Key Formulas to Remember — CFA Level I (Preparation & Exam Strategy)

You already practiced timing and exam strategies. Now stop fumbling for formulas like you forgot your coffee. This is the concentrated espresso shot: the formulas you should have tattooed on the inside of your brain (or at least on a 3x5 flashcard).

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Why this matters (building on Practice & Time Management)

You practiced pacing and full mocks, so you know: every second counts. Memorized formulas = fewer mental gymnastics, faster calculations, fewer errors. Combine this with the brain-dump at the start technique (you learned in Practice Exam Strategies) and you shave minutes off dozens of items. Also, recall Risk Management frameworks — many formulas (VaR, portfolio variance, duration) are literal links between quantitative theory and risk decisions. Learn them. Use them. Flex them on the exam.

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How to use this page

• First: keep reading like it’s a popcorn thriller — with selective highlighting.
• Second: make flashcards grouped by topic.
• Third: practice writing these from memory under 3 minutes (brain-dump).

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High-priority formulas (by topic)

Time Value of Money (TVM)

• Future value (single sum): FV = PV * (1 + r)^n
• Present value (single sum): PV = FV / (1 + r)^n
• Annuity PV: PV_ann = PMT * [1 - (1 + r)^(-n)] / r
• Perpetuity: PV_perp = PMT / r
• Growing perpetuity: PV = PMT1 / (r - g) (r > g)

Example (quick): PV of a $100 payment forever at 4% = 100 / 0.04 = 2,500.

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Fixed Income

• Price of a bond: Price = Sum[CF_t / (1 + y)^t] (coupons + redemption)
• Current yield: current yield = Annual coupon / Price
• Yield approximation (if needed): YTM is solved iteratively; use calculator
• Macaulay duration: D = (Sum[t * PV(CF_t)] / Price)
• Modified duration: D_mod = D_Mac / (1 + y)
• Approx. price change: ΔP ≈ -D_mod * Δy * P + 0.5 * Convexity * (Δy)^2 * P

Quick tip: Duration ≈ weighted average time to cash flows — tells sensitivity to yield.

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Portfolio & Asset Pricing

• Expected portfolio return: E(R_p) = Σ w_i * E(R_i)
• Portfolio variance (two assets): σ_p^2 = w1^2 σ1^2 + w2^2 σ2^2 + 2 w1 w2 Cov(1,2)
• General matrix form: σ_p^2 = w' Σ w
• CAPM (expected return): E(R_i) = R_f + β_i * [E(R_m) - R_f]
• Beta of portfolio: β_p = Σ w_i β_i
• Sharpe ratio: (R_p - R_f) / σ_p
• Treynor ratio: (R_p - R_f) / β_p
• Jensen's alpha: α = R_p - [R_f + β_p (R_m - R_f)]

Example: Two-asset variance gives real intuition about diversification; correlation matters.

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Statistics & Probability

• Arithmetic mean: x̄ = Σ x_i / n
• Geometric mean (returns): (Π (1 + r_i))^(1/n) - 1
• Variance (sample): s^2 = Σ (x_i - x̄)^2 / (n - 1)
• Standard deviation: s = sqrt(s^2)
• Covariance: Cov(X,Y) = Σ (x_i - x̄)(y_i - ȳ) / (n - 1)
• Correlation: ρ = Cov(X,Y) / (σ_X σ_Y)
• Z-score: z = (x - μ) / σ

Quick memory trick: correlation = Cov scaled between -1 and 1.

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Corporate Finance & Ratios

• WACC: WACC = Σ (w_i * r_i * (1 - T_c)) for debt components; + weight_equity * r_equity (no tax shield)
• CAPM for cost of equity: r_e = R_f + β (R_m - R_f)
• Dividend Discount Model (one-stage): P_0 = D_1 / (r - g)
• DuPont decomposition (3-step): ROE = Net profit margin * Asset turnover * Equity multiplier
• EPS: EPS = (Net income - Preferred dividends) / Weighted average shares

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Derivatives & Parity

• Forward/futures (no dividends): F_0 = S_0 * (1 + r_f)^T
• Option payoffs: Call = max(S_T - K, 0); Put = max(K - S_T, 0)
• Put-Call parity (European): C - P = S_0 - K / (1 + r)^T

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Risk Metrics (link to Risk Management)

• Portfolio VaR (parametric): VaR = z_{α} * σ_portfolio * Portfolio value (z_{α} is critical z for confidence level; use absolute value)
• Historical VaR: use empirical distribution — remember, VaR ≠ expected shortfall!

From Risk Management: you used portfolio variance and distributions. VaR is just applying those to capital at risk — memorize the z-values, and how to scale volatility across time: σ_T = σ_daily * sqrt(T).

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Study/Exam tactics for formulas (practical — you use Time Management skills here)

1. Brain-dump: Immediately write the handful of TVM, CAPM, DuPont, VaR, Duration, and NPV formulas on your scratch paper.
2. Group flashcards: By topic (TVM, fixed income, portfolio, stats). Practice 5-min recall drills daily.
3. Use mnemonics: e.g., TVM: "PV in, FV out: multiply by (1+r)^n." Shake-and-repeat.
4. Practice under timed conditions: Do formula-only quizzes in 10 minutes. If you can’t reproduce it cold, you’ll choke on exam day.
5. Work examples, not just passive reading: Write one quick numeric example after each formula until it feels wrong not knowing it.

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Quick reference table (cheat-sheet style)

Topic	Key formula(s)
TVM	FV = PV(1+r)^n ; PV = FV/(1+r)^n ; PV annuity = PMT * [1 - (1+r)^-n]/r
Bonds	Price = Σ CF_t/(1+y)^t ; Macaulay D = Σ t*PV(CF_t)/Price
Portfolio	E(R_p)=Σ w_iE(R_i) ; σ_p^2 = w'Σw
CAPM/WACC	E(R)=R_f+β(R_m-R_f) ; WACC = Σw_i r_i(1-T)
Risk	VaR = z * σ_p * Value ; σ_T = σ_daily * sqrt(T)

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Final mic-drop (closing)

Memorize the skeleton formulas. Practice them until your fingers know them by reflex. You already practiced pacing and full-mock strategies — now make formula recall automatic so exam-time thinking can be strategic instead of frantic. In other words: train your brain to be a math ninja, not a panicked calculator.

"Formulas are the muscles; practice is the gym. Skip the gym, and your brain will flail at question 12." — Your wildly helpful TA