Comprehensive Study Guide: Investments and Capital Markets

The Investment Process, Objectives, and Constraints

  • Investment as Deferred Consumption:

    • Investing is fundamentally deferred consumption — choosing to wait and forego spending today to accumulate greater purchasing power for the future.

    • An Investment Policy Statement (IPS) acts as a strategic roadmap, formalizing an investor's objectives and constraints.

  • IPS Objectives and Risk Tolerance:

    • Objectives require balancing desired returns against acceptable risk tolerance.

    • Risk tolerance consists of two distinct dimensions that do not always align:

    1. Ability to take risk: Financial capacity, determined by wealth, income stability, time horizon, and obligations.

    2. Willingness to take risk: Psychological comfort level with market volatility and potential financial loss.

  • Five Practical Investor Constraints:

    • Resources: The minimum initial sum required to invest, ongoing capital availability, and associated transaction costs.

    • Horizon: The specific timeframe when funds will be needed (e.g., retirement date, house purchase).

    • Liquidity: The ease and speed with which an asset can be converted to cash without suffering a significant price concession.

    • Taxes: Focuses on maximizing after-tax returns, requiring consideration of the investor's current and expected future marginal tax bracket.

    • Unique Circumstances: One-off restrictions such as employer matching terms, insider trading restrictions, conflicts of interest, ethical exclusions, or legal mandates.

  • Four Core Investment Strategies:

    1. Investment Management: Deciding whether to self-manage investments or hire professional management.

    2. Market Timing: Attempting to buy and sell securities to anticipate future market direction.

    3. Asset Allocation: Deciding how to distribute capital across broad asset classes (e.g., stocks, bonds, cash).

    4. Security Selection: Selecting specific individual securities within each chosen asset class.

  • Asset Allocation vs. Security Selection Performance Impact:

    • Empirical research demonstrates that Asset Allocation accounts for ≈90%\approx 90\% of portfolio performance variability, whereas Security Selection accounts for only ≈10%\approx 10\%.

    • Most individual investors incorrectly focus on stock-picking, but broad market movements dominate returns. For example, during the 20082008 Financial Crisis, bonds broadly outperformed equities; skilled individual stock selection within equities failed to protect investors because stocks moved together downward.

  • Risk Tolerance Questionnaire and Case Analysis:

    • Risk tolerance scores range from 1010 (extremely conservative) to 4545 (extremely aggressive).

    • Sample empirical participant data:

    • Lynn: Age 2323, Female, Little/no experience, Score 1313

    • Ananya: Age 5050, Female, Little/no experience, Score 1919

    • Isabel: Age 2828, Female, Little/no experience, Score 3737

    • Brigit: Age 3838, Female, Little/no experience, Score 3535

    • Lauren: Age 2222, Female, Little/no experience, Score 1919

    • Khalil: Age 2929, Male, Little/no experience, Score 2020

    • Imelda: Age 5959, Female, Less than average experience, Score 1818

    • Homer: Age 5454, Male, Average experience, Score 2727

    • Ximena: Age 2525, Male, Average experience, Score 3838

    • Marie: Age 2121, Female, More than average experience, Score 4040

    • Case Comparative Analysis (Marie vs. Imelda):

    • Marie (2121 years old, Accounting major, Score 4040): Long horizon (30+30+ years), aggressive risk tolerance. Traditional equity allocation rule-of-thumb: 100−21=79%100 - 21 = 79\% equity, or 110−21=89%110 - 21 = 89\% equity.

    • Imelda (5959 years old, College Professor, Score 1818): Short horizon (5–105\text{--}10 years), conservative risk tolerance. Traditional equity allocation rule-of-thumb: 100−59=41%100 - 59 = 41\% equity, or 110−59=51%110 - 59 = 51\% equity.

Risk tolerance score and time horizon score matrix

  • AAII Model Portfolios and Historical Performance:

    • Aggressive Portfolio (90%90\% Stock / 10%10\% Fixed): Time horizon 20+20+ years, very risk tolerant; seeks substantial growth; very low income. Average annual growth: 8%8\%. Worst year: −37%-37\%. Historical annualized returns (1-yr/5-yr/10-yr1\text{-yr} / 5\text{-yr} / 10\text{-yr}): 16.3%/12.8%/11.6%16.3\% / 12.8\% / 11.6\%.

    • Moderate Portfolio (60%60\% Stock / 40%40\% Fixed): Time horizon 15+15+ years, tolerates some risk; seeks moderate growth and low income. Average annual growth: 7%7\%. Worst year: −21%-21\% . Historical annualized returns (1-yr/5-yr/10-yr1\text{-yr} / 5\text{-yr} / 10\text{-yr}): 12.0%/9.9%/9.0%12.0\% / 9.9\% / 9.0\%.

    • Conservative Portfolio (40%40\% Stock / 60%60\% Fixed): Time horizon 10+10+ years, not risk tolerant; seeks low growth and moderate income. Average annual growth: 6%6\%. Worst year: −12%-12\%. Historical annualized returns (1-yr/5-yr/10-yr1\text{-yr} / 5\text{-yr} / 10\text{-yr}): 8.1%/7.7%/6.7%8.1\% / 7.7\% / 6.7\%.

    • Strategic vs. Tactical Asset Allocation: Strategic Asset Allocation defines long-term target baseline asset weights; Tactical Asset Allocation represents short-term temporary deviations from strategic targets to exploit market views.

Financial Markets, Brokers, and Account Types

  • Brokerage Service Tiers:

    • Full-Service Brokers: Provide comprehensive individual advice, financial planning, proprietary research, and execution (e.g., Merrill Lynch, Morgan Stanley, Edward Jones). High cost structure.

    • Discount and Online Brokers: Offer direct execution and online tools with dramatically reduced or zero commissions (e.g., Charles Schwab, Fidelity, E*TRADE).

    • Robo-Advisors: Fully automated, algorithm-driven portfolio construction and rebalancing without human advisors (e.g., Betterment, Wealthfront, Schwab Intelligent Portfolios). Lowest cost structure.

