Risk Assessment In Investment Portfolios

How to calculate Beta for Unlisted firms? A common interview question in Finance. Follow me (Peeyush) for more such simple concept breakdowns How do you value companies that are coming with an IPO, or a recently listed one. We need a discount rate, but we do not have the price history to calculate Beta. What do we do here? We can take Beta of similar firms, or average of Betas of firms in the sector, but there is an issue here. Beta tells us about firm specific risk – which can be attributed to operating leverage (business risk) and financial leverage (Debt) Since we choose firms from the same sector, operating leverage should be similar for all. However, financial leverage could be different. So it may be incorrect to take a simple average of betas of sector peers. Solution? The most common solution is to “Un-lever” and “Re-lever” the Betas. How? Assume a new steel company is getting listed. 1) Find Beta for similar firms (SAIL, JSW Steel etc) using stock prices (levered beta) 2) Un-lever the Beta for each firm using the below formula Unlevered Beta = Levered Beta / (1 + ((Debt/Equity)(1-tax rate))) Unlevered Beta is the Beta of the firm after removing the effect of capital structure. Simply put, the Beta of the firm assuming it had no debt 3) Take an average of the Unlevered Betas, to find Sector Unlevered Beta 4) Finally, Re-lever the average Unlevered Beta using the firm’s own D/E ratio (using the same formula above) When is this useful? When the firm has no price history. Or if the price history is a bit skewed, making statistical beta unreliable. Note that there may be other methods as well, but this is the most commonly used and simple method. ---- I help students build a career in #finance through my writing. Do go through some of my earlier posts if you aspire for a career in #valuation or #investmentbanking

Attention property owners, facilities managers, and developers: when incorporating solar panels and battery storage systems into your buildings, it's essential to consider fire protection and risk management. The increasing presence of solar panels on commercial buildings, coupled with the advancements in battery storage technology, offers significant benefits for energy efficiency. However, these systems also introduce new challenges regarding fire safety. Solar photovoltaic (PV) systems and battery storage operate at high voltages, potentially posing fire risks if not properly installed or maintained. While these risks are relatively rare in the UK, fires involving these systems can be challenging to extinguish and can escalate rapidly due to the stored energy, combustible materials, and high voltages involved. Common risks associated with these systems include loose connections, damaged wiring, or faults in inverters, which can lead to overheating, arcing, or electrical fires. Since PV systems are often installed on rooftops, fires may not be immediately detected, causing significant damage before intervention. Battery storage systems, particularly those using lithium-ion technology to store excess solar power, can experience thermal runaway if damaged or overcharged, potentially resulting in severe fires or explosions. Even when the main power is off, PV systems can still generate electricity, posing risks to emergency responders and maintenance personnel. Improper installation or retrofitting of these systems may lead to inadequate separation from other building components, increasing the risk of fire spreading to critical areas like roof voids or occupied spaces. Whether overseeing a warehouse, office building, or school, it is crucial to integrate renewable energy systems into comprehensive fire risk assessments. Ensure that detection systems, signage, and maintenance protocols are regularly updated and effective in mitigating potential fire risks. . #FireSafety #RenewableEnergy #RiskManagement

