1997 Risk Model delivered in Excel format to the financial market.
The HSBC James Capel Portfolio Analyser is tailored to the unusual structure
of the Australian sharemarket – the high concentration of mining companies.
It consists of a spreadsheet that analyses the risk of a portfolio of Australian
equities.
The Portfolio Analyser highlights the overall risk of a portfolio against a
number of different benchmarks and, importantly, the sources of this risk
in terms of both stocks and sectors.
The style views approach enables assessment of the portfolio using more
than one paradigm. This allows investors to better allocate stocks to
match their views of sector groupings, or the risk of the portfolio.
The key benefit of the Portfolio Analyser over rival products is its ability to
interrogate the engine, rather than being presented with a “black–box”
approach.
Pairs
This page lists all the significant correlations between pairs of different stocks –
both significantly positive and negative correlations.
This information is useful in looking for arbitrage opportunities in the market.
For example, two companies’ share prices and dividend returns might move
closely together – perhaps due to a similar sector exposure. If their share price
returns move out of sync, for no apparent reason, we have the basis for a
possible pairs trading opportunity.
Dokumen tersebut membahas tentang Pedoman Dasar Karang Taruna (PDKT) yang mengatur tentang tujuan, asas, struktur organisasi, keanggotaan, kepengurusan, program kerja, dan sumber pendanaan Karang Taruna. PDKT disahkan oleh Kementerian Sosial RI untuk memandu kegiatan Karang Taruna di seluruh Indonesia.
Karang Taruna merupakan organisasi pembinaan remaja yang didirikan pada 1960 di Jakarta. Karang Taruna bertujuan menanggapi persoalan masyarakat dan mengantisipasi krisis sosial kaum muda melalui kegiatan ekonomi, seni budaya, dan peningkatan kemandirian. Karang Taruna telah berkembang melalui berbagai fase sejak didirikan hingga saat ini.
Materi Manajemen Organisasi Karang Taruna.pptxPrihWardoyo2
Dokumen tersebut merangkum tentang pelatihan Karang Taruna di Kabupaten Sleman tahun 2022. Karang Taruna adalah organisasi generasi muda yang bertujuan untuk mengembangkan potensi dan kemampuan generasi muda serta meningkatkan kesejahteraan sosial. Pelatihan ini membahas tentang peraturan, prinsip, tujuan, status hukum, tugas, fungsi, keanggotaan, pengurus, pembina, pendanaan, dan program Karang Taruna.
Dokumen tersebut merupakan peraturan tentang Anggaran Dasar dan Anggaran Rumah Tangga Karang Taruna. Dokumen ini mengatur tentang tujuan, fungsi, keanggotaan, organisasi, pengurusan, mekanisme kerja, dan pengukuhan pengurus Karang Taruna di tingkat desa/kelurahan hingga nasional.
Dokumen tersebut membahas tentang Pedoman Dasar Karang Taruna (PDKT) yang mengatur tentang tujuan, asas, struktur organisasi, keanggotaan, kepengurusan, program kerja, dan sumber pendanaan Karang Taruna. PDKT disahkan oleh Kementerian Sosial RI untuk memandu kegiatan Karang Taruna di seluruh Indonesia.
Karang Taruna merupakan organisasi pembinaan remaja yang didirikan pada 1960 di Jakarta. Karang Taruna bertujuan menanggapi persoalan masyarakat dan mengantisipasi krisis sosial kaum muda melalui kegiatan ekonomi, seni budaya, dan peningkatan kemandirian. Karang Taruna telah berkembang melalui berbagai fase sejak didirikan hingga saat ini.
Materi Manajemen Organisasi Karang Taruna.pptxPrihWardoyo2
Dokumen tersebut merangkum tentang pelatihan Karang Taruna di Kabupaten Sleman tahun 2022. Karang Taruna adalah organisasi generasi muda yang bertujuan untuk mengembangkan potensi dan kemampuan generasi muda serta meningkatkan kesejahteraan sosial. Pelatihan ini membahas tentang peraturan, prinsip, tujuan, status hukum, tugas, fungsi, keanggotaan, pengurus, pembina, pendanaan, dan program Karang Taruna.
Dokumen tersebut merupakan peraturan tentang Anggaran Dasar dan Anggaran Rumah Tangga Karang Taruna. Dokumen ini mengatur tentang tujuan, fungsi, keanggotaan, organisasi, pengurusan, mekanisme kerja, dan pengukuhan pengurus Karang Taruna di tingkat desa/kelurahan hingga nasional.
Dokumen tersebut membahas mengenai penyempurnaan penyelenggaraan trantibumlinmas di tingkat desa, meliputi:
1. Penguatan kelembagaan satuan pelindungan masyarakat (Satlinmas) di desa
2. Peningkatan kapasitas personil Satlinmas
3. Peningkatan kinerja Satlinmas melalui berbagai program pemberdayaan
Dokumen tersebut membahas tentang Sistem Keamanan Lingkungan (Siskamling) yang bertujuan menciptakan situasi yang aman dan tentram serta meningkatkan kesadaran masyarakat dalam pencegahan gangguan ketertiban. Siskamling diselenggarakan melalui kerja sama antara polisi, masyarakat, dan aparat pemerintah lokal dengan Forum Kemitraan Polisi dan Masyarakat sebagai fasilitatornya. Pos Kamling bertugas menjaga
Dokumen tersebut membahas tentang pemberdayaan pekerja sosial masyarakat. Ia menjelaskan pengertian, tujuan, dan peran pekerja sosial masyarakat. Dokumen ini juga menjelaskan prinsip dan aspek pemberdayaan pekerja sosial masyarakat seperti peningkatan kapasitas, pemberdayaan kelembagaan, dan apresiasi kinerja. Arah kebijakan pemberdayaan mencakup peningkatan pemahaman
Anggaran rumah tangga KARANG TARUNA BHAKTI MANDIRI 02Nie Andini
Dokumen tersebut merupakan Anggaran Rumah Tangga Karang Taruna Bhakti Mandiri 02 Palabuan tahun 2013 yang mengatur tentang struktur organisasi, keanggotaan, pemilihan ketua, tugas dan wewenang pengurus karang taruna.
1) Dokumen tersebut merupakan laporan perkiraan intelijen singkat mengenai kunjungan pejabat penting ke Kabupaten Nias
2) Ada kemungkinan terjadinya unjuk rasa atau gangguan karena ketidakpuasan masyarakat terhadap kinerja BRR
3) Polri bersiap mengamankan kunjungan tersebut secara terencana bekerja sama dengan instansi terkait.
Permendagri no. 18 tahun 2018 tentang lembaga kemasyarakatan desa dan lembaga...Pemdes Seboro Sadang
Peraturan Menteri ini mengatur tentang Lembaga Kemasyarakatan Desa (LKD) dan Lembaga Adat Desa (LAD) yang bertujuan untuk meningkatkan partisipasi masyarakat dalam pembangunan desa dan menjamin kelancaran pelayanan pemerintahan desa. LKD dan LAD dibentuk berdasarkan prakarsa masyarakat dan berperan sebagai mitra pemerintah desa, antara lain dengan menampung aspirasi masyarakat dan turut serta d
TUPOKSI KEPALA DESA DAN PERANGKAT DESA.pptxSaripudin19
Dokumen tersebut membahas tentang tugas pokok dan fungsi Kepala Desa dan Perangkat Desa dalam penyelenggaraan pemerintahan di desa. Kepala Desa bertanggung jawab atas penyelenggaraan pemerintahan desa, pembangunan desa, pembinaan kemasyarakatan, dan pemberdayaan masyarakat desa. Perangkat Desa membantu Kepala Desa dalam pelaksanaan tugas tersebut di bidang umum, perencanaan, keuangan, pemer
A pessoa descrita tem grande elevação e nobreza de caráter. O amor e o altruísmo fazem parte de sua personalidade, assim como a moral e bondade. Busca influenciar positivamente através da sabedoria.
Keputusan Bupati Barito Selatan membentuk Kelompok Kerja Operasional Pembinaan Pos Pelayanan Terpadu dan Sekretariat Tetap Kabupaten untuk meningkatkan koordinasi dan pembinaan Pos Pelayanan Terpadu di wilayah Kabupaten Barito Selatan. Kelompok Kerja ini akan melakukan revitalisasi Pos Pelayanan Terpadu, pembinaan, pemantauan, dan pelaporan kegiatan.
Dokumen tersebut membahas tentang penyelenggaraan ketertiban umum, ketenteraman, dan perlindungan masyarakat di Desa Badegan Kecamatan Badegan tahun 2023. Dokumen tersebut menjelaskan dasar hukum, pengertian, peran desa, kegiatan, pelaksanaan, dan satuan perlindungan masyarakat (Satlinmas) dalam menyelenggarakan ketertiban umum dan perlindungan masyarakat di desa.
Dokumen tersebut membahas tentang pengertian, kedudukan, fungsi, wewenang, hak, kewajiban, larangan, pemberhentian, rapat, aspirasi masyarakat, hubungan kerja, keuangan, dan peran Badan Permusyawaratan Desa di Kabupaten Bekasi secara singkat.
Alpha Risk Analyser - Risk Analysis in terms of Value versus GrowthColin Ritchie
Alpha Investment Management
Alpha Risk Analyser
Risk Analysis in terms of Value versus Growth
Six months to June 30th 1999.
Combining in-house statistical factor Risk Model with bottom up Valuation. Incorporating the relationship of bond yield to valuation; interest rate sensitivity to portfolio risk; and explaining these relationships using Value versus Growth terminology.
1. The Australian equity market has increased 24% from its March low but remains below levels from three years ago. The report predicts continued bull market conditions with the All Ordinaries index reaching 3,650, implying almost 15% total returns over the next 12 months.
2. Small cap stocks have outperformed recently but now appear relatively expensive. Overall, the market appears fairly valued based on the "rule of 20" and prospective earnings yield relative to bonds.
3. The consensus view is that stronger world growth may benefit resources over banks, but the report finds resource stocks trading at higher valuations and lower yields compared to the major banks. The portfolios recommended overweight banks and include only one major miner.
