Investments

Units

1. 1

   The investment environment

   4 lessons

   1. Real and financial assetsTell real assets from financial assets, name the three classes of financial assets (fixed income, equity, derivatives) by the claim each one gives, and read the risk return tradeoff on a mean versus standard deviation chart.
   2. Asset classes and financial instrumentsSurvey the main instruments (money market securities, Treasury, municipal and corporate bonds, common and preferred stock, options and futures), compute a T-bill yield and a tax-equivalent yield, and build a price-weighted and a value-weighted index.
   3. How securities are tradedTrace an Atlas share from issuance through resale, choose a buy order against a quote, and calculate the effects of buying on margin or selling short.
   4. Mutual funds and other investment companiesCompute a fund's net asset value, tell open-end funds, closed-end funds, ETFs and hedge funds apart by how they trade, and show with numbers how expense ratios and loads compound over decades.
2. 2

   Risk and return

   4 lessons

   1. Holding period, arithmetic and geometric returnsCompute a holding period return, the arithmetic and geometric averages of a run of returns, a dollar-weighted return (IRR), and a real return with the Fisher equation, and say which average answers which question.
   2. Expected return and standard deviationCompute the expected return, variance and standard deviation of an asset from a scenario table and from historical data, and use the normal distribution to say how likely a return range is.
   3. Risk premiums and the Sharpe ratioDefine excess return and the risk premium, compute the Sharpe ratio as premium per unit of standard deviation, use it to rank two funds, and compare the historical risk premiums and Sharpe ratios of stocks, bonds and bills.
   4. Value at risk and tail riskCompute value at risk and expected shortfall for a normal return distribution, read both from historical data, and explain how skewness, kurtosis and fat tails make the normal answer too optimistic.
3. 3

   Portfolio theory

   4 lessons

   1. Risk aversion and utilityScore a risky portfolio with the mean-variance utility U = E(r) − 0.5Aσ², find its certainty equivalent, draw indifference curves in the mean-σ plane, and compute the risk premium an investor with risk aversion A needs.
   2. The capital allocation lineCombine a risk-free asset with a risky portfolio, write the mix's E(rC) = rf + y(E(rP) − rf) and σC = yσP, draw the capital allocation line with slope equal to the Sharpe ratio, find the optimal risky share y* = (E(rP) − rf)/(Aσ²), and rank funds by Sharpe ratio.
   3. Two risky assets and correlationCompute the expected return and variance of a portfolio of a stock fund and a bond fund, σp² = w²σS² + (1 − w)²σB² + 2w(1 − w)ρσSσB, see how the correlation ρ bends the opportunity set, and find the minimum variance portfolio.
   4. The efficient frontier and separationBuilds Markowitz's efficient frontier, finds the tangency (optimal risky) portfolio, and explains the separation property and the limits of diversification.
4. 4

   Asset pricing models

   4 lessons

   1. The single index modelWrites the index model R_i = alpha + beta R_M + e, separates systematic and firm-specific variance, and estimates alpha and beta from a regression line.
   2. The capital asset pricing modelDerives the CAPM from the market portfolio and the capital market line, draws the security market line, and computes alpha as distance from the SML.
   3. Arbitrage pricing theoryExplains multifactor models and Ross's arbitrage pricing theory, showing how a mispriced well-diversified portfolio creates an arbitrage, with a two factor numerical example.
   4. Fama-French and factor modelsExplains the Fama-French three factor model (market, SMB, HML), the Carhart momentum factor and how factor loadings are estimated and used.
5. 5

   Market efficiency and behavioral finance

   4 lessons

   1. The efficient market hypothesisExplains weak, semistrong and strong form efficiency, the random walk, and implications for technical analysis, fundamental analysis and passive investing.
   2. Event studies and tests of efficiencyComputes abnormal returns and cumulative abnormal returns around an announcement and reads the CAR graph as a test of semistrong efficiency.
   3. Market anomaliesCovers the size effect, value effect, momentum, post earnings announcement drift and the debate between risk-based and mispricing explanations.
   4. Behavioral financeExplains prospect theory's value function, overconfidence, mental accounting, framing, the disposition effect and limits to arbitrage that let mispricing persist.
6. 6

   Bond prices and yields

   4 lessons

   1. Bond pricing and yield to maturityPrices bonds from coupons and face value, computes yield to maturity, yield to call and realized compound yield, and explains accrued interest and clean versus dirty prices.
   2. The term structure of interest ratesComputes forward rates from spot rates, and explains the expectations, liquidity preference and market segmentation theories of the yield curve.
   3. DurationComputes Macaulay duration as a weighted average time of cash flows and modified duration, and uses it to estimate price change for a yield change.
   4. Convexity and immunizationAdds convexity to the duration price estimate, draws the price yield curve, and immunizes a liability by matching duration, contrasting with cash flow matching.
7. 7

   Equity valuation

   4 lessons

   1. Macroeconomic and industry analysisExplains top-down analysis, business cycle sensitivity, cyclical and defensive industries, and the industry life cycle in fundamental analysis.
   2. Dividend discount modelsApplies the constant growth DDM, sustainable growth g = ROE x b, the present value of growth opportunities and multistage DDMs.
   3. Price-earnings ratiosLinks P/E to growth opportunities and the required return, and uses P/E, P/B, P/S and EV/EBITDA comparables with their pitfalls.
   4. Free cash flow modelsComputes FCFF and FCFE from financial statements and values the firm and its equity by discounting at WACC and the cost of equity respectively.
8. 8

   Options

   4 lessons

   1. Option contracts and payoff diagramsExplains calls and puts, moneyness, intrinsic and time value, and draws payoff and profit diagrams for long and short calls and puts.
   2. Option strategies and put-call parityDraws protective puts, covered calls, straddles and spreads, and derives put-call parity C + PV(X) = P + S0 with an arbitrage example.
   3. Binomial option pricingPrices a call with a one period binomial tree using the hedge ratio and risk-neutral probability, then extends to two periods.
   4. The Black-Scholes modelApplies the Black-Scholes formula with d1 and d2, explains each input's effect on value, implied volatility and the option delta.
9. 9

   Futures, forwards and swaps

   4 lessons

   1. Futures markets and mechanicsContrasts forwards and futures, explains the clearinghouse, marking to market, margin accounts and convergence of futures and spot prices.
   2. Futures pricing and cost of carryDerives the spot futures parity F0 = S0(1 + rf - d)^T by a cost of carry arbitrage and applies it to stock index futures.
   3. Hedging and speculating with futuresHedges a stock portfolio with index futures using beta, computes the number of contracts, and explains basis risk.
   4. Interest rate swapsExplains a plain vanilla fixed for floating interest rate swap, its cash flows, and how firms use swaps to change the duration of assets or liabilities.
10. 10

    Portfolio performance evaluation

    4 lessons

    1. Risk-adjusted performance measuresComputes the Sharpe ratio, Treynor measure, Jensen's alpha, information ratio and M squared for sample funds and explains when each is appropriate.
    2. Style analysis and attributionExplains Sharpe style analysis and decomposes excess return into asset allocation and security selection effects with a performance attribution table.
    3. Active versus passive managementCompares active and passive investing with evidence on mutual fund persistence and fees, and the Treynor-Black model for combining active and index portfolios.
    4. Investment policy and the processWrites an investment policy statement with return and risk objectives and constraints (liquidity, horizon, taxes, regulation, unique needs) and strategic asset allocation.