include amount.4 Around 50% of emissions from
river flooding, torrential rainfall, drought, new buildings are embedded in the
wildfire, thunderstorms and tsunamis. construction materials. The other half
Secondary perils are often not modeled arises from operation of the building.5
and have historically received little This sets the real estate industry before
monitoring from the insurance industry. the dual challenge of creating spaces that
Though the annual costs of both types are more efficient in use while reducing
of climate event are increasing, the share the up-front carbon emissions involved
represented by secondary perils is growing. in construction and refurbishment. This
should be kept in mind as we concentrate
The overwhelming majority of climate on identifying climate risks for existing
scientists and academics agree that global assets.
warming is caused by human activity.2
Figure 1
Global insured losses from climate events
Primary perils Secondary perils/effects of primary perils Total 5-year moving average
USD bn (2020 prices)
140
120
100
80
60
40
20
0
2012
2016
2000
2002
2004
2006
2008
2010
2014
2018
1990
1994
1992
1996
1998
1980
1984
1982
1986
1988
2020
Source: Swiss RE (2021); “In 5 charts: natural catastrophes in a changing climate”,
https://www.swissre.com/risk-knowledge/mitigating-climate-risk/sigma-in-5-charts.html
Figure 2
Annual global temperature anomalies since 1820
Degrees Celsius
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1830
1870
2010
1850
1880
1920
2000
1940
1910
1960
1990
1900
1820
1930
1840
1970
1860
1890
1950
1980
2020
Source: Berkley Earth; temperature anomalies relative to the Jan 1951-Dec 1980 average.
16 Risk & Reward #01/2022 | Managing climate risk – a 21st century approach for commercial real estate investorsFigure 3
Buildings and construction share of global energy and energy-related CO2 emissions (2020)
Energy Emissions
Residential 22% 17%
Non-residential 8% 10%
Energy Emissions Buildings construction industry 6% 10%
Other construction industry 6% 10%
Other industry 26% 23%
Buildings and Buildings and
Transport 26% 23%
construction construction
share in total: 42% share in total: 47% Other 6% 6%
Source: IEA (2021a).
Financial impacts of climate risk volatility, higher insurance costs, lower
on real estate capital growth, higher financing rates
Determining the financial impact of and reduced liquidity for commercial
extreme weather on real estate is complex properties (table 1). In the most severe
Determining the the financial and extends far beyond calculating the cases, a property could become a
impacts of extreme weather potential repair costs of a building. Climate stranded asset with its capital value
on real estate is complex. risk can influence real estate pricing via reduced to zero.
various channels, with effects varying in
severity and longevity. A recent United The UNEPFI report found that the financial
Nations Environment Programme Finance consequences of climate risk to real estate
Initiative (UNEPFI) report presents a depend on multiple conditions. One key
meta-analysis of research into such finding was that access to information on
impacts as reduced rental income, longer risks is a contributing factor in valuation
re-leasing times, greater cash flow and pricing, with evidence that better
Table 1
Potential effects of climate risk on commercial real estate asset performance
Broad Transmission Specific financial consequences
impact channel
Effects on Income • Reduced rent from fall in demand
cash flow • Reduced occupancy rate from fall in demand
• Longer to re-let space/weaker tenants
• Changes to feasible uses impacting on income
Outgoings • Increased operating costs (building services)
• Increased capital costs (repair/restoration)
• Higher insurance premiums to reflect higher risks
• Higher property taxes (clean up and mitigation
costs)
Effects on Risk • Greater cash flow volatility
capitalization premiums • Reduced liquidity/saleability of asset
rate • Reduced insurability of asset
• Greater site and location risks
Expected • Reduced rental prospects for location
growth • Increased depreciation for non-resilient buildings
• Reduced future occupancy rates
• Increased operating and capital costs, taxes, etc.
Effects on Cost of • Higher margins stemming from increased risk
financing finance • Higher DSCRs to cover cash flow volatility
Availability • Reduced willingness to lend in location
of finance • Lower amounts lent/more security sought
• Fewer potential equity partners
Source: Clayton J, van de Wetering J, Sayce S & Devaney S (2021); UNEPFI report “Climate risk and commercial property
values: a review and analysis of the literature”.
17 Risk & Reward #01/2022 | Managing climate risk – a 21st century approach for commercial real estate investorsinformation leads to greater awareness, Subcategory metrics are also available,
acceptance and integration of climate such as the expected flood return period
impacts on transacted prices. (i.e., flood frequency in years), rainfall
intensity and inundation level from a
Measuring climate risk 1-in-100-year flood.