Dokumen tersebut membahas mengenai penyempurnaan penyelenggaraan trantibumlinmas di tingkat desa, meliputi:
1. Penguatan kelembagaan satuan pelindungan masyarakat (Satlinmas) di desa
2. Peningkatan kapasitas personil Satlinmas
3. Peningkatan kinerja Satlinmas melalui berbagai program pemberdayaan
Dokumen tersebut membahas tentang Sistem Keamanan Lingkungan (Siskamling) yang bertujuan menciptakan situasi yang aman dan tentram serta meningkatkan kesadaran masyarakat dalam pencegahan gangguan ketertiban. Siskamling diselenggarakan melalui kerja sama antara polisi, masyarakat, dan aparat pemerintah lokal dengan Forum Kemitraan Polisi dan Masyarakat sebagai fasilitatornya. Pos Kamling bertugas menjaga
Dokumen tersebut membahas tentang pemberdayaan pekerja sosial masyarakat. Ia menjelaskan pengertian, tujuan, dan peran pekerja sosial masyarakat. Dokumen ini juga menjelaskan prinsip dan aspek pemberdayaan pekerja sosial masyarakat seperti peningkatan kapasitas, pemberdayaan kelembagaan, dan apresiasi kinerja. Arah kebijakan pemberdayaan mencakup peningkatan pemahaman
Anggaran rumah tangga KARANG TARUNA BHAKTI MANDIRI 02Nie Andini
Dokumen tersebut merupakan Anggaran Rumah Tangga Karang Taruna Bhakti Mandiri 02 Palabuan tahun 2013 yang mengatur tentang struktur organisasi, keanggotaan, pemilihan ketua, tugas dan wewenang pengurus karang taruna.
1) Dokumen tersebut merupakan laporan perkiraan intelijen singkat mengenai kunjungan pejabat penting ke Kabupaten Nias
2) Ada kemungkinan terjadinya unjuk rasa atau gangguan karena ketidakpuasan masyarakat terhadap kinerja BRR
3) Polri bersiap mengamankan kunjungan tersebut secara terencana bekerja sama dengan instansi terkait.
Permendagri no. 18 tahun 2018 tentang lembaga kemasyarakatan desa dan lembaga...Pemdes Seboro Sadang
Peraturan Menteri ini mengatur tentang Lembaga Kemasyarakatan Desa (LKD) dan Lembaga Adat Desa (LAD) yang bertujuan untuk meningkatkan partisipasi masyarakat dalam pembangunan desa dan menjamin kelancaran pelayanan pemerintahan desa. LKD dan LAD dibentuk berdasarkan prakarsa masyarakat dan berperan sebagai mitra pemerintah desa, antara lain dengan menampung aspirasi masyarakat dan turut serta d
TUPOKSI KEPALA DESA DAN PERANGKAT DESA.pptxSaripudin19
Dokumen tersebut membahas tentang tugas pokok dan fungsi Kepala Desa dan Perangkat Desa dalam penyelenggaraan pemerintahan di desa. Kepala Desa bertanggung jawab atas penyelenggaraan pemerintahan desa, pembangunan desa, pembinaan kemasyarakatan, dan pemberdayaan masyarakat desa. Perangkat Desa membantu Kepala Desa dalam pelaksanaan tugas tersebut di bidang umum, perencanaan, keuangan, pemer
A pessoa descrita tem grande elevação e nobreza de caráter. O amor e o altruísmo fazem parte de sua personalidade, assim como a moral e bondade. Busca influenciar positivamente através da sabedoria.
Keputusan Bupati Barito Selatan membentuk Kelompok Kerja Operasional Pembinaan Pos Pelayanan Terpadu dan Sekretariat Tetap Kabupaten untuk meningkatkan koordinasi dan pembinaan Pos Pelayanan Terpadu di wilayah Kabupaten Barito Selatan. Kelompok Kerja ini akan melakukan revitalisasi Pos Pelayanan Terpadu, pembinaan, pemantauan, dan pelaporan kegiatan.
Dokumen tersebut membahas tentang penyelenggaraan ketertiban umum, ketenteraman, dan perlindungan masyarakat di Desa Badegan Kecamatan Badegan tahun 2023. Dokumen tersebut menjelaskan dasar hukum, pengertian, peran desa, kegiatan, pelaksanaan, dan satuan perlindungan masyarakat (Satlinmas) dalam menyelenggarakan ketertiban umum dan perlindungan masyarakat di desa.
Dokumen tersebut membahas tentang pengertian, kedudukan, fungsi, wewenang, hak, kewajiban, larangan, pemberhentian, rapat, aspirasi masyarakat, hubungan kerja, keuangan, dan peran Badan Permusyawaratan Desa di Kabupaten Bekasi secara singkat.
Alpha Risk Analyser - Risk Analysis in terms of Value versus GrowthColin Ritchie
Alpha Investment Management
Alpha Risk Analyser
Risk Analysis in terms of Value versus Growth
Six months to June 30th 1999.
Combining in-house statistical factor Risk Model with bottom up Valuation. Incorporating the relationship of bond yield to valuation; interest rate sensitivity to portfolio risk; and explaining these relationships using Value versus Growth terminology.
1. The Australian equity market has increased 24% from its March low but remains below levels from three years ago. The report predicts continued bull market conditions with the All Ordinaries index reaching 3,650, implying almost 15% total returns over the next 12 months.
2. Small cap stocks have outperformed recently but now appear relatively expensive. Overall, the market appears fairly valued based on the "rule of 20" and prospective earnings yield relative to bonds.
3. The consensus view is that stronger world growth may benefit resources over banks, but the report finds resource stocks trading at higher valuations and lower yields compared to the major banks. The portfolios recommended overweight banks and include only one major miner.
Capital Expenditure Survey 2003
Capital spending continues to decline in nearly all industries, continuing a
trend that began in the mid-1990s when manufacturing productivity began
to increase markedly. The continuing uncertainty in most economies has
put pressure on manufacturers to cut spending, resulting in a steady decline
for several years now despite increasing revenues. Helping to fuel the
cost-cutting fire are the mega-mergers between industrial giants that have
racked up billions in savings as companies increase their manufacturing
economies of scale and eliminate duplicate functions.
ARC’s CapEx index tracks capital expenditures, total revenue, total assets,
EBIT, and return on assets (ROA) for 56 companies in 10 target industries,
representing $2.4 trillion in annual revenue. Companies in the index
generate revenue from most global markets and many
spread their manufacturing around the globe. Of the 56
companies, 64 percent have their headquarters in North
America, 27 percent in Europe, and 9 percent in Asia.
This report provides an overview of the coal mining market in China in three main sections. First, it analyzes the size of China's coal mining market from 2008-2010 and identifies the major market areas. Second, it examines the top 10 companies in the industry by sales revenue and market share. Third, it evaluates the market structure and shares by company ownership as well as import and export trends of coal mining products. The report aims to present a comprehensive picture of the current state and key players influencing China's coal mining market.
This document is a capstone project report analyzing the Australia grocery market which is dominated by Woolworth and Coles with over 60% combined market share. The report includes an introduction outlining the research topic and background. It then provides a literature review on relevant anti-combination laws, the effects of monopoly, and risk analysis. The report also describes the data collection and analysis methodology to be used. It will analyze factors related to the grocery industry and identify hypotheses about whether the current monopoly is optimal for the Australian market and consumers. The conclusion will forecast if other competitors could become major players by utilizing appropriate short- and long-term strategies.
This report analyzes the dyestuff market in China. It examines the size of the Chinese dyestuff market and identifies hot areas. It also analyzes the top 10 companies in the industry and discusses the market share and structure in China. The report provides an overview of dyestuff imports and exports as well as industry standards. It summarizes key statistics about the Chinese dyestuff industry.
Quiz-Essay Paper 3 – Capital Structure and Financial Leverage .docxcatheryncouper
Quiz-Essay Paper 3 – Capital Structure and Financial Leverage Risk
INTRODUCTION: Enter historical EBIT for your non-financial company and determine your optimal
capital structure for shareholder value (EPS) and Risk (beta-driven WACC). For purposes of enterprise
planning and/or acquisitions, a strategic view of capital structure across alternative debt/capital ratios
and operating earnings scenarios is essential. You are encouraged to develop more than one earnings
scenario – a probability distribution of EBIT is best thought not required for this assignment.
If you discover issues or are unsure of how to deal with negative EBIT, growth or cash flow from your
selected company’s financial statements, please let me know. Additional information on writing the QEP
is posted in our course, under the Content-Student Resources-Checklists – be sure to take advantage of
this, as it will prove quite helpful for this and following papers. Finally, although we don’t grade your
writing process directly– plan to start on time with preliminary research, draft, revision(s), and finalize
steps.
Contact EWC (Resources Menu-EWC) to make sure your paper is written in a manner that is in scope
and carries the most impact. Let me know if you feel like you might be getting stuck or need clarification
on developing analytic perceptions or have scope questions.
SPECIFICS OF THE ASSIGNMENT: In this assignment, you will write a 1 1/2 – 2 page narrative analysis of
your selected non-financial company’s optimal capital structure for shareholder value and cost. Base
your analysis on example spreadsheet provided or similar framework covering shareholder value and
risk for capital structure. No year over year, point to point recitations please.
Calculate and use financial leverage inputs of the example spreadsheet using descriptive statistics (e.g.,
mean, median, standard deviation, geometric mean, rolling average, min, max, etc.) see example Excel
worksheet [Content] or other sources. Use descriptive statistics for key financial leverage inputs in your
narrative analysis for best grade (e.g., discuss mean relative to median, standard deviation, reversion to
the mean, scenarios, rolling average trend, etc.).
For Optimal Capital Structure Analysis:
Typically, the analyst finds the mean or median ratio and standard deviation for each of the financial
leverage inputs group and re-calculates an estimated WACC and EPS of the subject company as if
company performance had shifted due to different levels of debt. Multiple scenarios of estimated
WACC and EPS are presented to demonstrate a reasonable range estimate of optimal capital structure.
What might be a reasonable HighLowMostLikely WACC-EPS pre-acquisition? How might H-L-ML change
if an acquisition were to optimize the capital structure? For best grade show before optimal capital
structure and after optimal capital structure.
