Investment Management
How assets are priced, how risk gets paid, and how to think clearly when real money and real people are involved.
Every dot is a portfolio. Mix five asset classes at random and the cloud draws its own boundary: the efficient frontier. The red line from the risk-free rate touches it once, at the tangency portfolio. Most of this course leads up to that picture.
A framework that outlasts the market you learn it in
Products change, tickers disappear, and interest rates move in directions no one predicted. The ideas in this course are the ones that still hold after all of that.
The course gives students the theory and the quantitative tools to understand how financial instruments are priced and how they are used in investment decisions. It is rigorous and critical about investing rather than a tour of current practice.
Students learn to value an asset from forecasts of its cash flows and the risks those cash flows carry. Common stocks get the most attention. Fixed-income securities and options each get their own full treatment. Along the way the course builds the economic and statistical models that connect risk to expected return, from Markowitz's mean–variance analysis to the CAPM and multifactor models. It then asks two questions the models leave out: who actually holds the shares, and what happens when the people trading them are not perfectly rational.
- Read the investment environment. Tell real assets from financial ones, map the asset classes, and explain how an order becomes a trade.
- Value a company from the top down. Move from the macroeconomy to the industry to the firm, and turn financial statements into a price.
- Price and hedge a bond. Link price to yield, read the term structure, and measure interest-rate risk with duration and convexity.
- Think in contingent claims. Draw the payoff of any option position and explain what drives its premium.
- Build the optimal portfolio. Quantify risk, diversify it, allocate capital, and price the risk that is left with the CAPM and factor models.
- Account for people. Explain how institutional owners shape firms and markets, and how predictable biases leave marks on prices.
The investment environment, its tools, and its machinery
Before pricing anything, we need to know what is being traded, where it trades, who stands in the middle, and what a trade costs.
Paper claims on real things
A society's wealth is its factories, land, software and know-how. A stock or a bond is a claim on the income those real assets produce, and financial markets decide who holds which claim.
Investment management is usually taught as two decisions made in order. Asset allocation decides how much goes into broad classes such as stocks, bonds and cash. Security selection then picks the specific holdings inside each class. Most of the long-run difference between two investors comes from the first decision, even though most financial news covers the second.
| Asset | Arithmetic mean | Geometric mean | Std. deviation | Worst year | $1 became |
|---|
One day, one company, one question about AI spending
After the Chinese startup DeepSeek said its R1 model cost a small fraction of what U.S. labs spend to train, Nvidia fell nearly 17% and lost about $589 billion of market value, the largest one-day loss for any U.S. company. The Nasdaq fell about 3% while the Dow rose. That split is a clear example of an industry-specific shock rather than a market-wide one, a distinction that becomes the core of Part V.
Supply the savings
They buy the claims directly or, far more often, through funds and retirement plans.
Demand the capital
They issue stocks and bonds to pay for real assets and public spending.
Stand in the middle
Banks, investment companies, insurers and pension funds pool money, spread risk and lower costs.
A field guide to what gets traded
Every instrument sits somewhere on a short list: the money market, the bond market, the equity market, and the derivatives built on top of them. Indexes summarize each of them in one number.
Why a 3.5% muni can beat a 5% corporate
Interest on most municipal bonds is exempt from federal income tax. To compare the two fairly, convert the muni yield into the taxable yield that would leave the investor with the same after-tax income.
Two ways to average a market
The Dow Jones Industrial Average adds up 30 share prices. The S&P 500 weights each firm by its market value. Move the prices below and watch the two methods disagree on what "the market" did.
Start: ABC $25 with 20M shares; XYZ $100 with 1M shares.
From an order to a price
A market is a list of standing promises: buy up to here, sell down to there. Liquidity is how much of that list you can use before the price moves against you.
| Order | What it says | What it guarantees | The risk |
|---|---|---|---|
| Market | Trade now at the best available price | Execution | The price, in a thin or fast market |
| Limit buy / sell | Trade only at this price or better | Price | It may never fill |
| Stop-loss | Become a market sell if the price falls to the stop | A trigger | Gaps: the fill can be far below the stop |
| Stop-buy | Become a market buy if the price rises to the stop | A trigger | Buying at the top of a squeeze |
Leverage cuts both ways: margin and short sales
Buying on margin means borrowing part of the purchase price from the broker. The investor's equity is the asset value minus the loan, and when equity falls below the maintenance requirement, the broker issues a margin call. A short sale runs the same logic in reverse: the loss is unlimited because the price has no ceiling.
