Risk and Return Trade-offs

Reexamining the Performance of Passive Options Strategies More than 40 years ago, Merton et al. published two papers examining the performance of passive options strategies. At the time of their studies, options data was not widely available, so they used historical volatility to calculate options prices. Since then, the options market has become highly liquid, with significant structural changes. A recent article reexamines the strategies studied by Merton et al., along with additional strategies, using actual options data from the period 2012 to 2023. Findings: -The original option strategies recommended by Merton et al. no longer provide a favorable return-to-risk ratio, likely due to assumptions in their simulation-based approach. -Recent data show that simple options strategies no longer add value to a portfolio or index. -However, three dynamic options strategies have outperformed the S&P 500 Index on a return-to-risk basis. -The favorable performance observed in prior studies can be replicated by incorporating simple market regime signals into strategy construction. -The Protective Put (PPUT) strategy consistently outperforms the S&P 500 Index on a return-to-risk basis. -Adding a simple logic of avoiding puts after a one-standard-deviation drawdown enables PPUT to outperform the index on a return basis with significantly lower risk. -A possible reason for the PPUT strategy's superior performance is that increased use of covered call strategies by firms reduces implied volatility levels, underpricing tail risk. Join the quant community—subscribe to the newsletter! Link in profile. References: -Andrew Kumiega, Greg Sterijevski, and Eric Wills, Black–Scholes 50 Years Later: Has the Outperformance of Passive Option Strategies Finally Faded?, International Journal of Financial Studies 12: 114. -Merton, Robert C., Myron S. Scholes, and Mathew L. Gladstein. 1978. The Returns and Risk of Alternative Call Option Portfolio Investment Strategies. Journal of Business 51: 183–242. -Merton, Robert C., Myron S. Scholes, and Mathew L. Gladstein. 1982. The Returns and Risks of Alternative Put-Option Portfolio Investment Strategies. Journal of Business 55: 1–55. #options #portfoliomanagement #quantitativeresearch Abstract Slightly over fifty years ago, the Black–Scholes option pricing model revolutionized investing by enabling a shift from linear to non-linear payoff structures. Myron Scholes later published two papers documenting the performance of passive option strategies that outperformed the underlying index on a risk–return basis. The options market has evolved considerably over the last fifty years from an open outcry trading structure with options being single-listed to a high-frequency computer-based market. This paper re-evaluates the trilogy of foundational studies to determine whether passive-option-enhanced portfolios still produce superior performance in the current high-frequency options market environment.

Modern Portfolio Theory (MPT) & CAPM: Why “RIP CAPM” is Premature The recent discussions around “RIP CAPM” raise an important question—is the Capital Asset Pricing Model truly obsolete, or does it still hold foundational value in finance? Let’s break it down. 1. What Modern Portfolio Theory (MPT) Teaches Us → Efficient Frontier: Maximizing returns for a given risk level by optimizing asset allocation. → Risk-Return Trade-off: Higher risk should be compensated by higher expected returns. → Diversification: Reducing unsystematic risk by investing in a variety of assets. 2. CAPM: The Bridge from MPT to Practical Pricing CAPM builds on MPT by establishing a clear relationship between risk and expected return: rᵢ(t) = βᵢ rₘ(t) + αᵢ(t) → Beta (β): Measures an asset’s sensitivity to overall market movements. → Alpha (α): Represents excess return not explained by market risk. CAPM asserts that, in an efficient market, α should be zero, meaning investors cannot consistently “beat the market” without taking additional risk. 3. Understanding the Graphs in the Image The image visually explains how market returns (SP500) influence asset returns (XYZ stock): → Left Graph (Daily Returns Over Time): • Shows the movement of a stock (XYZ) in relation to the S&P 500 (market returns). • The fluctuations illustrate how stocks generally follow market trends but with varying degrees of volatility. → Right Graph (Market vs. Stock Relationship): • Plots XYZ’s returns against the S&P 500 to show its sensitivity to market movements (β₁). • The slope represents the stock’s beta (β)—a steeper slope means higher market dependence. • Alpha (α) is the intercept, representing excess returns independent of the market. • CAPM predicts that α should be zero in an efficient market, implying that systematic risk alone determines expected returns. 4. Why Critics Say “RIP CAPM” CAPM’s assumptions—such as a single-factor risk model, no transaction costs, and rational investors—are often seen as oversimplifications. Newer models like the Fama-French 3/5-factor models and Arbitrage Pricing Theory (APT) incorporate additional factors such as size, value, and profitability to address these limitations. Critics argue that CAPM fails to fully capture real-world market behavior. 5. Why CAPM Still Matters Despite its limitations, CAPM remains essential for several reasons: → Foundational Tool: It is the starting point for understanding asset pricing. Criticizing CAPM without understanding it is like dismissing the Black-Scholes model just because more complex option pricing models exist. → Practical Use Cases: • Cost of Equity Calculations: Used in corporate finance for WACC estimation. → Simplicity: In many cases, a one-factor model provides sufficient insights without unnecessary complexity. #CAPM #RiskManagement #QuantitativeFinance #AssetPricing #PortfolioManagement #FinancialMarkets #InvestmentStrategies #Trading #FinancialEngineering