Ask me if you have questio ...
- The portfolio generated a profit of €88,299 from equity investments, €10,904 from fixed income, and incurred a loss of €30,016 from hedging, resulting in an overall profit of €69,187.
- The portfolio consisted of 70% in equities, 22% in fixed income, and 5% in an alternative investment (hedging) strategy, with the remaining 3% as fees.
- Dividends generated €11,988 in additional profits.
This report analyzes the canned meat and poultry market in China. It discusses the size of the market and identifies hot areas with high import levels. It ranks the top 10 companies and analyzes their market share. Finally, it examines import and export trends, product standards, and lists major importers in China.
This report analyzes the biscuit market in China. It discusses the size of the Chinese biscuit market and identifies hot areas based on production and import levels in different provinces. It also analyzes the top 10 companies in the industry and examines the market share and structure in China. The report provides data on market shares held by imports, foreign enterprises, and companies of different ownership types. It also lists relevant industry standards and major biscuit importers in China.
The document provides an overview of Antero Resources Corporation. It contains forward-looking statements regarding estimates, plans, expectations and guidance. It cautions that actual results could differ materially from forward-looking statements due to risks and uncertainties inherent in the natural gas and oil business. The company has achieved significant reductions in well costs in both the Marcellus and Utica shales through improvements in drilling times, lateral lengths, stages per well, and costs per thousand feet.
This document provides an overview and agenda for a presentation on successful planning strategies for life and investments. It discusses Barry Mendelson's background and experience in financial services. It also summarizes Just Plans Etc., the firm he founded, which provides financial planning and investment management. The presentation agenda covers investment planning, personal planning, and charitable giving strategies.
Impact of Risk Free and Risky Asset on Portfolio ReturnAtif Ahmed
The document analyzes the impact of risk-free and risky assets on portfolio returns. It examines data from 10 stocks listed on the Karachi Stock Exchange from July 2013 to June 2015 to create two portfolios. Descriptive statistics are calculated for the individual stocks and indexes. The risky portfolio includes the 10 stocks from various industries, while the risk-free portfolio contains treasury bills. Correlations between the stocks and market index are mostly positive, except for treasury bills. The purpose is to analyze risk and returns of the portfolios to minimize risk through diversification across unrelated industries.
Create a financial analysis report with our topic-specific Detailed Investment Analysis Powerpoint Presentation Slides. The content ready investment evaluation PowerPoint complete deck has various professional looking PPT slides such as introduction to investments, objectives of portfolio management, types of investment, market scenario overview investment instruments, securities portfolio, analysis and valuation of equity securities, industry analysis PESTEL, SWOT analysis, discounted cash flow method, financial statement analysis, company cash flow statement, issues inefficient markets, technical analysis types, investment in special situations, fixed income and leveraged securities, bond valuation system, reinvestment risk table, type of convertible securities, options analysis, warrants summarization overview, derivative products, put and call options, stock index futures and options, stock indexes comparison table, broaden the investment perspective, international security market highlights, global market trends, mutual funds investment criteria overview, investment in real estate, diversified real estate classification, KPIs and dashboards, etc. Download investment management presentation deck to showcase asset allocation management plan. Give folks an example of your high degree of erudition with our Detailed Investment Analysis Powerpoint Presentation Slides. Be able to display impressive credentials.
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OPXS is a monopoly provider of laser-protected periscopes to the US military. It has no competitors after acquiring its previous major rival. OPXS revenues and profits have steadily increased in recent years due to increased military spending on vehicles like tanks that use its products. The company trades on the OTC market, which may suppress its valuation. However, its current valuation of EV/revenue of 0.76x and EV/EBITDA of 8.8x presents an attractive risk/reward given its dominant market position and growth prospects from military spending increases and commercial expansion plans.
This report analyzes the confectionery market in China, including the size of the market and changes over time, key regions in China, and the top 10 companies. It examines the market share and structure based on different types of enterprises. The report also evaluates import/export trends and provides an overview of industry standards and major importers in China. Key statistics on the sales, production, profits, assets, and growth of the confectionery industry in China are presented.
Examine the components of investment management with our content ready Portfolio Analysis PowerPoint Presentation Slides. The topic-specific investment strategies PowerPoint complete deck has various content ready PPT slides such as introduction to investments, objectives of portfolio management, types of investment, market scenario overview investment instruments, securities portfolio, analysis and valuation of equity securities, industry analysis PESTEL, SWOT analysis, discounted cash flow method, financial statement analysis, company cash flow statement, investment in special situations, fixed income and leveraged securities, bond valuation system, reinvestment risk table, type of convertible securities, options analysis, warrants summarization overview, derivative products, put and call options, stock index futures and options, stock indexes comparison table, broaden the investment perspective, international security market highlights, global market trends, mutual funds investment criteria overview, investment in real estate, diversified real estate classification, KPIs and dashboards, etc. Download this visually appealing easy to use financial management PPT slide to showcase factors of investing. Bedeck your ideas with our Portfolio Analysis PowerPoint Presentation Slides. Your audience will get glued onto them.
Poonawalla Fincorp’s Strategy to Achieve Industry-Leading NPA Metricsshruti1menon2
Poonawalla Fincorp Limited, under the leadership of Managing Director Abhay Bhutada, has achieved industry-leading Gross Non-Performing Assets (GNPA) below 1% and Net Non-Performing Assets (NNPA) below 0.5% as of May 31, 2024. This success is attributed to a strategic vision focusing on prudent credit policies, robust risk management, and digital transformation. Bhutada's leadership has driven the company to exceed its targets ahead of schedule, emphasizing rigorous credit assessment, advanced risk management, and enhanced collection efficiency. By prioritizing customer-centric solutions, leveraging digital innovation, and maintaining strong financial performance, Poonawalla Fincorp sets new benchmarks in the industry. With a continued focus on asset quality, digital enhancement, and exploring growth opportunities, the company is well-positioned for sustained success in the future.
13 Jun 24 ILC Retirement Income Summit - slides.pptxILC- UK
ILC's Retirement Income Summit was hosted by M&G and supported by Canada Life. The event brought together key policymakers, influencers and experts to help identify policy priorities for the next Government and ensure more of us have access to a decent income in retirement.
Contributors included:
Jo Blanden, Professor in Economics, University of Surrey
Clive Bolton, CEO, Life Insurance M&G Plc
Jim Boyd, CEO, Equity Release Council
Molly Broome, Economist, Resolution Foundation
Nida Broughton, Co-Director of Economic Policy, Behavioural Insights Team
Jonathan Cribb, Associate Director and Head of Retirement, Savings, and Ageing, Institute for Fiscal Studies
Joanna Elson CBE, Chief Executive Officer, Independent Age
Tom Evans, Managing Director of Retirement, Canada Life
Steve Groves, Chair, Key Retirement Group
Tish Hanifan, Founder and Joint Chair of the Society of Later life Advisers
Sue Lewis, ILC Trustee
Siobhan Lough, Senior Consultant, Hymans Robertson
Mick McAteer, Co-Director, The Financial Inclusion Centre
Stuart McDonald MBE, Head of Longevity and Democratic Insights, LCP
Anusha Mittal, Managing Director, Individual Life and Pensions, M&G Life
Shelley Morris, Senior Project Manager, Living Pension, Living Wage Foundation
Sarah O'Grady, Journalist
Will Sherlock, Head of External Relations, M&G Plc
Daniela Silcock, Head of Policy Research, Pensions Policy Institute
David Sinclair, Chief Executive, ILC
Jordi Skilbeck, Senior Policy Advisor, Pensions and Lifetime Savings Association
Rt Hon Sir Stephen Timms, former Chair, Work & Pensions Committee
Nigel Waterson, ILC Trustee
Jackie Wells, Strategy and Policy Consultant, ILC Strategic Advisory Board
Budgeting as a Control Tool in Government Accounting in Nigeria
Being a Paper Presented at the Nigerian Maritime Administration and Safety Agency (NIMASA) Budget Office Staff at Sojourner Hotel, GRA, Ikeja Lagos on Saturday 8th June, 2024.
Navigating Your Financial Future: Comprehensive Planning with Mike Baumannmikebaumannfinancial
Learn how financial planner Mike Baumann helps individuals and families articulate their financial aspirations and develop tailored plans. This presentation delves into budgeting, investment strategies, retirement planning, tax optimization, and the importance of ongoing plan adjustments.
“Amidst Tempered Optimism” Main economic trends in May 2024 based on the results of the New Monthly Enterprises Survey, #NRES
On 12 June 2024 the Institute for Economic Research and Policy Consulting (IER) held an online event “Economic Trends from a Business Perspective (May 2024)”.
During the event, the results of the 25-th monthly survey of business executives “Ukrainian Business during the war”, which was conducted in May 2024, were presented.
The field stage of the 25-th wave lasted from May 20 to May 31, 2024. In May, 532 companies were surveyed.
The enterprise managers compared the work results in May 2024 with April, assessed the indicators at the time of the survey (May 2024), and gave forecasts for the next two, three, or six months, depending on the question. In certain issues (where indicated), the work results were compared with the pre-war period (before February 24, 2022).
✅ More survey results in the presentation.
✅ Video presentation: https://youtu.be/4ZvsSKd1MzE
5 Compelling Reasons to Invest in Cryptocurrency NowDaniel
In recent years, cryptocurrencies have emerged as more than just a niche fascination; they have become a transformative force in global finance and technology. Initially propelled by the enigmatic Bitcoin, cryptocurrencies have evolved into a diverse ecosystem of digital assets with the potential to reshape how we perceive and interact with money.
5 Compelling Reasons to Invest in Cryptocurrency Now
HSBC Portfolio Risk Analyser
1. HSBC James Capel Australia
Member HSBC Group
HSBC James Capel: Portfolio research 1
November 1997 Portfolio research
Portfolio Analyser
Risk analysis of Australian equities
The HSBC James Capel Portfolio Analyser is tailored to the unusual structure
of the Australian sharemarket – the high concentration of mining companies.
It consists of a spreadsheet that analyses the risk of a portfolio of Australian
equities.
The Portfolio Analyser highlights the overall risk of a portfolio against a
number of different benchmarks and, importantly, the sources of this risk
in terms of both stocks and sectors.
