Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon -- Ralph Goldsticker
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This presentation shows how to use Cumulative Contribution Charts to visualize the relationships between investment horizon and volatility and the behavior of volatilities and correlations through time. With that information the researcher can select the sampling period and window that reflects the investment horizon and expected market environment.
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Source: http://qwafafew.org/index.php/files/page/visualizing_the_time_series_behavior_of_volatility_serial_correlation_and_i/san_francisco/
Visualizing the Effects of Holding Period and Data Window on Calculations of ...Ralph Goldsticker
This presentation shows how to use Cumulative Contribution Charts to visualize the relationships between investment horizon and volatility and the behavior of volatilities and correlations through time. With that information the researcher can select the sampling period and window that reflects the investment horizon and expected market environment.
Highlights the "errors" academics make when conducting applied investment research. Describes the standards that should be observed to make the research more useful to investment managers.
Callan's director of Hedge Fund Research, Jim McKee, explores the advantages of momentum-based investing strategies, which profit from market trends in whichever direction. He discusses the rationale behind them, how they are defined and harnessed for different diversification needs, and whether they are appropriate for fund sponsors.
Momentum investing has grown in popularity. As with all investments the devil is in the details. For momentum it boils down to trading costs and protecting one self from crowded trades leading to sharp drawdowns.
Visualizing the Effects of Holding Period and Data Window on Calculations of ...Ralph Goldsticker
This presentation shows how to use Cumulative Contribution Charts to visualize the relationships between investment horizon and volatility and the behavior of volatilities and correlations through time. With that information the researcher can select the sampling period and window that reflects the investment horizon and expected market environment.
Highlights the "errors" academics make when conducting applied investment research. Describes the standards that should be observed to make the research more useful to investment managers.
Callan's director of Hedge Fund Research, Jim McKee, explores the advantages of momentum-based investing strategies, which profit from market trends in whichever direction. He discusses the rationale behind them, how they are defined and harnessed for different diversification needs, and whether they are appropriate for fund sponsors.
Momentum investing has grown in popularity. As with all investments the devil is in the details. For momentum it boils down to trading costs and protecting one self from crowded trades leading to sharp drawdowns.
While U.S. stocks finished the quarter with positive results, a range of global assets lost ground as bond yields jumped and commodity prices fell. The portfolio’s emphasis on U.S. equities and an underweight to interest rate risk, while helpful, did not offset declines across a range of global investments. The fund continues to pursue a flexible balance of risk exposures.
Express measurement of market volatility using ergodicity conceptJack Sarkissian
Don't we want to base our trading decisions on current market conditions? Then why should we rely on time averages only because they are simple to comprehend? We can get current market volatility a lot faster by applying the ERGODICITY concept to financial markets. Ensemble averaging allows to measure market volatility quickly, based on only two points in time and is as relevant to volatility measurement as the traditional measures.
Webinar on Structured Investing - A deliberate and thoughtful investment process designed to help you achieve your lifetime financial goals and focus on what matters most to you, whether it is putting your children through college, philanthropy or a secure retirement.
There is a cost to indexing that most investors are unaware of. It is called “reconstitution.”
A blog post is scheduled for 8 Feb 2017 discussing this article.
http://wp.me/p2Oizj-Hh
While U.S. stocks finished the quarter with positive results, a range of global assets lost ground as bond yields jumped and commodity prices fell. The portfolio’s emphasis on U.S. equities and an underweight to interest rate risk, while helpful, did not offset declines across a range of global investments. The fund continues to pursue a flexible balance of risk exposures.
Express measurement of market volatility using ergodicity conceptJack Sarkissian
Don't we want to base our trading decisions on current market conditions? Then why should we rely on time averages only because they are simple to comprehend? We can get current market volatility a lot faster by applying the ERGODICITY concept to financial markets. Ensemble averaging allows to measure market volatility quickly, based on only two points in time and is as relevant to volatility measurement as the traditional measures.