Investment companies: what a fee really costs
Mutual funds and ETFs pool savings, diversify them and handle the administration. The price is an expense ratio, sometimes plus a load. The fee is quoted as a small percentage of assets, but it is charged every year, so its cost compounds.
| Vehicle | Priced at | Trades | Distinctive feature |
|---|---|---|---|
| Open-end mutual fund | NAV, once a day | With the fund itself | Shares created and redeemed on demand |
| Closed-end fund | Market price | On an exchange | Often trades at a discount to NAV |
| Exchange-traded fund | Market price ≈ NAV | Intraday, on an exchange | In-kind creation keeps price near NAV; tax efficient |
| Unit investment trust | NAV | Redeemed with sponsor | Fixed, unmanaged portfolio |
| Hedge fund | Periodic NAV | Restricted | Lightly regulated; leverage, shorting, performance fees |
Security analysis: from the economy to one share price
Fundamental analysis runs from the top down. Start with the economy, narrow to the industry, then read the firm's own statements and turn everything into a value per share.
The economy sets the tide
A firm's earnings depend on GDP growth, interest rates, inflation, exchange rates and policy long before they depend on its managers. An analyst has to be able to read the economy.
| Firm | Type | Beta |
|---|
Betas on the S&P 500 ETF (SPY), 60 monthly returns to Aug 2026. Firms whose sales track the cycle carry higher market sensitivity.
| Family | Moves | Examples |
|---|---|---|
| Leading | Before the economy | Yield-curve spread, building permits, initial jobless claims, new orders, stock prices, consumer expectations |
| Coincident | With the economy | Nonfarm payrolls, industrial production, personal income, manufacturing and trade sales |
| Lagging | After the economy | Duration of unemployment, inventories-to-sales, prime rate, unit labor costs, CPI for services |
A share is worth the cash it will pay
Intrinsic value is the present value of all future dividends, discounted at the return investors require. The rest of the chapter is about making that infinite sum usable.
Growth is not the same as value
Split a price into the value of the current earnings stream, if all of it were paid out, plus the present value of growth opportunities. Reinvesting creates value only when the firm earns more on new capital than its investors require.
E₁ = $5.00, k = 12.5%.
| Firm | PVGO as a share of price | Share |
|---|
The course's own calculation from the September 2, 2026 snapshot: E₁ = analysts' forward EPS, k from the CAPM with a 5% equity premium, PVGO = P₀ − E₁/k. A negative value means the market prices the firm below the value of its current earnings stream.
When growth is temporary: the two-stage model
Few firms can grow faster than the economy forever. A multistage model forecasts dividends year by year while growth is unusual, then switches to the Gordon formula once the firm matures. The classroom case is Better Mousetraps: a new product lifts growth to 20% for four years, then competitors catch up and growth falls to 5%. The last dividend was $1.00 and investors require 10%.
Valuing the firm, not just the dividend
Many firms pay little or nothing in dividends and return cash through buybacks instead. S&P 500 companies spent a record $942.5 billion on buybacks in 2024, against $629.6 billion in dividends. Free-cash-flow models avoid the problem by valuing the cash the business generates, whatever the firm later does with it.
A first dividend as a signal
Meta announced its first-ever dividend, $0.50 a quarter, together with a $50 billion buyback. The stock jumped about 20% the next day. The dividend itself was small relative to the share price; the market was reacting to what it said about management's confidence in future cash flow, which is Miller and Modigliani's information effect.
| Approach | Core question | Tools | Weak spot |
|---|---|---|---|
| Discounted cash flow | What will it pay, and how risky is that? | DDM, two- and three-stage models, FCFF/FCFE | Terminal value dominates |
| Relative (multiples) | What do similar firms sell for? | P/E, P/B, P/S, EV/EBITDA, PEG | Inherits the peers' mispricing |
| Contingent claim | What is the flexibility worth? | Option pricing on real assets | Inputs rarely observable |
Taking ROE apart
Two firms can report the same return on equity for opposite reasons. The DuPont decomposition shows which lever (margin, turnover or leverage) is producing it.
When the auditor walks away
After a short-seller report in August 2024, Super Micro Computer delayed its annual 10-K. In October its auditor, Ernst & Young, resigned, saying it could no longer rely on management's representations. Ratios can only be as good as the statements they come from, which is why earnings quality is part of the analysis.
Reading the words: textual analysis
A 10-K contains a few pages of numbers and tens of thousands of words. The words carry information the ratios miss: tone, hedging, what management chose to change, and what it left unsaid. Textual analysis turns that language into measurements that can be tested against returns, earnings and corporate outcomes, and it is now a standard part of finance research.
