HD and Dean's List Full Course Notes

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HD and Dean's List Extensive Complete Course Notes. Covering every topic and lecture for the whole term. Topics covered: Part 1 (Weeks 1 to 3, Returns, Risk and Portfolio Theory): Weeks 1 and 2 (Returns, Risk and Portfolio Theory): Holding period return formula (HPR = (P_T minus P_0 plus D) divided by P_0), arithmetic vs geometric averages (use cases and distinction), annualising from monthly data (mean x 12, std dev x sqrt(12), variance x 12, covariance x 12), expected return using probability-weighted scenarios, portfolio expected return as weighted average. Variance and standard deviation (probability-weighted and sample formulas), covariance formula and sample covariance, correlation coefficient (rho = Cov divided by sigma_i x sigma_j, range negative 1 to plus 1). The N x N covariance matrix (diagonal elements are variances, off-diagonal are covariances), portfolio variance using cell-by-cell multiplication of the covariance matrix, covariance between two portfolios formula. Three-asset portfolio fully worked example (E[r] = , sigma = , diversification benefit = ). Weeks 2 and 3 (Mean-Variance Frontier and Capital Allocation): Mean-variance utility function (U = E[r] minus (1/2) x A x sigma^2), risk aversion coefficient A (risk averse A greater than 0, neutral, loving), dominance principle, finding A for indifference between two portfolios. Global Minimum Variance Portfolio (GMVP) as the starting point of the efficient frontier, minimum variance frontier (MVF) and the efficient region above GMVP, long-short vs long-only portfolios. Capital Allocation Line (CAL) construction (E[r_C] = r_f plus (Sharpe ratio) x sigma_C), Sharpe ratio as slope of CAL, optimal weight in risky portfolio (y* = (E[r_P] minus r_f) divided by (A x sigma_P^2)). Sharpe ratio domination proof (worked example with assets X and Z), two-fund separation theorem (all investors hold same P* regardless of risk aversion; only allocation between P* and r_f differs), complete portfolio construction. Markowitz optimisation using Excel Solver (minimise variance subject to target return and budget constraints), tracing the MVF, finding P* by maximising the Sharpe ratio, iLab 1 five-stock efficient frontier step-by-step procedure. Two-asset GMVP analytical formula (omega_1 = (sigma_2^2 minus Cov_12) divided by (sigma_1^2 plus sigma_2^2 minus 2 x Cov_12)), optimal complete portfolio worked examples for investors with A = 3 and A = 5. Diversification mathematics: N equal assets formula (Var = sigma^2/N plus (N minus 1)/N x rho x sigma^2), systematic risk floor as N approaches infinity, numerical example showing risk declines from 30% to Part 2 (Weeks 3 to 5, Asset Pricing Models): Weeks 3 and 4 (Capital Asset Pricing Model): CAPM assumptions (mean-variance optimisers, homogeneous expectations, risk-free borrowing and lending, perfect markets, price takers), the market portfolio M (contains all risky assets in proportion to market cap), Capital Market Line (CML) slope = (E[r_M] minus r_f) divided by sigma_M. Beta formula (beta_i = Cov(r_i, r_M) divided by Var(r_M) = rho_{iM} x sigma_i divided by sigma_M), equivalent forms, portfolio beta as weighted average, beta of the market = 1, interpretation of beta (aggressive, defensive, zero, negative). Security Market Line (E[r_i] = r_f plus beta_i x MRP), alpha as deviation from SML (positive = underpriced, negative = overpriced), reward-to-risk parity condition, CML vs SML distinction (total risk vs systematic risk on x-axis). Full CAPM worked example (three stocks, market cap weights, betas, expected returns, complete portfolio with 30% in risk-free). CAPM risk decomposition (total variance = systematic plus idiosyncratic, sigma_epsilon^2 = sigma_i^2 minus beta_i^2 x sigma_M^2), idiosyncratic variance approaches zero as N increases, systematic floor remains. BRK and AAPL worked example (risk decomposition, covariance between stocks, equal-weight portfolio check). CAPM equilibrium mechanism (price adjustment until alpha = 0), reward-to-risk parity verified with two-asset market worked example. CAPM empirical evidence (supporting: positive beta-return relationship; contradicting: Fama-French 1992, size effect, value effect, momentum, low-volatility anomaly), rational vs behavioural responses, equity premium puzzle (historical 5 to 8%, A = vs A greater than 20 paradox, proposed explanations: survivorship bias, transaction costs, loss aversion, rare disasters). Weeks 4 and 5 (Single Index Model and Active Portfolio Management): SIM return equation (r_i = alpha_i plus beta_i x r_M plus epsilon_i), three key assumptions (zero mean noise, uncorrelated with market, uncorrelated across stocks), expected return, variance decomposition, and covariance formulas under SIM. Parameter reduction advantage (N plus 2 vs N(N plus 1)/2 plus N for full matrix). Alpha