Webinar on Structured Investing - A deliberate and thoughtful investment process designed to help you achieve your lifetime financial goals and focus on what matters most to you, whether it is putting your children through college, philanthropy or a secure retirement.
There is a cost to indexing that most investors are unaware of. It is called “reconstitution.”
A blog post is scheduled for 8 Feb 2017 discussing this article.
http://wp.me/p2Oizj-Hh
In this PPT, review and explain the types of trend and pattern analysis. Every dataset is unique, and the identification of trends and patterns in the underlying the data is important. If a business wishes to produce clear, accurate results, it must choose the algorithm and technique that is the most appropriate for a particular type of data and analysis.
The five steps in financial planning, forecasting internalexternal .pdfamrahlifestyle
The five steps in financial planning, forecasting internal/external finds is critical. With today\'s
economic and interest rate market conditions, along with the volitility of the captial markets,
what factors would you emphasize when you are preparing your forecasts?
Solution
Connect with Vanguard > vanguard.com Executive summary. Some say the long-run outlook for
U.S. stocks is poor (even “dead”) given the backdrop of muted economic growth, already-high
profit margins, elevated government debt levels, and low interest rates. Others take a rosier view,
citing attractive valuations and a wide spread between stock earnings yields and Treasury bond
yields as reason to anticipate U.S. stock returns of 8%–10% annually, close to the historical
average, over the next decade. Given such disparate views, which factors should investors
consider when formulating expectations for stock returns? And today, what do those factors
suggest is a reasonable range to expect for stock returns going forward? We expand on previous
Vanguard research in using U.S. stock returns since 1926 to assess the predictive power of more
than a dozen metrics that investors would know ahead of time. We find that many commonly
cited signals have had very weak and erratic correlations with actual subsequent returns, even at
long investment horizons. These poor Vanguard research October 2012 Forecasting stock
returns: What signals matter, and what do they say now? Authors Joseph Davis, Ph.D. Roger
Aliaga-Díaz, Ph.D. Charles J. Thomas, CFA 2 predictors include trailing values for dividend
yields and economic growth, the difference between the stock market’s earnings yield and
Treasury bond yields (the so-called Fed Model), profit margins, and past stock returns. We
confirm that valuation metrics such as price/earnings ratios, or P/Es, have had an inverse or
mean-reverting relationship with future stock market returns, although it has only been
meaningful at long horizons and, even then, P/E ratios have “explained” only about 40% of the
time variation in net-of-inflation returns. Our results are similar whether or not trailing earnings
are smoothed or cyclically adjusted (as is done in Robert Shiller’s popular P/E10 ratio). The
current level of a blend of valuation metrics contributes to Vanguard’s generally positive outlook
for the stock market over the next ten years (2012–2022). But the fact that even P/Es—the
strongest of the indicators we examined—leave a large portion of returns unexplained
underscores our belief that expected stock returns are best stated in a probabilistic framework,
not as a “point forecast,” and should not be forecast over short horizons. The variation of
expected returns Forming reasonable long-run return expectations for stocks and other asset
classes can be important in devising a strategic asset allocation. But what precisely are
“reasonable” expectations in the current environment, and how should they be formed? For
instance, should investors expect t.
Originally published in 2005. Abstract: Over the years many commodity trading advisors, proprietary traders, and global macro hedge funds have successfully applied various trend following methods to profitably trade in global futures markets. Very little research, however, has been published regarding trend following strategies applied to stocks. Is it reasonable to assume that trend following works on futures but not stocks? We decided to put a long only trend following strategy to the test by running it against a comprehensive database of U.S. stocks that have been adjusted for corporate actions. Delisted companies were included to account for survivorship bias. Realistic transaction cost estimates (slippage & commission) were applied. Liquidity filters were used to limit hypothetical trading to only stocks that would have been liquid enough to trade, at the time of the trade. Coverage included 24,000+ securities spanning 22 years. The empirical results strongly suggest that trend following on stocks does offer a positive mathematical expectancy, an essential building block of an effective investing or trading system.