Climate risk is not a singular metric, but
refers to multiple, interacting risks that can Democratizing climate risk data
compound and cascade, making it very The Moody’s tool can be used to evaluate
difficult to estimate. Measuring climate risk the climate risk of almost any location
requires quantifying both the likelihood across the globe, including IRE’s entire
and consequences of climate change in a direct real estate holdings, which comprise
particular location. Here, we focus on the more than 500 commercial assets across
physical elements of climate risk rather North America, Asia, Oceania and Europe.
than ’transition risks’, i.e., the potential
costs from moving towards a less polluting, Moody’s subscription-based model allows
greener economy. Though still important, users to generate location-specific climate
transition risks have fundamentally risk scorecards. These reports are detailed
different characteristics to physical climate and valuable, but optimizing their use at
risks and should therefore be modeled and IRE required building additional tools to
analyzed separately. better visualize and disseminate the data.
The information could not be easily
Assessing a specific location’s vulnerability accessed by the wider IRE teams who did
to future climate events has traditionally not have a Moody’s ESG login. So, in order
been the remit of a handful of highly skilled to leverage the information for better
professionals such as actuaries or investment and asset management
academics, and it required access to decision making, we needed to democratize
private datasets plugged into specialized our climate risk process – in particular
software. But growing awareness of and streamlining the delivery of information to
interest in climate risk have broadened teams involved in the appraisal of asset
demand for these tools. Recent acquisitions (transaction teams) and those
advancements in geospatial modeling managing existing assets and funds (asset
techniques coupled with the emergence of and fund managers).
open-source data and software has helped
proliferate climate risk services available to The solution found by IRE’s Strategic
businesses and organizations. Analytics team was a Climate Risk
Dashboard, which links directly to Moody’s
To understand the exposure of IRE’s global database and allows users to instantly
property portfolio to climate change, we identify the climate risk exposure of each
needed a tool with consistent and robust address they enter. The dashboard displays
scoring across various countries, regions the risks pertaining to our portfolio assets
and sectors. Moody’s ESG Solutions and summarizes and filters risks by fund,
(previously Four Twenty Seven) is a leading using maps and charts to highlight key
provider of physical climate and information.
environmental risk analysis with a climate
risk application well-suited for a globally Benchmarking asset risk
diversified asset manager like IRE. Investments do not happen in a vacuum.
While the clear first step in contextualizing
Moody’s methodology is deeply data climate risk is to democratize the asset-
driven and leverages large public and level data, further understanding can be
Moody’s methodology is private databases to generate more than achieved by considering how one
deeply data driven. 25 underlying risk indicators, each linked investment compares to another for insight
to known business consequences of into the relative risk. This can be done by
climate change. Scoring is forward looking benchmarking, or matching an asset’s
and focuses on thresholds near the tail end climate risk against other locations in the
of the risk distribution because such surrounding area. For instance, a well-
events are the most likely sources of located property with access to plenty of
disruption and damage – especially as amenities might see its locational benefits
extreme events grow in severity and/or outweigh its climate risk. However, it may
frequency. High-level risk indicators in still be more ideal to own a relatively less
Moody’s service include exposure to risky asset in the same area to minimize
floods, heat stress, hurricanes and the climate risk while enjoying the benefits
typhoons, sea level rise, water stress, of the amenities.
wildfires, and also earthquakes (which are
technically a geological hazard rather than Our benchmarking is achieved by utilizing
a climate risk but have also been included Moody’s ESG scoring on strategically
due to increasing client demand). generated sample points within a
boundary of interest (submarket, block
Moody’s risk scores are standardized group, etc.). With a series of sample
(ranging from 0 to 100) and globally points now available, the scores can be
comparable. The assigned risk levels summarized at the defined boundary
(none, low, medium, high, red flag) aid levels, and scores of individual assets
interpretability. For example, a flood risk of interest can be placed within the
score of 70/100 equates to a high risk level distribution. Figure 4 shows a building in
and means a location is susceptible to Tokyo and how its flood risk compares to
some flooding and inundation during the surrounding area. In this location, the
rainfall or riverine flood events. low score conveys that the asset is not
18 Risk & Reward #01/2022 | Managing climate risk – a 21st century approach for commercial real estate investorsFigure 4
A benchmarking example
Risk: Red Flag High Medium Low None
Benchmark count
100
Asset and benchmark scores
75
50
25
0
25 50 75
Score (lower is better)
Source: IRE Strategic Analytics.
very exposed to flood risk. However, as North American wildfires
the distribution in figure 4 shows, there In the summer of 2021, several areas in
are parts of Tokyo with high risk values, western North America experienced
meaning that the sample building might historic wildfires while much of the region
be a well-positioned asset, close to experienced record high temperatures.
