Portfolio Management

Portfolio optimization as a sequential decision problem This one is for my followers in finance… For anyone who is solving nonlinear (Markowitz-style) portfolio models, there is an immediate way to improve the performance of your model.   First, you have to recognize that your portfolio model is a *policy*  for making decisions over time managing your portfolio. While finding an optimal solution to your model is nice, what matters is how the *policy* performs over time (see graphic below). Typically the policies are tested on historical data (“backtesting”).   Solving a Markowitz model would produce an optimal policy if there were no transaction costs, but this is not the case. There has been considerable attention devoted to using approximate dynamic programming to solve the dynamic program, but this is not necessary.   What you want to do is to parameterize your Markowitz model. For example, the importance of transaction costs depends on the volatility of the asset. Imagine multiplying the transaction cost for asset i times a coefficient \theta_i. Using \theta_i = 1 gives you the solution you already have, so optimizing \theta (I am not saying this is easy) is guaranteed to produce a better solution.   The idea of parameterizing a Markowitz model-policy is described in section 13.2.4 of my book at https://lnkd.in/dB99tHtM  (“tinyurl.com/” with “RLandSO”). I recommend using Jim Spall’s SPSA algorithm (see section 5.4.4) for optimizing \theta.    Yes, this is stochastic optimization. No, you don’t need Bellman’s equation or scenario trees. :)

Performance analysis is where risk models meet fundamental theses. 'Advanced Portfolio Management' describes the state of that art. Chapter 8 bullets, with math & comments. Let know if you'd like the excel. *1) Factor vs. Idio Decomp* "The Earth rotates around the Sun at a speed of 67,000mph. When I go for my occasional run, my own speed is in the tens of thousands of miles per hour. Should I take credit for this amazing performance?" Risk models prevent conflation of stock-specific, 'idiosyncratic' performance with macro or 'factor'-driven returns. Step one is to aggregate exposures, model relationships, and predict volatility. But the second, at least as important step for fundamental equities investors is single stock & portfolio performance decomp. Why has a stock moved the way it has over the past year? This week? Today? Why has a PM / analyst / fund performed as it did? *2) "Annotate the Idio" * Performance analysis itself spins into two distinct threads: First, how do we analyze investor performance: - Hit rates on factor vs. single stock (idio) bets - Skill in stock selection vs. sizing - Earnings vs. ex-earnings P&L - Similar-investor crowding Analyzing performance this way does several things: It informs that investor's compensation, promotion, success. It drives capital allocation, and more subtly, helps elicit the residual signal necessary to build "back books" on top of fundamental portfolios. But most important, it creates feedback loops in fundamental stock picking. Instead of 'better decisions next time', it identifies where decisions are already excellent, and where they are poor or mediocre. Incrementalist, continuous improvement compounded can be the difference between long-term success and failure. The second thread is single stock research: What KPIs, narratives, & data drive residual performance in this name or sector? Are we focused on single stock research, or conflating idio and macro? Tracking residual performance focuses research on what has fundamentally mattered to a stock, instead 'playing macro PM' in your names. "The simple fact is that factors can find infinite ways to mar your performance, but cannot tell you how to be profitable." *3) Sizing vs. Selection; Breadth; Information Ratios* Stylized math on sizing vs. selection, breadth, and translating hit rates and idio %s into Information & Sharpe Ratios attached. But stepping back, what Gappy describes is a synthesis. Between the analytical decomposition of risk & performance on the one hand, And, on the other, excellence in fundamental single stock research. Historically, the two have remained separated. But the accelerating future is a closer pairing of these two functions, in which the insights from each side drive iteration & excellence in the other. As Gappy points out, "quantitative analysis is helpful in itself, but it is most helpful when it is combined with detailed, qualitative knowledge.”