Taking on Wall Street: A Comparative Study of Strategies Sourced from "The Pr...Quantopian
A unique set of data comprised of strategy returns sourced through traditional means from managers (“the pros”) and from strategies developed on Quantopian’s platform (“the crowd”) is analyzed. We detect distinct groups of strategy styles within the data: In particular, some "crowd" strategies fall into their own clusters distinct from those within the "pro" data set. A few do overlap as well. We go on to analyze the various strategy groups with respect to environmental conditions and risk factors (among other relevant features), teasing out differences in trading styles.
Ultimately we judge how well “the crowd” is doing so far, in terms of being able to compete with the established managers not only in terms of performance but also with respect to risk management and overall novelty and diversification in the trading styles that have emerged. Finally we address general notions (and pitfalls) of building meta strategies from manager return streams.
This presentation was part of QuantCon 2015 hosted by Quantopian. Visit us at: www.quantopian.com.
International capital flows and financial vulnerabilities in emerging market ...Macropru Reader
http://www.bis.org/publ/othp25.pdf
International capital flows and financial vulnerabilities in emerging market economies: analysis and data gaps -
By Nikola Tarashev, Stefan Avdjiev and Ben Cohen
Note submitted to the G20 International Financial
Architecture Working Group
August 2016
Markus Brunnermeier - Keynote at World Finance Conference "Safe Assets" Macropru Reader
Princeton Professor Markus Brunnermeier - Keynote at World Finance Conference "Safe Assets"
Presentation Date:
Saturday, July 30, 2016
Location:
New York City, Cooper Union
http://scholar.princeton.edu/markus/presentations/keynote-word-finance-conference
Adrian, Crump, Vogt - Nonlinearity and Flight-to-Safety in the Risk-Return Tr...Macropru Reader
Adrian, Crump, Vogt - Nonlinearity and Flight-to-Safety in the Risk-Return Tradeoff for Stocks and Bonds (wp at https://www.newyorkfed.org/research/staff_reports/sr723.html )
Capital Flow Measures and Research ChallengesMacropru Reader
Linda Goldberg, NYFed Research (and BIS Visiting Scholar) https://www.bis.org/ifc/events/sat_semi_rio_jul15/1_goldberg_presentation.pdf "'Capital Flow Measures and Research Challenges"
July 2015 Keynote Presentation, BCB / CEMLA / IFC , Rio de Janeiro.
Global Imbalances and Currency Wars at the ZLBMacropru Reader
GLOBAL IMBALANCES AND CURRENCY WARS AT THE ZLB.
Ricardo J. Caballero, Emmanuel Farhi, Pierre-Olivier Gourinchas
Working Paper 21670 http://www.nber.org/papers/w21670
BIS Quarterly Chart Pack - September 2015, Bank for International SettlementsMacropru Reader
BIS Quarterly Chart Pack - September 2015, Bank for International Settlements http://www.bis.org/publ/qtrpdf/r_qt1509_charts.pdf "we will publish a regular chart pack of key graphs" https://twitter.com/HyunSongShin/status/643068234103713792
Peterson Institute for International Economics (OECD Research Director Catherine Mann, July 9, 2015); BIS Annual Report (BIS Executive Claudio Borio, June 28, 2015) - Productivity (economics research)
"Global Pricing of Risk and Stabilization Policies" -- IMFS Working Lunch: To...Macropru Reader
source file: http://www.imfs-frankfurt.de/fileadmin/user_upload/Events_Presentations_Programs_Flyer/IMFS_Working_Lunch_Tobias_Adrian.pdf
IMFS Working Lunch with Tobias Adrian, New York Fed, on July 1, 2015
"Global Pricing of Risk, Monetary Policy, and Financial Stability"
event website: http://www.imfs-frankfurt.de/de/veranstaltungen/imfs-working-lunches-und-seminare/2015.html
Author web site: http://newyorkfed.org/research/economists/adrian/index.html (IMFS presenter)
Author web site: http://newyorkfed.org/research/economists/vogt/index.html
Global Liquidity and Monetary Policy TransmissionMacropru Reader
Global Liquidity and Monetary Policy Transmission
Hyun Song Shin - Bank for International Settlements (BIS)
Liquidity and Market Efficiency – Alive and Well? http://www.suerf.org/helsinki2015
6th joint conference organised by SUERF and Bank of Finland
Helsinki, 3 July 2015
Three BIS research themes in the 2015 Annual ReportMacropru Reader
"Three BIS research themes in the 2015 Annual Report"
http://www.bis.org/speeches/sp150628b.htm
slides from Hyun Song Shin 신현송 (appended by MapoReader)
Economic Adviser and Head of Research
85th Annual General Meeting, June 2015
Bank for International Settlements
Rethinking Macro Policy III - Session 2: Macro-Prudential Tools: Gathering Evidence
IMF Spring Meetings - April 15, 2015
..................................
