What is Macaulay Duration and what is its mathematical formula?

The weighted average maturity of a bond's cash flows: MacD = [∑ (t * CF_t / (1 + y)^t)] / Bond Price, measured in years.

In M&A finance, when is an all-stock acquisition immediately accretive to the acquirer's Earnings Per Share (EPS)?

When the acquiring company trades at a higher Price-to-Earnings (P/E) multiple than the target company (excluding transaction costs and post-merger integration synergies).

What is Implied Volatility (IV) and how is it obtained from market option prices?

The forward-looking expected standard deviation of underlying asset returns implied by market option prices; calculated by numerically inverting the Black-Scholes formula using observed market premiums.

Distinguish between the Capital Market Line (CML) and the Security Market Line (SML).

The CML evaluates efficient portfolios plotting expected return against total risk (σ); the SML applies to all individual assets and portfolios, plotting expected return against systematic risk (β) based on CAPM.

What is Delta-Neutral Hedging and why does it require dynamic rebalancing?

A trading strategy creating a portfolio with net Delta = 0 to insulate against small price moves; dynamic rebalancing is required because Gamma causes Delta to change continuously as underlying price moves.

What is the Volatility Smile/Smirk observed in equity index options markets?

A pattern where deep out-of-the-money puts trade at higher implied volatilities than at-the-money options, reflecting market pricing of negative skewness and tail-risk crashes.

What is the Sortino Ratio and why is it preferred for asymmetric return profiles?

Sortino Ratio = (R_p - R_target) / Downside Deviation; it penalizes only harmful downside volatility below a target return rather than total standard deviation, which penalizes upside gains.

Define Option Theta and explain why it represents the cost of holding long options.

Theta (Θ = -∂V/∂T) measures the rate of decay of an option's market value over time; long options suffer continuous value decay as expiration approaches (negative theta).

What are the two major categories of M&A synergies?

Operating synergies (revenue enhancements through cross-selling and cost savings via economies of scale/streamlined SG&A) and Financial synergies (lower cost of capital, increased debt capacity, tax shields).

What is the Markowitz Efficient Frontier in portfolio theory?

The locus of optimal portfolios in expected return versus standard deviation space that offer the highest expected return for a defined level of risk, or the lowest risk for a given target return.

Define DV01 (Dollar Value of an 01 / PVBP).

The absolute dollar change in a bond's price or portfolio value resulting from a 1 basis point (0.01% or 0.0001) shift in yield: DV01 ≈ ModD * Price * 0.0001.

What is the Tangency Portfolio in Modern Portfolio Theory?

The unique optimal portfolio of risky assets located at the point where the Capital Allocation Line is tangent to the Efficient Frontier, maximizing the Sharpe Ratio.

What do N(d1) and N(d2) represent in the Black-Scholes-Merton option pricing framework?

N(d1) is the option Delta (the sensitivity ∂C/∂S and the replication hedge ratio); N(d2) is the risk-neutral probability that the call option finishes in-the-money at expiration (S_T > K).

What are the terminal payoff formulas for long call, short call, long put, and short put options?

Long Call: max(0, S_T - K); Short Call: -max(0, S_T - K); Long Put: max(0, K - S_T); Short Put: -max(0, K - S_T).

What is a Leveraged Buyout (LBO) and what creates shareholder equity returns in an LBO?

The acquisition of a company funded predominantly with substantial borrowed debt (60-80%); returns are generated via debt paydown using target company free cash flow (deleveraging), operational margin expansion, and exit multiple expansion.

What is the Capital Allocation Line (CAL) and what represents its slope?

A line graph showing risk-return combinations created by mixing a risk-free asset with a portfolio of risky assets; its slope is the Sharpe Ratio of the risky portfolio.

State the Sharpe Ratio formula and its interpretation.

Sharpe Ratio = (R_p - R_f) / σ_p; measures excess portfolio return earned per unit of total portfolio volatility.

Define Option Gamma and explain where it achieves its maximum value.