𝐓𝐡𝐞 𝐀𝐬𝐩𝐢𝐫𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐈𝐧𝐯𝐞𝐬𝐭𝐨𝐫 𝐅𝐫𝐚𝐦𝐞𝐰𝐨𝐫𝐤 𝐢𝐧 𝐏𝐫𝐚𝐜𝐭𝐢𝐜𝐞: Showing affluent investors how risky their portfolio 𝘳𝘦𝘢𝘭𝘭𝘺 are ⚠️ This week, I want to give you a few practical insights into my work as a Financial Advisor - starting this week with how we use the Aspirational Investor Framework (as re-introduced last week!) in practice. Today, let's start with a story about risk. 𝐋𝐚𝐬𝐭 𝐲𝐞𝐚𝐫, 𝐈 𝐦𝐞𝐭 𝐚𝐧 𝐚𝐟𝐟𝐥𝐮𝐞𝐧𝐭 𝐢𝐧𝐝𝐢𝐯𝐢𝐝𝐮𝐚𝐥 𝐰𝐡𝐨 𝐡𝐚𝐝 𝐬𝐮𝐜𝐜𝐞𝐬𝐬𝐟𝐮𝐥𝐥𝐲 𝐬𝐨𝐥𝐝 𝐭𝐡𝐞𝐢𝐫 𝐛𝐮𝐬𝐢𝐧𝐞𝐬𝐬 𝐟𝐨𝐫 𝐚 𝐥𝐨𝐰 𝐞𝐢𝐠𝐡𝐭-𝐟𝐢𝐠𝐮𝐫𝐞 𝐚𝐦𝐨𝐮𝐧𝐭. Since the exit a few years back, they’d been very active as an investor - buying not only a personal property, but also investing substantial sums into both venture capital funds and direct venture capital investments. As the ‘tech bubble’ of ‘19-21 burst, they reached out to me to assist them with a critical view of their current investment setup. One thing that we focus on at Cape May Wealth Advisors is making sure that our clients can always maintain their lifestyle - more precisely, by designing their Market Bucket so that it is invested in a way, and large enough, to have the highest probability of generating the required income over 10, 30, or 50 years. 𝐀𝐧𝐝 𝐭𝐡𝐚𝐭 𝐰𝐚𝐬 𝐚 𝐯𝐢𝐞𝐰 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞 𝐜𝐥𝐢𝐞𝐧𝐭 𝐡𝐚𝐝 𝒏𝒐𝒕 𝐜𝐨𝐧𝐬𝐢𝐝𝐞𝐫𝐞𝐝, 𝐢𝐧𝐬𝐭𝐞𝐚𝐝 𝐟𝐨𝐜𝐮𝐬𝐢𝐧𝐠 𝐦𝐨𝐫𝐞 𝐨𝐧 𝐭𝐡𝐞 𝐨𝐯𝐞𝐫𝐚𝐥𝐥 (𝐜𝐨𝐧𝐬𝐢𝐝𝐞𝐫𝐚𝐛𝐥𝐞) 𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞𝐢𝐫 𝐰𝐞𝐚𝐥𝐭𝐡. So when we categorized their assets according to the Aspirational Investor logic, things became a bit more clear: They had most of their assets invested in the Aspirational Bucket, and most of their Market Bucket in illiquid, long-term investments. 𝐀𝐧𝐝 𝐢𝐭 𝐛𝐞𝐜𝐚𝐦𝐞 𝐜𝐥𝐞𝐚𝐫 𝐭𝐨 𝐭𝐡𝐞𝐦 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞𝐲 𝐡𝐚𝐝 𝐦𝐮𝐜𝐡 𝐦𝐨𝐫𝐞 𝐫𝐢𝐬𝐤 𝐭𝐡𝐚𝐧 𝐭𝐡𝐞𝐲 𝐡𝐚𝐝 𝐰𝐚𝐧𝐭𝐞𝐝 𝐭𝐨 𝐭𝐚𝐤𝐞, 𝐞𝐱𝐩𝐨𝐬𝐢𝐧𝐠 𝐭𝐡𝐞𝐦𝐬𝐞𝐥𝐯𝐞𝐬 𝐭𝐨 𝐬𝐢𝐠𝐧𝐢𝐟𝐢𝐜𝐚𝐧𝐭 𝐢𝐥𝐥𝐢𝐪𝐮𝐢𝐝𝐢𝐭𝐲 𝐫𝐢𝐬𝐤. It wasn't unlikely that in a market downturn, their combination of hard-to-sell illiquid investments and a drawdown in their liquid portfolio would leave them with little to no liquidity for their day-to-day expenses. The other banks they worked with never brought up that risk, focusing either on the overall size of the client’s assets or simply just caring about what (shrinking) liquid portfolio they had managed. Thanks to the Framework, they realized that their investment strategy didn’t quite suit them as well as they thought - and luckily were able to make them the required adjustments to not become 'insolvent' in an eventual downturn.