Chair: Stanley Fischer
Robert Rubin
Hyun Song Shin
Paul Tucker
IMF's Global Financial Stability Report, April 2015 (Chapter 3 - Asset Management and Financial Stability) summary of graphics highlights slideshow for @macropru
This paper evaluates the capacity of emerging market economies (EMEs) to moderate the domestic impact of global financial and monetary forces through their own monetary policies.
Gingko App for Economics https://gingkoapp.com/
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Gingko gives you a place to clarify your thoughts.
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Get it on the Chrome App Store https://chrome.google.com/webstore/detail/gingko-app/dpgfhngpppagnmfjocmhlioockncfgjn too!
Macroprudentialism VOX EU ebook December 2014Macropru Reader
Macroprudentialism is now part of the standard macroeconomic toolkit but it involves a set of relatively untested policies. This new Vox eBook collects the thinking of a broad range of leading US and European economists on the matter. A consensus emerges on broad objectives of macroprudential supervision, but important disagreements remain among the authors. http://www.voxeu.org/content/macroprudentialism
Financial stability risks: old and new - Brookings presentation by Hyun Song...Macropru Reader
Hyun Shin’s presentation slides on financial stability risks, old and new http://www.brookings.edu/~/media/Blogs/Up%20Front/2014/12/04%20financial%20stability%20risks/shin_presentation.pdf @BIS_org @HyunSongShin @BrookingsInst Brookings December 4, 2014
"Financial 'deglobalization'?: Capital Flows, Banks, and the Beatles" -- Kris...Macropru Reader
Deglobaslisation -- Kristin Forbes, Bank of England Monetary Policy Committee Member, MIT Professor -- Speech at Queen Mary University, London Tuesday 18 November 2014 -- "Financial 'deglobalization'?: capital flows, banks, and the Beatles"
Kang Tae Soo -- Riksbank Macroprudential Conference Stockholm, Sweden, Nove...Macropru Reader
Kang Tae Soo -- Riksbank Macroprudential Conference Stockholm, Sweden, November 2014
....
http://www.riksbank.se/en/Financial-stability/Macroprudential-Policy-Conference-November-2014/
Macroprudential Policy Conference, November 2014
Sveriges Riksbank and the International Monetary Fund are jointly hosting the conference Macroprudential Policy - Implementation and Interaction with other Policies in Stockholm on 13-14 November.
The conference will bring together representatives of national authorities and international organizations to share their knowledge and experience in the evolving field of macroprudential policy.
The financial crisis showed that ensuring the health of individual components of the financial system is not sufficient to guarantee overall financial stability. Macroprudential policy recognizes the importance of systemic risk and the need to develop regulations that address systemic risk and help to build resilience in the entire financial system.
Financial Assets: Debit vs Equity Securities.pptxWrito-Finance
financial assets represent claim for future benefit or cash. Financial assets are formed by establishing contracts between participants. These financial assets are used for collection of huge amounts of money for business purposes.
