CFP Exam Formulas

Question 1

V=D₁/r−g

D₁ = next year’s dividend
r = the investor’s required rate of return
g = the dividend growth rate

Answer 1

Constant Growth Dividend Discount Model (DDM)

Calculates the value of a dividend-paying security (with constant dividend growth) in dollar terms.

Question 2

r=D₁/P + g

D₁= next year’s dividend
P = market price paid for a security
g = the dividend growth rate

Answer 2

Expected Rate of Return

The rate an investor should expect based on the price paid for a security.

Question 3

COV_ij=ρ_ijσ_iσ_j

ρ_ij = correlation between securities i and j
σ_i = standard deviation of security i
σ_j = standard deviation of security j

Answer 3

Covariance

Measures how one security behaves as a direct result of another.

Positive COV = aligned
Negative COV = inverse

Question 4

σ_p=√W²_i σ²_i + W²_jσ²_j + 2(W_iW_jCOV_ij

W_i = weight of stock ‘i’
W_j = weight of stock ‘j’
σ_i = standard deviation of stock ‘i’
σ_j = standard deviation of stock ‘j’
COV_ij = covariance between ‘i’ and ‘j’

Answer 4

Weighted Standard Deviation of a Two-Asset Portfolio

Provides the weighted standard deviation for a two-stock portfolio.

Question 5

β_i=COV_im / σ²_m
=P_imσ_iσ_m

σ_i = standard deviation of the individual security
ρ_im = correlation between an individual security and the market
COV_im = covariance between an individual security and the market
σ_m = standard deviation of the market

Answer 5

Beta

Provides risk as a measure of volatility relative to that of the market.

Question 6

σ_r √(∑ⁿ_t=1 (r_t−r¯)² / n

σ_r = standard deviation of results from the expected return
Σ = summation of all terms
n = number of periods being considered
r_t = actual return
r¯ = average return

Answer 6

Standard Deviation of a Population

Identifies the deviation of a single security over a series of periods of return.

Very Unlikely on Exam! More likely - Standard Devaition of a Sample

Question 7

S_r √ (∑ⁿ_t=1 (r_t−r¯)² / n−1

S_r = standard deviation of results from the expected return
Σ = summation of all terms
n = number of periods being considered
r_t = actual return
r¯ = average return

Answer 7

Standard Deviation of a Sample

Identifies the deviation of a single security over a series of periods of return.

Keystrokes HP 10bII+:
20, ∑+
15, ∑+ …
[SHIFT], 7 (x¯, y¯) = (mean)
[SHIFT], 8 (sx, sy) = (standard deviation)

Question 8

r_i=r_f+(r_m−r_f)β_i

r_i = the investor’s required rate of return
r_f = risk-free rate (T-Bill rate serves this end)
r_m = return of the market (S&P 500 or some broad index)
β_i = beta of the security being measured for the required return

Answer 8

Capital Asset Pricing Model (CAPM)

Used to determine a theoretically appropriate required rate of return of an asset.

market risk premium is the same as (r_m−r_f)

Question 9

α_p = r_p − [r_f + (r_m−r_f)β_p]

α_p = difference of return from the amount required by investors
r_p = return of the portfolio
r_f = risk-free rate of return
r_m = return of the market
β_p = Beta of the portfolio being measured

Answer 9

Jensen’s Performance Index (Alpha)

Measures the performance of a portfolio manager relative to the performance of the market.

market risk premium is the same as (r_m−r_f)

Question 10

T_p = r_p−r_f / β_p

T_p = Treynor Index
r_p = return of the portfolio
r_f = risk free rate of return
β_p = beta of the portfolio being measured

Answer 10

Treynor Ratio

Measures the risk-adjusted performance of a portfolio manager.

Need to compare 2 ore more investments. Higher is better

Use when R² > .70
If not use Sharpe ratio

Question 11

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

c = rate of interest paid on the coupon
t = number of periods to maturity
y = Yield to Maturity (as a %)

Answer 11

Duration

Identifies the length of time the discounted cash flow of a bond remains outstanding.

Question 12

ΔP / P = −D[Δy / 1+y]

ΔP = the dollar change in price.
P = price of a bond.
ΔPP = % price change of bond.
(-D) = the duration in terms of years used as a negative value.
∆y = the % change in interest rates. If they go down, this number should be negative.
1+y = 1 + yield to maturity

Answer 12

Change of Bond Price

States the change of price that will occur in a bond as interest rates change.

Question 13

IR=R_p−R_B / σ_A

R_p = return of a portfolio
R_B = return of a benchmark
σ_A = tracking error of active return

Answer 13

Information Ratio

Measures return above benchmark divided by standard deviation.

a relative (or comparative) value. Higher the better.

Question 14

EAR=(1+i/n)ⁿ−1

i = interest rate
n = number of periods

Answer 14

Effective Annual Rate

Accounts for intra-year compounding.

Question 15

TEY = r / (1−t)

r = nominal rate of return
t = investor’s marginal tax rate (as a decimal)

Answer 15

Taxable Equivalent Yield

Provides the return that is required on a taxable investment to make it equal to the return on a tax-exempt investment.

Question 16

AM=a₁+a₂+a₃+…+a_n / n

a = rate of return for given period
n = number of periods

Answer 16

Arithmetic Mean

Offers the average of a set of numerical values, calculated by adding them together and dividing by the number of terms in the set.

Question 17

S_P=r_p−r_f / σ_p

S_p = sharpe Index
r_p = return of the portfolio
r_f = risk free rate of return
σ_p = standard deviation of the portfolio being measured

Answer 17

Sharpe Ratio

Measures the risk-adjusted performance of a portfolio in terms of standard deviation.

Need to compare 2 or more investments. Higher is better

Use when R² < .70
If not use Traynor ratio

Question 18

HPR=[(1+r₁)×(1+r₂)×…(1+r_n)]−1

r = rate of return for given period
n = number of periods

Answer 18

Holding Period Return

Provides the total return received from holding an asset or portfolio of assets over a period of time.

Question 19

√(1+r1)×(1+r2)×…(1+rn)n−1

n = number of periods
r = rate of return for given period