  • SIPC Protection vs. FDIC Insurance:

    • Securities Investor Protection Corporation (SIPC): Insures brokerage accounts up to \\text{\\$500,000} total per customer (\text{\\$250,000} cash limit) if the brokerage firm fails or suffers fraud. It does NOT cover market losses.

    • FDIC: Insures bank deposits against bank insolvency.

    • Broker Legal Duties: Brokers owe customers a duty of reasonable care, but are not inherently fiduciaries unless an explicit advisory agreement exists. Commission compensation models create potential conflicts of interest, such as "churning" (excessive trading to generate commissions).

  • Brokerage Account Types and Transactions:

    • Cash Account: Securities are paid for in full; borrowing and leverage are strictly prohibited.

    • Cash Account Execution Worked Example:

    • Setup: Open account, deposit \\text{\\$10,000}, purchase 100100 shares of stock at \\text{\\$80/share}, pay \\text{\\$50} commission.

    • Calculation: \text{\\10,000} - (100 \times \text{\\80}) - \text{\\50} = \text{\\1,950} cash remaining.

    • Portfolio state: \\text{\\$1,950} cash plus \\text{\\$8,000} market value in stock.

    • Margin Account: Allows buying securities on credit using capital borrowed from the broker.

  • Tax-Advantaged Retirement Accounts:

    • Company-Sponsored Plans (401(k)401(k), 403(b)403(b)): Employee contributions via payroll deduction lowering current taxable income; employers often provide matching contributions.

    • Contributions Tax Benefit Worked Example: An investor in a 15%15\% tax bracket making a \\text{\\$12,000} pre-tax contribution saves .15 \times \text{\\12,000} = \text{\\1,800} in current taxes, resulting in an out-of-pocket cost of only \\text{\\$10,200}.

    • Traditional IRA / 401(k)401(k) vs. Roth IRA / 401(k)401(k):

    • Traditional: Pre-tax contributions today (tax-deferred growth); distributions fully taxed as ordinary income upon withdrawal in retirement. Preferred if expecting a lower tax bracket in retirement.

    • Roth: After-tax contributions today; capital gains and dividends grow tax-free; qualified withdrawals in retirement are entirely tax-free. Preferred for younger investors in low current tax brackets.

  • Margin Trading Mechanics and Leverage Math:

    • Key Definitions:

    • Margin: The percentage of account equity provided directly by the investor.

    • Call Money Rate: The benchmark interest rate brokers pay banks to borrow funds, passed to margin clients.

    • Initial Margin: Minimum equity percentage required at position opening (Federal Reserve Regulation T sets minimum at 50%50\%).

    • Maintenance Margin: Minimum equity percentage required at all times.

    • Margin Call: A demand by the broker for cash/collateral when account equity drops below maintenance margin.

    • Merck & Co. (MRK) Margin Purchase Example:

    • Setup: Buy 1,0001,000 shares of MRK at \\text{\\$50/share} (\text{\\$50,000} total cost). Initial margin = 60%60\%, Maintenance margin = 30%30\%, Margin loan interest rate = 11%11\%.

    • Opening Balance Sheet: Assets = \\text{\\$50,000} stock; Liabilities = \\text{\\$20,000} loan; Equity = \\text{\\$30,000} (60%60\% margin).

    • Scenario A: Stock Price Rises to \\text{\\$60}:

      • Position Value = 1,000 \times \text{\\60} = \text{\\60,000}.

      • Owed = \\text{\\$20,000} principal + \\text{\\$2,200} annual interest (11\% \times \text{\\$20,000}) = \\text{\\$22,200}.

      • Net Payoff = \text{\\60,000} - \text{\\22,200} = \text{\\$37,800}.

      • Margined Return = \frac{\text{\\37,800} - \text{\\30,000}}{\text{\\30,000}} = \frac{\text{\\7,800}}{\text{\\$30,000}} = +26.00\%.

      • Unmargined Return (600600 shares bought with \\text{\\$30,000} cash) = +20.00%+20.00\%.

    • Scenario B: Stock Price Falls to \\text{\\$40}:

      • Position Value = \text{\\$40,000}. Owed = \\text{\\$22,200}.

      • Net Payoff = \text{\\40,000} - \text{\\22,200} = \text{\\$17,800}.

      • Margined Return = \frac{\text{\\17,800} - \text{\\30,000}}{\text{\\30,000}} = \frac{-\text{\\12,200}}{\text{\\$30,000}} = -40.67\%.

      • Unmargined Return = −20.00%-20.00\%.

      • Current Margin % = \frac{\text{\\40,000} - \text{\\20,000}}{\text{\\40,000}} = \frac{\text{\\20,000}}{\text{\\$40,000}} = 50.00\% (above 30%30\% maintenance margin).

    • Margin Call Trigger Price Formula:     \nP^* = \frac{\text{Amount Borrowed}}{\text{Shares} \times (1 - \text{Maintenance Margin})}\n         P^* = \frac{\text{\\20,000}}{1,000 \times (1 - 0.30)} = \frac{\text{\\20,000}}{700} = \text{\\$28.57 per share}     MRK must fall 43%43\% from \\text{\\$50} to \\text{\\$28.57} to trigger a margin call.

    • Short-Term Holding Period Annualization:

    • Sell after 33 months (9090 days) at \\text{\\$53}.

    • Interest owed = \text{\\20,000} \times 11\% \times \frac{90}{360} = \text{\\550}.

    • Net cash = \text{\\53,000} - \text{\\20,550} = \text{\\$32,450}. Net profit = \\text{\\$2,450}.

    • Holding Period Return (HPR) = \frac{\text{\\2,450}}{\text{\\30,000}} = 8.17\%.

    • Effective Annual Rate (EAR): EAR=(1+0.0817)4−1≈36.9%\text{EAR} = (1 + 0.0817)^4 - 1 \approx 36.9\%.

  • Short Sales Mechanics and Risks:

    • Mechanics: Selling shares borrowed from a broker today, aiming to buy them back ("cover") later at a lower price.

    • AT&T (T) Short Sale Worked Example:

    • Setup: Short 100100 shares of AT&T at \\text{\\$30/share} (\text{\\$3,000} market value). Initial margin = 50%50\% (\text{\\$1,500} cash deposit), Maintenance margin = 40%40\%.