Two major Types: Debt Securities and Equity Securities.
Debt Securities are Also known as fixed-income securities or instruments. The type of assets is formed by establishing contracts between investor and issuer of the asset.
• The first type of Debit securities is BONDS. Bonds are issued by corporations and government (both local and national government).
• The second important type of Debit security is NOTES. Apart from similarities associated with notes and bonds, notes have shorter term maturity.
• The 3rd important type of Debit security is TRESURY BILLS. These securities have short-term ranging from three months, six months, and one year. Issuer of such securities are governments.
• Above discussed debit securities are mostly issued by governments and corporations. CERTIFICATE OF DEPOSITS CDs are issued by Banks and Financial Institutions. Risk factor associated with CDs gets reduced when issued by reputable institutions or Banks.
Following are the risk attached with debt securities: Credit risk, interest rate risk and currency risk
There are no fixed maturity dates in such securities, and asset’s value is determined by company’s performance. There are two major types of equity securities: common stock and preferred stock.
Common Stock: These are simple equity securities and bear no complexities which the preferred stock bears. Holders of such securities or instrument have the voting rights when it comes to select the company’s board of director or the business decisions to be made.
Preferred Stock: Preferred stocks are sometime referred to as hybrid securities, because it contains elements of both debit security and equity security. Preferred stock confers ownership rights to security holder that is why it is equity instrument
<a href="https://www.writofinance.com/equity-securities-features-types-risk/" >Equity securities </a> as a whole is used for capital funding for companies. Companies have multiple expenses to cover. Potential growth of company is required in competitive market. So, these securities are used for capital generation, and then uses it for company’s growth.
Concluding remarks
Both are employed in business. Businesses are often established through debit securities, then what is the need for equity securities. Companies have to cover multiple expenses and expansion of business. They can also use equity instruments for repayment of debits. So, there are multiple uses for securities. As an investor, you need tools for analysis. Investment decisions are made by carefully analyzing the market. For better analysis of the stock market, investors often employ financial analysis of companies.
BONKMILLON Unleashes Its Bonkers Potential on Solana.pdfcoingabbar
Introducing BONKMILLON - The Most Bonkers Meme Coin Yet
Let's be real for a second – the world of meme coins can feel like a bit of a circus at times. Every other day, there's a new token promising to take you "to the moon" or offering some groundbreaking utility that'll change the game forever. But how many of them actually deliver on that hype?
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
Abhay Bhutada Leads Poonawalla Fincorp To Record Low NPA And Unprecedented Gr...Vighnesh Shashtri
Under the leadership of Abhay Bhutada, Poonawalla Fincorp has achieved record-low Non-Performing Assets (NPA) and witnessed unprecedented growth. Bhutada's strategic vision and effective management have significantly enhanced the company's financial health, showcasing a robust performance in the financial sector. This achievement underscores the company's resilience and ability to thrive in a competitive market, setting a new benchmark for operational excellence in the industry.
where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
5 Tips for Creating Standard Financial ReportsEasyReports
Well-crafted financial reports serve as vital tools for decision-making and transparency within an organization. By following the undermentioned tips, you can create standardized financial reports that effectively communicate your company's financial health and performance to stakeholders.
Yes of course, you can easily start mining pi network coin today and sell to legit pi vendors in the United States.
Here the telegram contact of my personal vendor.
@Pi_vendor_247
#pi network #pi coins #legit #passive income
#US
3. Concerns about standard approaches to modeling risk for
investors with longer investment horizons
100% quantitative / systematic approaches may not fully capture
data and market complexities.
Estimates may be overly dependent on the date sample and
sampling frequency.
• If volatility and correlations are investment horizon dependent,
modeling with shorter-term returns may produce poor
estimates of longer-term risk.
• Volatilities, correlations and serial correlations may vary over
time.
• Estimates can be sensitive to a few observations.