One of the most widely used models for calculating the required rate of return on equity investments is the Capital Asset Pricing Model (CAPM). Developed by financial economists in the 1960s, the CAPM provides a formula for determining a theoretically appropriate required rate of return that investors should expect, given the risk of an investment. The key component of CAPM is beta, which measures the volatility of an asset's returns relative to the overall market. A beta greater than 1 indicates that an asset is more volatile than the market, while a beta less than 1 means it is less volatile. The rationale behind CAPM is that investors require a rate of return greater than the risk-free rate to compensate for the risk taken. The amount of compensation depends on the asset's beta; the higher the beta, the greater the perceived risk and, thus, the higher the required return premium. While the CAPM has its limitations and makes some assumptions, it provides a standardized model for calculating expected returns that are widely used by investors, corporations, and academics. Estimating a company's cost of equity capital using CAPM is a crucial input for valuation models and capital budgeting decisions. No model is perfect, but CAPM offers a relatively simple yet powerful framework for relating risk to expected return. Understanding and applying CAPM is essential knowledge for any finance professional.

REGIME-DEPENDENT BETA: WHY YOUR SINGLE MARKET SENSITIVITY ESTIMATE IS DANGEROUSLY WRONG 📊 Standard finance approaches relies on a single beta coefficient to measure market sensitivity. But here's the uncomfortable truth: beta dramatically shifts across economic regimes, and using static estimates can expose portfolios to massive unintended risk. A comprehensive analysis of major asset classes reveals that regime-conditional beta modeling fundamentally changes our understanding of market sensitivity and portfolio risk exposure. The Hybrid Bootstrap-Copula Framework: - ARMA(1,1)-GARCH(1,1) models capture each asset's marginal dynamics - Bivariate copulas preserve dependence structures with market factor - Monte Carlo simulation generates forward-looking alpha/beta distributions - 5,000 scenarios across Normal, Bull, Bear, and Crisis regimes Critical Findings from Forward Beta Analysis: • Mega-cap equity betas compress during Bear/Crisis vs Bull markets • Gold maintains positive, equity-like sensitivity even in crisis periods • Crypto and silver exhibit amplified high-beta behavior under stress • 80% confidence intervals reveal substantial estimation uncertainty • Traditional "low-beta" assets can become high-beta when you need hedging most Strategic Applications: ✅ Risk Budgeting: Use regime-conditional betas for accurate position sizing ✅ Dynamic Hedging: Anticipate beta shifts before they impact portfolios ✅ Stress Testing: Model how correlations break down in crisis scenarios ✅ Asset Allocation: True diversifiers show β < 0 in crisis conditions As markets become increasingly interconnected and regime shifts more frequent, the assumption of constant beta has become a critical blind spot in modern portfolio management. Regime-dependent modeling provides the forward-looking framework essential for navigating tomorrow's volatility with today's decisions. How are you currently accounting for beta instability in your risk models, and what role does regime analysis play in your portfolio construction process? I am open to collaborations applying it beyond equities, commodities and cryptos. #QuantitativeFinance #RiskManagement #PortfolioTheory #BetaModeling #RegimeAnalysis #MonteCarloSimulation #AssetAllocation #FinancialEngineering

For aspiring quants: Last year, I evaluated a strategy that "beat the S&P 500 by 20%." Impressive, right? Then I ran it through a simple CAPM risk model. Turns out, the strategy was just 2x leveraged beta with extra steps. It didn't beat the market - it just borrowed more money to buy the market. Worse: It was delivering only 60% of the return you'd expect for that level of risk. Here's the problem most backtests hide: They show you total return. They don't show you risk-adjusted return. A real example: UPRO (3x leveraged S&P 500 ETF) Edgar Alcántara and I analyzed leveraged ETFs using CAPM for our open-source course and found that:: ·      UPRO takes on 3.04x the volatility (β = 3.04) ·      But delivers only 2.04x the cumulative returns ·      That's 67% of what you'd expect for the risk taken The chart below shows the decomposition: The green line is what CAPM predicts UPRO should return. The blue line is what it actually returns. The gap? Inefficiencies from volatility drag, transaction costs, and behavioral factors. This isn't "alpha." It's inefficient beta. For those building careers in quant finance: Before you present any strategy, decompose it through a risk model: → How much return comes from market exposure? → How much from factor tilts? → How much from genuine alpha? The question isn't "did it outperform?" The question is "was it worth the risk?" Want to learn how to do this analysis? I've built a full tutorial on CAPM and risk-adjusted returns in my open-source Portfolio Management Course (developed with Edgar Alcántara): https://lnkd.in/ebsTPNQ7 Module 4.1-4.4 covers exactly this type of analysis with Python code. Read the full paper: "Leveraged Portfolios Risk Analysis" https://lnkd.in/eVFh-sme This analysis was conducted independently using publicly available data. All views are my own. What's your experience? Where have you seen backtests that looked great but didn't account for risk? #QuantFinance #RiskManagement #PortfolioManagement