    • Balance Sheet at Inception:

      • Assets: Cash Proceeds (\text{\\$3,000}) + Margin Deposit (\text{\\$1,500}) = \\text{\\$4,500}.

      • Liabilities: Securities Short (\text{\\$3,000}). Account Equity = \\text{\\$1,500} (50%50\% margin).

    • Stock Price Falls to \\text{\\$20/share}:

      • Value of shares owed = 100 \times \text{\\20} = \text{\\2,000}.

      • Gain = \text{\\10/share} \times 100 = \text{\\1,000}.

      • New Account Equity = \text{\\1,500} + \text{\\1,000} = \text{\\$2,500}.

      • New Margin % = \frac{\text{\\2,500}}{\text{\\2,000}} = 125\%.

    • Short Interest and Squeeze Dynamics:

    • Short Interest: Total number of shares currently sold short.

    • Tesla (TSLA) Data Check-In (Settlement July 15, 2026): Short interest = 70.6M70.6\text{M} shares (down 10.7%10.7\% from 79.1M79.1\text{M}). Days-to-cover = 1.781.78 days based on average daily volume of 39.7M39.7\text{M} shares.

    • Asymmetric Risk: Long positions carry bounded downside (maximum loss is 100%100\% of capital). Short positions carry theoretically unlimited loss potential because share prices can rise without ceiling.

    • GameStop (GME) Case Study: Shares surged from \approx \text{\\$18} (Jan 8, 2021) to an intra-day close near \\text{\\$325} (Jan 29, 2021), forcing massive short squeezes. By August 2026, GME traded back near \\text{\\$18/share}.

Securities Mechanics: Debt, Equity, and Derivatives

  • Three Major Security Families:

    1. Interest-Bearing (Debt): Money market and fixed-income debt.

    2. Equity: Common stock and preferred stock.

    3. Derivatives: Futures contracts and options contracts.

  • Debt Instruments (Money Market vs. Fixed Income):

    • Money Market Instruments: Short-term debt (<1< 1 year maturity at issuance), single cash payment at maturity (e.g., T-bills, CDs, commercial paper). Quoted on a discount basis (compute price from rate).

    • Fixed-Income Securities: Longer-term debt (>1> 1 year maturity at issuance), fixed payment schedule (e.g., T-notes, T-bonds, corporate bonds, municipal bonds).

    • Anatomy of a Bond Issuance:

    • Issuer: Borrower issuing the bond (corporation, government, agency).

    • Principal (Face Value): Amount repaid at maturity (typically \\text{\\$1,000} or \\text{\\$100} per bond).

    • Coupon Rate: Annual interest rate paid to bondholders, usually semiannually.

    • Maturity Date: Settlement date when principal is repaid and bond retires.

    • Credit Rating: Agency default risk assessment (AAA to D).

    • Call Provision: Issuer's right to redeem early after a call-protection period.

    • Covenants: Contractual protective provisions limiting issuer behavior (e.g., debt caps).

    • Use of Proceeds: Defined operational purpose for raised funds.

    • 3M Company (MMM) Bond Quote Reading Example:

    • Fields: Coupon = 3.125%3.125\%, Maturity = Sep 19, 2046, Last Price = \\text{\\$67.92} per \\text{\\$100} face value, Yield to Maturity (YTM) = 5.72%5.72\%, Callable = Yes (next call Mar 2036).

    • Discount Mechanics: Price below par (67.92<10067.92 < 100) implies YTM (5.72%5.72\%) > Coupon (3.125%3.125\%) because buyers recover the discount at maturity.

    • Debt Risks:

    1. Default (Credit) Risk: Risk that borrower fails to pay principal or interest.

    2. Interest-Rate Risk: Inverse relationship between interest rates and bond prices (Rates rise →\rightarrow Price falls; Rates fall →\rightarrow Price rises).

    3. Illiquidity Risk: Inability to sell quickly at fair market value.

  • Equity Securities (Common vs. Preferred):

    • Common Stock: Residual ownership claim; variable dividends; voting rights (usually one share, one vote); values fluctuate with firm performance.

    • Preferred Stock: Priority claim over common stock for fixed dividends and liquidation distribution; typically limited or no voting rights.

    • Dual-Class Voting Structure: Founders retain control via super-voting shares.

    • Corporate Voting Multipliers: Groupon (150150 votes/share), Zynga (7070), Facebook (1010), Google (1010), LinkedIn (1010), Zillow (1010).

    • Nordstrom (JWN) Stock Quote Reading Example:

    • Last Price = \\text{\\$24.14} (+0.08%+0.08\%), Prev Close = \\text{\\$24.12}, Open = \\text{\\$24.10}, Day's Range = \\text{\\24.11}\text{--}\\text{\\24.16}, 52-wk52\text{-wk} Range = \\text{\\16.79}\text{--}\\text{\\24.99}, Volume = 556,796556,796, Avg Volume = 2,537,2482,537,248, Market Cap = \\text{\\$3.98B}, P/E (TTM) = 15.2815.28, EPS (TTM) = \\text{\\$1.58}, Beta (5Y5\text{Y}) = 2.602.60, Div & Yield = \\text{\\$0.76} (3.09%3.09\%).

  • Derivatives (Futures vs. Options):

    • Primary Asset: Issued by a firm/government to directly raise capital.

    • Derivative Asset: Value derived from an underlying asset; traded between investors without capital reaching the issuing firm.

    • Futures Contracts: Mandatory obligation to trade at a set price on a future date. Zero upfront cost (no premium).

    • Quotes Example:

      • Crude Oil (Jun 2025): Last = \\text{\\$68.45/barrel}, Change = +\\text{\\$0.62}, Prior Settle = \\text{\\$67.83}, Volume = 248,310248,310

      • Gold (Jun 2025): Last = \\text{\\$2,651.40/oz}, Change = +\\text{\\$12.30}, Prior Settle = \\text{\\$2,639.10}, Volume = 176,254176,254

    • Futures Leverage Examples:

      • Crude Oil (1,0001,000 barrels): Contract value = \\text{\\$68,450}, Initial margin = \\text{\\$6,000} (≈11×\approx 11\times leverage). A 3%3\% price move causes a ±34%\pm 34\% equity swing.