Novice investors often make the mistake of choosing an investment based solely on projected returns. A projected 30% average annual return looks phenomenal on paper… But it doesn’t paint the full picture. Projected returns don’t take into account the very real risks involved in a real estate deal. This is where risk-adjusted returns come in. Simply put, risk-adjusted return is a calculation that determines an investment's expected return while accounting for the level of risk. This ratio is shown as a percentage and takes into account general risks that could negatively impact the return of the investment, such as market risk or volatility. For instance, an investor with less risk tolerance may prefer to invest in a higher quality property in a top-tier market with an expected rate of 4% compared to a lower class building in a less desirable, tertiary market with an expected rate of 12%. While the 12% may seem more appealing at first glance, it carries more risk due to the quality of the asset and market location. Certain investments inherently carry more risks than others with variances in income, expenses, and returns because of downside volatility, among other factors. Overall, if you're considering investing in real estate, it's essential to understand the concept of risk-adjusted return, how to calculate it, and how it can be used to make informed investment decisions. Don't fall into the trap of solely considering projected returns without taking into account the level of risk involved.

When it comes to private commercial real estate, one thing’s clear: not all returns are created equal. It’s easy to get caught up in flashy numbers—20% IRR here, 3x equity multiple there. But here’s the deal: 𝗿𝗲𝘁𝘂𝗿𝗻𝘀 𝗮𝗹𝗼𝗻𝗲 𝗱𝗼𝗻’𝘁 𝘁𝗲𝗹𝗹 𝘁𝗵𝗲 𝘄𝗵𝗼𝗹𝗲 𝘀𝘁𝗼𝗿𝘆. The question you really need to ask is: 𝗪𝗵𝗮𝘁’𝘀 𝘁𝗵𝗲 𝗿𝗶𝘀𝗸 𝗯𝗲𝗵𝗶𝗻𝗱 𝘁𝗵𝗼𝘀𝗲 𝗿𝗲𝘁𝘂𝗿𝗻𝘀? Here’s what I’ve learned: A higher return might come with a higher risk profile. Think of a 20% return with shaky assumptions versus a 16% return built on solid ground. 𝗧𝗵𝗲 𝗺𝗮𝗻𝗮𝗴𝗲𝗿 𝗺𝗮𝘁𝘁𝗲𝗿𝘀. The right team can make or break a deal. Experience, transparency, and alignment with investors are non-negotiable. 𝗗𝗲𝗯𝘁 𝗶𝘀 𝗮 𝗱𝗼𝘂𝗯𝗹𝗲-𝗲𝗱𝗴𝗲𝗱 𝘀𝘄𝗼𝗿𝗱. It can amplify rewards—or risks. Understanding the capital stack and stress-testing the deal is key. 𝗧𝗵𝗲 𝘁𝘆𝗽𝗲 𝗼𝗳 𝗮𝘀𝘀𝗲𝘁 𝗰𝗼𝘂𝗻𝘁𝘀. A fully leased apartment building? Different game than a ground-up mixed-use development. Real estate investing isn’t about chasing the highest number on the page. It’s about 𝗯𝗮𝗹𝗮𝗻𝗰𝗶𝗻𝗴 𝗿𝗲𝘁𝘂𝗿𝗻 𝘄𝗶𝘁𝗵 𝗿𝗶𝘀𝗸, 𝗽𝗮𝗿𝘁𝗻𝗲𝗿𝗶𝗻𝗴 𝘄𝗶𝘁𝗵 𝘁𝗵𝗲 𝗿𝗶𝗴𝗵𝘁 𝗽𝗲𝗼𝗽𝗹𝗲, 𝗮𝗻𝗱 𝗺𝗮𝗸𝗶𝗻𝗴 𝗱𝗲𝗰𝗶𝘀𝗶𝗼𝗻𝘀 𝘁𝗵𝗮𝘁 𝗮𝗹𝗶𝗴𝗻 𝘄𝗶𝘁𝗵 𝘆𝗼𝘂𝗿 𝗴𝗼𝗮𝗹𝘀. P.S. 𝘏𝘢𝘷𝘦 𝘺𝘰𝘶 𝘦𝘷𝘦𝘳 𝘣𝘦𝘦𝘯 𝘵𝘦𝘮𝘱𝘵𝘦𝘥 𝘣𝘺 𝘩𝘪𝘨𝘩 𝘳𝘦𝘵𝘶𝘳𝘯𝘴, 𝘰𝘯𝘭𝘺 𝘵𝘰 𝘥𝘪𝘴𝘤𝘰𝘷𝘦𝘳 𝘵𝘩𝘦 𝘳𝘪𝘴𝘬𝘴 𝘸𝘦𝘳𝘦 𝘵𝘰𝘰 𝘴𝘵𝘦𝘦𝘱? 𝘓𝘦𝘵’𝘴 𝘵𝘢𝘭𝘬—𝘪𝘵’𝘴 𝘢 𝘭𝘦𝘴𝘴𝘰𝘯 𝘸𝘰𝘳𝘵𝘩 𝘴𝘩𝘢𝘳𝘪𝘯𝘨.