Ralph Goldsticker 3
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
4. Modeling risk using only shorter-term returns may produce
poor estimates of longer-term risks.
• Standard deviations may not grow with the square root of time.
• Correlations may be investment horizon dependent.
Ralph Goldsticker 4
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
5. Volatility varied with data window and sampling frequency.
• Volatility is dependent on market and economic environments.
Both uncertainty and risk aversion vary through time.
• Time diversification versus momentum depends on the environment.
• Time-based techniques such as exponential weighting and moving
window may not properly capture market cycles and regimes.
• Volatility was higher after 1996
than before.
• Later period showed short-term
reversal and longer-term
momentum.
• Early period showed longer-term
reversal (time diversification).
Ralph Goldsticker 5
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
6. Stock versus bond correlation varied over time.
Correlation increased with investment horizon.
• Correlations depend on the underlying environment.
• Time-based techniques such as exponential weighting and moving
window may not properly capture market cycles and regimes.
• Stocks and bonds positively
correlated through 1999.
• Stocks and bonds negatively
correlated since.
• Correlations increased with
investment horizon in both
periods.
Ralph Goldsticker 6
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
7. Objective:
Modeling risk to match the investment horizon
1. What holding period for returns?
• Higher frequency returns provide more precise estimates.
(More degrees of freedom.)
But:
• Volatility may not grow with time.
• Correlations may depend on holding period.
• Adjusting for serial correlations and cross-correlations won’t
capture episodic impacts from different types of news arriving at
different frequencies.
• Cash Flows • Growth Rates • Discount Rates
1. What data sample do we use?
•Future more likely to look like recent than distant past.
But:
• Distant events provide evidence of what could happen.
• May have view on which past periods resemble expected future.
Ralph Goldsticker 7
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
8. Use judgment to incorporate investment horizon and
environment into risk forecasts.
Rather than relying on rules and ever more complex models,
1. Use cumulative contribution charts to visually examine the behavior
of volatilities and correlations.
• Through time
• As function of return period
2. Use judgment to select the return period and data window that you
believe represents the future environment.
Ralph Goldsticker 8
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
9. Calculating cumulative contribution to variance
2. Contribution to variance for period t =
Returnt - Average Return 2
Total number of periods - 1
3. Cumulative contribution to variance =
:Ll Returnt t - Average Return 2
Total number of periods - 1
Note: Use variance rather than standard deviation because variance grows linearly with
time.
Ralph Goldsticker 9
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
10. Interpreting Cumulative Contribution to Variance Charts
Constant Volatility (simulated returns)
• Higher volatility results in steeper line.
• Lines end at annualized variance.
Ralph Goldsticker 1
0
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
11. Interpreting Cumulative Contribution to Variance Charts
Time Varying Volatility (simulated returns)
• Slope of line changes as volatility changes.
• Lines end at annualized variance of full sample.
Ralph Goldsticker 11
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
12. Examples of cumulative contribution to variance charts
1. Chart of cumulative contribution to 1-month variance
2. Cumulative contribution to variance versus rolling variance.
3. Cumulative contribution to variance versus length of return period
4. Variance estimated using daily versus monthly returns
5. Variance estimated 1-month versus 3- and 12-month returns
6. Variance estimated 12-month versus 24- and 36-month returns
Ralph Goldsticker 12
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
13. Cumulative contribution to variance of 1-month returns
Observations:
• Ends at 2.48%% (full period variance)
• Steeper than average slope shows high
volatility from 1972 to 1976.
• Slope of line from 1977 to 1987 shows
volatility was lower than early 1970s,
but higher than subsequent period.
• Crash of October 1987 is visible.
• Steeper slope shows higher volatility
during and post the Tech Bubble.
• Future will look like the post October
1987 period
Ralph Goldsticker 13
14. Rolling volatility doesn’t provide the same insights as
cumulative contribution to variance chart.
Observations:
• Rolling volatility is affected by data
leaving the sample.