So you're thinking of building an #electrolyzer to make green #hydrogen. But how much #wind, #solar and #battery capacity do you need to power the electrolyzer in order to minimize the cost of hydrogen it produces? BloombergNEF has just the tool you need to find out - the Hydrogen Electrolyzer Optimization Model (H2EOM). A vastly enhanced version 2.0 was published yesterday by my brilliant colleagues Xiaoting Wang and Ulimmeh-Hannibal Ezekiel. For an example project in #California, the optimal setup for a 1MW electrolyzer is to power it by 1.14MW of wind and 0.83MW of solar, skipping the batteries. That gives you a levelized cost of hydrogen (LCOH) or $4.63 per kilogram and a utilization rate of 65% on your electrolyzer (excluding any #IRA #45V #taxcredits). If you wanted to increase the utilization rate to 90%, you'd need to be happy with a #LCOH of $7.28 per kilogram as you pay for batteries, as well as more solar and wind capacity. Users can do this modeling for any location on the planet by using BNEF's Solar- and Wind Capacity Factor Tool to get 8,760h of capacity factor data anywhere. Users can tweak any cost and financing assumption to suit their project, making this a super versatile tool for #H2 modeling. Oh, and did I say you can model up to 50 projects at once? BNEF clients can download the model here: https://lnkd.in/e9vTYc7G

PORTFOLIO OPTIMIZATION WITH UNCERTAINTY: BAYESIAN MEAN-VARIANCE 📊 In portfolio construction, the classical mean-variance optimization often produces extreme, unstable allocations due to parameter estimation errors. Bayesian Mean-Variance elegantly addresses this challenge by incorporating uncertainty directly into the optimization process. 🎯 This approach updates prior beliefs with observed data to create more robust portfolios through Bayesian inference: μ_post = (Σ_prior^(-1) + T·Σ_sample^(-1))^(-1) · (Σ_prior^(-1)·μ_prior + T·Σ_sample^(-1)·μ_sample) When properly implemented, Bayesian portfolio optimization involves three core elements: 📌 Prior Specification: Setting initial beliefs about expected returns, typically using market equilibrium or equal-weight assumptions as a conservative starting point 📈 Likelihood Function: Incorporating historical return data to update beliefs, with sample size T determining the weight given to observed versus prior information 🔄 Posterior Distribution: Combining prior and likelihood to obtain updated parameter estimates that reflect both beliefs and data Key steps to implement Bayesian Mean-Variance: 1. Define prior distributions for expected returns (often μ ~ N(μ₀, τ²Σ)) 2. Calculate posterior parameters using precision-weighted averaging 3. Optimize portfolio using posterior estimates instead of raw sample statistics 4. Apply standard mean-variance optimization with updated parameters 5. Monitor shrinkage intensity as new data arrives Applications in modern portfolio management: • Institutional Portfolios: Managing large diversified portfolios with parameter uncertainty • Robo-Advisory: Providing stable allocations for retail investors • Multi-Asset Strategies: Combining assets with limited historical data • Dynamic Rebalancing: Adapting portfolios as market regimes change • Risk Management: Reducing concentration risk from estimation errors By shrinking extreme positions toward more balanced allocations, Bayesian Mean-Variance delivers portfolios that are both theoretically sound and practically robust—particularly valuable when historical data is limited or market conditions are uncertain! 💡 #PortfolioOptimization #BayesianFinance #QuantitativeFinance #RiskManagement #InvestmentStrategy

