Present Value & Asset Pricing Flashcards

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Present Value

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The current worth of a future cash flow discounted at a rate. It is calculated as $PV = \frac{C}{(1+r)^t}$ for a single cash flow of $C$ received in $t$ years.

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Perpetuity PV

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A perpetuity pays a fixed cash flow $C$ forever. Its present value equals $PV = \frac{C}{r}$, highlighting the inverse relationship between payment size and required return.

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Annuity PV

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An annuity pays $C$ each period for a finite number of periods $n$. The present value is $PV = C \cdot \frac{1 - (1+r)^{-n}}{r}$, reflecting thefinite horizon discounting.

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Net Present Value

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NPV is the sum of the present values of all cash flows from a project minus the initial investment. A positive NPV means the project adds value and should be undertaken.

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Yield to Maturity

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YTM is the discount rate that makes the present value of all a bond's cash flows equal to its market price. It reflects the overall expected return if held to maturity.

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Bond Valuation

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Bonds are valued by discounting their predetermined cash flows (coupons and principal) at the appropriate rate. Price moves inversely with yields: as yields rise, prices fall.

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Stock Valuation

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Stocks are valued by the present value of expected future dividends and prices, with the Gordon Growth Model often used for steady growth: $P_0 = \frac{D_1}{r - g}$.

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Gordon Growth Model

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The price today when dividends grow at rate $g$ is $P_0 = \dfrac{D_1}{r - g}$, where $D_1$ is the next-period dividend and $r$ is the required return.

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CAPM

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CAPM links risk and expected return: $E(R_j) = R_f + \beta_j \, [E(R_M) - R_f]$, where $\beta_j$ measures a stock's sensitivity to the market.

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Market Efficiency

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Market efficiency forms (Weak, Semi-Strong, Strong) describe how quickly prices reflect information. Weak-form uses past prices; strong-form includes private information.

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Beta

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Beta measures a security's systematic risk relative to the market. A beta > 1 implies higher sensitivity to market moves; < 1 implies lower sensitivity.

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Forward Pricing

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For an asset with continuous yield $q$, the forward price is $F_{0,T} = S_0 \, e^{(r - q)T}$; without dividends, $F_{0,T} = S_0 e^{rT}$.

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Margin in Futures

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Margin accounts require an initial margin and maintenance margin. Prices are marked to market daily, and margin calls occur if the balance falls below the maintenance level.

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Options: Payoff

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A long call payoff is $\max(S_T - K, 0)$, while a long put payoff is $\max(K - S_T, 0)$. This defines the asymmetric risk-reward of option positions.

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Put-Call Parity

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Put-call parity states $C - P = S_0 - K e^{-rT}$, linking the prices of calls and puts with the same strike and maturity to prevent arbitrage.

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Binomial Pricing

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In a one-period binomial model, the risk-neutral probability is $q = (e^{r\Delta t} - d)/(u - d)$, and option prices are computed by replication or risk-neutral expectation.