      • Gold (100100 oz): Contract value = \\text{\\$265,140}, Initial margin = \\text{\\$11,000} (≈24×\approx 24\times leverage). A 3%3\% price move causes a ±72%\pm 72\% equity swing.

    • Option Contracts: Right, not obligation, to trade at a specified strike price (KK) on or before expiration. Buyer pays an upfront Premium.

    • Call Option: Right to BUY underlying asset.

    • Put Option: Right to SELL underlying asset.

    • Styles: American (exercise anytime before expiration) vs. European (exercise at expiration only).

    • Option Payoff Summary:

    • Long Call: Max Loss = Premium; Profit when S−K>PremiumS - K > \text{Premium}; Unlimited upside.

    • Short Call: Max Gain = Premium; Loss grows as stock rises (Unlimited downside).

    • Long Put: Max Loss = Premium; Profit when K−S>PremiumK - S > \text{Premium}; Max Gain when S→0S \rightarrow 0 (K−PremiumK - \text{Premium}).

    • Short Put: Max Gain = Premium; Loss grows as stock falls (Max Loss when S→0S \rightarrow 0).

Call option payoff diagram for long call and short call positions

  • Nike (NKE) Option Chain Quote Example (Stock Price = \\text{\\$71.52}, March Expiration, Contract Multiplier = 100100 shares):

    • Strike \\text{\\$67.50}: Call Last = \\text{\\$6.10}, Put Last = \\text{\\$2.05}

    • Strike \\text{\\$70.00}: Call Last = \\text{\\$4.70}, Put Last = \\text{\\$3.10} (Contract Premium = \text{\\4.70} \times 100 = \text{\\470})

    • Strike \\text{\\$72.50}: Call Last = \\text{\\$3.40}, Put Last = \\text{\\$4.30}

    • Strike \\text{\\$75.00}: Call Last = \\text{\\$2.30}, Put Last = \\text{\\$5.80}

  • Stock vs. Option Leverage Comparative Worked Example:

    • Capital = \\text{\\$15,000}. Stock initial price = \\text{\\$150/share}.

    • Strategy 1 (Outright Stock): Buy 100100 shares at \\text{\\150} = \text{\\15,000}.

      • Stock rises to \\text{\\$165} (+10%+10\%): Value = \\text{\\$16,500}, Profit = +\\text{\\$1,500} (+10%+10\%).

      • Stock falls to \\text{\\$135} (−10%-10\%): Value = \\text{\\$13,500}, Loss = -\text{\\$1,500} (−10%-10\%).

    • Strategy 2 (Call Options): Buy \\text{\\$150} strike calls at \\text{\\$10} premium (\text{\\$1,000/contract}). Buy 1515 contracts controlling 1,5001,500 shares.

      • Stock rises to \\text{\\$165} (+10%+10\%): Option Payoff = (165 - 150) \times 1,500 = \text{\\$22,500}. Net Profit = \text{\\22,500} - \text{\\15,000} = +\text{\\$7,500} (+50%+50\%).

      • Stock falls to \\text{\\$135} (−10%-10\%): Options expire worthless (\text{\\$0} payoff). Net Loss = -\text{\\$15,000} (−100%-100\%).

  • Quote Location Resources: Bonds (FINRA / TRACE at finra.org), Futures (CME Group at cmegroup.com), Options (CBOE at cboe.com), Stocks (Yahoo Finance at finance.yahoo.com).

Primary and Secondary Stock Markets

  • Private Equity (PE) Fundamentals:

    • PE provides equity financing for nonpublic companies.

    • Debt fails when borrowing capacity is exhausted or terms limit flexibility. PE accepts equity risk, taking ownership stakes and board control, realizing returns via exit (sale, recapitalization, or IPO).

    • PE Fund Structure: Closed-end, finite-lived vehicle (≈10-year\approx 10\text{-year} life). Investors make commitments upfront, called over time, with capital returned upon liquidity exits.

    • Clawback Provision Worked Example (\text{\\$1,000} invested, 20%20\% carried interest fee):

    • Year 1: +25%+25\% return \rightarrow \text{\\$250} profit per \\text{\\$1,000}. Manager accrues 20\% \times \text{\\250} = \text{\\50} fee.

    • Year 2: −10%-10\% loss →\rightarrow Accumulated 2-year profit drops to \\text{\\$125} per \\text{\\$1,000}.

    • At Liquidation: Total earned fee = 20\% \times \text{\\250} \text{ accumulated net profit... wait, } 20\% \times \text{\\125} = \text{\\$25}. Clawback requires manager to return half of the Year-1 fee (\text{\\$25} returned). Net fee paid = \\text{\\$25}.

    • Three Flavors of Private Equity:

    1. Venture Capital (VC): High-risk start-ups. Staged financing (ground-floor →\rightarrow mezzanine), active operational management, funding withheld if milestones missed, exit via sale or IPO.

    2. Middle Market: Established, profitable, small/family-owned firms. Growth capital to expand beyond region, allows founders to cash out, introduces professional management.

    3. Leveraged Buyout (LBO): Acquires all public shares to take company private. Funded with heavy debt; activity tracks credit markets (peaked in 2007).

  • Primary vs. Secondary Markets:

    • Primary Market: New securities sold; proceeds flow directly to issuing firm.

    • IPO (Initial Public Offering): First public sale ("unseasoned").

    • SEO (Seasoned Equity Offering): Additional shares sold by an already public company (General cash offer to public or Rights offer to existing owners).

    • Secondary Market: Existing shares traded among investors; no capital reaches the firm.

  • IPO Mechanics and Underwriter Spread:

    • Underwriter Spread Calculation Example:

    • Step 1 (Underwrite): Investment banker purchases 2M2\text{M} shares from company at \\text{\\$10/share} (\text{\\$20M} capital raised).

    • Step 2 (Resell): Banker resells shares to public at \\text{\\$11/share}.

    • Step 3 (The Spread): Underwriter spread = \text{\\11} - \text{\\10} = \text{\\$1/share} (\frac{\text{\\1}}{\text{\\11}} \approx 9\%, typical range 7–10%7\text{--}10\%).

