The Long View · 2026-10-12
Both numbers get called profit, and they can differ by 50 percent or more in the same year. The four wedges that drive them apart, a full worked example, and what each red flag actually indicates.
Recency bias makes the last two years of market history feel like the next ten. Work through the arithmetic of buying high and selling low, see the base-rate data on forecasts, and build a checklist that survives both bull and bear markets.
Continue readingPrice-to-book compares a stock price to the accounting value of what the company owns. Here is the formula, two fully worked examples, why P/B suits banks and breaks on software companies, and where it fits among valuation metrics.
Continue readingWhen a company buys back its own shares, your slice of it grows — but only if the price was fair. The EPS math of buybacks, when they help, when they waste money, and where to find them in filings.
Continue readingLeave it, roll it to an IRA, move it to the new plan, or cash it out — the four 401(k) options compared with actual numbers, including what cashing out a $60,000 balance really costs.
Continue readingThe one-fund retirement default explained: what a glide path does, what target-date fees cost over 30 years with exact math, and the blind spots worth knowing.
Continue readingA high yield is only half the story. How the payout ratio — from earnings and from free cash flow — separates sustainable dividends from future cut candidates.
Continue readingRebalance on a schedule or on a threshold? A worked $100,000 example shows what a 5-percentage-point band actually triggers, how much the discipline was worth in one bull-then-bust sequence, and why frequency alone answers the wrong question.
Continue readingNo other account deducts money on the way in, shelters growth, and waives tax on the way out. A fully worked 30-year example shows what the three breaks are worth together — and the one mistake that throws most of the value away.
Continue readingTwo portfolios can earn the same average return and end with very different balances, because the order of those returns decides how much a withdrawal costs. This guide runs the same sequence two ways and shows how much the ordering alone is worth.
Continue readingProfit is an accounting opinion; cash is a fact. This walkthrough builds a cash flow statement line by line from a fictional company, shows why a profitable business can still run short of cash, and sets out the three tests worth running before trusting a reported profit.
Continue readingA gain is not taxed when the price rises, only when the position is sold — and the rate applied depends on how long it was held. This walkthrough covers cost basis, holding periods, loss offsets, and the after-tax arithmetic of a single sale.
Continue readingA 1% fee looks like a rounding error beside a 6% return. Run both through 30 years of compounding and the fee removes roughly 24% of the ending balance. Here is the arithmetic, worked in full.
Continue readingA balance sheet is a snapshot rather than a story: what a company owns, what it owes, and what is left for shareholders. A worked example, the ratios that fall out of it, and what it cannot tell you.
Continue readingA dividend is not extra money on top of the share price — the price adjusts by roughly the amount paid. How yield, payout ratio and total return fit together, worked out step by step.
Continue readingThe most counterintuitive line in finance, explained with a bond you can price on a calculator. Includes the full discounting arithmetic, a duration shortcut, and why bond funds behave differently from bonds held to maturity.
Continue readingThe price-to-earnings ratio is the most quoted number in investing and one of the least understood. Here is the arithmetic behind it, one fully worked example, and the four situations where it quietly stops meaning anything.
Continue readingThe Roth versus traditional question is not about which account is better. It is about the tax rate you face now versus the one you face later. Here is the arithmetic that turns a debate into a single comparison.
Continue readingA fund can earn 8% a year while the people who own it earn 6%. The difference is called the behavior gap, and it comes from when money arrives rather than what it buys. Here is the arithmetic behind it, and the specific habits that close it.
Continue readingRevenue, gross profit, operating income, net income, EPS — an income statement is one subtraction chain read top to bottom. Here is what each line measures, which ratios matter, and the three places the numbers can be framed to mislead.
Continue readingThe stock/bond split is the one decision that changes your results more than any fund pick. Here is the arithmetic of expected return, the arithmetic of a bad year, and a fully worked rebalancing example — with the assumptions stated at every step.
Continue readingIndex investing is popular because the arithmetic is hard to argue with, not because it is exciting. This walkthrough covers what an index fund actually is, what fees do over decades, and the exact steps from brokerage account to first purchase.
Continue readingA stock quote packs a dozen numbers onto one screen and most people ignore half of them. Here is what price, bid-ask spread, volume, market cap, P/E, dividend yield and the 52-week range each actually tell you.
Continue readingYou have money to invest and one decision to make first: all at once, or in installments? The historical data favors lump sum more often than intuition suggests — but the reasons people still choose DCA are rational, and here is the arithmetic on both sides.
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