Core Viewpoint - Despite the prevailing narrative about the decline of personal computers and the challenges faced by legacy companies like HP Inc (NYSE:HPQ), the stock exhibits an upward bias due to its unique performance characteristics and strong cash flow generation [1][5]. Group 1: Stock Performance - Over the past 52 weeks, HPQ stock has experienced a loss of approximately 32%, with a 12% decline in the last month [2]. - The concept of non-ergodicity explains the discrepancy between the stock's poor performance and its upward bias, as HPQ tends to recover slowly between sell-offs [3]. Group 2: Market Position and Fundamentals - The assertion that personal computers are "dead" is misleading; while the market for PCs is mature, they remain essential infrastructure for work, and their role is unlikely to diminish even with advancements in quantum computing [4][5]. - HPQ generates significant free cash flow of $2.8 billion, indicating that it is not a dead business model and deserves more recognition than it currently receives [5]. Group 3: Trading Strategy - Retail traders have the advantage of pricing risk non-monotonically, allowing for strategic trading opportunities that differ from institutional approaches [6][7]. - A forecasted price range for HPQ stock over the next 10 weeks is between $21.80 and $22.80, with a peak probability density around $22.30, indicating an upward bias [10]. - Under current market conditions, a non-monotonic risk model suggests a potential price peak of $24.20, contrasting with traditional models that predict $22.30 [12]. Group 4: Options Strategy - A recommended trading strategy involves a 23/24 bull call spread expiring on February 20, 2026, which could yield a maximum payout of over 163% if HPQ stock rises above the $24 strike price [15]. - An alternative 23/25 bull spread could generate a maximum payout of over 257%, but the significant probability decay between the strikes makes the 23/24 spread a more favorable option [16].

Core Viewpoint - AST SpaceMobile Inc (NASDAQ:ASTS) has shown strong performance this year, but its stock is highly volatile, leading to potential challenges for options traders [1][2] Group 1: Stock Performance and Market Sentiment - ASTS stock has experienced a decline, which may be linked to insider selling and year-end tax-related share sales by major stakeholders [3] - Despite the company's progress in satellite launches and securing contracts, there is a prevailing sentiment that the stock is undervalued, although this reasoning may be flawed [4][5] Group 2: Mispricing Analysis - The concept of mispricing needs to be quantified to assess probabilities, as terms like "undervalued" are subjective and unbounded [6][7] - Analyzing a 10-week price data strand reveals that the stock has shown a downward trend, with only four up weeks in the last ten weeks [10] Group 3: Probability and Trading Strategy - The expected forward 10-week price range for ASTS stock is projected to be between $62 and $92, with peak probability density between $76 and $81, indicating a structural arbitrage of approximately 8.71% [11] - A recommended trading strategy is the 75/80 bull call spread expiring on February 20, 2026, which requires a net debit of $210 and offers a maximum profit of $290, translating to over 138% [12][14] - The probability density significantly decreases for prices above $80, making it less sensible to target outcomes beyond this range [15][16]

Core Viewpoint - The price of gold has surged to over $4,500 per ounce, with projections suggesting it could reach $5,000 next year and potentially $6,000 in the long term, driven by macroeconomic factors and central bank purchases [3][4]. Gold Market Overview - Earlier this year, gold was forecasted to reach $3,000 due to concerns over U.S. fiscal policies impacting Treasury yields, with a notable increase from a previous record of $2,696 per ounce [1][2]. - Currently, gold's total market value stands at approximately $31.5 trillion, making it significantly larger than Nvidia Corp's market value [3]. Price Projections - J.P. Morgan Global Research anticipates gold prices could push towards $5,000 next year, with a long-term scenario suggesting $6,000, based on macro factors rather than recent market hype [4]. Mining Sector Dynamics - The mining sector may take up to 18 years for projects to become fully productive, and supply constraints due to rising extraction difficulties could exert upward pressure on gold prices [5]. - Mining companies have been slow to respond to rising prices, indicating potential for a positive rerating in the sector [4]. Market Volatility and Non-Ergodicity - The commodities market, including gold, is characterized by high volatility compared to blue-chip equities, which may affect investment returns [6]. - Non-ergodicity in the gold market can lead to mismatches between actual and expected returns, posing challenges for leveraged and synthetic exposure [7][8]. Investment Products - Direxion offers two ETFs, NUGT and DUST, allowing investors to speculate on gold miners' performance, with NUGT aiming for 200% of the positive performance and DUST for 200% of the inverse [9][10]. - These ETFs provide a straightforward mechanism for speculation, reducing the complexity typically associated with options trading [11]. ETF Performance - The NUGT ETF has gained 477% since the start of the year and over 166% in the past six months, although volume accumulation has faded recently [13]. - Conversely, the DUST ETF has declined 90% since January and nearly 72% in the last six months, despite a recent volume trend indicating potential contrarian interest [15].