    • Syndicate: Underwriting group formed to share risk.

    • IPO Step-by-Step: 1. Appoint banker →\rightarrow 2. Design issue (firm commitment, best efforts, or Dutch auction) →\rightarrow 3. File prospectus with SEC (preliminary "red herring") →\rightarrow 4. SEC approval →\rightarrow 5. Announce ("tombstone" ads) and sell.

  • Secondary Market Venues and NYSE vs. Nasdaq:

    • Dealer: Holds inventory; posts Bid (buy price) and Ask (sell price); earns Ask-Bid Spread.

    • Broker: Holds no inventory; acts as customer agent earning commissions.

    • NYSE ("Big Board"):

    • Founded 1792 Buttonwood Agreement. Went public in 2006 (1,366 seats converted to annual trading licenses at \approx \text{\\$50,000/year}). Merged with Euronext (2007); acquired by ICE (2013). Early 2025: 2,1322,132 listed companies representing ≈30%\approx 30\% of global equity trading.

    • Hybrid auction market featuring Designated Market Makers (DMMs), Floor Brokers, and Supplemental Liquidity Providers (SLPs).

    • Nasdaq:

    • Launched 1971. Electronic dealer network with no physical trading floor. Opened to ECNs in late 1990s. Early 2025: 3,300+3,300+ listed companies; higher share volume, smaller average market caps.

    • Market Disruptions & Safeguards:

    • May 6, 2010 Flash Crash: DJIA fell −9%-9\% in minutes due to automated trading software algorithms and liquidity withdrawal.

    • Circuit Breakers: Marketwide trading halts triggered at 7%7\% decline; single-stock trading halts added.

    • Other Venues: Third market (off-exchange trading of exchange-listed stocks), Fourth market (direct institutional trading), OTC Markets / FINRA.

Stock Market Orders, Types, and Risks

  • Market vs. Limit Orders:

    • Market Order: Fill immediately at best available price. Buy fills at lowest ask; Sell fills at highest bid. Execution certain, price uncertain.

    • Limit Order: Fill only at specified price or better (Buy at limit or lower; Sell at limit or higher). Price certain, execution uncertain.

  • Stop Orders and Stop-Limit Orders:

    • Stop Order: Trigger price converts order into a Market Order.

    • Stop-Sell (Stop-Loss): Placed below current price to cap long position losses. Risk: Price gapping causes execution far below stop price.

    • Stop-Buy: Placed above current price to cap short position losses. Risk: Price gapping causes execution far above stop price.

    • Stop-Limit Order: Trigger price converts order into a Limit Order.

    • Sell Stop-Limit: Placed below price; triggers a limit sell. Risk: Fast crash leaves order unfilled if price drops below limit.

    • Buy Stop-Limit: Placed above price; triggers a limit buy. Risk: Fast rally leaves order unfilled above limit.

    • Stop price and limit price need not be identical (e.g., \\text{\\$45} stop trigger, \\text{\\$44} limit price).

  • Order Types Reference Matrix:

    • Market Buy: Buy at best price available immediately.

    • Market Sell: Sell at best price available immediately.

    • Limit Buy: Buy at limit price or lower; forgo if not met.

    • Limit Sell: Sell at limit price or higher; forgo if not met.

    • Stop Buy: Converts to market buy when price crosses stop from below.

    • Stop Sell: Converts to market sell when price crosses stop from above.

    • Stop-Limit Buy: Converts to limit buy when price crosses stop from below.

    • Stop-Limit Sell: Converts to limit sell when price crosses stop from above.

  • NYSE Ban on Stop Orders:

    • In 2015, NYSE eliminated stop orders after the August 24, 2015 market crash where blue-chip stocks plunged up to 21%21\% due to cascading stop orders acting as "land mines." Brokers replicate stop functionality internally.

Stock Market Indexes and Weighting Schemes

  • Dow Jones Industrial Average (DJIA):

    • Composed of 3030 large American industrial firms. Price-weighted index.

    • Four Index Dimensions: Market covered, types of stocks included, number of stocks included, weighting scheme.

    • Price Staleness: Inactive constituent trading causes stale prices, shifting true index levels.

  • Price-Weighted vs. Value-Weighted Index Mechanics:

    • Price-Weighted (e.g., DJIA): Higher-priced stocks exert greater weight regardless of firm size. Distorted by stock splits; requires divisor adjustments.

    • Value-Weighted (e.g., S&P 500): Shares weighted by market capitalization (Shares Outstanding×Price\text{Shares Outstanding} \times \text{Price}). Immune to stock splits.

  • Comparative Worked Example (Betty Co. & Gray Bull):

    • Setup: Betty Co. (10M10\text{M} shares, \\text{\\10} \rightarrow \\text{\\11}), Gray Bull (20M20\text{M} shares, \\text{\\20} \rightarrow \\text{\\25}).

    • Price-Weighted Calculation:

    • Beginning average price = \frac{\text{\\10} + \text{\\20}}{2} = \text{\\$15}.

    • Ending average price = \frac{\text{\\11} + \text{\\25}}{2} = \text{\\$18}.

    • Price-Weighted Return = \frac{\text{\\18} - \text{\\15}}{\text{\\$15}} = +20\%.

    • Value-Weighted Calculation:

    • Beginning total value = (10\text{M} \times \text{\\10}) + (20\text{M} \times \text{\\20}) = \text{\\100M} + \text{\\400M} = \text{\\$500M}.

    • Ending total value = (10\text{M} \times \text{\\11}) + (20\text{M} \times \text{\\25}) = \text{\\110M} + \text{\\500M} = \text{\\$610M}.

    • Value-Weighted Return = \frac{\text{\\610M} - \text{\\500M}}{\text{\\$500M}} = +22\%.

  • Stock Splits and Divisor Adjustments:

    • Gray Bull splits 5-for-15\text{-for-}1 (price drops \\text{\\20} \rightarrow \\text{\\4}). To prevent a phantom crash from \\text{\\$15} to \frac{\text{\\10} + \text{\\4}}{2} = \text{\\$7}:

    • Solve for new divisor dd:     \n    \frac{\text{\\10} + \text{\\4}}{d} = 15 \Rightarrow \frac{14}{d} = 15 \Rightarrow d = \frac{14}{15} \approx 0.93333\n    

    • Divisors drop below 1.01.0 after cumulative stock splits.