The style views approach enables assessment of the portfolio using more
than one paradigm. This allows investors to better allocate stocks to
match their views of sector groupings, or the risk of the portfolio.
The key benefit of the Portfolio Analyser over rival products is its ability to
interrogate the engine, rather than being presented with a “black–box”
approach.
Contact
+61-3-9229+ Ext
Colin Ritchie 3572
colin.ritchie@hsbcib.com
2. November 1997 Portfolio Analyser
2 HSBC James Capel: Portfolio research
Contents
Overview – getting to know portfolio risk ....................................................................... 3
Entering a portfolio ........................................................................................................... 4
Summary statistics............................................................................................................ 5
Overall break-down of tracking variance ........................................................................ 6
Sensitivity analysis of tracking variance ......................................................................... 7
Stocks outside the portfolio........................................................................................................9
Stock contributions to tracking variance....................................................................... 10
Tracking error – popular misconceptions ..................................................................... 11
Tracking error & residual error....................................................................................... 13
Beta & residual error ....................................................................................................... 13
Vasicek beta adjustment ...........................................................................................................14
Stock statistics ................................................................................................................. 15
Price-earnings ratio, coefficient of variation & dividend yield...............................................15
Slicing & dicing................................................................................................................ 16
Sector analysis – ASX break-down...........................................................................................16
Size analysis...............................................................................................................................17
Value growth analysis ...............................................................................................................18
Industrial portfolio plot..............................................................................................................18
Cluster analysis..........................................................................................................................19
Pairs .................................................................................................................................. 19
Spearmans correlation.................................................................................................... 21
Style views ....................................................................................................................... 22
Engine............................................................................................................................... 23
Tracking error of portfolio returns relative to a benchmark...................................................23
Estimating the covariance matrix of the residual returns of stocks in the index .................24
Portfolio Analyser – Benchmark menu.....................................................................................25
Australian Research Team contacts .............................................................................. 26
The screen dumps illustrated on page 1 and throughout this document are for illustrative purposes. Data shown is calculated as at the
date appearing “on screen”, 30 September 1997.
3. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 3
Overview – getting to know portfolio risk
The Portfolio Analyser contains a series of worksheets to help equity managers
form a new portfolio, or better understand aspects of an existing portfolio. It
concentrates on the overall risk of the portfolio that is represented by the beta of
the portfolio relative to the benchmark. Not only does the analyser give a break-
down of stocks’ contributions to the portfolio beta, it also highlights the impact
on tracking variance of stocks selected both within the portfolio, and those
excluded from the portfolio – the active portfolio.
The beta of the portfolio is the measure of the expected sensitivity to
movements in the benchmark – the overall risk of the portfolio. The beta
explains most of its expected returns. However, unless the portfolio is identical
to the benchmark, a slight tracking deviation exists.
The tracking deviation is analysed and attributed between different stocks and
sectors. The Portfolio Analyser will, for example, highlight those stocks that
make up most of the likely volatility in the excess returns of the portfolio against
the benchmark. In particular, this volatility may be due to stocks excluded from
the portfolio. (Not only is the inclusion of a stock in a portfolio an active
decision, but so too its exclusion.)
Industry break-up of the sharemarket
Resources
25%
Industrials
75%
The Australian sharemarket is markedly different to overseas sharemarkets due
to its high concentration of resources companies. At the end of September 1997,
resources companies represented 24.9% of the market capitalisation of the
ASX’s All Ordinaries index. Given that the resources stocks’ relative share price
returns tend to move in opposite directions to the industrial stocks’ relative
returns, this may lead to unintentional “bets” occurring in the portfolio. Also,
companies that may be classified as industrial stocks can display positive
covariance with resources stocks. For instance, ICI Australia and Simsmetal both
present high correlations with resources stocks due to the nature of the drivers
of their respective businesses.
In most instances, an experienced equity manager will be aware of the areas or
stocks that might generate surprises in the portfolio’s returns. The purpose of
the Portfolio Analyser is to highlight unintentional bets that may have emerged
in an Australian portfolio.
Tracking deviation analysed
and attributed to stocks and
sectors
Resources companies
represent 24.9% of the
Australian market
4. November 1997 Portfolio Analyser
4 HSBC James Capel: Portfolio research
Entering a portfolio
The portfolio is entered into the Portfolio analysis worksheet. This can be done
manually, or stocks and weightings can be cut and pasted from an existing
product. You are also able to start with a base portfolio, clear an existing
portfolio ready to enter a new one, or re-base your portfolio stock weights to
add to 100% – via the Benchmark menu (see the insert “Portfolio Analyser –
Benchmark menu” on page 25 for more details.) The company name column
will automatically show whether the stock entered exists in the database. If the
portfolio includes some cash, a separate security code can be entered as CASH,
accompanied by the appropriate weighting.
When you have finished entering the portfolio, select a different benchmark via
the Benchmark menu and/or push the [RUN] button. Once the [RUN] button has
been pushed all the worksheets will be updated, yielding summary statistics and
graphs related to your portfolio.
Portfolios can be cut and
pasted to/from existing
products
HSBC James Capel - Portfolio Analyser Date: 30-Sep-97
ASX code weight Company name Summary Statistics - Benchmark All Ordinaries
100.0%
1 AMC 2.4% Amcor Portfolio Benchmark
2 ANZ 7.4% ANZ Banking Group Beta 1.05 1.00
3 BHP 14.1% BHP Tracking error p.a. 2.8% 0.00%
4 BIL 2.8% Brambles Industries Tracking variance 0.078% 0.00%
5 BOR 2.1% Boral - All Ordinaries volatility 13.3%
6 CBA 6.9% Commonwealth Bank
7 CCL 4.1% Coca-Cola Amatil Price-earnings ratio
8 CML 3.2% Coles Myer 1997 17.7 18.3
9 CSR 2.5% CSR 1998 16.2 16.1
10 FBG 2.2% Foster's Brewing Group 1999 14.1 14.2
11 FLCBS 0.4% Fletcher - Building
12 FLCES 0.5% Fletcher - Energy Earnings growth
13 FLCFS 0.4% Fletcher - Forest 1998 9.2% 13.1%
14 FLCPS 0.5% Fletcher - Paper 1999 14.6% 13.4%
15 LLC 3.6% Lend Lease Corp
16 NAB 13.1% National Australia Bank Earnings uncertainty
17 NCP 6.0% News Corporation coefficient of variation
18 NCPDP 4.6% News Corporation preferred 1998 9.4% 10.0%
19 PDP 1.7% Pacific Dunlop 1999 8.8% 10.0%
20 RIO 5.8% Rio Tinto
21 WBC 6.7% Westpac Banking Corp Dividend yield
22 WMC 3.2% WMC 1997 3.4 3.6
23 WOW 2.2% Woolworths 1998 3.7 3.9
24 WPL 3.8% Woodside Petroleum 1999 4.2 4.4
25
26 Dividend growth
27 1998 7.9% 8.9%
28 1999 12.7% 11.4%
29
30 Overall breakdown of Tracking variance
31
5. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 5
Summary statistics
The first box details the summary risk and valuation statistics. In order they are:
Beta: this measures the expected average sensitivity to a movement in the
benchmark returns. A figure of 1.10 means that the portfolio is 10% more
sensitive to a movement in the benchmark. For example, if the benchmark rises
by 10% the portfolio would, on average, rise by 11%. The beta of a portfolio
accounts for most of its expected volatility around the index. The beta of the
portfolio is derived from the individual stocks’ betas which, in turn, have been
adjusted using a Vasicek adjustment (see the insert “Vasicek beta adjustment”
on page 14 for more details).
Tracking error: although the beta explains most of the volatility of a portfolio
around the index, a slight residual error usually remains. This residual error is
caused by stock-specific events (say, an operational failure) or specific industry
events (eg, the removal of a fuel rebate) that is not related to the overall market
effects.
The tracking error incorporates this residual error by measuring the standard
deviation of the excess returns of the portfolio (for more details on the actual
calculation refer to the section titled “Engine” on page 23.) A figure of say, 2%,
suggests that the portfolio will display returns, in the majority of instances
(65%), in a band of plus or minus 2% around the difference between the mean
return of the portfolio and the benchmark. Note: refer to the section titled
“Tracking error –popular misconceptions” on page 11.
Tracking variance: this figure is the tracking error squared. In analysing the
tracking error of the portfolio against the benchmark, the tracking variance is
used because mathematically only variance can be added and subtracted – not
standard deviations (tracking error).
Price-earnings ratio: the current price of each stock is divided by the actual
and expected EPS estimates for the calendar years detailed to derive the price-
earnings ratio (PE) for each stock. These PE ratios are then market-weighted and
portfolio-weighted (by weighting the reciprocal of the PE ratio, the earnings
yield) to measure respective PE ratios.
Earnings growth: the earnings growth of the market and the portfolio are the
implied percentage growth rates in the PE ratio of the portfolio and market.
Earnings uncertainty: the standard deviation of the consensus estimates of
the mean EPS for each stock is divided by its mean EPS. This has the effect of
standardising a level of uncertainty in the EPS estimates for each stock –
normally referred to as the coefficient of variation (CV). These CVs are then
market and portfolio-weighted for each calendar year.
Dividend yield: the dividends of each of the stocks are divided by the current
price of each stock to derive their respective dividend yields. These dividend
yields are then market-weighted and portfolio-weighted to measure their
respective dividend yields.
Dividend growth: the dividend growth of the market and the portfolio are the
implied percentage growth rates in the dividends of the portfolio and market.
Tracking variance is best for
manipulating data
6. November 1997 Portfolio Analyser
6 HSBC James Capel: Portfolio research
Overall break-down of tracking variance
In analysing the tracking error of the portfolio against the benchmark, the
tracking variance is used because, mathematically, only variances can be added
and subtracted. The chart below provides a quick snapshot of the level of extra
risk flowing into the portfolio because certain stocks, or groups of stocks, tend to
move together – either in the same or opposite directions. This extra risk is
referred to as the “sector effect”, and it is a more general in its application than
just looking at the sector exposures as defined by the ASX.