definition and calculation, active vs passive distinction. Treynor-Black 8-step active portfolio construction procedure (compute alphas and idiosyncratic variances, reward-to-risk ratios, proportional weights, active portfolio parameters alpha_A and beta_A and sigma_epsilon_A^2, unadjusted weight omega_A^0, beta-adjusted weight omega_A*, optimal risky portfolio P*, Sharpe ratio improvement using Information Ratio: S_P*^2 = S_M^2 plus IR^2). Full Treynor-Black worked example (assets X and Y, omega_A* = , S_P* = vs S_M = ). SIM regression in practice (OLS intercept = alpha, slope = beta, R^2 = rho^2_{i,M}), Blume beta adjustment ( plus x raw beta), SIM vs CAPM comparison table (origin, factor, alpha, main use, covariance formula, idiosyncratic risk). iLab 2 SIM estimation procedure (10 stocks, excess returns regression, beta and alpha via SLOPE and INTERCEPT, idiosyncratic variance from residuals, SIM covariance matrix construction, Treynor-Black active weights, comparison with Markowitz frontier). Week 5 (Multi-Factor Models): Limitations of CAPM and SIM (single market factor insufficient: Fama and French 1992). Fama-French-Carhart four-factor model equation (E[R_i] = alpha_i plus beta_M x lambda_M plus beta_SMB x lambda_SMB plus beta_HML x lambda_HML plus beta_MOM x lambda_MOM). Factor definitions and construction: Market factor (value-weighted market excess return), SMB Small Minus Big (long bottom half by market cap, short top half, 50th percentile cut), HML High Minus Low (long top 30% by book-to-market, short bottom 30%), MOM Momentum (long past 12-month winners, short losers, exclude most recent month). Typical historical factor premiums (MRP approx to 5%, SMB approx 3 to 5%, HML approx 3 to 4%, MOM approx 1 to 4%). Chevron worked example (factor loadings applied to compute E[r] = ). Value premium debate (rational distress risk view of Fama-French vs behavioural extrapolation bias view of Lakonishok, Shleifer and Vishny 1994, evidence post-1990s). Part 3 (Weeks 6 and 7, Market Efficiency and Behavioural Finance): Weeks 6 and 7 (Efficient Market Hypothesis and Behavioural Finance): EMH definition, three forms comparison table (weak form: reflects all past price and volume data, implication: technical analysis cannot generate alphas; semi-strong form: reflects all public information, implication: fundamental analysis on public data cannot generate alphas; strong form: reflects all information including private, implication: insiders cannot consistently earn alphas). EMH violation analysis (eight observation scenarios with violation status and reasoning: positive average returns do not violate, zero autocorrelation is consistent, buying after 10% rise violates weak form, low dividend yield strategy violates semi-strong, pre-announcement insider data violates strong form only, half of funds outperforming in a year does not violate, persistent winner funds violates semi-strong, negative weekly autocorrelation violates weak form). Key empirical anomalies (size effect, value effect, momentum: Jegadeesh and Titman 1993 violates weak form, January effect, post-earnings announcement drift PEAD as semi-strong violation, caveat on transaction costs and data mining). Behavioural finance and overconfidence (mechanism 1: miscalibration causes underestimation of sigma_epsilon^2, inflating alpha/sigma_epsilon^2 ratio and over-weighting active positions; mechanism 2: better-than-average effect and over-trading, Barber and Odean 2000; mechanism 3: familiarity bias and home country bias leading to under-diversification). Behavioural bias table (overconfidence, under-reaction, over-reaction, representativeness, anchoring, herding with descriptions and market effects). Active vs passive management comparison table (strategy, theoretical basis, costs, net performance, evidence, appropriate conditions). Active vs passive conclusion (passive indexing dominates in expectation if markets are semi-strong efficient). Part 4 (Weeks 8 and 9, Fixed Income Securities): Week 8 (Bond Basics, Pricing, YTM and Holding Period Return): Bond types table (zero-coupon, coupon bond, floating rate note). Bond pricing formulas (zero-coupon: P = F divided by (1 plus y)^T; YTM: y = (F/P)^(1/T) minus 1; coupon bond: P = C x annuity factor plus F x discount factor). Price-yield relationship (inverse; at par when y = coupon rate, at discount when y greater than coupon rate, at premium when y less than coupon rate). Three worked bond pricing examples. Holding period return (HPR = (C plus P_sell minus P_buy) divided by P_buy, three-step calculation), convexity asymmetry demonstrated (yield rise gives smaller loss than yield fall gives gain), three-scenario HPR worked example (base case , case b at 5% yield gives , case c at 3% yield gives , asymmetry = gain vs loss). No-arbitrage bond pricing (fair value = sum of zero-coupon bond prices replicating cash flows, if mispriced: buy or short and capture