  • Reindexing Series to Base 1,000:

    • Formula: Reindexed Value=Raw ValueBase Raw Value×1,000\text{Reindexed Value} = \frac{\text{Raw Value}}{\text{Base Raw Value}} \times 1,000.

    • Series Example (Base Raw Value Year 1 = 1,6871,687):

    • Year 1: 1,6871,687×1,000=1,000.00\frac{1,687}{1,687} \times 1,000 = 1,000.00

    • Year 2: 1,7891,687×1,000=1,060.46\frac{1,789}{1,687} \times 1,000 = 1,060.46

    • Year 3: 1,8001,687×1,000=1,066.98\frac{1,800}{1,687} \times 1,000 = 1,066.98

    • Year 4: 1,7001,687×1,000=1,007.71\frac{1,700}{1,687} \times 1,000 = 1,007.71

Investment Companies: Structure, Fees, and Performance

  • Scale of Mutual Funds Industry:

    • ≈1980\approx 1980: 5 million5\text{ million} Americans held mutual funds.

    • January 2024: 121 million121\text{ million} owners across 72 million72\text{ million} U.S. households holding \\text{\\$26 trillion} in assets.

  • Core Fund Concepts:

    • Pooled Ownership: Investors hold pro-rata claims on a unified portfolio.

    • Professional Management: Compensation paid to investment advisors.

    • Daily NAV Pricing: Net Asset Value per share calculated daily:     \n    \text{NAV} = \frac{\text{Market Value of Assets} - \text{Liabilities}}{\text{Shares Outstanding}}\n    

  • Open-End vs. Closed-End Funds:

    • Open-End Fund: Sells and redeems shares directly with investors at NAV daily; share count floats with inflows/outflows.

    • Closed-End Fund (≈500\approx 500 CEFs vs. ≈7,500\approx 7,500 open-end funds): Fixed share count issued once; shares trade on exchange between investors at market prices (persistently trade at discounts to NAV).

Investment company classification taxonomy tree

  • Regulated Investment Company (RIC) Taxation:

    • RIC status eliminates corporate income tax (pass-through entity).

    • Qualification requirements: Hold almost all assets in securities, use ≤5%\le 5\% of assets per single security acquired, pass through all realized income.

  • Fund Fee Types and Hidden Costs:

    • Front-End Load: Upfront sales charge when buying (up to ≈8.5%\approx 8.5\%).

    • Back-End Load: Sales charge when redeeming (declines over time).

    • 12b−112b-1 Fee: Annual marketing/distribution fee (≤1.00%\le 1.00\% allowed; 0.25%0.25\% common).

    • Management Fee: Paid to advisor (0.25%–1.50%/yr0.25\%\text{--}1.50\%/\text{yr}).

    • Expense Ratio: Reported recurring cost ratio.

    • Turnover Rate: Proxy for trading costs (unreported directly; higher turnover increases trading costs and capital gains taxes).

  • Fee Drag Worked Examples:

    • Front-End Load Calculation Example (Common Sense Growth Fund):

    • \text{NAV} = \\text{\\$13.91}, Offer Price = \\text{\\$15.20}.

    • Load Dollar Amount = \text{\\15.20} - \text{\\13.91} = \text{\\$1.29}.

    • Load % = \frac{\text{\\1.29}}{\text{\\15.20}} = 8.49\%.

    • Day 1: \text{\\$100} buys only \approx \\text{\\$91.51} in fund assets.

    • Annual Fee Deduction Worked Example (\text{\\$10,000} initial, 8.00%8.00\% gross return, 1.00%1.00\% expense ratio):

    • Year 1: No fee = \text{\\$10,800.00}; With expenses (7.00%7.00\%) = \text{\\$10,700.00}; Drag = \text{\\$100.00}.

    • Year 2: No fee = \text{\\$11,664.00}; With expenses = \text{\\$11,449.00}; Drag = \text{\\$215.00}.

    • Year 3: No fee = \text{\\$12,597.12}; With expenses = \text{\\$12,250.43}; Drag = \text{\\$346.69}.

    • Total drag exceeds simple fee subtraction due to lost compounding on fee dollars.

    • 40-Year40\text{-Year} Wealth Compounding Fee Drag (\text{\\$400/month}, 10%10\% annual return):

    • 0%0\% fee: \text{\\$2,529,632}

    • 1%1\% fee: \text{\\$1,872,528}

    • 2%2\% fee: \text{\\$1,396,403} (A 2%2\% annual fee erases \approx \\text{\\$1.13M} or ≈45%\approx 45\% of ending wealth).

Fee drag on ending balance over 40 years

  • Fund Categories and Equity Style Box:

    • Money Market Funds: Target stable \\text{\\$1.00} NAV (not guaranteed). Falling below \\text{\\$1.00} is called "breaking the buck." Taxable vs. Tax-Exempt (VMSXX national muni, VCTXX California muni).

    • Stock Funds: Categorized by Objective (VEIPX Equity Income), Size (VEXPX Explorer), Geography (VTIAX Total International), Theme (VGENX Energy Opportunities).

    • Blended / Target-Date Funds: VWELX Wellington Fund (active stock/bond mix), VFORX Target Retirement 2040 Fund (automatic glide path shifting away from equities near retirement).

    • Equity Style Box: 3×33 \times 3 grid mapping Size (Large, Mid, Small) against Valuation (Value, Blend, Growth).

  • Performance Evaluation and Morningstar Star Ratings:

    • Sequence: Match strategy to benchmark →\rightarrow Align time basis and total returns net of fees →\rightarrow Adjust for risk.

    • Star ratings are backward-looking historical risk-adjusted rankings; expense ratios are far stronger predictors of future relative performance.

  • ETFs, ETNs, and Leveraged Fund Traps:

    • Exchange-Traded Funds (ETFs): Traded intraday on exchanges; in-kind creation/redemption provides tax efficiency. Examples: SPY (S&P 500), DIA (Dow 30), QQQ (Nasdaq-100), ARKK (ARK Innovation active).