Ever wondered about the differences between traditional automation, AI automation, and AI agents? It’s a question I get asked a lot, so I put together this infographic, for all of you! 1️⃣ Traditional Automation ↳ Primarily rule-based: think straightforward RPA (Robotic Process Automation), basic factory robots, or simple scripted IT tasks. ↳ Great for repetitive processes with predictable, static conditions. ↳ Still struggles with unpredictable changes, requiring frequent reprogramming by humans. ↳ Tools: UiPath, Blue Prism, Automation Anywhere — these remain the dominant RPA solutions, but they’re increasingly integrating AI for tasks like document understanding. 2️⃣ AI Automation ↳ How It Works: Machine Learning and other AI approaches to learn from data and adapt with minimal human intervention. ↳ Adapts to changing inputs—like email spam filters that get better over time or AI chatbots that refine responses. ↳ Examples: Fraud detection systems, recommendation engines, advanced chatbots. ↳ Tools/ Frameworks: → Gumloop: A rising platform that lets teams prototype, test, and deploy AI models with minimal coding → Zapier: For connecting AI-driven workflows to thousands of apps 3️⃣ AI Agents ↳ How they differ: These go beyond pattern recognition to reason, plan, and act autonomously. ↳ They actively make contextual decisions in real time, learning from ongoing interactions. ↳ Examples: Self-driving cars orchestrating traffic decisions, personal AI research assistants scouring data for insights, or “smart” systems that can optimize supply chains on the fly. ↳ Tools/ Frameworks: → CrewAI: Focuses on real-time collaboration and multi-agent systems with a Pythonic design → LangChain: A framework that enables developers to build applications powered by large language models, suitable for creating custom AI agents. → AutoGen: An open-source Python-based framework by Microsoft, designed for developers to create advanced AI agents with minimal coding → RASA: Open-source framework for building intelligent chatbots and voice assistants with advanced NLU → LangGraph: LangChain-created tool for building and managing complex generative AI agent workflows using graph-based architectures. → OpenAI Swarm: Experimental framework for lightweight, customizable multi-agent systems focusing on flexible task delegation and coordination. 𝌭 Foundational LLMs/SLMs : → Open-source models from Mistral AI models, Microsoft Phi, Google Gemma models, DeepSeek AI models, Perplexity R1-1776, Meta llama models, Alibaba Group Qwen models → Closed-source models from OpenAI, Anthropic, Perplexity, Google 🚀 Top-Inference providers- Fireworks AI, Groq, Cerebras Systems I’d love to hear your experiences: Have you implemented AI agents recently? Any favorite frameworks or tools you think are game-changers? Share below 👇 -------- Share this post with your network ♻️ Follow me (Aishwarya Srinivasan) for more AI insights, news, and educational content!

Most PMs are prioritizing the wrong things. It’s not about building the most features. 𝗜𝘁’𝘀 𝗮𝗯𝗼𝘂𝘁 𝗯𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝘁𝗵𝗲 𝗿𝗶𝗴𝗵𝘁 𝗼𝗻𝗲𝘀. When everything feels urgent, the real skill is choosing what 𝘯𝘰𝘵 to do. Here are quick, proven techniques to simplify your prioritization process: 🚦 𝗦𝘁𝗮𝗿𝘁 𝘄𝗶𝘁𝗵 𝘁𝗵𝗲 𝗯𝗶𝗴 𝗽𝗶𝗰𝘁𝘂𝗿𝗲 → Mission: Why does this product exist? → Vision: Where are we headed? → Strategy: What will get us there? → Goals: What matters 𝘳𝘪𝘨𝘩𝘵 𝘯𝘰𝘸? → Metrics: What do we measure to stay on track? But the real challenge? Balancing speed, strategy, and stakeholder alignment. My top 5 frameworks to help you navigate a backlog: 🟢 𝗥𝗜𝗖𝗘 𝗦𝗰𝗼𝗿𝗶𝗻𝗴 Evaluate projects based on: ↳ Reach: How many users will it impact? ↳ Impact: What’s the effect on each user? ↳ Confidence: How sure are we about our estimates? ↳ Effort: How much time will it take? RICE score: (Reach × Impact × Confidence) / Effort 🟢 𝗪𝗦𝗝𝗙 (𝗪𝗲𝗶𝗴𝗵𝘁𝗲𝗱 𝗦𝗵𝗼𝗿𝘁𝗲𝘀𝘁 𝗝𝗼𝗯 𝗙𝗶𝗿𝘀𝘁) WSJF helps you build what’s most valuable—fast: ↳ Job Size: How big or complex is the work ↳ Cost of Delay = User-Business Value + Time Criticality + Risk Reduction / Opportunity Enablement WSJF Score = Cost of Delay ÷ Job Size 🟢 𝗠𝗼𝗦𝗖𝗼𝗪 𝗠𝗲𝘁𝗵𝗼𝗱 This method clarifies priorities and sets expectations: ↳ Must have: Essential features. ↳ Should have: Important but not critical. ↳ Could have: Nice to have. ↳ Won’t have: Not for this time. 🟢 𝗩𝗮𝗹𝘂𝗲 𝘃𝘀. 𝗖𝗼𝗺𝗽𝗹𝗲𝘅𝗶𝘁𝘆 𝗠𝗮𝘁𝗿𝗶𝘅 Plot your initiatives on a 2x2 grid: ↳ High Value, Low Complexity: Quick wins. ↳ High Value, High Complexity: Strategic projects. ↳ Low Value, Low Complexity: Fill-ins. ↳ Low Value, High Complexity: Time sinks. 🟢 𝗞𝗮𝗻𝗼 𝗠𝗼𝗱𝗲𝗹 Classify features based on customer satisfaction: ↳ Must-be: Basic expectations. ↳ Performance: More is better. ↳ Attractive: Delightful surprises. The best product teams don’t rely on a single technique. They blend methods based on goals, clarity, and team dynamics. Let’s stop guessing and start building smarter. 📌 𝗪𝗮𝗻𝘁 𝗮 𝗱𝗲𝘁𝗮𝗶𝗹𝗲𝗱 𝗯𝗿𝗲𝗮𝗸𝗱𝗼𝘄𝗻 𝗼𝗳 𝘁𝗵𝗲𝘀𝗲 𝗽𝗿𝗶𝗼𝗿𝗶𝘁𝗶𝘇𝗮𝘁𝗶𝗼𝗻 𝘁𝗲𝗰𝗵𝗻𝗶𝗾𝘂𝗲𝘀? Product Map dives deeper with clear examples and resources. Here is the link to the detailed guide on Prioritization 👇 https://lnkd.in/e2tQCiHp ♻️ Repost to share the value. 📩 Which technique works best for your team? Let’s discuss this in comments!

