Investment Analysis 2026 - Rebalanced Exam Flashcards

Vocabulary flashcards generated from Investment Analysis 2026 lecture transcript.

Consumption timing

Financial markets allow investors to shift consumption across time by saving or borrowing.

Indifference curves

Combinations of expected return and risk that give the same utility. More risk requires more expected return; higher risk aversion makes the curve steeper.

Investment process

Investment process: how an investor organizes portfolio decisions, including asset allocation and security selection.

Top-down vs bottom-up analysis

Top-down starts with broad asset allocation and then selects securities. Bottom-up starts with attractive individual securities and lets the portfolio composition emerge.

Active vs passive management

Active management seeks mispriced securities or market timing but has higher costs. Passive management avoids these attempts and holds a diversified portfolio at lower cost.

Money and capital markets

Money market vs capital market: Money markets contain short-term, liquid, relatively low-risk instruments. Capital markets contain longer-term and generally riskier securities. Money-market instruments: Examples include T-bills, certificates of deposit, commercial paper, bankers' acceptances, Eurodollars, repos, federal funds, brokers' calls and SOFR-linked instruments.

Common vs preferred stock

Common stock: Ownership claim with voting rights, residual claim on assets/income and limited liability. Return comes from dividends and capital gains. Preferred stock: Hybrid of debt and equity: usually fixed income and no voting power; payments are dividends rather than interest.

Financial intermediaries and investment banks

Financial intermediaries: Institutions such as investment companies, pension funds, banks and insurers that channel funds between savers and borrowers. Investment bank: Provides specialized services such as IPOs/SEOs and markets securities in the primary market.

IPO and SEO

IPO: first public sale of a firm's shares. SEO: additional equity issue by an already public firm.

SPAC

Special Purpose Acquisition Company: a listed shell company that raises cash first and later acquires a private operating company.

Bid-ask spread

Bid is the dealer's buying price; ask is the selling price. Ask minus bid is the bid-ask spread and an implicit trading cost.

HFT, dark pools and IEX

HFT uses very fast automated trading. Dark pools allow trading without displaying orders publicly. IEX uses design features intended to reduce speed advantages.

Short sale

Profit from a decline in a security price: borrow stock, sell it, later buy it back, return it, and pay the borrowing fee. $\text{Profit} = P(t=0) - P(t=1) - \text{fee}$.

Originate-to-hold/distribute and securitization

Originate to hold vs originate to distribute: Originate to hold: lender keeps originated loans. Originate to distribute: loans are originated and then sold or securitized, allowing claims on the pool to be sold to investors. Securitization: Process of pooling loans and transforming their cash flows into tradable securities.

RMBS and tranches

RMBS pool residential mortgages. Tranching divides cash flows into claims with different seniority and credit risk.

CDO and CDO-squared

A CDO pools debt exposures and issues tranches. A CDO-squared is backed partly by tranches of other CDOs, increasing structural complexity.

Credit risk and CDS

Credit risk is the risk that a borrower fails to meet promised payments. A CDS transfers default risk from protection buyer to protection seller in exchange for a premium.

Synthetic CDO

A synthetic CDO obtains credit exposure mainly through derivatives such as CDS contracts rather than by owning the underlying bonds or loans.

Systemic risk

Risk that distress at institutions or markets disrupts the broader financial system through interconnected exposures, funding problems or fire sales.

Financial-crisis mechanism

High leverage, weak underwriting, securitization, falling housing prices and interconnected credit exposures amplified losses across the financial system.

Investment companies and NAV

Investment companies pool investor funds. $\text{NAV per share} = \frac{\text{market value of assets} - \text{liabilities}}{\text{shares outstanding}}$.

Open-end vs closed-end funds

Open-end funds issue and redeem shares at NAV. Closed-end fund shares trade between investors and can trade above or below NAV.

REITs and hedge funds

REIT: Investment organization similar to a closed-end fund that invests in real estate or loans secured by real estate. Hedge fund: Investment organization with substantially less regulation than mutual funds in the lecture classification.

Mutual-fund costs

Investor returns can be reduced by loads, management fees, operating expenses and trading costs.