    • Leveraged ETFs (e.g., SPXL 3X S&P 500 Bull): Utilize daily resets. Daily reset causes severe path-dependent compounding drift over long periods; S&P +33%+33\% over 2 years does NOT yield SPXL +99%+99\%.

    • ETFs vs. ETNs: ETFs represent fund equity ownership; Exchange-Traded Notes (ETNs) are unsecured bank debt notes carrying bank credit/default risk.

  • Hedge Funds and Fee Mechanics (2/202/20):

    • Restricted to accredited investors (\text{\\$1M} net worth or \text{\\$200k/year} income).

    • 2/202/20 Structure: 2%2\% annual management fee on assets; 20%20\% performance fee on profits above high-water mark / hurdle rate.

Historical Risk and Return Principles

  • Compounding Wealth Scenarios ("Millionaire Question"):

    • Scenario 1: Invest \text{\\$300/month} at 9%9\% tax-deferred →36.34\rightarrow 36.34 years to reach \text{\\$1,000,000}.

    • Scenario 2: Invest \text{\\$500/month} at 12%12\% tax-deferred →25.50\rightarrow 25.50 years to reach \text{\\$1,000,000}.

  • Two Fundamental Lessons of Financial History:

    1. Risk is Rewarded: Investors earn substantial positive risk premiums for bearing risk over time.

    2. More Risk, More Return: Greater potential return accompanies greater risk.

  • Measuring Return Formulas and Worked Examples:

    • Total Dollar Return Formula:     \n    \text{Total Dollar Return} = \text{Dividend Income} + \text{Capital Gain (or Loss)}\n    

    • Harley-Davidson Example: 200200 shares bought at \text{\\$50/share} (\text{\\$10,000}), sold at \text{\\$55.60} (\text{\\$11,120}), \text{\\$80} total dividends (\text{\\$0.40/share}).

    • Dollar Return = \text{\\80} + (\text{\\11,120} - \text{\\10,000}) = \text{\\80} + \text{\\1,120} = \text{\\1,200}.

    • Total Percent Return Formula:     \n    \text{Total Percent Return} = \text{Dividend Yield} + \text{Capital Gain Yield} = \frac{D_{t+1}}{P_t} + \frac{P_{t+1} - P_t}{P_t}\n    

    • Harley-Davidson Percent Return = \frac{\text{\\0.40}}{\text{\\50.00}} + \frac{\text{\\5.60}}{\text{\\50.00}} = 0.8\% + 11.2\% = 12.0\%.

    • Concannon Plastics Worked Example:

    • Setup: Invest \text{\\$1,400} at \text{\\$35/share} (4040 shares). One year later: price = \text{\\$49/share}, dividend = \text{\\$1.40/share}.

    • Dollar Return: Capital gain = 40 \times \text{\\14} = \text{\\560}; Dividends = 40 \times \text{\\1.40} = \text{\\56}; Total = \text{\\$616}.

    • Percent Return: Capital gain yield = \frac{\text{\\14}}{\text{\\35}} = 40\%       Dividend yield = \frac{\text{\\1.40}}{\text{\\35}} = 4\%       Total = 40%+4%=44%40\% + 4\% = 44\%. Check: \frac{\text{\\616}}{\text{\\1,400}} = 44\%.

    • Annualizing Holding Period Returns (EAR):     \n    \text{EAR} = (1 + \text{HPR})^m - 1 \quad \text{where } m = \frac{12}{\text{Months Held}}\n    

    • Moderna Example: Buy at \text{\\$28.00}, sell after 44 months at \text{\\$29.40} (no dividend).

    • \text{HPR} = \frac{\text{\\29.40} - \text{\\28.00}}{\text{\\$28.00}} = 5\%. m=124=3m = \frac{12}{4} = 3

    • EAR=(1+0.05)3−1=0.1576 or 15.76%\text{EAR} = (1 + 0.05)^3 - 1 = 0.1576 \text{ or } 15.76\%.

  • Century of Financial Market History (1926–20241926\text{--}2024 Data):

    • Growth of \text{\\$1.00} Invested at Year-End 19251925 (Log Scale Values):

    • Small-Company Stocks: \text{\\$61,816.03}

    • Large-Company Stocks: \text{\\$17,894.03}

    • Long-Term Government Bonds: \text{\\$129.02}

    • U.S. Treasury Bills: \text{\\$24.46}

    • Inflation (CPI): \text{\\$17.65}

Value of $1 invested since 1925 across asset classes

  • Average Annual Returns and Standard Deviations (1926–20241926\text{--}2024):

    • Small-Company Stocks: Avg Return = 16.0%16.0\%, Std Dev = 30.9%30.9\%

    • Large-Company Stocks: Avg Return = 12.3%12.3\%, Std Dev = 19.7%19.7\%

    • Long-Term Corporate Bonds: Avg Return = 6.7%6.7\%, Std Dev = 8.4%8.4\%

    • Long-Term Government Bonds: Avg Return = 5.5%5.5\%, Std Dev = 10.2%10.2\%

    • U.S. Treasury Bills (Risk-Free Rate): Avg Return = 3.3%3.3\%, Std Dev = 3.1%3.1\%

    • Inflation: Avg Rate = 3.0%3.0\%, Std Dev = 3.9%3.9\%

  • Historical Risk Premiums (Over T-Bills 3.3%3.3\%):

    • Large-Company Stocks Risk Premium: 12.3%−3.3%=9.0%12.3\% - 3.3\% = 9.0\%

    • Small-Company Stocks Risk Premium: 16.0%−3.3%=12.7%16.0\% - 3.3\% = 12.7\%

    • Long-Term Corporate Bonds Risk Premium: 6.7%−3.3%=3.4%6.7\% - 3.3\% = 3.4\%

    • Long-Term Government Bonds Risk Premium: 5.5%−3.3%=2.2%5.5\% - 3.3\% = 2.2\%

  • Historical vs. Forward-Looking Forecasts: Historical large-stock risk premium (9.0%9.0\%) vs. Economist Survey median forward-looking risk premium estimate (7.0%7.0\% across 226226 financial economists).