I’ve reviewed > 400 portfolios this year. Observation #1: The ones that got interviews weren’t the prettiest. They were the clearest. → Clear intent (what roles they’re targeting) → Clear structure (who they helped + what changed) → Clear thinking (how they made decisions) Observation #2: Hiring managers responded best to portfolios that made it easy to scan, not admire. → 3-5 second headlines that told the story → Metrics up top, visuals in the middle, lessons at the end → Less storytelling. More signal. Observation #3: The portfolios that ‘failed’? → Opened with “Hi, I’m Alex and I love solving problems” → Contained 30+ screenshots with no explanation → Didn’t articulate business impact or their role → Had no opinion, no POV, no process If I were applying today? → I’d restructure my case studies to lead with outcomes → I’d add a design philosophy section to show how I think → I’d cut 40% of the fluff and focus on what actually matters → I’d communicate my USP and elevator pitch up front Your portfolio isn’t a gallery. It’s a business case for why you’re worth hiring. ----- Just thought I'd share this after reviewing some notes over the weekend. Hope it helps! ----- #ux #tech #design #ai #business #careers

Dear MBA Class of 2027 - Stop Sending Resumes. Start Sending Links. That’s how I cracked my internship. While batchmates were polishing buzzwords, I was polishing Power BI visuals. While others pitched “cross-functional synergy”, I built a working currency converter app in Excel. I’m not a core techie. Not a pure management type either. I sit in that powerful middle lane -> techno-functional. So I took a different route: Built few real-world projects: 1) Mandi Price Tracker App - fetches daily prices from multiple agricultural markets via REST APIs 2) Excel Scenario Simulator - runs 8 business scenarios in parallel with dynamic inputs 3) Power BI Dashboard - visualizes pan-India Clean Energy metrics using live REST API data 4) Monte Carlo Simulator - models risk & return for an 8-stock equity portfolio in Excel Then I did this: -Created a personal website -Links to live dashboards -Gave video demos over Zoom calls Recruiter’s first line: “This is refreshing. Let’s skip the usual.” Two weeks later, internship in hand. -- MBA Class of 2027 - here’s the playbook if you’re targeting techno-functional roles: 1) Don't just say “I know tools” - show business thinking through them 2) Skip fluff. Build lean, relevant, real-world solutions 3) Make your portfolio easy to click, demo-ready, and story-rich Forget big words. Be demo-ready. Be impressive in 10 seconds or less.