Overall break-down of tracking variance
0.00% 0.02% 0.04% 0.06% 0.08%
Stock specific
effect
Sector effect
Total
The remainder is the risk flowing from the respective stock weightings. This is a
function of how heavily weighted in the portfolio the stock is relative to the
benchmark, and/or the volatility of the stock’s returns relative to the benchmark.
The ratio between specific variance and the “sector effect” can be used as a
measure of the managers strategy. For instance, if the intended strategy is one
of “stock picking”, then the expectation would be for a small fraction of the risk
being due to the “sector effect”.
Sector effect shows the
extra risk in the portfolio –
certain stocks tend to
move together
7. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 7
Sensitivity analysis of tracking variance
The chart below shows the sensitivity of the tracking variance to changes in the
weightings of stocks in the portfolio. From the total portfolio of stocks the top 10
diversifying stocks and the bottom 10 least-diversifying stocks are displayed.
The term “diversifying” means that an increase in the relative weighting of a
stock in the portfolio will reduce the tracking variance of the portfolio.
Conversely, an increase in weighting of the least-diversifying stocks will
increase the tracking variance and, in turn, the tracking error of the portfolio.
These sensitivity measures are a helpful guide to index funds or low-tracking
funds that need to tightly control the tracking error around the benchmark.
As an example of this sensitivity analysis, we’ll assume that the tracking error of
the portfolio is too high. Looking at the chart below, the most-diversifying stock
in the portfolio is WMC. Buying more WMC will reduce the tracking variance.
However, increasing the weighting of one stock means that the weighting of
another stock will need to fall. The best pick would be to reduce the weighting of
The News Corporation (NCP).
-0.0080% -0.0060% -0.0040% -0.0020% 0.0000% 0.0020% 0.0040% 0.0060% 0.0080%
WMC
RIO
BHP
FBG
PDP
FLCFS
FLCPS
FLCBS
FLCES
CSR
NCP
NCPDP
WBC
WPL
ANZ
CBA
CCL
CML
NAB
LLC
Most
diversifying
Least
diversifying
The actual calculations would run as follows:
Firstly, the current tracking error is a low 2.8%. The tracking variance is 0.078% –
this is the term that is used to calculate the new tracking variance and ultimately
the tracking error (see the section “Tracking variance” on page 5 for details).
Sensitivity analysis
highlights the most-
diversifying and least-
diversifying stocks
8. November 1997 Portfolio Analyser
8 HSBC James Capel: Portfolio research
A 1% increase in the relative weighting in WMC should decrease the tracking
variance by 0.00604% (see the previous chart.) Similarly, a 1% decrease in the
weighting of NCP will reduce the tracking variance by 0.00754%.
Therefore, the final tracking variance should be 0.07785% minus 0.00604% (the
increase in WMC) and minus 0.00754% (the decrease in NCP) which equals
0.06427%. This equates to a tracking error, the standard deviation, of 2.535%. In
other words, the changes in the relative weightings of WMC and NCP have
reduced the tracking error from 2.790% to 2.535%.
Another way to calculate the new tracking error would be to perform the
operation on the spreadsheet, as shown below:
Summary Statistics - Benchmark All Ordinaries
Portfolio Benchmark
Beta 1.05 1.00
Tracking error p.a. 2.560% 0.00%
Tracking variance 0.066% 0.00%
As expected, the tracking error has dropped. But it is a little higher than expected
using the numbers derived from the sensitivity analysis. The reason for the slight
difference is that the sensitivity analysis uses the “instantaneous” change in the
relative weights of each stock. It is roughly equal to a 1% change in the relative
weights of each stock in the portfolio. (see the end of the section titled “engine”
on page 23 for the calculation of “sensitivity to tracking variance”).
9. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 9
Tracking variance – stocks outside the portfolio
The previous example only dealt with the contribution of stocks in the portfolio to
the tracking variance. However, stocks within the benchmark, but not in the
portfolio, also contribute to variance. Hence, the top 10 most-diversifying stocks
and bottom least-diversifying stocks in the benchmark can also be examined.
With the press of a button these stocks can be viewed. The chart on the previous
page can also be viewed in tabular form. The table below shows the contribution
of the top 10 most-diversifying stocks and the bottom 10 least-diversifying stocks
from the total benchmark to tracking variance.
Sensitivity analysis of tracking variance
115 CRT -0.0156%
114 EMP -0.0153%
113 CRI -0.0148%
112 CMX -0.0132%
111 SVR -0.0128%
110 KGM -0.0124%
109 MMC -0.0122%
108 SBM -0.0120%
107 AWA -0.0118%
106 QNI -0.0117%
1 NCP 0.0075%
2 NCPDP 0.0074%
3 WBC 0.0069%
4 WPL 0.0065%
5 ANZ 0.0060%
6 CBA 0.0055%
7 CCL 0.0054%
8 CML 0.0051%
9 NAB 0.0047%
10 LLC 0.0042%
As can be seen from the table above, a 1% increase in Consolidated Rutile (CRT)
has a far greater effect on decreasing variance, than the previous example of a
1% increase in WMC. At the same time, NCP remains the least-diversifying stock.
Therefore, the final tracking variance should be 0.07785% minus 0.0156% (the
increase in CRT) and minus 0.00754% (the decrease in NCP), which equals
0.05474%.
This equates to a tracking error of 2.340%. In other words, the changes in the
relative weightings of Consolidated Rutile (CRT) and NCP have reduced the
tracking error from 2.790% to 2.340%.
Showbenchmark
stocks
10. November 1997 Portfolio Analyser
10 HSBC James Capel: Portfolio research
Stock contributions to tracking variance
The “Contribution of stocks to the tracking variance” chart displays the
contribution of the top 15 stocks to the tracking variance of the portfolio. A
smaller portfolio of nine stocks is shown below for clarity.
NAB
12% NCP
10%
WBC
9%
ANZ
9%
CBA
7%NCPDP
7%
WPL
5%
CCL
4%
CML
3%
Remainder
33%
This break-up of the tracking variance is different to the sensitivity of the
tracking variance to each stock. A stock may represent a large slice of the overall
tracking variance of the portfolio, yet there may be other stocks that can
generate a bigger change in the tracking error from a 1% change in their relative
weighting in the portfolio.
Normally, the two tables are related but there can be instances, such as an
overweighting or underweighting in the larger capitalisation stocks, when they
differ. Some stocks due to the way they covary with other stocks on the portfolio
might subtract tracking variance from the total portfolio. Negative contributions
are still highlighted in the pie chart but are displayed near the remainder.
Also, only stocks in the portfolio are displayed in the pie chart. It is quite possible
that there are other stocks in the market that affect the tracking error more than
the companies in the portfolio. For a complete listing of all the stocks in the
benchmark and their contribution to the tracking variance refer to the worksheet
“Risk rankings”.
The table on the next page is an extract from the “Risk ranking” worksheet. Here
you can not only see the contribution of tracking variance of stocks within the
physical portfolio, but also those within the active portfolio. That is, stocks within
the benchmark, that are actively excluded from the portfolio. Of interest, in this
example, is the fact that Comalco (CMC) is the seventh-largest positive
contributor to tracking variance through its exclusion from the portfolio. The
portfolio, in this case, being the 20 Leaders index, against the All Ordinaries as
the benchmark.
Tracking variance break-up
differs from the sensitivity
of tracking variance to
each stock
11. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 11
Contribution of all stocks in the benchmark to Tracking variance
Ranking ASX % contribution
code
1 NAB 11.6%
2 NCP 9.6%
3 WBC 9.3%
4 ANZ 8.9%
5 CBA 7.4%
6 NCPDP 7.3%
7 CMC 6.4% Not in Portfolio
8 WPL 5.1%
9 CCL 4.2%
366 WFT -1.4% Not in Portfolio
367 SGB -2.6% Not in Portfolio
368 WMC -7.1%
369 RIO -8.3%
370 BHP -14.7%
Tracking error – popular misconceptions
It is worth discussing some popular misconceptions about tracking errors of
portfolios. Tracking errors measure the volatility of the excess returns of a
portfolio. They are often viewed as a measure of the potential returns that a fund
manager can add to a portfolio.
For example, a particularly low tracking error is perceived to flow from a
portfolio that closely tracks the index returns. In fact, fund managers running
active portfolios are often criticised if their tracking errors are too low.
Conversely, fund managers with high tracking errors are perceived to be
aggressive, and have the potential to add a significant excess return to the
portfolio.
But how correct are these notions?
Depending upon a critical assumption, they are misleading. The critical
assumption is the expected return from the portfolio after taking into account the
sensitivity of the portfolio to the market index.
The excess returns of a portfolio can be shown to be a function of three
elements. Firstly:
excess returns = returns of portfolio minus returns of market index.
Now the sensitivity of the portfolio against the market, or beta, accounts for the
majority of its return. So the returns of the portfolio could be rewritten as:
returns of portfolio = a constant return
plus beta of the portfolio
times returns of the index
plus a random residual return.
E[r] = rP
- rM
rP
= αα P
+ ββP
*rM
+ εε
12. November 1997 Portfolio Analyser
12 HSBC James Capel: Portfolio research
Therefore, the excess returns of the portfolio are:
excess returns = a constant return
plus (beta of the portfolio – 1)
times returns of the index
plus a random residual return.
In other words, the excess returns of a portfolio against the index are determined
by:
a constant return (that reflects the return added by a fund manager over
time);
the beta of the portfolio; and
a random residual return due to specific company or industry effects.
The average excess return is simply:
average excess return = a constant return
plus (beta of the portfolio – 1)
times average return of the index.
(The random residual return disappears given that, on average, it is equal to 0.)
Now, the important point is that the tracking error is the standard deviation of
the excess returns around this average. To be precise, the tracking variance (the
standard deviation squared) is equal to:
tracking variance = (beta of the portfolio - 1)
2
times variance of the index returns
plus variance of residual returns.
For more details on actual calculation refer to the “Engine” spreadsheet.
When the beta of the portfolio is equal to 1.0, the same as the market index, the
average excess return collapses to the constant return or value-added by the
fund manager. Therefore, the tracking variance is the dispersion of returns
around this constant return. In theory, a fund manager could exhibit a markedly
low tracking error, but an extremely high constant return over the index. In this
case, it would be incorrect to assume that a low tracking error equates to an
index-type performance, unless, it is assumed that the fund manager’s returns
will, on average, be equal to the index.