Mutual-fund performance

Performance should be evaluated after costs and relative to an appropriate benchmark; higher costs mechanically reduce investor returns, all else equal.

Morningstar style box

Classifies equity funds by firm size and investment style, helping investors compare funds with similar mandates.

Value vs growth stocks

Value stocks have relatively low prices compared with fundamentals such as book value; growth stocks have relatively high valuations and stronger expected growth.

Holding-period return

$r_{t+1} = \frac{P_{t+1} - P_t + D_{t+1}}{P_t}$.

Log return

$r_{t+1} = \text{ln}(P_{t+1}) - \text{ln}(P_t)$.

Empirical distribution

Probability distribution constructed from historical realized returns; counting realized returns within intervals estimates the underlying distribution.

Expected return from states

$E(r) = \frac{\text{s}}{\text{ps}} r_s$.

Normal return distribution

A normal distribution is symmetric and fully characterized by mean and variance.

Empirical returns and fat tails

Empirical asset returns often show more extreme observations than the normal distribution; fat tails imply extreme returns occur more frequently.

Risk profile

A return distribution is summarized not only by expected return but also by dispersion and tail behavior.

Return risk and future wealth

Uncertain returns imply uncertain future wealth; greater return volatility produces a wider distribution of possible future wealth.

Value at Risk

One-number summary combining expected return and risk. A 95% one-year VaR sets a loss threshold exceeded with 5% probability.

Value at Risk (95%)

$\text{VaR}_t = W_t (1.645 \times \text{sd} - \text{mean})$.

Interpretation of 95% VaR

If VaR = 19.81, there is a 5% probability the portfolio loses more than 19.81 over the specified period. VaR gives a threshold, not the size of losses beyond it.

Log-return approximation

For small returns: $\text{ln}(1 + r) \text{ is approximately } r$.

Additivity of log returns

$r_{0,T} = \frac{\text{sum}_{t=1}^T}{r_t}$.

Expected return across horizons

$\text{mean}_{\text{LF}} = H \times \text{mean}_{\text{HF}}$.

Variance and volatility across horizons

$\text{var}_{\text{LF}} = H \times \text{var}_{\text{HF}}\text{; therefore } \text{sd}_{\text{LF}} = \text{sqrt}(H) \times \text{sd}_{\text{HF}}$.

VaR across horizons

$\text{VaR}_{t,\text{annual}} = W_t (1.64 \times \text{sd}_{\text{annual}} - \text{mean}_{\text{annual}})$.

Risk premium vs Excess return

Excess return is realized risky return minus $R(f)$. Risk premium is expected excess return: $E[R(p)] - R(f)$.

Mean-variance utility

$U = E(r) - \frac{1}{2} A \text{var}(r)$.

Mean-Variance Indifference Curve

Combinations of expected return and risk giving equal utility. More risk requires more expected return. Higher A means greater risk aversion and a steeper indifference curve. An investor's own indifference curves cannot intersect; curves of different investors can.

Diversification and covariance

Diversification: Holding many risky assets can reduce portfolio risk because firm-specific risk diversifies away. Diversification cannot eliminate systematic risk. Diversification insight: covariance: In a well-diversified portfolio, a security's contribution to portfolio risk depends on its covariance with other securities, not simply on its own variance.

Covariance matrix ̓

Covariance matrix contains variances on the diagonal and covariances off-diagonal; $\text{cov}_{ij} = \text{corr}_{ij} \text{sd}_i \text{sd}_j$.

Variance of an N-asset portfolio

$\text{var}_p = \frac{\text{sum}_i \text{sum}_j}{w_i w_j \text{cov}(r_i, r_j)}$.

Diversification as n increases

Equal-weighted portfolio variance: With $w_i = \frac{1}{n}$, portfolio variance contains n variance terms and n(n-1) covariance terms. Diversification as n approaches infinity: Individual variance is diversified away; portfolio variance approaches the common covariance component.

Certainty equivalent

The risk-free rate that gives the same utility as the risky portfolio.

