Investments Final exam Info

Comprehensive practice flashcards reviewing modern portfolio theory, asset pricing models (CAPM, index models, SML), regression analytics, and income-producing commercial/multi-family real estate fundamentals.

Capital Market Line (CML)

The line representing efficient portfolios formed by combining the risk-free asset and the market portfolio under CAPM assumptions, defined by the equation $E(R_p) = R_f + [E(R_M) - R_f] \times \frac{\sigma_p}{\sigma_M}$.

Systematic Risk

Market-wide, nondiversifiable risk caused by economy-wide shocks (such as recessions or interest rate changes) that affects many securities and is priced under the CAPM.

Unsystematic Risk

Firm-specific or idiosyncratic risk resulting from unique company events (such as a product recall) that can be eliminated through diversification in a broad portfolio.

Beta ($\beta$)

A measure of a security's sensitivity to market movements in a linear covariance sense, defined mathematically as $\beta_i = \frac{\text{Cov}(R_i, R_M)}{\text{Var}(R_M)}$.

Market Risk Premium

The expected return of the market portfolio in excess of the risk-free rate, expressed as $E(R_M) - R_f$, representing a forward-looking forecast rather than a known constant.

Capital Asset Pricing Model (CAPM) Equation

The equilibrium asset pricing relationship stating that an asset's required expected return equals the risk-free rate plus its beta times the market risk premium: $E(R_i) = R_f + \beta_i [E(R_M) - R_f]$.

Portfolio Beta

The weighted average of the constituent asset betas in a fully invested portfolio, calculated as $\beta_P = \sum w_i \beta_i$.

Global Minimum Variance Portfolio (GMVP)

The portfolio of risky assets that produces the lowest possible portfolio variance and standard deviation, obtained by optimizing weights subject to $\sum w_i = 1$ and long-only constraints ($w_i \ge 0$).

Maximum Sharpe Portfolio

The optimal risky tangency portfolio that maximizes the Sharpe ratio, offering the steepest capital allocation line and the highest excess return per unit of total risk.

Multi-Asset Portfolio Variance (Matrix Form)

The mathematical formula used to compute portfolio variance across multiple risky assets using the covariance matrix $\mathbf{\Sigma}$, expressed as $\sigma_P^2 = \mathbf{w}'\mathbf{\Sigma}\mathbf{w}$.

Complete Portfolio

An investor-specific allocation combining the optimal risky portfolio and the risk-free asset (such as T-bills) based on an individual's personal risk tolerance.

Efficient Frontier

The set of optimal portfolios within the feasible set that maximizes expected return for each level of standard deviation, or minimizes standard deviation for a given target expected return.

Separation Property

The investment principle dividing portfolio choice into two independent tasks: first determining the optimal risky portfolio (identical for all investors), and second choosing the allocation between that risky portfolio and the risk-free asset.

Single-Index Model

A linear asset pricing model relating security returns to a single common market factor plus a firm-specific surprise, given by $R_i = \alpha_i + \beta_i R_M + e_i$.

Single-Index Variance Decomposition

The partitioning of an individual security's total variance into systematic variance and firm-specific (residual) variance, calculated as $\sigma_i^2 = \beta_i^2 \sigma_M^2 + \sigma^2(e_i)$.

Sharpe Ratio ($S_P$)

A measure of risk-adjusted performance that calculates the expected excess return earned per unit of total portfolio risk: $S_P = \frac{E(r_P) - r_f}{\sigma_P}$.

Capital Allocation Line (CAL)

A straight line depicting the risk-return combinations available by mixing a risk-free asset with a specific risky portfolio, expressed by the equation $E(r_C) = r_f + S_P \sigma_C$.

Diversification Benefit ($DB$)

The measure of how much portfolio standard deviation falls below the weighted average of individual asset standard deviations in a long-only two-asset portfolio: $DB = w_A \sigma_A + w_B \sigma_B - \sigma_P$.

