CFA Level I · Cheat Sheet
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| Problem Type | Formula | Key Adjustment | ||
|---|---|---|---|---|
| Single Lump Sum | FV = PV × (1 + r)^N | Solve for any variable | ||
| PV = FV / (1 + r)^N | ||||
| Ordinary Annuity (end of period) | PV = PMT × [1 – (1+r)^(–N)] / r | Most common in CFA | ||
| FV = PMT × [(1+r)^N – 1] / r | ||||
| Annuity Due (beginning of period) | Multiply ordinary annuity by (1 + r) | Worth MORE than ordinary | ||
| Perpetuity (pays forever) | PV = PMT / r | No N variable | ||
| Effective Annual Rate (EAR) | EAR = (1 + APR/m)^m – 1 | m = compounding periods/year | ||
| Continuous Compounding | EAR = e^r – 1 | Rare but possible | ||
| Scenario | Setup | Answer | ||
| Mortgage ($200k, 6% annual, 30 years) | Monthly rate = 0.5%, N = 360; solve for PMT | ~$1,199/month | ||
| Endowment (pay $500k/year forever, 5% return) | PV = $500k / 0.05 | $10,000,000 needed | ||
| Multi-cash flows ($10k in 5yr + $15k in 8yr, 7% discount) | Discount each separately; sum PVs | ~$15,868 total PV | ||
| Mean Type | Formula / Use | When to Use | ||
| Arithmetic Mean | Σ(X_i) / N | Expected return in ONE future period | ||
| Geometric Mean | [(1+R₁)(1+R₂)…(1+Rₙ)]^(1/n) – 1 | Actual compound return over multiple periods | ||
| Weighted Mean | Σ(w_i × X_i) | Portfolio return; unequal data weights | ||
| Median | Middle value when ordered | Skewed data; outliers present | ||
| Mode | Most frequent value | Categorical data | ||
| Measure | Formula | Use | ||
| Variance | Σ(X_i – mean)² / (n–1) | Note: n–1 for sample (Bessel's correction) | ||
| Standard Deviation (σ) | √Variance | Risk in original units; most common in finance | ||
| Coefficient of Variation (CV) | σ / mean | Compare risk across assets with different returns | ||
| Range | Max – Min | Quick spread measure; sensitive to outliers | ||
| Property | Characteristic | Finance Implication | ||
| Skewness = 0 | Symmetric distribution | Mean = Median = Mode | ||
| Positive Skewness | Long right tail; mean > median | Upside surprise potential | ||
| Negative Skewness | Long left tail; mean < median | DANGEROUS: large losses more likely | ||
| Excess Kurtosis > 0 | Fatter tails than normal | More extreme events (2008 crisis pattern) | ||
| Excess Kurtosis = 0 | Normal distribution | 68–95–99.7 rule applies | ||
| Rule | Coverage | Notes | ||
| Chebyshev's Inequality | ≥ (1 – 1/k²) within k σ | Works for ANY distribution | ||
| k=2: ≥ 75% | k=3: ≥ 89% | Non-parametric; conservative | ||
| Normal Distribution | 68% within 1σ | 95.4% within 2σ | 99.7% within 3σ | Parametric; assumes normality |
| Pair | Distinction | |||
| Arithmetic vs. Geometric Mean | Arithmetic = single-period expected return; Geometric = multi-period realized compound return | |||
| Ordinary Annuity vs. Annuity Due | Ordinary: payments END of period; Due: payments BEGIN of period (multiply by 1+r) | |||
| Variance vs. Standard Deviation | Variance is squared; Std Dev in original units; use Std Dev for risk comparisons | |||
| APR vs. EAR | APR is stated rate; EAR accounts for intra-year compounding; compare investments using EAR | |||
| Sample Variance (n–1) vs. Population Variance (n) | Use |
Aligned to the CFA Institute Level I curriculum.
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