Diversification hasn’t stopped working—it’s investors who stopped using it properly. From 2010 to 2025, US large-cap equities crushed everything else. Any move into bonds, hedge funds, or alternatives looked like dead weight. But the flaw wasn’t diversification. It was refusing to use leverage intelligently . That’s where capital efficiency comes in. Instead of borrowing directly, investors can access embedded or delegated leverage inside assets and structures. Small caps, emerging markets, private equity, higher-duration bonds—they deliver more exposure per dollar. Hedge funds and portable alpha combine equity beta with diversifiers in a capital-light way. Done well, this frees balance sheet space for real diversification without watering down returns . The chart comparing four portfolio types makes it obvious. A simple 60/40 delivered ~6% returns, with equity risk dominating. Add hedge funds and alternatives at low vol, returns fell. Lever it back—returns recovered. Use delegated leverage (private equity, portable alpha, higher-vol hedge funds)—you get the same uplift, without explicit borrowing. The outcome is the same, the optics are cleaner . Here’s the friction. Investors often reject high-vol strategies because the line item looks uncomfortable—even if the portfolio impact is the same. That “line-item trap” kills efficiency. The job isn’t to minimize visible drawdowns in each bucket—it’s to maximize the resilience and growth of the whole portfolio. Bottom line: capital efficiency isn’t exotic. It’s discipline. Use structures that embed leverage intelligently, avoid overpriced high-beta or duration plays, and think total portfolio, not line items. The only free lunch is diversification. Capital efficiency is how you actually eat it. Would you pay up for embedded leverage if it frees capital elsewhere? Do you judge alternatives by line-item P&L—or by portfolio contribution? Is private equity in your book a growth bet or a capital-efficiency tool? Would you accept higher vol in a slice if total portfolio risk falls? For more see our Nomura CIO Corner: https://lnkd.in/e4TCax_g #CapitalEfficiency #Diversification #PrivateEquity #HedgeFunds #PortableAlpha #Alternatives #Nomura #CIO #Macro

ACCOUNTING SOFTWARE vs ERP SYSTEMS 🧮 💻 Financial systems make or break a business - but how do you know which one is right for YOU? Choosing the right financial management solution can save your business THOUSANDS of dollars while setting you up for future growth. ➡️ THE CORE DIFFERENCE Most folks think these are the same thing, but they're not. Accounting software handles your transactions and financial reporting. That's it. ERP is the entire orchestra - connecting everything from accounting to inventory to HR to sales. ➡️ FEATURE SHOWDOWN Your typical accounting package includes: - General ledger stuff - Accounts receivable/payable - Bank recon tools - Invoicing capabilities - Financial reports - Tax features - Some basic inventory tracking Meanwhile, ERP systems give you: - Everything above PLUS - Serious inventory management - Full warehouse systems - Supply chain tools - Complete HR management - Production scheduling - Data analytics/dashboards ➡️ WHICH SIZE FITS YOU? Accounting software makes sense if: - You're small/medium sized - Have one main location - Deal with simple finances - Run a service business - Have under 50 team members ERP becomes necessary when: - You're mid-sized or larger - Operate multiple locations - Manufacture or distribute products - Deal with complex financials - Have 50+ people on payroll ➡️ TIMING IS EVERYTHING With accounting software, you're looking at: - 1-2 weeks to pick one - A few days to set it up - 1-2 weeks for basic config - Another week for data transfer - Few days training the team - About a week to go live TOTAL: 1-2 months from start to finish ERP timelines are a whole different story: - 1-3 months just gathering requirements - 1-2 months picking the right system - Several weeks for initial setup - 2-4 months configuring everything - 2-6 months on customization - 2-5 months moving data and testing TOTAL: 3-6 months before you're fully operational ➡️ WHAT'S THE DAMAGE? Accounting software won't crush your budget: - $10-200 monthly per user - $0-2,000 for implementation help - $0-2,000 for training - 0-20% annual maintenance - Minimal IT investment TOTAL: As little as $50 / month to get started ERP systems demand serious investment: - $15,000 to $1M+ licensing - $150-500+ monthly per user - $50,000-250,000+ implementation & customization - Major IT infrastructure needs TOTAL: $10,000-250,000 minimum ➡️ POPULAR SOLUTIONS Accounting software players: - QuickBooks - Xero - FreshBooks - Wave Major ERP contenders: - NetSuite - Microsoft Dynamics - Acumatica - Odoo - SAP ➡️ MAKING THE RIGHT CALL The right solution comes down to several key factors: - Look at your 3-year plan. Multiple locations coming? ERP might save pain later. - Count your departments. More teams needing the same data = stronger case for ERP. - Be honest about your budget. Start with accounting software if money's tight. === What system runs YOUR finances right now? Drop me a comment below 👇