Gamma (Γ = ∂^2V/∂S^2 = ∂Δ/∂S) measures the rate of change of Delta relative to underlying asset price; it peaks when the option is At-The-Money (ATM) close to expiration.

How is a synthetic long stock position constructed using European options?

By purchasing a call option and selling a put option with identical strike price (K) and expiration date (T): S_0 ≈ C - P + K * e^(-r*T).

State the Black-Scholes-Merton formula for the price of a European call option.

C = S_0 * N(d_1) - K * e^(-r*T) * N(d_2), where d_1 = [ln(S_0/K) + (r + σ^2/2)*T] / (σ * √T) and d_2 = d_1 - σ * √T.

What is Modified Duration and how does it estimate bond price sensitivity to interest rate shifts?

ModD = MacD / (1 + y/m); it estimates the percentage change in bond price for a 100 bps yield change: ΔP / P ≈ -ModD * Δy.

State Put-Call Parity for European options on non-dividend paying underlying stocks.

C + K * e^(-r*T) = P + S_0, where C is call price, P is put price, K is strike, S_0 is current spot price, r is risk-free rate, and T is time to maturity.

State the Modern Portfolio Theory (MPT) formula for the variance of a two-asset portfolio.

σ_p^2 = w_1^2 * σ_1^2 + w_2^2 * σ_2^2 + 2 * w_1 * w_2 * Cov(R_1, R_2) = w_1^2 * σ_1^2 + w_2^2 * σ_2^2 + 2 * w_1 * w_2 * ρ_(1,2) * σ_1 * σ_2.

What is a Credit Default Swap (CDS) and how does it protect the buyer?

A bilateral financial contract where the protection buyer pays a periodic spread/premium to the seller in exchange for a contingent payoff if a referenced borrower suffers a defined credit event (e.g., default, restructuring).

Define Option Vega and state how implied volatility changes affect long option holders.

Vega (ν = ∂V/∂σ) measures option price sensitivity to a 1% change in implied volatility; all long calls and puts have positive Vega, gaining value when volatility expands.

What are the primary differences between forward contracts and futures contracts?

Forwards are private OTC bilateral agreements with customizable terms and settlement at maturity, bearing counterparty credit risk; Futures are standardized contracts traded on public exchanges, cleared by a central clearinghouse, and marked to market daily with margin accounts.

State the second-order Taylor expansion bond price change formula combining Modified Duration and Convexity.

ΔP / P ≈ -ModD * Δy + 0.5 * Convexity * (Δy)^2.

State the Treynor Ratio formula and explain when it is preferable to the Sharpe Ratio.

Treynor Ratio = (R_p - R_f) / β_p; preferred when evaluating sub-portfolios or funds held within a broader, well-diversified portfolio where unsystematic risk has already been diversified away.

What is a plain vanilla Interest Rate Swap and how do the counterparties exchange cash flows?

An OTC derivative agreement where one counterparty pays a fixed interest rate on a notional principal and receives a floating reference rate (e.g., SOFR), while the other party does the opposite.

What is Bond Convexity, and why is positive convexity advantageous to a bondholder?

The second derivative of bond price with respect to yield (curvature of price-yield curve); positive convexity means price rises more when yields fall than it drops when yields rise by the same amount.

Define Option Delta and state its theoretical values for call and put options.

Delta (Δ = ∂V/∂S) measures the change in option price per $1 change in underlying asset price; ranges from 0 to +1 for long calls and 0 to -1 for long puts.

State Jensen's Alpha formula and interpret what a positive alpha signifies.

α = R_p - [R_f + β_p * (R_m - R_f)]; a positive alpha signifies that the portfolio manager generated returns exceeding the risk-adjusted benchmark predicted by CAPM.

