Items on the CFP Sheet to Familiarize but not Memorize

Question 1

Dividend Growth Model

V = D1 / (r - g)
r = (D1 / P) + g

Answer 1

Example: A company plans to pay $3.00 dividends next year (4% growth). At $45 stock price:

r=3/45+0.04=0.0667+0.04=10.67%

Question 2

Holding Period Return (HPR)

HPR = (1 + r1)(1 + r2)…*(1 + rn) - 1

Answer 2

Returns: 10%, -5%, 8%
HPR = (1.10 × 0.95 × 1.08) - 1 = (1.1274) - 1 = 0.1274 or 12.74%

Question 3

Covariance = ρᵢⱼσᵢσⱼ

Answer 3

Example:
Correlation between A and B is 0.3, σA = 10%, σB = 20%.
COV = 0.3 × 0.10 × 0.20 = 0.006

Question 4

Annualized Return = ⁿ√(1+r₁)×…×(1+rₙ) - 1

Question 5

σ of portfolio with 2 risky assets = √(Wᵢ²σᵢ² + Wⱼ²σⱼ² + 2WᵢWⱼCOVᵢⱼ)

Answer 5

Example:
60% in Asset A (σ = 12%), 40% in Asset B (σ = 18%), COV = 0.008
σp = √[(0.6² × 0.12²) + (0.4² × 0.18²) + 2 × 0.6 × 0.4 × 0.008]
σp = √[0.005184 + 0.005184 + 0.00384] = √0.014208 ≈ 11.93%

Question 6

Beta

βᵢ = (ρᵢₘσᵢ)/σₘ

βᵢ = COV₍ᵢₘ₎ / σₘ² = ρ₍ᵢₘ₎ × σᵢ / σₘ

Answer 6

Correlation with market = 0.7, σᵢ = 15%, σₘ = 10%
β = 0.7 × 0.15 / 0.10 = 1.05

Question 7

Population Standard Deviation

σ = √[Σ(rₜ - r̄)²/n]

Answer 7

Example:
Returns: 5%, 7%, 6%.
Mean = 6%.
σᵣ = √[((5-6)² + (7-6)² + (6-6)²)/3] = √[(1+1+0)/3] = √(2/3) ≈ 0.8165%

Question 8

Sample Standard Deviation

S = √[Σ(rₜ - r̄)²/(n-1)]

Answer 8

Example:
Returns: 5%, 7%, 6%.
Sᵣ = √[(1+1+0)/2] = √(2/2) = 1%

Question 9

CAPM: rᵢ = rf + (rₘ - rf)βᵢ

Answer 9

Example:
Risk-free = 2%, market = 8%, β = 1.2
rᵢ = 2% + (8%-2%)×1.2 = 2% + 7.2% = 9.2%

Question 10

Jensen’s Alpha

αₚ = r̄ₚ - [r̄_f + (r̄ₘ - r̄_f)βₚ]

Answer 10

Example:
Portfolio return = 11%, risk-free = 3%, market = 9%, β = 1.1
αₚ = 11% - [3% + (9%-3%)×1.1] = 11% - [3% + 6.6%] = 11% - 9.6% = 1.4%

Question 11

Treynor Ratio

Tₚ = (r̄ₚ - r̄_f)/βₚ

Answer 11

Portfolio return = 10%, risk-free = 2%, β = 1.25
Tₚ = (10%-2%) / 1.25 = 8% / 1.25 = 6.4%

Question 12

Sharpe Ratio

Sₚ = (r̄ₚ - r̄_f)/σₚ

Answer 12

Example:
Portfolio return = 9%, risk-free = 2%, σₚ = 11%
Sₚ = (9%-2%) / 11% = 7% / 11% ≈ 0.64

Question 13

Information Ratio

IR = (Rₚ - R_B)/σ_A

Answer 13

Example:
Portfolio beats benchmark by 2%, active risk = 4%
IR = 2% / 4% = 0.5

Question 14

Macauley Duration (bond)

D = (1+y)/y - [(1+y) + t(c-y)]/[c((1+y)ᵗ -1) + y]

Answer 14

5-year bond, 6% coupon, YTM = 5%
D = (1.05/0.05) - [(1.05 + 5(0.06-0.05)) / (0.06((1.05^5)-1) + 0.05)]
D ≈ 4.46 years

Question 15

Bond Price Change (Duration Approximation)

ΔP/P ≈ -D[Δy/(1+y)]

Answer 15

Duration = 4, yield increases by 0.5% (from 5% to 5.5%)
ΔP/P = -4 × (0.005 / 1.05) ≈ -1.9%

Question 16

Taxable Equivalent Yield (TEY)

TEY = r/(1 - t)

Answer 16

Example:
Municipal bond yield = 3%, tax rate = 32%
TEY = 0.03 / (1 - 0.32) = 0.03 / 0.68 ≈ 4.41%

Question 17

Effective Annual Rate (EAR)

EAR = (1 + i/n)ⁿ - 1

Answer 17

Example:
Nominal rate = 8%, compounded quarterly (n=4)
EAR = (1 + 0.08/4)^4 - 1 = (1.02)^4 - 1 ≈ 8.24%

Question 18

Arithmetic Mean

AM = (Σaₜ)/n

Answer 18

Example:
Returns: 4%, 8%, -2%, 10%
AM = (4+8-2+10)/4 = 20/4 = 5%

Question 19

Spot Rate (N-Year)

₁R_N = [Π(1 + E(ₜr₁))]¹/ᴺ - 1

Answer 19

Example:
Year 1 rate = 2%, expected year 2 rate = 3%, expected year 3 rate = 4%
R₃ = [(1.02) × (1.03) × (1.04)]^(1/3) - 1 ≈ (1.092)^(1/3) - 1 ≈ 2.97%