📈 BUILD SMARTER PORTFOLIOS: THE POWER OF MEAN-VARIANCE OPTIMIZATION Investing is all about balancing risk and return, but how do we analytically find the optimal balance? That's where mean-variance portfolio optimization comes in—a method pioneered by Harry Markowitz that remains fundamental in modern finance. 🔹 The Core Idea: We construct a portfolio that minimizes risk (variance) for a given level of expected return. By leveraging the covariance between assets, we determine the ideal asset weights to diversify risk efficiently. 🔹 Key Takeaways: ✅ Mathematical Optimization: Using first-order conditions and Lagrange multipliers, we derive optimal weights for assets. ✅ Efficient Frontier: The set of optimal portfolios that offer the highest return for each level of risk. ✅ Practical Implementation: Modern computational tools (e.g., R, Python, and quadratic programming) make optimization accessible. 🔹 Why It Matters: Mean-variance portfolio optimization is the foundation of all advanced portfolio optimization techniques developed later. While it may not always be applied directly in practice, it remains a benchmark for evaluating the effectiveness of newer portfolio strategies. Many modern approaches, from robust optimization to machine learning-based asset allocation, are often compared against the mean-variance portfolio to assess their improvements in risk-return trade-offs. This approach is truly a cornerstone of modern finance and continues to shape investment decision-making. ➡ How do you approach portfolio construction? ➡ What challenges have you faced in optimizing asset allocation? #Finance #Investing #PortfolioOptimization #QuantitativeFinance #RiskManagement

Risk and reward go hand and hand. If you decrease your risk exposure, you decrease your expected return. But if you combine two assets with similar risk profiles, but whose correlations do not match, you can lower portfolio risk without necessarily lowering expected returns. GLD launched in 2004. Its standard deviation has been 16.83% versus 16.54% for that of the S&P 500, and their drawdowns have been -45% and -55% respectively. Both the S&P 500 and GLD have returned an identical 9.7% per year over this period. It is not a coincidence that two assets with similar risk profiles produced similar returns. A portfolio of 50% GLD and 50% SPY would therefore have also produced 9.7% over this period (10.4% if you rebalanced annually back to the target weightings), but the standard deviation of the portfolio drops to 11.79% and the portfolio drawdown drops to 32%. This represents a 28% reduction in std. deviation, and a 40% reduction in drawdown, with no corresponding reduction in returns as illustrated by the Blue line in the graph below. The reason why AGG bonds are a poor diversifier is that they have a much lower std. deviation than stocks. So while they lower risk, they lower return at essentially the same rate. Meaning you are no further along on a risk-adjusted basis. The way to reduce the systematic risk of equities in a portfolio is to find diversifiers with similar risk profiles to stocks. You WANT their higher volatility to offset stock risk. If you're looking for ways to add value to your portfolio, drop the low risk bonds for true diversifiers.