• Rolling volatility doesn’t identify start
and end points of volatility regimes.
• Rolling volatility spiked after October
1987, but fell 36 months later.
• Rolling volatility ranged from 8% to 22%.
Cumulative contribution to variance
showed more stable behavior.
Ralph Goldsticker 14
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
15. Implied volatility doesn’t provide the same insights as the
cumulative contribution to standard deviation.
14
Observations:
• Implied volatility moves more due to
changes in the price of volatility (cost of
insurance) than changes in expected
volatility.
• Implied volatility for all 3 horizons spiked
above 30% in response to market
moves.
• Cumulative contribution to variance of
monthly returns showed more stable
behavior. More appropriate for
investors with longer horizons.
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
16. Cumulative contribution to variance charts show the effects
of serial correlations and/or pace of news arrival.
• Variance increasing with holding period
• Positive serial correlation (momentum / under reaction)
• Some types of news arrives at lower frequency.
• Variance decreasing with holding period.
• Negative serial correlation (time diversification / over reaction /
reversal)
Ralph Goldsticker 15
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
17. Volatility of daily returns has been higher than monthly
returns since the mid 1990s.
Observations:
• Higher standard deviation of daily
returns for the full period shows
reversal at daily level.
• From 1974 though 1997, other than
1987 Crash, similar slopes for daily and
1-month lines. Little serial correlation in
daily returns during that period.
• Future will look like period since 1997.
Monthly vol will be less than daily vol.
• From 1997 through 2013, daily returns
line is steeper than 1-month. Volatility
of 20.5% versus 16.0%. Model risk using monthly returns.
16
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
18. Higher variance of 3- and 12-month returns shows positive
serial correlation or impact of lower frequency news.
Observations:
• Full period variances increased with
holding period, reflecting positive serial
correlation (momentum) in 1-month
and 3-month returns.
• Most of the positive serial correlation at
the 12-month horizon occurred from
• Similar slopes of lines for 1-month and
3-month returns suggests that the
positive serial correlation of 1-month
returns was episodic.
• Should not use monthly returns to
forecast annual volatility without an
1995 through 2008. adjustment.
18
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
19. Data shows time diversification at multi-year horizons.
Pattern was reversed during and after the Tech Bubble.
Observations:
• Time diversification at longer horizons.
Variances decreased with holding
period.
• Trending market during and after Tech
Bubble appears as 36-month rising
faster than 12-month and 24-month.
• Reversal of Financial Crisis losses
appears as 12-month rising faster than
24-month and 36-month.
• Assume some time diversification at 36-
month investment horizon.
Ralph Goldsticker 19
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
20. Volatility Summary
Volatility and serial correlations varied through time.
Full period behavior:
• Short-term reversals:
Daily volatility was higher than monthly.
• Medium-term momentum:
Volatility of 3- and 12-month returns was higher than 1-month
• Long-term time diversification:
Volatility of 24- and 36-month returns were lower than 12-month.
But:
• Volatility of monthly returns was higher during the 1970s and 1980s.
• Positive serial correlation of annual returns during and after the Tech
Bubble
Ralph Goldsticker 20
Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
21. II. Cumulative contribution to correlation charts provide
insights into the behavior of correlations over time.
Estimating correlations requires addressing the same issues as
estimating volatility.
Cumulative Contribution to Correlation charts provide insights that
assist in deciding:
• What holding period do we use for returns?
• What time period do we use to estimate the statistics?
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
22. Calculating cumulative contribution to correlation
1. Correlation(Stocks, Bonds) =
Covariance (Stocks,Bonds)
Std Dev Stocks × Std Dev (Bonds)
2. Covariance(Stocks, Bonds ) =
:L((Stk Rett − Avg Stk Ret) × (Bnd Rett − Avg Bnd Ret))
Total number of periods − 1
3. Cumulative Contribution to Correlation(Stock, Bond) =
:Lt ((Stock Returnt − Avg Stk Ret) × 1 (Bond Returnt − Avg Bnd Ret))
(Total number of periods − 1) × Std Dev Stocks × Std Dev(Bonds)
Note: Covariances grow linearly with time, so contributions to correlations are linear
as well.