risk-free profit), worked arbitrage example ($ fair value vs $120 market price, profit calculation). Week 9 (Term Structure, Forward Rates, Duration and Immunisation): Spot rates (y_t = YTM of zero-coupon bond maturing in t years), bootstrapping spot rates from coupon bonds sequentially. Implied forward rate formula ((1 plus y_t)^t x (1 plus forward) = (1 plus y_{t+n})^{t+n}), general n-year forward rate formula. Full bootstrapping worked example (Bonds E, F, G to derive y_1 = , y_2 = , y_3 = , y_4 = , pricing Bond H = $, computing 2-year forward rate 2f4 = ). Term structure theories comparison table (expectations hypothesis: forward rates are unbiased predictors; liquidity preference theory: forward rate = expected future spot rate plus liquidity premium; market segmentation theory: independent supply and demand per maturity). Forward rate decomposition under liquidity preference with worked example (2f3 = , L = , E[2y3] = ). Macaulay duration formula (weighted average time to cash flows), modified duration (D_mod = D_mac divided by (1 plus y)), duration rule (Delta_P divided by P = negative D_mod x Delta_y), five duration properties (zero-coupon = maturity, coupon bond less than maturity, higher coupon shorter, higher yield shorter, perpetuity = (1 plus y)/y). Full duration calculation worked example (4-year 10% coupon at y = 5%, D_mac = years, D_mod = , price change estimate vs actual showing $ convexity error). Immunisation principles (match D_assets = D_liabilities and PV assets = PV liabilities, must rebalance as time passes), single-liability immunisation worked example (liability $100 in 3 years, bonds A and B with D = 2 and D = 6, omega_A = , omega_B = , dollar amounts and units of each bond, verification at y = 9%). Multi-liability immunisation worked example (two liabilities, D_liability = years, solving for bond weights). Bond duration deep dive (price risk vs reinvestment risk and why they exactly cancel at the duration horizon, duration of special bond types, portfolio duration as weighted average). Convexity concept and example (duration is linear approximation, actual price-yield relationship is convex, yield rise gives smaller actual loss than duration predicts, yield fall gives larger actual gain, both directions benefit bondholder, asymmetry = the convexity benefit). Two-period immunisation rebalancing necessity explained. Part 5 (Week 10, Derivatives and Options): Week 10 (Options): Option fundamentals (call and put, buyer vs writer, American vs European), four-row option type table (long call, short call, long put, short put with buyer's right, exercise condition, profit at expiry formula). Moneyness definitions (ITM, ATM, OTM), intrinsic value and time value, break-even formulas. 10-contract CBA call option worked example (three scenarios: ITM profit $1,600, ATM loss $2,500, OTM loss $2,500). Option strategies comparison table (protective put, covered call, bull spread, straddle with components, payoff profile, motivation), protective put vs covered call worked example ($50 stock with $45 put and $55 call). Binomial option pricing model (setup: up factor u and down factor d, no-arbitrage condition u greater than e^(rT) greater than d), four-step procedure (calculate payoffs, find hedge ratio Delta, value riskless portfolio, solve for call price), risk-neutral pricing approach (p = (e^(rT) minus d) divided by (u minus d), C_0 = e^(-rT) x (p x C_u plus (1 minus p) x C_d), interpretation of p as mathematical construct not true probability). Full one-period binomial worked example (S_0 = $100, u = , d = , r = , X = $100, Delta = , C_0 = $ verified via both hedge portfolio and risk-neutral methods). Two-period binomial extension worked example (S_0 = $100, u = , d = , r = 5% discrete, X = $100, p = , C_0 = $ verified both node-by-node and direct calculation). Black-Scholes formula (C = S_0 x N(d_1) minus X x e^(-rT) x N(d_2), d_1 and d_2 formulas, five inputs, assumptions: log-normal returns, constant volatility, continuous trading, no dividends, frictionless markets, constant risk-free rate). Black-Scholes worked example (S_0 = $, X = $50, T = years, r = , sigma = 45%, C = $, P = $ via put-call parity). Put-call parity (C plus X x e^(-rT) = P plus S_0, derivation from payoff equivalence of call plus PV(X) and put plus stock, arbitrage if violated). Option Greeks table (delta, gamma, vega, theta, rho with definitions, sign for long call, economic meaning), delta hedging in practice (sell 1 call with delta = , buy shares, near-zero net exposure, rebalancing as delta changes due to gamma, ATM delta = , deep ITM delta = 1, deep OTM delta = 0). Convexity of bond prices extended analysis (duration rule linear approximation, d^2Price/dy^2 greater than 0, price rises more on yield fall than falls on yield rise, convexity term = (1/2) x C x (Delta_y)^2 always positive, example asymmetry: actual $ gain vs $ estimated on 1% yield fall).