Navigating Rooftop Solar Hazards While Rooftop Solar PV panels are an excellent step toward sustainability, they introduce unique hazards that demand proactive management. With a steep growth in such installations, both in terms of scale and complexity, the risk profile for building owners and emergency responders also rapidly changes. According to industry data and NFPA insights, key hazards include: # Electrical Shock from high-voltage systems that remain energized even after primary power is shut off. # Fire Risks that might difficult to access and manage on the roof of a structure. # Integrity of the roofing structure with added weight of large arrays of PV Modules can compromise and contribute to roof collapse during or after a fire. # Large arrays of PV Modules under fire can complicate roof access and generate toxic emissions, hindering effective firefighting and emergence response. Implementing loss minimization measures as recommended by NFPA Codes like NFPA 1, NFPA 70B, NFPA 70E, NFPA 855 isn’t just about compliance, it’s about resilience. These measures, including pre-planning and specialized training for facility teams, which are essential to mitigate risks before they escalate. Key Action Steps: # Prioritize Pre-Planning that collaborate with local fire services to ensure they are familiar with a site rooftop layout and shutdown procedures. # Adherence to NFPA certified installation and maintenance standards to minimize electrical and fire ignition risks. # Invest in Training to equip response teams with the knowledge to handle properties with rooftop solar features. A sustainable future is a safe future. It's important that all green energy transitions are backed by robust safety and loss prevention strategies. #SolarEnergy #FireSafety #RenewableEnergy #RiskManagement #NFPA #BuildingSafety #Sustainability #GreenEnergy #tataaigriskengineering #tataaig Video Source: @TheFMGroup Youtube Channel

Zero-Beta CAPM: In the world of Quantitative Finance, the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), and Mossin (1966), is widely known. This model states that the expected excess return* of an asset is proportional to the expected excess return of the market portfolio**, with the proportionality constant being the asset's beta. However, there is another lesser-known version of the CAPM that does not assume the existence of a riskless asset, and is therefore known as the Zero-Beta CAPM. This model was developed by Fisher Black, co-creator of the Black-Scholes model, in Black (1972). The zero-beta CAPM is obtained under the same assumptions of the Mean-Variance analysis, with the extra assumption that all investors have homogeneous expectations. The formula below presents the expression of the zero-beta CAPM of Black (1972). In the formula: - R_i is the expected return of the ith market asset. - R_p^M is the expected return of the market portfolio (assumed to be different from the global minimum-variance portfolio). - beta_i^M is the beta of the ith asset. - The term in parentheses is the difference between the expected return of the market portfolio and the expected return of the portfolio orthogonal*** to the market portfolio. As can be seen from the formula, the zero-beta CAPM can be obtained from the standard CAPM by simply replacing the return of the risk-free asset with the expected return of the portfolio orthogonal to the market portfolio. A detailed derivation of the Zero-Beta CAPM, as well as the standard CAPM, with all the assumptions and intermediate results with proofs, can be found in Noguer et al. (2025), a book I co-authored with Dr Miquel Noguer i Alonso and Julian Antolin: https://lnkd.in/dEeVCVJj (*) The expected excess return of an asset is equal to its expected return minus the return of the riskless asset. (**) The market portfolio is the portfolio of risky assets that has the same weights as the market. (***) Two portfolios are orthogonal if the covariance of their returns is zero. References: - Black (1972): "Capital Market Equilibrium With Restricted Borrowing," Journal of Business, 45 (3), 444-455. - Lintner (1965): "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets", Review of Economics and Statistics, 47 (1), 13-37. - Mossin (1966): "Equilibrium in a Capital Asset Market", Econometrica, 34 (4), 768-783. - Noguer, Bueno-Guerrero and Antolín (2025): "Quantitative Portfolio Optimization: Advanced Techniques and Applications", Wiley. - Sharpe (1964): "Capital Asset Prices: A Theory of Market Equilibrium Under Condition of Risk", Journal of Finance, 19 (3), 425-442. #finance #mathematics #markets