Want to break into asset management? Learn what portfolio managers do. Successful investing isn’t just about picking stocks—it’s about structuring portfolios that balance risk and return. Whether you're managing billions or just starting out, these concepts are essential. 📈 Modern Portfolio Theory (MPT) – The foundation of diversification. Investors seek the optimal balance of risk and return by combining assets efficiently. ⚖ Risk-Return Tradeoff – Higher returns come with higher risk. The key is knowing how much risk is worth taking. 📊 Efficient Frontier – The set of portfolios offering the highest expected return for a given level of risk. If your portfolio isn’t on this curve, it’s inefficient. 📍 CML vs. SML I. Capital Market Line (CML) – Shows the risk-return tradeoff for efficient portfolios (market risk). II. Security Market Line (SML) – Used in CAPM, showing expected return based on an asset’s beta (systematic risk). 🔎 Investment Styles I. Value Investing – Buying undervalued assets (Buffett, Graham). II. Growth Investing – Targeting high-growth stocks (think tech & innovation). III. Momentum Investing – Riding market trends and technical signals. IV. Factor Investing (Smart Beta) – Using data-driven factors like size, value, or volatility to enhance returns. 🏗 Portfolio Construction & Risk Management I. Asset Allocation – Strategic (long-term) vs. Tactical (short-term, market-driven). II. Diversification – Reducing risk by spreading investments across assets. III. Hedging & Derivatives – Protecting portfolios using options, swaps, and futures. IV. Monte Carlo Simulations – Stress-testing portfolios under different market conditions. 📊 Performance Measurement & Attribution I. Sharpe Ratio, Sortino Ratio, Information Ratio – Measuring risk-adjusted returns. II. Alpha & Beta – How much return comes from skill (alpha) vs. market movement (beta). III. Treynor Ratio – Return per unit of market risk. IV. Attribution Analysis – Breaking down where portfolio returns actually come from (market exposure vs. active decisions). Portfolio management is a combination of strategy, risk control, and performance measurement. If you want to stand out in finance, understand these principles inside out. Which investment strategy do you find most interesting? Follow me, Afzal Hussein, to break into finance faster. #Finance #Banking #Careers

📈 Volatility-Managed Portfolios Hello #FinanceCommunity, This paper by Moreira and Muir on volatility-managed portfolios warrants your attention. The authors challenge prevailing assumptions about risk and return, finding that certain volatility-managed portfolios can offer higher risk-adjusted returns. This runs counter to long-held theories. 🔑 Key Takeaways: 1️⃣ Risk-Adjusted Returns: The paper introduces a strategy that scales monthly returns by the inverse of their previous month's realized variance. This simple yet effective approach can significantly improve alphas and Sharpe ratios. 2️⃣ Contrarian Approach: Interestingly, the strategy advises taking less risk during high-volatility periods, including recessions and financial crises. This is contrary to the popular belief that these are the times to take more risks. 3️⃣ Utility Gains: The strategy offers substantial utility gains for mean-variance investors, making it a robust and profitable approach. 4️⃣ Challenges to Existing Models: The findings pose a challenge to representative agent models and macro-finance models, suggesting that an investor’s willingness to take stock market risk must be higher in periods of high stock market volatility. 5️⃣ Robustness: The strategy is robust to realistic transaction costs and leverage constraints, making it practical for real-world implementation. If you're interested in asset pricing, risk management, or portfolio optimization, this paper is worth a read. It not only offers actionable insights but also opens up new lines of inquiry in the finance research community. #Finance #AssetPricing #RiskManagement #PortfolioOptimization

Everyone wants returns. Few understand the risk behind them. The conversations usually start the same way: "What kind of returns can I expect?" Fair question. But here's a better one: "What risk am I taking to get those returns?" In real estate investing, not all returns are created equal. And if you don’t understand the risk behind the return, you’re not investing—you’re gambling. Let's break it down: 1. Development (Highest Risk) -> No cash flow for 2+ years. -> Heavy exposure to construction delays, cost overruns, and interest rates. -> Projected IRR: 18–20%+ if everything goes perfectly. 2. Value Add (Moderate-High Risk) -> Requires significant renovations or operational turnaround. -> Returns depend on execution, timing, and market conditions. -> Projected IRR: 15–18% if executed well. 3. Core Plus (Lower Risk, More Predictable) -> Stabilized assets in strong markets with light value enhancements. -> Cash flow from day one with long-term appreciation. -> Projected IRR: 13–15% with lower downside risk. In today’s environment, Core Plus provides the strongest risk-adjusted profile. The challenge? Many of these assets are traded at negative leverage (interest rate is higher than the asset's cap rate). That's exactly why we are acquiring Heritage Square: -> Cap rate is higher than interest rate (RARE) = high cash flow -> 95% occupied, Class A construction -> Immediate cash flow and quarterly distributions -> 15%+ projected IRR -> Acquired well below replacement cost We’re not just chasing upside—we’re protecting your downside. Before you invest, ask yourself: Am I being fairly compensated for the risk I'm taking? Want to see how we de-risk investments without sacrificing returns? Download the full investment deck here: www.invest-heritage.com Not an offer to invest. Open to accredited investors only.