Similarly, a high tracking variance is only one part of the equation. The other
part is the average expected returns that are likely to be added by the fund
manager.
E[r] = αα P
+ (ββP
-1)*rM
+ εε
Average excess return
E = αα P
+ (ββP
-1)*rM
VP
= (ββP
-1)
2
*VM
+ Vεε
Tracking variance is one
part of the equation – the
other is average expected
return added by the fund
manager
13. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 13
Tracking error & residual error
How does the tracking error relate to the residual error of the stock and the
portfolio?
Following on from the previous section, the tracking variance incorporates the
measure of the residual variance, plus the beta of the portfolio. The reason that
the beta of the portfolio enters into the equation is that the tracking error is
defined as the volatility of the excess returns of the portfolio around the
benchmark. Whereas the residual variance is the volatility of the portfolio returns
around the beta-adjusted benchmark returns (or the line of best fit).
If the portfolio displays a beta of 1.0, that is, the same as the benchmark, the
residual error and the tracking error are equivalent (VP
= (βP
-1)
2
*VM
+ Vε , if βP
=
1.0 then VP
= Vε). However, as the beta moves away from 1.0 the tracking
variance increases above the residual variance. The tracking error could be
visualised as the deviation of the stocks or portfolio returns in the graph below,
from another line of best fit which has a slope of 1.0 (the benchmark beta).
The risk space (either residual or tracking variance) can be selected on the first
spreadsheet, “Portfolio analysis”, by choosing the Risk space option under the
Benchmark menu. The full Benchmark menu has been detailed in the shaded
insert on page 25.
-10
-8
-6
-4
-2
0
2
4
6
8
-15 -10 -5 0 5 10 15
Beta =slope
of line
Stock returns
Benchmark
returns
Residual error =
standard deviation
of residuals
Beta & residual error
The beta is calculated using the preceding 48 months of returns of each stock
(including dividends) against the accumulation indices of each benchmark. The
beta provides a measure of the average sensitivity of each stock to a movement
in the benchmark. Note that the beta has been constructed using a Capital Asset
Pricing model where the returns from the risk-free rate have been subtracted
from the monthly returns of each stock (the 90-day bank bill accumulation index
has been used).
14. November 1997 Portfolio Analyser
14 HSBC James Capel: Portfolio research
Finally, the betas have been adjusted for each stock, using a so-called Bayesian
adjustment. This adjustment helps to provide a better estimate of the future
beta of the stock. The adjustment is known as a Vasicek adjustment and
basically pulls the beta back towards 1.0, (the market beta) if the estimation
error in the beta is higher than other stocks’ betas (see the insert “Vasicek beta
adjustment” below for more details).
The residual error of each stock is the standard deviation of each stock’s returns
around the beta-adjusted market returns. The residual error and beta of a stock is
graphed on the page opposite.
The beta of the stock can be pictured as the line of best fit between the stock
returns and the market returns (before the Vasicek adjustment). The more
sensitive the stock to the market, the higher the beta and the more steeply
inclined is the slope of the line. The residual error is a measure of the dispersion
of the “unexplained” part of the returns around the line of best fit (or beta).
These errors are assumed to fall in a normal bell-shaped distribution around the
line of best fit. The residual error is measured in terms of one standard
deviations given that this captures the majority of the residual returns.
Vasicek beta adjustment
The beta of a stock is an important component in the calculations of the risk-adjusted returns. Originally, beta
factors were simply estimated from past data by least-squares regression procedures. The least-squares
technique consists of fitting a linear relationship between monthly rates of return of a stock and the market
index so that the sum of squared differences between the stock’s actual returns and forecast returns are
minimised.
The Vasicek beta adjustment provides a better estimate of the future beta of a stock. It does this by
incorporating some additional information outside the sample of returns of the stocks and the market index.
This additional information is the fact that the beta of the market must be 1.0. This information is combined
with the sample estimator, the least-squares estimator of the beta, using Bayesian statistics.
The formula for the adjustment is detailed below;
Beta`i= 1/m
2
+ Betai/s
2
1/m
2
+ 1/s
2
where:
Beta`i is the Vasicek adjusted beta of stock i
Betai is the least squares estimator beta of stock i
s is the standard error of Betai
m is the market weighted average of all the standard errors of betai
For an example, assume a stock’s unadjusted beta is 1.50 with a low degree of accuracy, indicated by a 0.60
standard error. This compares to a market beta and standard error of 1.0 and 0.36, respectively. The adjusted
beta would be:
Beta`I = (7.7 + 4.2) = 11.9 = 1.13
(7.7 + 2.8) 10.5
In other words, a beta of 1.13 provides a better estimate of the “underlying beta”.
For more information refer to "A note on Cross-Sectional Information in Bayesian Estimation of Security
Betas", Journal of Finance 28 (December 1973), pp1233-1239.
Betas are modified via a
Vasicek adjustment
15. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 15
Stock statistics
This spreadsheet details a number of risk and valuation statistics for each stock.
This is a report page and no information needs to be entered on this
spreadsheet.
HSBC James Capel - Portfolio Analyser
ASX code Company name weight Price Index Beta Residual
30-Sep-97 weight error p.a.
Total 100.0% Portfolio 54.02% 1.05 2.8%
1 AMC Amcor 2.4% 8.69$ 1.31% 1.106 11.6%
2 ANZ ANZ Bank 7.4% 11.28$ 3.99% 1.010 17.1%
3 BHP BHP 14.1% 16.08$ 7.61% 1.144 13.7%
4 BIL Brambles Industries 2.8% 28.75$ 1.50% 1.084 14.8%
5 BOR Boral 2.1% 4.18$ 1.13% 0.927 14.6%
6 CBA Commonwealth Bank 6.9% 17.04$ 3.72% 0.969 13.5%
7 CCL Coca Cola Amatil 4.1% 14.77$ 2.19% 1.015 25.1%
The first table, as shown above, simply lists the stocks entered from the portfolio
analysis page. The next table lists the share price, benchmark index weight, the
beta and tracking error (see the section “Beta and residual error” on page 13 for
more details).
Price-earnings ratio, coefficient of variation & dividend yield
The remaining tables on the Stock analysis page, shown below, list the price-
earnings ratio (PE), the coefficient of variation (CV), and the dividend yield (DY)
for each stock in the portfolio.
1997 PE 1998 PE 1999 PE 1998 CV 1999 CV 1997 DY 1998 DY 1999 DY
17.7 16.2 14.1 9.4% 8.8% 3.4 3.7 4.2
21.6 17.8 14.9 7.2% 9.0% 4.4 4.6 4.7
13.1 12.4 11.5 4.6% 6.9% 4.3 5.0 5.6
19.0 16.8 14.4 11.6% 14.2% 3.2 3.2 3.8
26.4 22.8 20.2 3.1% 3.8% 2.6 2.7 2.7
27.0 19.5 15.2 9.6% 8.8% 3.6 3.8 4.3
12.9 12.9 11.9 2.7% 4.1% 6.0 6.5 7.1
44.7 40.6 35.3 9.5% 12.0% 1.3 1.4 1.5
The PE ratio is defined as the current price divided by the estimated earnings
per share (EPS) for each calendar year.
The CV measures the degree of dispersion of analysts’ estimates around the
mean EPS. Low CV figures indicate that analysts’ forecasts are tightly
clustered around the mean – implying lower earnings risk.
The dividend yield is defined as the estimated dividend per share divided by
the current price for each year.
16. November 1997 Portfolio Analyser
16 HSBC James Capel: Portfolio research
Slicing & dicing
This spreadsheet slices up the tracking variance of the portfolio into different
risk perspectives. These risk perspectives may change over time and are a
function of how investors view the Australian sharemarket. The advantage of
this sort of technique is that we are not bound by a certain risk model or
paradigm in analysing the Australian sharemarket. For example, stocks could be
classified into a “bottom-up” risk classification, perhaps by balance sheet and
earnings risk. However, at other times, style classification may be more
important – growth versus value stocks. By using different views of risk we are
unlikely to be surprised by the emergence of a new clustering of stocks in the
portfolio.
The risk perspectives are based on two different techniques – a classification
technique and a factor analysis. The first classifies stocks by either
membership or non-membership of certain groupings or sectors. There are
three different views of the portfolio risk based on this method:
ASX sector break-down;
small and large-capitalised segmentation; and
value and growth views.
The other method looks at the correlations of different stocks’ returns. If two
stocks display similar return profiles, irrespective of their ASX sector
classification, it might suggest that they are being affected by certain common
factors. By unravelling the correlations of all the stocks, a number of common
factors can be identified as driving the returns of stocks.
Using a factor analysis of the correlations of all stocks, the Australian market
divides neatly into basically industrial stocks and resources stocks. These sector
groupings are different to the ASX break-down – for example ICI tends to display
a return profile similar to resources stocks. Further, these sector groupings are
not just based on membership or non-membership of the sectors. A loading or
sensitivity for each stock is calculated for each factor.
An advantage of this factor analysis is that the stocks’ returns reveal potentially
new groupings in the Australian market – which would not be evident using a
simple classification system based on a certain risk model or paradigm.
Sector analysis – ASX break-down
The chart opposite compares the portfolio against the ASX sector groupings and
weightings. Additionally, the tracking variance is attributed between the different
sectors and graphed in the bar chart.
If the beta is different to 1.0 then part of the tracking error will be due to the
higher or lower sensitivity of the portfolio against the index. This extra risk is
classified as “market risk” because a higher or lower beta is equivalent to taking
an increased or decreased bet on the market.
Another use of this spreadsheet is in analysing the sectors weights in different
benchmarks. For example, what are the two largest sector weightings in the ex-
ASX 100 index? The answer: Property Trusts and Miscellaneous Industrials!