| Measure | The idea | What the evidence shows |
|---|---|---|
| Tone | Share of negative and positive words | Finance-specific negative words in a 10-K relate to filing-date returns, volume and later volatility. Loughran & McDonald (2011) |
| Media pessimism | Negative words in a daily market column | High pessimism predicts downward pressure on prices, followed by a reversal. Tetlock (2007) |
| Readability | Fog index, length, file size | Firms with lower earnings file harder-to-read annual reports (Li, 2008). File size is a simple, robust readability proxy (Loughran & McDonald, 2014). |
| Changes from last year | Similarity between consecutive 10-Ks | Firms that change their language substantially later underperform, and prices react slowly. Cohen, Malloy & Nguyen (2020) |
| Tone management | Tone beyond what fundamentals justify | Unusually positive tone in earnings releases predicts weaker future earnings. Huang, Teoh & Zhang (2014) |
| Deception cues | Word choice on conference calls | Linguistic models flag later-restated quarters better than chance. Larcker & Zakolyukina (2012) |
| Product text | Similarity of business descriptions | Text-based industry networks capture competitors that standard codes miss. Hoberg & Phillips (2016) |
| Political risk | Political topics in earnings-call transcripts | Firm-level political risk varies widely within industries and affects hiring and investment. Hassan et al. (2019) |
| Writing for machines | Disclosure when algorithms read filings | As machine downloads rise, firms avoid words that dictionaries score as negative. Cao, Jiang, Yang & Zhang (2023) |
| Man + machine | AI forecasts compared with analysts | An AI model beats most analysts, and combining the two does better than either alone. Cao, Jiang, Wang & Yang (2024) |
A lesson about large language models and evidence
Two widely shared working papers claimed that ChatGPT-style models could read financial statements and filings better than people. Both were withdrawn by their own authors in 2025 after replication attempts failed. The methods are promising, but a working paper is not a result until it survives replication and peer review. That standard applies to AI research as much as to anything else in this course.
Fixed income and the price of time
A bond is the cleanest valuation problem in finance: the cash flows are written in the contract. The difficulty is that the discount rate keeps changing, and this part is about measuring and managing that risk.
Price and yield move in opposite directions
A bond's price is the present value of its coupons and its principal. When market yields rise, those fixed payments are worth less today, and the price falls.
Interest-rate risk, measured
Duration turns a bond's maturity, coupon and yield into one number that answers a practical question: how much will this position lose if rates rise by one percentage point?
| Holding the rest fixed, if… | Duration | Why |
|---|---|---|
| Maturity rises | Rises (usually) | Cash flows arrive later |
| Coupon rises | Falls | More value arrives early |
| Yield rises | Falls | Distant cash flows are discounted more heavily |
| It is a zero-coupon bond | = maturity | There is only one cash flow |
| It is a perpetuity | (1+y)/y | Finite even though maturity is infinite |
Asset–liability management: duration on both sides of the balance sheet
Banks, insurers and pension funds all hold assets to meet liabilities, and both sides are exposed to interest rates. A bank funds long-term loans with deposits that can leave at any time. A pension fund owes benefits decades from now, so its liabilities have a longer duration than almost any bond it can buy. What matters is the mismatch: how far the two sides move apart when rates change.
Immunization funds a dated obligation with a portfolio whose duration equals the horizon. If rates rise, the bond loses value but its coupons are reinvested at higher rates. If rates fall, the reverse happens. With duration matched to the horizon, the two effects offset. The textbook case: a 5-year obligation of $14,693.28 funded with $10,000 of 8%, six-year bonds, whose duration is 5 years.
When the hedge itself becomes the risk: UK pension funds
UK defined-benefit pension funds used leveraged liability-driven investment (LDI) to match their long-duration liabilities. After the September 2022 fiscal announcement, 30-year gilt yields rose about 130 basis points in three trading days. Collateral calls forced funds to sell gilts, which pushed yields higher still. The Bank of England bought £19.3 billion of gilts between September 28 and October 14 to stop the spiral. The hedge was right in principle, but the leverage and collateral needed to hold it created a liquidity problem.
A duration mismatch becomes a bank run
Silicon Valley Bank had invested deposits in long-dated Treasuries and mortgage-backed securities just before the fastest rate increases in four decades. When it sold about $21 billion of securities at a $1.8 billion loss and announced a capital raise, depositors withdrew funds, and regulators closed the bank two days later. It is a real case of the asset–liability problem that immunization is meant to solve.
Indexing
Match a bond index's duration and sector weights; accept the market's pricing.
Immunization
Set asset duration equal to liability duration so price risk and reinvestment risk offset each other.
Swaps & rate bets
Substitution, intermarket spread, rate anticipation and riding the yield curve.
Contingent claims: paying for the right, not the obligation
An option splits a payoff at a threshold. That single idea covers portfolio insurance, executive pay, corporate debt and the market's fear gauge.
Build a position, see its payoff
Every option strategy is a combination of four basic shapes. Choose one below, change the inputs, and compare the value at expiration with the Black–Scholes value today.