Complete portfolio: one risky portfolio + risk-free asset

$E(r_C) = y E(r_p) + (1-y) r_f = r_f + y [E(r_p) - r_f]$. $\text{sd}_C = y \text{sd}_p$.

Capital Allocation Line (CAL)

$E(r_C) = r_f + \frac{\text{sd}_C}{\text{sd}_p} [E(r_p) - r_f]$.

Sharpe ratio

$S = \frac{E(r_p) - r_f}{\text{sd}_p}$.

Optimal risky allocation

$y^* = \frac{E(r_p) - r_f}{A \text{var}_p}$.

Expected return: two risky assets

$E(r_p) = w_D E(r_D) + w_E E(r_E)\text{, with } w_D + w_E = 1$.

Variance: two risky assets

$\text{var}_p = w_D^2 \text{var}_D + w_E^2 \text{var}_E + 2 w_D w_E \text{cov}_{DE}$.

Perfect positive correlation

When rho=1, portfolio SD is the weighted sum of asset SDs. The assets move perfectly together, so there is no diversification benefit.

Perfect Hedge Asset

With rho=-1, suitable weights can produce sigma_P=0, giving a perfect hedge.

Global Minimum Variance Portfolio

Portfolio of risky assets with the lowest possible variance. Its weights depend on the covariance structure, not on expected returns.

Efficient frontier

Set of risky portfolios offering the highest expected return for a given risk; it starts at the GMV portfolio.

Optimal portfolio without a risk-free asset

Investor chooses the point on the efficient frontier tangent to the highest attainable indifference curve; the choice depends on risk aversion A.

Tangency portfolio

With a risk-free asset, choose the risky portfolio that maximizes the Sharpe ratio; the CAL from r_f is tangent to the efficient frontier.

Finding the optimal complete portfolio

First find tangency portfolio P, then choose $y^* = \frac{E(r_P) - r_f}{A \text{sd}_P^2}$; invest 1-y* in the risk-free asset.

Mean-Variance Frontier with K Risky Assets

Contains the minimum-variance portfolio for every target expected return. The upper and lower boundary forms the mean-variance frontier.

Efficient portfolios with K risky assets

An efficient portfolio gives the highest expected return for a given variance; only the upper part of the mean-variance frontier is efficient.

Optimal complete portfolio with K risky assets: three-stage approach

1. Find efficient frontier. 2. Find tangency portfolio by maximizing Sharpe ratio. 3. Combine tangency portfolio with rf according to investor risk aversion.

Portfolio weight vector

For K risky assets, w is the weight vector and vector_iota is a K x 1 vector of ones. w_{rf} = 1 - w' \text{vector_iota}.

Excess-return vector

r^e = r_p - r_f \text{vector_iota}; $\text{mean}^e = E(r^e)$; $\text{var}(r^e) = \text{Sigma}$.

Mean-variance optimization in matrix notation

$\text{max}_w r_f + w' \text{mean}^e - \frac{1}{2} A w' \text{Sigma} w$.

Optimal weights in matrix notation

FOC(w): $\text{mean}^e - A \text{Sigma} w = 0$. $w^* = A^{-1} \text{Sigma}^{-1} \text{mean}^e$; w_{rf} = 1 - w^{*\text{T}} \text{vector_iota} = 1 - \text{vector_iota}' w^*.

Exogenous Risk

Risk from an asset/exposure already given and not freely tradable as part of the investor's portfolio choice.

Portfolio with Exogenous risk

With K risky assets and existing position q in an asset with return $r_q$, r_C = r_f + w' (r^e - r_f \text{vector_iota}) + q r_q. Investor optimizes w, not q.

Mean and Variance with Exogenous Risk

Expected return includes $q \text{mean}_q$; variance includes $w' \text{Sigma} w$, the exogenous-risk variance, and covariance between tradable assets and the exogenous exposure.

Optimal portfolio with exogenous risk

$w_q^* = A^{-1} \text{Sigma}^{-1} \text{mean}^e - q \text{Sigma}^{-1} \text{cov}_{rq}$.

Speculative Demand

$A^{-1} \text{Sigma}^{-1} \text{mean}^e$: the portfolio the investor would optimally choose without the exogenous risk.