Slicing the tracking
variance into different risk
perspectives
17. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 17
HSBC James Capel - Portfolio Analyser
1. Sector Analysis - ASX breakdown % contribution
ASX code Sector Portfolio Index Difference to tracking variance
1 GOLD 0.0% 2.6% -2.6% 9.4%
2 METALS 3.2% 5.3% -2.1% 16.1%
3 DIVRES 19.9% 12.0% 7.9% -20.0%
4 ENERGY 4.4% 5.1% -0.8% 6.9%
5 UTILITIES 0.0% 0.9% -0.9% 0.6%
6 DEVCON 3.6% 3.8% -0.2% 3.5%
7 BLDMAT 5.0% 4.4% 0.5% 4.8%
8 ALCTOB 2.2% 1.8% 0.4% -0.8%
9 FOODHH 4.1% 3.4% 0.6% 2.7%
10 CHEMIC 0.0% 1.1% -1.1% 2.9%
11 ENGIN 0.0% 0.7% -0.7% 0.9%
12 PAPER 3.3% 1.9% 1.4% 0.4%
13 RETAIL 5.4% 3.8% 1.6% 4.1%
14 TRANSP 2.8% 3.0% -0.2% 4.2%
15 MEDIA 10.6% 9.0% 1.6% 19.9%
16 BANKS 34.0% 21.6% 12.5% 35.3%
17 INSUR 0.0% 2.8% -2.8% -1.2%
18 TELECOM 0.0% 0.2% -0.2% 0.3%
19 INVFIN 0.0% 2.0% -2.0% 0.6%
20 PROPTY 0.0% 4.8% -4.8% -3.3%
21 HEALTH 0.0% 1.2% -1.2% 2.4%
22 MISIND 0.0% 1.5% -1.5% 0.9%
23 DIVIND 1.7% 4.5% -2.8% 3.5%
24 TOUR 0.0% 2.6% -2.6% 0.9%
cash 0.0% 0.0% 0.0% 0.0%
MARKET RISK (for tracking error) 5.0% 1
100.0% 100.0% 100.0%
GOLD
METALS
DIVRES
ENERGY
UTILITIES
DEVCON
BLDMAT
ALCTOB
FOODHH
CHEMIC
ENGIN
PAPER
RETAIL
TRANSP
MEDIA
BANKS
INSUR
TELECOM
INVFIN
PROPTY
HEALTH
MISIND
DIVIND
TOUR
-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0% 40.0%
GOLD
METALS
DIVRES
ENERGY
UTILITIES
DEVCON
BLDMAT
ALCTOB
FOODHH
CHEMIC
ENGIN
PAPER
RETAIL
TRANSP
MEDIA
BANKS
INSUR
TELECOM
INVFIN
PROPTY
HEALTH
MISIND
DIVIND
TOUR
Risk analysis by sector
Size analysis
The next view of the risk divides the portfolio into large and small capitalisation
stocks. These are further sub-divided into industrials and resources. Again, the
tracking variance is attributable across these different sectors. The definition of a
small capitalisation is a company classified in the so-called ex-ASX 100 index.
Risk Analysis by size
% contribution
2. Size Analysis Portfolio Index Difference to tracking variance
Industrials Large Top 100 72.6% 64.2% 8.3% 72.9%
Industrials Small Ex 100 0.0% 10.8% -10.8% 9.9%
Resources Large Top 100 27.4% 22.3% 5.2% 5.3%
Resources Small Ex 100 0.0% 2.7% -2.7% 7.0%
cash 0.0% 0.0% 0.0% 0.0%
MARKET RISK (for tracking error) 5.0%
100.0% 100.0% 100.0%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
Large
Industrials
Small
Industrials
Large
Resources
Small
Resources
One area to closely monitor in the Australian market is the risk from the small
resources stocks. Many of these companies are gold stocks that can display
significant volatility.
18. November 1997 Portfolio Analyser
18 HSBC James Capel: Portfolio research
Value growth analysis
Stocks have also been classified into a value, growth or other category. A
“value” stock denotes a company that is selling on a low price relative to its
expected earnings, cash flow or net tangible assets. Additionally, these
companies tend to sell on persistently low PE multiples – such as the banks. The
full list of the stocks included in the value group (and any other grouping) is
detailed in the “Style views” spreadsheet.
Risk Analysis by style
3. Value|Growth Analysis % contribution
Portfolio Index Difference to tracking variance
Industrials Value 36.2% 26.4% 9.8% 40.0%
Industrials Growth 21.0% 18.9% 2.1% 31.3%
Industrials Other 42.8% 54.7% -11.9% 23.7%
MARKET RISK (for tracking error) 5.0%
100.0% 100.0% 100.0%
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
Value
Industrials
Growth
Industrials
Other
Industrials
The “growth” label is applied to those stocks which tend to sell on a persistently
high share price relative to their current earnings, cash flow or net tangible
assets. However, they are not just the opposite of a value stock. Companies may
exhibit high PE ratios because current or expected earnings have collapsed. The
distinguishing trait of a growth stock is its strong comparative advantage against
its competitors – such as Coca-Cola Amatil.
Industrial portfolio plot
The final chart brings together some of the results of the previous risk tables.
4. Industrial portfolio plot - value|growth & large|small
% contribution Risk profile by style and size for industrials
Portfolio Index Difference to tracking variance
Industrials Large 72.6% 64.2% 8.3% 72.9%
Industrials Growth 21.0% 18.9% 2.1% 31.3%
Industrials Small 0.0% 10.5% -10.5% 9.8%
Industrials Value 36.2% 26.4% 9.8% 40.0%
0.0%
20.0%
40.0%
60.0%
80.0%
Large
Growth
Small
Value
For the industrial stocks in the portfolio the style is mapped against the
capitalisation bias. For example, is most of the risk coming from value and
smaller stocks? This analysis is particularly useful in assessing different
economic environments. In the Australian market, smaller capitalisation stocks
tend to perform better in a strengthening economy. Further, value stocks attract
more interest when the economy improves. In times of earnings downgrades
and economic uncertainty, a more defensive portfolio would be positioned in the
top right-hand quadrant of growth and larger capitalisation stocks.
19. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 19
Cluster analysis
This table adopts the factor analysis technique and looks at the most important
factor in the Australian market – the industrial/resources split
A weighted score is provide for the cluster. The more positive the number from
the industrial/resources factor, the more “industrial” like is the portfolio.
Conversely, a negative figure would indicate a portfolio of stocks that acts like
the resources companies. The industrial/resources split has always been the
most important decision in the Australian market (at least in terms of the All
Ordinaries index) and continues to dominate the correlation of stocks.
4. Cluster analysis
Factor exposures
Industrials/Resources
Portfolio exposure 0.265
Index exposure 0.167
0.098
Positive figures = Industrial type portfolio
Negative figures= Resource type portfolio
Pairs
This page lists all the significant correlations between pairs of different stocks –
both significantly positive and negative correlations.
This information is useful in looking for arbitrage opportunities in the market.
For example, two companies’ share prices and dividend returns might move
closely together – perhaps due to a similar sector exposure. If their share price
returns move out of sync, for no apparent reason, we have the basis for a
possible pairs trading opportunity.
Alternatively, pairs correlations might suggest that certain other stocks outside
the portfolio would provide a better exposure than the current stock in the
portfolio (due to better value fundamentals).
Industry Index wgt ASX code ASX code Spearmans correlation Industry Index wgt
PROPTY 0.16% APF AAD 0.400 TOUR 0.08%
METALS 0.90% CMC AAD 0.429 TOUR 0.08%
INVFIN 0.02% EQK AAD 0.542 TOUR 0.08%
DEVCON 0.03% MDC AAD 0.455 TOUR 0.08%
BLDMAT 0.03% WFI AAD 0.426 TOUR 0.08%
METALS 0.07% WSL AAD 0.469 TOUR 0.08%
BANKS 0.05% BEN ABC 0.491 BLDMAT 0.07%
The key data is in the middle of the table – two columns labelled ASX code and a
third column listing the correlation coefficient (Spearmans correlation). The
other columns are simply to sort the data by a number of criteria – ASX code,
index weight and industry. There are arrows above each column which when
selected will list a menu of different sector, ASX codes, or index weights. For
example, a listing of bank correlations and stocks above 1% index weight was
performed – see overleaf.
The more positive the
industrial/resources factor,
the more “industrial” like
the portfolio
20. November 1997 Portfolio Analyser
20 HSBC James Capel: Portfolio research
Industry Index wgt ASX code ASX code Spearmans correlation Industry Index wgt
DIVRES 7.61% BHP ANZ -0.403 BANKS 3.99%
BANKS 3.99% ANZ CBA 0.572 BANKS 3.72%
BANKS 3.99% ANZ NAB 0.468 BANKS 7.05%
DIVRES 3.13% RIO ANZ -0.414 BANKS 3.99%
BANKS 3.72% CBA ANZ 0.572 BANKS 3.99%
DIVRES 7.61% BHP CBA -0.424 BANKS 3.72%
DIVRES 3.13% RIO CBA -0.412 BANKS 3.72%
METALS 1.72% WMC CBA -0.612 BANKS 3.72%
BANKS 3.72% CBA NAB 0.510 BANKS 7.05%
BANKS 7.05% NAB ANZ 0.468 BANKS 3.99%
BANKS 7.05% NAB CBA 0.510 BANKS 3.72%
DIVRES 3.13% RIO NAB -0.448 BANKS 7.05%
METALS 1.72% WMC NAB -0.586 BANKS 7.05%
BANKS 3.63% WBC ANZ 0.561 BANKS 3.99%
BANKS 3.63% WBC CBA 0.428 BANKS 3.72%
Not surprisingly, most of the major banks are highly correlated to each other’s
returns (remember, this is after the market effect has been stripped out of the
returns for each of the stocks). ANZ Banking Group is positively correlated to
Commonwealth Bank of Australia to the tune of 0.572. But just how significant is
0.572? The maximum correlation is +1.0 (stocks move exactly in tandem) and the
minimum -1.0 (stocks move in exactly the opposite direction). Only the
significant correlation figures have been picked in the sense that there is only a
5% chance that these correlations are a “fluke” or random occurrence.
An interesting point from the above table is the strong negative correlation (that
is, they move in opposite directions) between many of the larger banks and
mining stocks.
21. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 21
Spearmans correlation
Variance and correlation provide a measure of linear association. They are
sensitive to outliers and may indicate association where none exists.