Options inside the balance sheet
Asset–liability managers deal with options even when they never trade one. Many bonds, mortgages and deposit accounts give one side the right to change the cash flows, and that right is an option. A homeowner can refinance when rates fall. A depositor can withdraw when rates rise. A policyholder can surrender a contract. Each of these moves cash flows in the direction that hurts the institution, which is why duration alone underestimates the risk.
| Where the option sits | Who holds it | When it hurts the institution | Typical hedge |
|---|---|---|---|
| Callable bonds, mortgages, MBS | Issuer or homeowner | Rates fall: assets prepay and must be reinvested at lower yields | Receiver swaptions, interest-rate floors, callable funding |
| Deposits | Depositor | Rates rise: funds leave or demand higher rates | Payer swaptions, interest-rate caps, shorter asset duration |
| Floating-rate loans with caps | Borrower | Rates rise above the cap and asset income stops rising | Buy caps to offset |
| Insurance and annuity guarantees | Policyholder | Rates or markets fall below the guaranteed level | Floors, equity puts, dynamic hedging |
| Surrender and withdrawal rights | Policyholder | Rates rise and policyholders move money elsewhere | Liquidity buffers, surrender charges, caps |
| If this rises… | Call | Put |
|---|---|---|
| Stock price S | ↑ | ↓ |
| Strike K | ↓ | ↑ |
| Volatility σ | ↑ | ↑ |
| Time to expiration T | ↑ | ↑ (usually) |
| Interest rate r | ↑ | ↓ |
| Dividend payouts | ↓ | ↑ |
Risk, return, and the price of bearing it
Why does anyone earn more than the T-bill rate? Because they hold risk that cannot be diversified away. This part measures risk, removes the part that can be diversified, and prices the part that remains.
Ninety-eight years in one picture
Stock returns are not a single number. They are a distribution with a center, a spread and occasional very bad years, and an investor has to decide how much of that distribution to hold.
How much risk should you take?
The only free lunch in finance
Combine assets that do not move together and portfolio risk falls faster than expected return. Diversification removes firm-specific risk. Market risk remains.
Only beta gets paid
Regress a stock's return on the market's. The slope is beta, the stock's exposure to risk that cannot be diversified away. The CAPM says beta, and only beta, earns a premium.
60 monthly returns, Sep 2021 – Aug 2026, against the S&P 500 ETF (SPY). Prices from Yahoo Finance, adjusted for dividends and splits.
Market
The excess return of the value-weighted market. The CAPM's single factor.
Small minus big
Small firms minus large firms. A size premium that compensates for risks the market beta does not capture.
High minus low
High book-to-market (value) minus low (growth). Cheap, out-of-favor firms historically earned more.
Markets are made of people
Most shares are owned by institutions and traded by humans. Both facts help explain which models work and where they fail.
Who owns the firm matters
Pension funds, mutual funds, insurers, endowments and hedge funds now own most U.S. equity. They can influence management by engaging with it (voice) or by selling (exit), and their incentives depend on how long they plan to hold.
A trading rate is a horizon
A fund's turnover ratio measures how much of its portfolio it replaces. Each replacement is one sale plus one purchase, so the fraction of positions that actually change hands is half the turnover. That fraction converts directly into an average holding period.
Not all institutions are alike
Bushee (1998) sorted institutions by two habits: how often they trade and how concentrated their portfolios are. The result is still the standard way to separate owners who monitor from owners who mostly trade. Click a region to see how each type behaves and what the evidence says.
Common ownership: when every rival has the same owners
The three largest index-fund sponsors, BlackRock, Vanguard and State Street, together form the largest shareholder in most large U.S. companies. Fichtner, Heemskerk & Garcia-Bernardo (2017) put the figure at 88% of S&P 500 firms. If the same funds own every airline, do the airlines compete less hard? The question is one of the most contested in finance.
Owners of the whole industry prefer softer competition
Azar, Schmalz & Tecu (2018) estimate that airline ticket prices are higher on routes where rival carriers share more of the same owners.
The link disappears under other measures
Dennis, Gerardi & Schenone (2022) find that the result is driven by how market share enters the ownership measure, not by ownership itself. The debate continues in finance, economics and antitrust policy.
Five decades of evidence
A short reading path through the research that shapes how we think about institutional owners, from monitoring and activism to price pressure and herding.
To understand the market, understand ourselves
The models assume rational investors, but decisions are made by people. Behavioral finance studies the predictable ways people depart from the models and asks why arbitrage does not always correct the resulting prices.
Choice 1: which would you take?
Choice 2: and now?
Trading is hazardous to your wealth
Across 66,465 brokerage households in 1991–96, the most active traders earned 11.4% a year net of costs, compared with 17.9% for the market. Overconfidence is expensive.
The market could not subtract
After the Palm IPO, 3Com's own shares were priced below the value of the Palm shares it still owned, implying a negative value for the rest of 3Com. Short-sale constraints kept arbitrageurs from closing the gap.
Nine decades of research, in order
Every formula in the course comes from an argument someone first had to make. Students meet the originals, and many of their authors later received the Nobel Prize.