Finanzas Corporativas — Avanzado (C1/C2) 2: Derivatives, Portfolio Theory, Fixed Income Analytics & M&A

[Español] Finanzas Corporativas: Option pricing mechanics, Greeks, Black-Scholes, Modern Portfolio Theory, duration/convexity analytics, and M&A transaction dynamics

Level: advanced
Languages: es → es
Cards: 32
Markdown: Finanzas Corporativas — Avanzado (C1/C2) 2: Derivatives, Portfolio Theory, Fixed Income Analytics & M&A (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	What is Macaulay Duration and what is its mathematical formula?	The weighted average maturity of a bond's cash flows: MacD = [∑ (t * CF_t / (1 + y)^t)] / Bond Price, measured in years.
2	In M&A finance, when is an all-stock acquisition immediately accretive to the acquirer's Earnings Per Share (EPS)?	When the acquiring company trades at a higher Price-to-Earnings (P/E) multiple than the target company (excluding transaction costs and post-merger integration synergies).
3	What is Implied Volatility (IV) and how is it obtained from market option prices?	The forward-looking expected standard deviation of underlying asset returns implied by market option prices; calculated by numerically inverting the Black-Scholes formula using observed market premiums.
4	Distinguish between the Capital Market Line (CML) and the Security Market Line (SML).	The CML evaluates efficient portfolios plotting expected return against total risk (σ); the SML applies to all individual assets and portfolios, plotting expected return against systematic risk (β) based on CAPM.
5	What is Delta-Neutral Hedging and why does it require dynamic rebalancing?	A trading strategy creating a portfolio with net Delta = 0 to insulate against small price moves; dynamic rebalancing is required because Gamma causes Delta to change continuously as underlying price moves.
6	What is the Volatility Smile/Smirk observed in equity index options markets?	A pattern where deep out-of-the-money puts trade at higher implied volatilities than at-the-money options, reflecting market pricing of negative skewness and tail-risk crashes.
7	What is the Sortino Ratio and why is it preferred for asymmetric return profiles?	Sortino Ratio = (R_p - R_target) / Downside Deviation; it penalizes only harmful downside volatility below a target return rather than total standard deviation, which penalizes upside gains.
8	Define Option Theta and explain why it represents the cost of holding long options.	Theta (Θ = -∂V/∂T) measures the rate of decay of an option's market value over time; long options suffer continuous value decay as expiration approaches (negative theta).
9	What are the two major categories of M&A synergies?	Operating synergies (revenue enhancements through cross-selling and cost savings via economies of scale/streamlined SG&A) and Financial synergies (lower cost of capital, increased debt capacity, tax shields).
10	What is the Markowitz Efficient Frontier in portfolio theory?	The locus of optimal portfolios in expected return versus standard deviation space that offer the highest expected return for a defined level of risk, or the lowest risk for a given target return.
11	Define DV01 (Dollar Value of an 01 / PVBP).	The absolute dollar change in a bond's price or portfolio value resulting from a 1 basis point (0.01% or 0.0001) shift in yield: DV01 ≈ ModD * Price * 0.0001.
12	What is the Tangency Portfolio in Modern Portfolio Theory?	The unique optimal portfolio of risky assets located at the point where the Capital Allocation Line is tangent to the Efficient Frontier, maximizing the Sharpe Ratio.
13	What do N(d1) and N(d2) represent in the Black-Scholes-Merton option pricing framework?	N(d1) is the option Delta (the sensitivity ∂C/∂S and the replication hedge ratio); N(d2) is the risk-neutral probability that the call option finishes in-the-money at expiration (S_T > K).
14	What are the terminal payoff formulas for long call, short call, long put, and short put options?	Long Call: max(0, S_T - K); Short Call: -max(0, S_T - K); Long Put: max(0, K - S_T); Short Put: -max(0, K - S_T).
15	What is a Leveraged Buyout (LBO) and what creates shareholder equity returns in an LBO?	The acquisition of a company funded predominantly with substantial borrowed debt (60-80%); returns are generated via debt paydown using target company free cash flow (deleveraging), operational margin expansion, and exit multiple expansion.