All areas with the largest wildfires
amenities but far enough away from To test the utility of the Moody’s ESG
had been properly scored as the low-lying areas to avoid being too scores using a real-world example, we
high-risk locations. risky. looked at the Moody’s wildfire scores for
locations in the Pacific Northwest. The
Recent extreme weather events: results proved encouragingly accurate:
Two case studies Apart from medium risk scores in British
Finally, we assess the validity and accuracy Columbia, all areas with the largest
of Moody’s ESG scores with the help of wildfires had been properly scored as
two case studies of recent climate events. high-risk locations (figure 5).
Figure 5 Figure 6 Figure 7
Moody’s wildfire scores Moody‘s heat scores Moody’s future extreme temperatures
sub-scores
Source: IRE Strategic Analytics. Source: IRE Strategic Analytics. Source: IRE Strategic Analytics.
19 Risk & Reward #01/2022 | Managing climate risk – a 21st century approach for commercial real estate investorsAdditionally, we analyzed Moody’s heat a large river running through its center.
scores to see if the record-high temperatures Almost all the sample points near a river
were something that could have been and/or at relatively low elevation had a
foreseen. While overall heat scores high or red flag risk level in Moody’s
(figure 6) did not seem to be good scoring system. Equally, sample locations
predictors, the subcategory score for with medium-to-low flood risk were
future change in extreme temperatures sufficiently distanced from a river and/or
(figure 7) seemed to provide a warning had much higher land elevations.
that extreme heat is only going to get
worse. This sub-score provides valuable Conclusion
information for investors, and the high Many real estate investors still ignore
scores for future change are supported extreme weather events as they are
by the events of summer 2021. unpredictable and difficult to quantify.
Nonetheless, climate-related events are
European floods expected to become more common and
In July 2021, a number of Western more severe, calling into question this style
European countries experienced extreme of approach: Investors can no longer afford
flooding. Worst affected were Germany, to leave climate risk information out of
Belgium, Netherlands and Austria. A total their decision making. IRE’s Climate Risk
of 242 deaths are attributed to the Dashboard is designed to deliver timely
Investors can no longer afford flooding, of which 196 were in Germany. and reliable information to identify and
to leave climate risk information To test the validity of Moody’s ESG scores, mitigate, or completely avoid, potential
we sampled flood risk scores across five climate risk exposure. This will ultimately
out of their decision making. towns devastated by the floods (Schönau help us better preserve and grow capital
am Königssee, Hagen, Schuld and Bad and deliver stronger and more secure
Neuenahr in Germany, and Hallein in returns for our clients.
Austria). Unsurprisingly, each town had
Notes
1 Swiss RE (2021) Natural catastrophes in 2020: secondary perils in the spotlight, but don’t forget primary-peril risks.
Sigma 1/2021.
2 For instance, Carbon Brief (2021) Mapped: How climate change affects extreme weather around the world. https://
www.carbonbrief.org/mapped-how-climate-change-affects-extreme-weather-around-the-world; NASA (2021)
Scientific Consensus: Earth’s Climate Is Warming. https://climate.nasa.gov/scientific-consensus/
3 Architecture 2030 (2021) The 2030 Challenge. https://architecture2030.org/2030_challenges/2030-challenge/
4 39% of CO2 emissions according to Architecture 2030; 37% of CO2 emissions and 36% of global energy
consumption according to the UN Environment Programme.
5 World Green Building Council (2021) Beyond the Business Case report 2021. https://www.worldgbc.org/business-
case
About the authors
Louis Wright Zachary Marschik
Associate Director, Global Strategic Analytics Associate Director, Global Strategic Analytics
Invesco Real Estate, London Invesco Real Estate, Dallas
Louis Wright is a real estate data scientist Zachary Marschik is a real estate data
and research analyst, responsible for scientist who develops data-driven models
covering real estate markets in France and and applications, in particular geospatial
Iberia as well as developing investment analyses, to reveal investment and
insights through data-driven models and operational insights. Zachary works with
applications, including geospatial analyses. IRE’s US investment professionals to
Louis works with IRE’s European investment further understanding of thematic trends
professionals to make sense of the themes on real estate markets and enable targeted
and trends facing real estate markets adjustment at asset level.
as well as exploring granular locational
differentiation.
20 Risk & Reward #01/2022 | Managing climate risk – a 21st century approach for commercial real estate investorsYou can also read