The Pearson’s product moment correlation coefficient uses residual returns. The
Spearmans correlation coefficient is based on the ranking of stocks’ returns.
This reduces the effect of outliers in the correlation. The correlation measure in
the HSBC James Capel Portfolio Analyser is calculated using a Spearmans
correlation statistic.
To demonstrate the effects of outliers on the Pearson’s correlation coefficient,
assume that the following five-monthly returns were exhibited for two stocks.
Stock A Stock B
1 1% 2%
2 2% 3%
3 4% 3%
4 5% 4%
Correlation statistic 0.8944
The correlation between the stocks is high at 0.89. Further we will assume that
this correlation reflects the majority of returns. However, there will always be
one unusual return month that upsets the figures. Say stock B exhibits a 10% fall
in period 3. The new numbers are displayed below.
Stock A Stock B
1 1% 2%
2 2% 3%
3 4% -10%
4 5% 4%
Correlation statistic -0.2508
The correlation statistic has now reversed to -0.25.
A better way to handle these rogue numbers is to use a more robust technique –
the Spearmans correlation coefficient.
The Spearmans correlation is based on the ranking of stocks’ returns. Instead of
using the returns for each period, a simple ranking is performed from 1 (the
lowest) to 4 (the highest). This means that rogue numbers simply affect the
ranking of the return not the absolute number. Continuing on the above example
(with the rogue minus 10% figure), the ranking of the stocks would be:
Stock A Stock B
rankings rankings
1 1 2
2 2 3
3 3 1
4 4 4
Correlation statistic 0.4000
The correlation statistic falls, but only to 0.40. When the sample of numbers and
rankings are larger, the correlation statistic is not overly disturbed by outlying
figures.
The Spearmans correlation coefficients are used in the factor analysis for the
Slicing & Dicing of the tracking variance.
Correlation provides a
measure of linear
associations between
stocks
22. November 1997 Portfolio Analyser
22 HSBC James Capel: Portfolio research
Style views
The “Style views” spreadsheet simply lists every stock in the All Ordinaries
index with its categorisation in the ASX sector, small/large capitalisation and
value/growth.
INDUSTRIAL/RESOURCE SIZE VIEW VALUE/GROWTH VIEWS
VIEW INDUSTRIAL RESOURCES INDUSTRIALS
LARGE SMALL LARGE SMALL VALUE GROWTH
TOP 100 EX 100 TOP 100 EX 100
AAA 0 1 0 0 0 1 0 0
AAD 1 0 0 1 0 0 0 1
ABC 1 0 0 1 0 0 0 0
ABF 0 1 0 0 0 1 0 0
ABG 1 0 0 1 0 0 0 0
ACH 1 0 0 1 0 0 1 0
ADB 1 0 0 1 0 0 1 0
ADZ 1 0 0 1 0 0 0 0
AFF 1 0 0 1 0 0 0 0
A part of the spreadsheet is displayed above. A ‘1’ indicates membership of the
particular sector and ‘0’ non-membership. These columns of numbers are then
used to pick out the relevant tracking variance contribution on the “Slicing &
Dicing” spreadsheet.
Apart from listing all the stocks that make up a particular sector, it can also be
used as a template to derive other sector perspectives of the Australian
sharemarket that more closely follow the investor’s perspective of risk.
23. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 23
Engine
The engine is where all the calculations are performed. The tracking or residual
error is calculated here and the sensitivity and contribution of each stock to the
tracking/residual variance. The workings of this sheet is for the aficionados of
portfolio analysis.
The calculations are based on a so-called “statistical model” which decomposes
the market residual covariance matrix into a smaller number of factors – using
factor analysis. The covariance matrix is based on a more robust estimator of
the correlations – the Spearmans correlation. The tracking variance and residual
variance is calculated using the formulae in the shaded boxes below.
Tracking error of portfolio returns relative to a benchmark
Variance (tracking returnsi) = (wp-βp.wi)` Σ (wp - βp.wi) + (βp-1)
2
. s
2
i
(1x1) (1xn) (nxn) (nx1) (1x1)
where:
n = the number of stocks in the index
wp = the weights of each stock in the portfolio – a nx1 vector of weights
wi = the weights of each stock in the index – a nx1 vector of weights
βp = a scalar representing the beta of the portfolio relative to the index
s
2
i = the variance of the index (per annum) – a scalar
Σ = the covariance matrix of the residual returns of stocks in the index – an nxn
matrix. This is estimated using a factor analysis of the Spearmans correlation
matrix.
The residual variance drops the last term:
Variance (residual returnsi) = (wp-βp.wi)` Σ (wp - βp.wi)
(1x1) (1xn) (nxn) (nx1)
The tracking error or residual error (the standard deviation) is simply the square
root of the above terms.
The estimation of the correlation matrix is a critical part of the calculation of the
tracking/residual variance. The correlation matrix is decomposed into a smaller
number of factors that represent most of the variation in the correlations of the
residual returns of stocks.
If the correlation matrix is not collapsed into a smaller number of factors the
spreadsheet would be overwhelmed by the number of calculations. Using the All
Ordinaries index, there are 350-plus different securities which means a matrix of
350 times 350 – that is, 122,500 figures.
A principal components analysis of the correlation matrix of the residual returns
of every stock in the index reveals that 15 factors capture most of the variation in
the matrix – roughly 75%. These 15 factors and the loadings of each stock on
each factor are detailed in the middle of the spreadsheet.
Covariance matrix is
decomposed using factor
analysis
24. November 1997 Portfolio Analyser
24 HSBC James Capel: Portfolio research
In reducing the correlation matrix to these 15 factors, specific risk that presents
as covariance is reduced. This leads to a correlation matrix that better reflects
the future. That is, it has less noise from past stock specific events than just
using a historical covariance matrix.
The sensitivity of the tracking/residual variance to a change in each stock’s
weighting is calculated by differentiating the tracking variance with respect to
each stock’s weighting in the portfolio:
Sensitivity of tracking variance =
δ
δ
[( . )` ( . ) ( ) . ]w B w w B w B s
w
p p i p p i p i
p
− − + −Σ 1 2 2
Estimating ΣΣ, the covariance matrix of the residual returns, ej
, of
stocks in the index
ej = Rj - Rf - (aj + bj •Ri )
(mx1) (mx1) (mx1) (mx1)
where bj= the Vasicek adjusted beta for each company, j, based on a sample of
48 months
Ri = the monthly logged returns (including dividends) for the index
Rj = the monthly logged returns (including dividends) for each stock
Rf = the monthly logged returns of the accumulation index of the 90 day
bill rate
Correlation (e1 , e2 , e3 .... ,en) = Ω
Ω = an nxn Spearmans correlation matrix of residual returns for each stock, e j
Using factor analysis – principal components technique, 15 factor loading vectors
are extracted from Ω
Ω = (λ1λ1` + λ2λ2` + λ3λ3` + ... λ15λ15`) + Ψ
(nxn) (nxn) (nxn)
where λk = the nx1 eigenvectors scaled by their respective eigenvalues
Ψ = the residual matrix
However, 15 factor loadings are not enough to specify the full communalities of
each stock – only 75% on average is estimated. Therefore, the diagonals of the
residual matrix are added to the matrix of multiplied eigenvectors – see below.
Ω` = (λ1
λ1
` + λ2
λ2
` + λ3
λ3
` + ... λ15
λ15
`) + Ψ`
where Ψ` is a diagonal matrix of the residual terms and Ω` is the estimated
correlation matrix.
The final step is to convert the estimated correlation matrix, Ω`, into a covariance
matrix
Σ = σ σ` • Ω`
(nxn) (nxn) (nxn)
where σ is a vector of nx1 standard deviation of each stock’s residual returns.
Fifteen factors capture 75%
of the correlation matrix
26. November 1997 Portfolio Analyser
26 HSBC James Capel: Portfolio research
Australian Research Team contacts
Melbourne Sydney Brisbane
Fax: (03) 9229 3577 Fax: (02) 9255 2555 Fax: (07) 3223 7890
Andrew Dalziel Head of Research (07) 3229 6199
Chris Bedingfield Property Trusts (02) 9255 2676
Justin Blaess Property Trusts (02) 9255 2681
Stephen Burns Property Trusts (02) 9255 2643
Nick Caley Insurance (02) 9255 2473
James Casey Food & Retail (03) 9229 3669
Jeff Emmanuel Banking (03) 9229 3685
Bill Etheridge Gold (02) 9255 2586
Kiera Grant Small Companies (02) 9255 2680
Amos Hill Assistant Economist (03) 9229 3584
Nola Hodgson Media (03) 9229 3658
Michael Kirby Commodities (03) 9229 3607
Peter Lucas Alcohol, Tourism & Leisure (03) 9229 3591
Amanda Miller Small Companies (07) 3229 6199
Andrew Perks Energy (03) 9229 3676
Kate Prendiville Property Trusts (02) 9255 2569
Michael Saba Equity Derivatives (03) 9229 3641
Umit Safak RIO, MIM, NBH, CMC, PAS, ABF, SVR (03) 9229 3560
Kessada Sawyer Small Companies (03) 9229 3665
Mark Skocic Food & Retail (03) 9229 3599
Stuart Smith Energy & Utilities (03) 9229 3570
Adam Spowers Telecommunications & Pay TV (02) 9255 2554
Andrew Sutherland Diversified Industrials, Engineering & Chemicals (03) 9229 3574
John Syropoulo Global Mining (London) (171) 336 4389
Peter Taubman Equity Derivatives (03) 9229 3662
Mario Traviati Energy (03) 9229 3569
Marcus Tuck Strategist & Chief Economist (03) 9229 3589
Cherie Zanette Banking (02) 9229 3686
Colin Ritchie Portfolio Research & Quantitative Analysis (03) 9229 3572
Geoff Thomas Research Data (03) 9229 3687
Martin Summons Research Editor (03) 9229 3609
27. November 1997 Portfolio Analyser
HSBC James Capel: Portfolio research 27
This research report has been prepared and issued by HSBC James Capel. HSBC
James Capel has based this document on information obtained from publicly
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verified. HSBC James Capel makes no guarantee, representation or warranty and
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