  • S&P 500 Monthly Volatility Case Study (20082008): Jan −6.0%-6.0\%, Feb −3.2%-3.2\%, Mar −0.4%-0.4\%, Apr +4.9%+4.9\%, May +1.3%+1.3\%, Jun −8.4%-8.4\%, Jul −0.8%-0.8\%, Aug +1.4%+1.4\%, Sep −8.9%-8.9\%, Oct −16.8%-16.8\%, Nov −7.2%-7.2\%, Dec +1.1%+1.1\%.

Risk vs return trade-off scatter plot

  • Risk Measurement (Variance and Standard Deviation Math):

    • Sample Variance Formula:     \n    \text{Var}(R) = \frac{\sum_{t=1}^N (R_t - \bar{R})^2}{N - 1}\n    

    • Standard Deviation Formula: SD(R)=Var(R)\text{SD}(R) = \sqrt{\text{Var}(R)}.

    • Hand Calculation Worked Example (Large-Company Stocks 2012–20152012\text{--}2015):

    • Year 20122012: Return = 16.00%16.00\%, Mean = 15.87%15.87\%, Diff = +0.13%+0.13\%, Squared = 0.00000.0000

    • Year 20132013: Return = 32.39%32.39\%, Mean = 15.87%15.87\%, Diff = +16.52%+16.52\%, Squared = 0.02730.0273

    • Year 20142014: Return = 13.69%13.69\%, Mean = 15.87%15.87\%, Diff = −2.18%-2.18\%, Squared = 0.00050.0005

    • Year 20152015: Return = 1.38%1.38\%, Mean = 15.87%15.87\%, Diff = −14.49%-14.49\%, Squared = 0.02100.0210

    • Sum of Returns = 63.46%63.46\% (Mean Rˉ=15.87%\bar{R} = 15.87\%). Sum of Squared Diffs = 0.04880.0488

    • Variance = 0.04884−1=0.04883=0.01625\frac{0.0488}{4 - 1} = \frac{0.0488}{3} = 0.01625

    • Standard Deviation = 0.01625=0.1275 or 12.75%\sqrt{0.01625} = 0.1275 \text{ or } 12.75\%.

  • Normal Distribution and the 68–95–99.768\text{--}95\text{--}99.7 Rule:

    • Large-company stock returns (Mean=12.3%\text{Mean} = 12.3\%, SD=19.7%\text{SD} = 19.7\%):

    • ±1σ\pm 1\sigma (68.26%68.26\% confidence interval): −7.4%-7.4\% to 32.0%32.0\%

    • ±2σ\pm 2\sigma (95.44%95.44\% confidence interval): −27.1%-27.1\% to 51.7%51.7\%

    • ±3σ\pm 3\sigma (99.74%99.74\% confidence interval): −46.8%-46.8\% to 71.4%71.4\%

Normal distribution curve for large-company stock returns

  • Historical Dow Jones Extreme Days (Since 1896):

    • Best Days (% Gain): 1933-03-15 (+15.34%+15.34\%), 1931-10-06 (+14.87%+14.87\%), 1929-10-30 (+12.34%+12.34\%), 2008-10-13 (+11.08%+11.08\%), 1987-10-21 (+10.15%+10.15\%).

    • Worst Days (% Loss): 1914-12-12 (−23.52%-23.52\%), 1987-10-19 (−22.61%-22.61\%), 2020-03-16 (−12.93%-12.93\%), 1929-10-28 (−12.82%-12.82\%), 1929-10-29 (−11.73%-11.73\%).

    • Comparing Return Averages (Arithmetic, Geometric, Dollar-Weighted):

  • Arithmetic Average: Answers "What was your return in an average year?" Best for short-term single-period forecasts.

  • Geometric Average: Answers "What was your average compound return per year?"     \n    \text{Geometric Return} = \left[ \prod_{t=1}^N (1 + R_t) \right]^{\frac{1}{N}} - 1\n    

    • Large-Company Stocks Example (2012–20152012\text{--}2015):       \n      \text{Geometric Return} = (1.1600 \times 1.3239 \times 1.1369 \times 1.0138)^{\frac{1}{4}} - 1 = 15.34\%\n      

  • Historical Comparison (1926–20241926\text{--}2024):

    • Large-Company Stocks: Geometric = 10.4%10.4\%, Arithmetic = 12.3%12.3\%, SD = 19.7%19.7\%

    • Small-Company Stocks: Geometric = 11.8%11.8\%, Arithmetic = 16.0%16.0\%, SD = 30.9%30.9\%

    • Long-Term Corporate Bonds: Geometric = 6.4%6.4\%, Arithmetic = 6.7%6.7\%, SD = 8.4%8.4\%

    • Long-Term Government Bonds: Geometric = 5.1%5.1\%, Arithmetic = 5.5%5.5\%, SD = 10.2%10.2\%

    • U.S. Treasury Bills: Geometric = 3.3%3.3\%, Arithmetic = 3.3%3.3\%, SD = 3.1%3.1\%

    • Inflation: Geometric = 2.9%2.9\%, Arithmetic = 3.0%3.0\%, SD = 3.9%3.9\%

  • Forecasting Rule: Arithmetic average runs too high for long multi-year forecasts; geometric average runs too low for short single-period forecasts.

  • Dollar-Weighted Return (Internal Rate of Return - IRR):

    • Measures performance taking into account cash flow additions and withdrawals.

    • Worked Cash Flow Example:

      • t=0t = 0: Initial investment = - \text{\\$1,000}

      • t=1t = 1: Additional investment = - \text{\\$4,000} (Year 1 return = +10%+10\%)

      • t=2t = 2: Ending balance = + \text{\\$4,845} (Year 2 return = −5%-5\%)

    • Calculation:       \n      \text{Dollar-Weighted Return} = \text{IRR}(-\text{\\1,000}, -\text{\\4,000}, \text{\\$4,845}) = -2.6\%\n      

    • Comparison: Arithmetic average = +2.5%+2.5\%, Geometric average = +2.23%+2.23\%, Dollar-weighted return = −2.6%-2.6\%. The investor experienced an absolute dollar loss because a large additional cash deposit (\text{\\$4,000}) was made immediately prior to a market decline.