Two-Asset Minimum-Variance Weight ($w_A^{MVP}$)

The mathematical formula for the weight assigned to asset A that minimizes total portfolio risk: $w_A^{MVP} = \frac{\sigma_B^2 - \text{Cov}(A,B)}{\sigma_A^2 + \sigma_B^2 - 2\,\text{Cov}(A,B)}$.

Target-Return Weight Formula

The formula used to determine the exact weight required in asset A to achieve a specified portfolio expected return: $w_A = \frac{E(r_{\text{Target}}) - E(r_B)}{E(r_A) - E(r_B)}$.

Investment Opportunity Set

The plotted curve of all possible combinations of expected return and standard deviation generated by varying the weights across available risky assets.

Mean–Variance Criterion

The rule establishing that portfolio A dominates portfolio B if $E(r_A) \ge E(r_B)$ and $\sigma_A \le \sigma_B$, with at least one inequality being strict.

Two-Asset Portfolio Variance Formula

The equation determining total risk for two risky assets: $\sigma_P^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \text{Cov}(A,B)$, where the interaction covariance term drives diversification.

Covariance from Correlation Formula

The formula calculating covariance between two assets from their correlation coefficient and individual standard deviations: $\text{Cov}(A,B) = \rho_{AB} \sigma_A \sigma_B$.

Expected Return ($E(r)$)

The probability-weighted mean of all potential return outcomes across economic states, calculated as $E(r) = \sum p_s r_s$.

Covariance ($\text{Cov}(r_A, r_B)$)

A statistical measure indicating whether return deviations from expected values for two assets tend to occur together, calculated as $\text{Cov}(r_A, r_B) = \sum p_s [r_{A,s} - E(r_A)][r_{B,s} - E(r_B)]$.

Correlation Coefficient ($\rho_{AB}$)

A standardized measure of the linear co-movement between two asset returns, bounded between $-1.00$ and $+1.00$, defined as $\rho_{AB} = \frac{\text{Cov}(r_A, r_B)}{\sigma_A \sigma_B}$.

Security Market Line (SML)

The visual benchmark line plotting expected return against systematic risk (beta) for all securities priced under CAPM, featuring a vertical intercept of $R_f$ and a slope equal to the market risk premium $E(R_M) - R_f$.

Forecast Alpha ($\alpha$)

The abnormal expected return of a security calculated as the difference between its independently estimated forecast return and its CAPM-required return: $\alpha = E(R_i) - [R_f + \beta_i (E(R_M) - R_f)]$.

Security Characteristic Line (SCL)

A fitted linear regression line plotting a security's historical excess return against the market's excess return, where the regression slope equals estimated beta ($\beta$) and the intercept equals regression alpha ($\alpha$).

Coefficient of Determination ($R^2$)

A regression statistic measuring the proportion of total sample variance in a security's excess return that is explained by the market excess return regressor.

Multi-Family Housing

Income-producing residential properties consisting of structures designed to house 5 or more families at the same time, as distinguished from 1-to-4 family single-family residences.

Market Absorption Rate

The period of time required for a newly constructed or renovated commercial property to lease up and reach a positive operational net cash flow.

Debt Service Coverage Ratio (DSC / DSCR)

A commercial lending underwriting capacity metric comparing cash flow to scheduled debt obligations, typically requiring a minimum threshold of $1.25$ or higher.

Effective Gross Income (EGI)

The total realized gross revenue of an income-producing property, calculated as Rental Income plus Other Income minus Vacancy and Collection Allowance minus Concessions.

Net Operating Income (NOI)

The net cash flow generated by an income-producing property before debt service, calculated as Effective Gross Income (EGI) minus Operating Expenses minus Capital Expenditures/Improvement Allowances.

Gross (Full-Service) Lease

A commercial property lease structure in which the landlord/owner pays all operating expenses while the tenant pays a fixed base monthly rent.

Triple Net (NNN) Lease

A lease agreement requiring the tenant to pay base rent plus utilities, property taxes, insurance, and specified capital/maintenance expenses.

Common Area Maintenance (CAM)

A pro rata fee charged to commercial tenants in multi-tenant properties to cover the shared maintenance costs of communal areas such as hallways, parking lots, landscaping, and security.