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
23. Interpreting Cumulative Contribution to Correlation Charts
Constant Correlation (simulated returns)
• Higher correlation results in steeper line.
• Negative correlation results in downward slope
• Lines end at full period correlation.
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
24. Interpreting Cumulative Contribution to Correlation Charts
Time Varying Correlation (simulated returns)
• Slope of line changes as correlation changes.
• Line ends at full period correlation.
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25. Cumulative contribution to correlation chart provides
insights unavailable using full period and rolling window.
• Slope of cumulative correlation
line shows the evolution of
correlations through time.
• Cumulative contribution shows
correlation of monthly stock and
bonds returns changed from
positive to negative Oct. 2000.
• Rolling correlation was zero in
October 2000, and didn’t get to
-.30 until 2002.
• Cumulative correlation is not
sensitive to data points dropping
out of the sample (e.g. Oct.
1987)
Correlation of
Monthly Returns
1972 - 2013 0.10
12/1972 – 9/2000 0.31
10/2000 – 12/2013 -0.37
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
26. Stock versus Bond correlation increased with holding
period.
• Investors should use a return
period that’s consistent with
their investment horizon.
• The correlation calculated
using 3-year returns was
larger than correlations
calculated using returns for
shorter periods.
• Higher degree of correlation
shows that there are regimes
and cycles that are not
captured in short-term
returns.
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
27. Cumulative contribution to correlation allows us to identify
turning points.
Holding Period for Return Calculation
Daily 1-Mth 3-Mth Annual 2-Year 3-Year
Full Period:
1972 - 2013
0.00 0.10 0.07 0.21 0.27 0.35
While Positive 0.32 0.31 0.38 0.53 0.60 0.62
While Negative -0.34 -0.37 -0.52 -0.65 -0.71 -0.71
Date Changed from
Positive to Negative *
Oct-97 Sep-00 Mar-98 Apr-99 Sep-99 Apr-02
• The correlations calculated using annual returns are roughly 1½ times the
correlations calculated using monthly returns.
• The correlations calculated using 3-year returns are roughly two times as large.
* Date of peak. All of the correlations turned negative at approximately the same time.
Much of the difference can be attributed to slower reaction of longer holding period returns.
E.g. The return for January 2000 is in the 3-year return through December 2002.
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28. Stock versus Bond correlation is regime dependent.
28
Macro Environment Correlation
1970s Changing inflation expectations +
1980s Falling interest rates +
1990s Capital flows into both stock and bond markets +
2000s Tech Bubble and Financial Crisis result in interest
rates responding to growth surprises.
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
29. Changes in the slope of lines highlights regimes
• The steep 3-year line
between 1975 and 1981
shows that the environment
of highly volatile inflation
expectations translated into
high stock-bond correlations
for longer-term investors.
• There wasn’t much variability
in correlations between 1972
and 2000 using daily and
monthly returns.
• The correlations were more
negative after the Tech
Bubble and Financial Crisis
than during the period
between.
Financial
Crisis
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
30. Correlation Summary
Charting time series contribution to correlation provides insights that
are obscured by rolling windows and other approaches.
1. Correlation between stocks and Treasuries was regime dependent.
• Positive through the Tech Stock Bubble
• Negative since
2. Correlation between US stocks and Treasuries increased with the
holding period.
• More positive when positive
• More negative when negative
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon
31. Discussion
• We use charts of cumulative returns to understand performance, why
shouldn’t we use similar tools to understand risk?
• While the presentation focused on the visualizing asset class risks
and correlations, similar cumulative contribution charts could be used
to visualize other types of risks such as serial correlation, tracking
error and information ratios.
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Visualizing the Time Series Behavior of Volatility, Serial Correlation and Investment Horizon