Hedging Demand

$q \text{Sigma}^{-1} \text{sd}_{rq}$: tradable-asset exposure that replicates the exogenous risk and is subtracted from speculative demand.

Exogenous Risk: Portfolio intuition

Desired portfolio equals the optimal portfolio without exogenous risk minus the tradable exposure already effectively held through the exogenous asset.

Hedging demand via OLS

Regress exogenous-asset return on tradable-asset returns. The regression coefficients describe how the exogenous exposure can be replicated using tradable assets.

Market Portfolio M

Portfolio containing all risky assets weighted by market values. Aggregating investors makes lending/borrowing cancel, leaving the market portfolio as the aggregate risky portfolio.

Market price of risk

$\frac{E(r_M) - r_f}{\text{sd}_M^2}$.

CAPM

$E(r_i) = r_f + \text{beta}_i [E(r_M) - r_f]$.

Beta

$\text{beta}_i = \frac{\text{cov}(r_i, r_M)}{\text{sd}_M^2}$.

Security Market Line

Graphical CAPM relation: x-axis beta, y-axis expected return, intercept r_f, slope E(r_M)-r_f.

CML vs SML

CML: efficient portfolios, risk measured by standard deviation. SML: individual assets/portfolios, risk measured by beta.

Alpha

$\text{alpha}_i = E(r_i) - (r_f + \text{beta}_i [E(r_M) - r_f])$.

Time-series CAPM test

$r_{it} - r_{ft} = \text{alpha}_i + \text{beta}_i (r_{mt} - r_{ft}) + \text{error}_{it}$. Test whether alpha_i differs significantly from zero.

Cross-sectional CAPM test

CAPM predicts cross-sectional differences in expected returns are explained by beta: expected returns should be linearly related to beta and nothing else.

Fama-MacBeth regression

For period t: $r_{it} = \text{gamma}_0 + \text{beta}_{it} \text{gamma}_1 + x_{i,t-1} \text{gamma}_2 + \text{error}_{it}$.

Beta estimation in Fama-MacBeth

Beta is unobserved and estimated from pre-period time-series data. Estimated beta contains measurement error because it is not the true beta.

Fama and French 1992

Cross-sectional study of stock returns using portfolios based on size and beta. Finds little/no beta-return relation; size is negatively related to returns and book-to-market also matters.

Fama-French three factor model

Extends CAPM with market beta, SMB (Small Minus Big, size) and HML (High Minus Low, book-to-market) to explain patterns beta alone does not.

Momentum

Stocks that performed well over the past six months tend to have higher expected returns over the next six months; often added as an additional factor.

Tangency portfolio in matrix notation

w_{\text{tangency}} = \frac{\text{Sigma}^{-1} \text{mean}^e}{\text{vector_iota}' \text{Sigma}^{-1} \text{mean}^e}.

Three-stage approach versus Big Bang approach

The three-stage approach finds the optimal complete portfolio by: (1) constructing the efficient frontier of risky assets, (2) finding the tangency portfolio by maximizing the Sharpe ratio, and (3) choosing the allocation between the tangency portfolio and the risk-free asset according to risk aversion A. The Big Bang approach directly obtains the optimal complete risky-asset weights with $w^* = A^{-1} \text{Sigma}^{-1} \text{mean}^e$.

Complete-portfolio vs tangency weights

w_{\text{tangency}} = \frac{w^*}{\text{vector_iota}' w^*}.

Variance and SD from state probabilities

$\text{var}(r) = \frac{\text{sum}_s}{\text{ps}} (r_s - E(r))^2\text{; } \text{sd}(r) = \text{sqrt}(\text{var}(r))$.

Mean-variance dominance

A portfolio dominates another if it has higher expected return with no more risk, or lower risk with no lower expected return.

Risk aversion and position on the CAL

On the same CAL, a more risk-averse investor chooses less exposure to the tangency portfolio and a point closer to r_f. A less risk-averse investor chooses more risky exposure and may borrow at r_f if y*>1.

Primary vs secondary market

Primary market: newly issued securities; issuer receives the proceeds. Secondary market: existing securities trade among investors.