16	What is the Capital Allocation Line (CAL) and what represents its slope?	A line graph showing risk-return combinations created by mixing a risk-free asset with a portfolio of risky assets; its slope is the Sharpe Ratio of the risky portfolio.
17	State the Sharpe Ratio formula and its interpretation.	Sharpe Ratio = (R_p - R_f) / σ_p; measures excess portfolio return earned per unit of total portfolio volatility.
18	Define Option Gamma and explain where it achieves its maximum value.	Gamma (Γ = ∂^2V/∂S^2 = ∂Δ/∂S) measures the rate of change of Delta relative to underlying asset price; it peaks when the option is At-The-Money (ATM) close to expiration.
19	How is a synthetic long stock position constructed using European options?	By purchasing a call option and selling a put option with identical strike price (K) and expiration date (T): S_0 ≈ C - P + K * e^(-r*T).
20	State the Black-Scholes-Merton formula for the price of a European call option.	C = S_0 * N(d_1) - K * e^(-rT) N(d_2), where d_1 = [ln(S_0/K) + (r + σ^2/2)T] / (σ √T) and d_2 = d_1 - σ * √T.
21	What is Modified Duration and how does it estimate bond price sensitivity to interest rate shifts?	ModD = MacD / (1 + y/m); it estimates the percentage change in bond price for a 100 bps yield change: ΔP / P ≈ -ModD * Δy.
22	State Put-Call Parity for European options on non-dividend paying underlying stocks.	C + K * e^(-r*T) = P + S_0, where C is call price, P is put price, K is strike, S_0 is current spot price, r is risk-free rate, and T is time to maturity.
23	State the Modern Portfolio Theory (MPT) formula for the variance of a two-asset portfolio.	σ_p^2 = w_1^2 * σ_1^2 + w_2^2 * σ_2^2 + 2 * w_1 * w_2 * Cov(R_1, R_2) = w_1^2 * σ_1^2 + w_2^2 * σ_2^2 + 2 * w_1 * w_2 * ρ_(1,2) * σ_1 * σ_2.
24	What is a Credit Default Swap (CDS) and how does it protect the buyer?	A bilateral financial contract where the protection buyer pays a periodic spread/premium to the seller in exchange for a contingent payoff if a referenced borrower suffers a defined credit event (e.g., default, restructuring).
25	Define Option Vega and state how implied volatility changes affect long option holders.	Vega (ν = ∂V/∂σ) measures option price sensitivity to a 1% change in implied volatility; all long calls and puts have positive Vega, gaining value when volatility expands.
26	What are the primary differences between forward contracts and futures contracts?	Forwards are private OTC bilateral agreements with customizable terms and settlement at maturity, bearing counterparty credit risk; Futures are standardized contracts traded on public exchanges, cleared by a central clearinghouse, and marked to market daily with margin accounts.
27	State the second-order Taylor expansion bond price change formula combining Modified Duration and Convexity.	ΔP / P ≈ -ModD * Δy + 0.5 * Convexity * (Δy)^2.
28	State the Treynor Ratio formula and explain when it is preferable to the Sharpe Ratio.	Treynor Ratio = (R_p - R_f) / β_p; preferred when evaluating sub-portfolios or funds held within a broader, well-diversified portfolio where unsystematic risk has already been diversified away.
29	What is a plain vanilla Interest Rate Swap and how do the counterparties exchange cash flows?	An OTC derivative agreement where one counterparty pays a fixed interest rate on a notional principal and receives a floating reference rate (e.g., SOFR), while the other party does the opposite.
30	What is Bond Convexity, and why is positive convexity advantageous to a bondholder?	The second derivative of bond price with respect to yield (curvature of price-yield curve); positive convexity means price rises more when yields fall than it drops when yields rise by the same amount.
31	Define Option Delta and state its theoretical values for call and put options.	Delta (Δ = ∂V/∂S) measures the change in option price per $1 change in underlying asset price; ranges from 0 to +1 for long calls and 0 to -1 for long puts.
32	State Jensen's Alpha formula and interpret what a positive alpha signifies.	α = R_p - [R_f + β_p * (R_m - R_f)]; a positive alpha signifies that the portfolio manager generated returns exceeding the risk-adjusted benchmark predicted by CAPM.