Financial Engineering & Portfolio Theory -CM2 Actuarial Exam

Explore irrational behavior in finance by examining the St. Petersburg paradox, how people misprice extreme events, and why emotions drive gambling and insurance choices.

Explore consumer choice theory by analyzing how rational buyers maximize utility through bundles of goods. Learn how diminishing marginal utility, indifference curves, and budget lines determine optimal purchases.

Explore utility functions and utility theory, from diminishing marginal utility of wealth to risk attitudes, including absolute and relative risk aversion, St. Petersburg paradox, and Lennix function.

Explore the axioms of utility—completeness, transitivity, continuity, and independence—and how they justify representing preferences with a utility function to maximize expected utility under risk.

Explore expected utility theory, risk attitudes, and the St. Petersburg paradox; compare expected utility with expected wealth and examine quadratic and power utility functions.

Explore stochastic dominance, including absolute dominance, first order dominance, and second order dominance, and how risk adverse investors use cumulative distributions to determine which investments dominate.

Explore behavioral economics in investment decisions, showing how psychology and social forces shape heuristics, including framing, herd instinct, anchoring, myopic loss aversion, mental accounting, and biases that drive choices.

Explore heuristics and rule-of-thumb shortcuts that oversimplify complex issues, how they can mislead in finance, politics, and marketing, and why slow, deliberate thinking protects against manipulation.

Explore framing as a manipulation technique that colors questions and packaging, shaping attitudes toward bonds, assets, and brands, and learn to spot how presentation influences decisions.

Explore how herd instinct shapes financial behavior, from copying peers in Bitcoin purchases to asset managers following peers, and how echo chambers and groupthink influence investment decisions.

Explore anchoring, a cognitive bias that uses a reference price to shape decisions, illustrated by salary negotiations and irrelevant data like ID numbers.

Explore myopic loss aversion, a bias that overemphasizes immediate losses and underemphasizes later ones. It explains why people prefer credit and may avoid investing because money today is worth more.

Explore mental accounting through a pricing experiment. Compare relative versus absolute price differences to show how people prioritize savings irrationally and why bank statements reflect absolute costs.

Explore four biases that shape financial judgments: self-serving bias, confirmation bias, availability bias, and familiarity bias. Recognize these biases to improve investment decisions and project choices.

Explore how stories shape financial decisions and asset prices, using bitcoin’s rise and crash as a narrative example. Learn to read market fears and hopes to anticipate price movements.

Learn how beliefs form—from authority, reason, and empirical truth—and why embracing doubt improves your decisions. Apply evidence-based thinking in finance, marketing, and politics to spot scams and make stronger choices.

Introduce measures of risk by defining market risk as the unexpected change in asset and liability prices, and preview variance, semivariance, value at risk, and expected shortfall.

Examine variance and semi-variance in portfolio theory, showing how high and low variance affect risk. See how variance covers all upside and downside, while semi-variance focuses on downside risk.

Explain shortfall probability by calculating the chance that returns fall below a threshold l; use the average return, a benchmark, zero, or negative values to indicate loss magnitude.

Explore value at risk as a 99% loss threshold over 12 months, note normal model limits with fat tails, and discuss expected shortfall as tail value at risk.

Explore expected shortfall, or tail VaR, as the average loss beyond a threshold. Focus on tail behavior, skewed distributions, and loss-related thresholds.

Explore how risk measures relate to utility functions through a quadratic utility that makes utility a linear combo of expected return and variance, justifying mean-variance portfolio theory.

This introduction to portfolio theory explains measuring risk, mean-variance analysis, diversification, and the debate between active and passive investing, with high-level coverage of multifactor models and capital asset pricing models.

Mean-variance portfolio theory guides investors to maximize return for a given risk or minimize risk for a return, defining risk as variance, using a quadratic utility function, and noting limitations.

This lecture outlines the mean-variance portfolio theory assumptions. It shows investments are chosen solely on risk and return, with no taxes, costs, or limits, and with known information.

Explore the opportunity set and the efficient frontier to identify portfolios that maximize return for a given risk, using mean, variance, and covariance.

Discover the diversification benefit, showing how the variance of returns declines when assets are independent and covariances vanish, and distinguish specific risk or alpha from systemic risk or beta.

Identify the optimal portfolio on the efficient frontier by diversifying two securities to maximize mean and minimize variance.

Examine capital asset pricing models as an extension of mean-variance portfolio theory, linking the market portfolio, risk-free rate, and beta to determine returns, while evaluating assumptions and security market line.

Explore how forward contracts transfer price risk from farmers to bankers, illustrating how derivatives hedge market risk with long and short positions tied to harvest prices.

Learn how futures are priced under no arbitrage, with strike equal to current price accumulated at the risk-free rate, and how dividends and oil during COVID affect pricing.

Learn how options grant the right to buy or sell, not obligations, and how premiums depend on duration, volatility, strike price, dividends, current price, risk-free rate, payoff graphs, and Greeks.

Explore how utility theory and insurance interact, analyzing absolute and relative risk aversion, a quadratic utility model, and premium pricing to equate expected and current utility.

Use a stochastic differential equation to model stock prices, derive a lognormal distribution, and assess the four-year variance and CEO surplus, plus put option hedge considerations such as premium.

Apply the Black-Scholes model to value a European call on a non-dividend stock and explain FITA, Delta, dividends, and put-call parity.

Calculate the probability the customer remains solvent after three years. Determine the interest rate needed for a 10% annual return under default risk using discounted cash flow.

Apply the inflation adjusted chain ladder method to a run-off triangle by deriving incremental claims from a cumulative table, adjusting for inflation using year indices, and computing outstanding claims.

Banks practice delta hedging with put options by selling shares to offset negative delta, then compare delta-based price updates with Black-Scholes estimates, and discuss gamma and vega implications.

explore ruin theory by defining the insurer's surplus process, discuss limitations, and compare finite versus infinite time ruin probabilities, using premium income and aggregate claims in a 500 policy example.