It was great to see such a strong response to the earlier post on geometric intuition behind portfolio diversification and Modern Portfolio Theory (MPT). Many insightful comments emphasized that working with just standard deviations and correlations isn’t enough to understand the full dynamics - and I couldn’t agree more! 🔍 In this follow-up, I wanted to connect that intuitive geometric view with something more familiar: regression analysis, particularly as it shows up in the Capital Asset Pricing Model (CAPM). MPT gives us a symmetrical view treating both assets in a pair equally and focusing on portfolio volatility. When we shift to projecting one asset onto another, symmetry breaks. But the view is very useful as in real-world cases like stock vs. index, we care about directional dependence. That’s the core of CAPM. CAPM models expected returns, and in practice, we often estimate beta by regressing stock returns on market returns. That naturally leads to the idea of residuals - the parts of a stock’s return not explained by market movements. And then, the intuitive geometry comes back in: - The beta component aligns with the market (projection) - The residual component is orthogonal (unexplained) 📌 In MPT, residuals are in the background - we focus on the total portfolio volatility, and not necessarily on the actual behaviour of an individual asset’s moves. With CAPM’s regression framing, residuals get to the centre stage. We can now explore their volatility, dynamics, and whether they hint at structural deviations from the market. ⚠️ Of course, real markets aren’t as clean as diagrams suggest. Residuals often contain structure - patterns, outliers, or volatility clustering, and betas themselves can shift across time. But the underlying framework gives foundation. Plus, the empirical regression linked to CAPM reveals more than just beta: it surfaces alpha - often interpreted as manager skill or model deviation, and it gives us a full path of residuals to investigate, which is often where things get interesting.. 🌍 For example, climate risk adds an important layer here. Traditional beta and residual analysis reflect historical patterns, but climate-related risks can cause new, non-linear shifts that break past correlations. Residuals may no longer be just noise - they can signal structural changes driven by climate impacts.

🛑When the Sun Turns Dangerous: The Hidden Fire Risk in Solar Panels 📌Solar energy is booming, but are we ignoring a silent threat? ☀️ ⚠️While solar panels are generally safe, fires do happen – and when they do, the consequences can be catastrophic for businesses, homes, and insurers. 📌MAJOR CAUSES OF SOLAR PANEL FIRES: 1️⃣ Poor Installation (60%+ of cases) Loose connections, underrated cables, or incorrect DC isolators create high-resistance points that arc and ignite. 2️⃣ Module Defects (Micro-cracks & Hotspots) Manufacturing flaws or physical damage cause localized overheating, melting the backsheet and leading to arc faults. 3️⃣ DC Arc Faults Unlike AC, DC arcs don't have a natural zero-crossing. Once initiated, they can sustain themselves – melting metal and starting fires. 4️⃣ Connector Mismatch Mixing connectors from different brands (e.g., MC4 with non-MC4) creates water ingress and resistance heating. 5️⃣ Rodent Damage Rats and squirrels chew through insulation, exposing live wires that short-circuit against the module frame. 6️⃣ Accumulated Debris & Shading Bird droppings, leaves, or partial shading cause reverse bias in cells, creating extreme hotspots (150°C+). ❓HOW TO REDUCE OR PREVENT SOLAR PANEL RISK: 🛡️ Before Installation: Use only IEC 61730 certified modules & DC cables Hire trained, certified installers (not the cheapest bid) Specify identical connectors (same brand & type) 🛡️ During Operation: Install DC arc fault detection devices (now mandatory in many codes) Perform thermal imaging surveys every 6-12 months Clean panels regularly; monitor for debris/shading Rodent-proofing: install mesh barriers around arrays. 🛡️ For Insurers & Risk Managers: Require commissioning reports & thermal scans Inspect for proper labeling, disconnect means, and rapid shutdown compliance