Core Viewpoint - Five Below is showing signs of renewed strength with significant holiday sales growth and an optimistic outlook for 2025, despite a slowdown in new store openings [1][2][5]. Financial Performance - The company opened 136 net new stores in the first three quarters of 2025 and expects to open a total of 150 for the year, a decrease from 227 in 2024 [1]. - Adjusted earnings per share are projected to be $6.325, representing a 25.5% increase from 2024 [1]. - Revenues are anticipated to rise by 22.4% in 2025 to $4.75 billion, driven by a 12.5% growth in same-store sales, which is 15.2 percentage points higher than in 2024 [1]. - Holiday sales increased by 23.2% to $1.47 billion, marking the second consecutive quarter with sales exceeding $1 billion [1]. Stock Performance - Five Below's stock has appreciated nearly 104% over the past 12 months, although it is down 14% from its all-time high of $237.86 in August 2021 [2]. - The stock's volatility is indicated by a relatively high standard deviation, with a recent strong buy recommendation from Barchart [3][5]. Store Expansion Strategy - The company aims to reach 3,500 stores across the U.S., with 1,907 stores as of November 1, 2025. At the current rate of 150 new stores per year, it would take over 10 years to achieve this target [6]. - The quality of new store locations is emphasized as crucial for long-term sales growth, rather than just the quantity of openings [7]. Pricing Strategy - The CEO highlighted a shift in value perception, incorporating price points above $5 to enhance customer experience and maintain gross margins [9][10]. - The gross margin for Q3 2025 was reported at 33.8%, the highest in five years, indicating effective pricing strategies [9]. Analyst Sentiment - Analysts are generally lukewarm about Five Below, with 52% rating it a buy and a target price of $203, which is only slightly above its current share price [11]. - The stock trades at a forward P/E of 31.9 based on 2025 EPS guidance, which is not significantly better than its valuation in 2026 [11]. Market Position - Five Below is positioned as a unique discount retailer, with a business model that may deliver higher margins compared to peers like Dollar General and Dollar Tree [12]. - The enterprise value is currently 2.87 times its trailing 12-month sales, which is considered high compared to its historical multiple of 4.16 times in August 2021 [12][13].

The basic mathematical concepts of standard deviation and variance are useful to investors. Compare variance versus standard deviation and calculate each. https://t.co/LmvS1zaR8J ...

Bitcoin Price Prediction - To reach $1 million, Bitcoin needs to double its price a little over three times [1][2] - The current doubling time for Bitcoin is approximately two years, but it is gradually increasing [1] - Based on the parallel core trend, Bitcoin could reach $1 million around 2033, potentially sooner with market bubbles [2] Volatility Analysis - The standard deviation of the core Bitcoin price trend is about 20% [3] - The standard deviation of Bitcoin bubbles has significantly decreased from over 100% to approximately 37% [3] - The volatility of Bitcoin bubbles is decreasing roughly as a reciprocal relationship to Bitcoin's age [4] Forecast Methodology - The forecast method considers both the parallel core mean and the bubble mean, along with the standard deviation size for the bubble [5] - The right tail of the bubble, specifically one and two standard deviations above the mean, indicates potential extreme prices [5][6] - There's an estimated 8% chance of Bitcoin price being one standard deviation above the bubble mean and only about a 1% chance of being two standard deviations above [6] Power Law Model - The ratio of price increase for the power core can be calculated by taking the inverse of Bitcoin's age, adding one, and raising that to the power law index of 58% [8] - At Bitcoin age 245 years, the parallel core median line is projected to be around $1 million [9][10]