Formulas and Ratios

Question 1

V = D1 / (r-g)

Answer 1

V = value of a dividend-paying security with constant dividend growth
D1 = next year’s dividend
r = req rate of return
g = div growth rate

Question 2

r = D1 / P + g

Answer 2

r = expected rate of return
D1 = next year’s dividend
g = div growth rate

Question 3

COVij=(ρij)(σi)(σj)

Answer 3

COVij = a measurement of the behavior of one security as a direct result of another
ρij = correlation between securities i and j
σi = std dev of security i
σj = std dev of security j

Question 4

σp=√[(Wi)^2 (σ1)^2+(Wj)^2 (σj)^2 + (2WiWjCOVij)]

Answer 4

σp = standard dev of a 2 asset portfolio
Wi = weight of stock ‘i’
Wj = weight of stock ‘j’
σi = standard deviation of stock ‘i’
σj = standard deviation of stock ‘j’
COVij = covariance between ‘i’ and ‘j’

Question 5

βi=(COVim)/(σm)^2=(Pim)(σi)/(σm)

Answer 5

βi = beta, provides risk as a measure of volatility relative to that of the market
σi = standard deviation of the individual security
ρim= correlation between an individual security and the market
COVim= covariance between an individual security and the market
σm = standard deviation of the market

Question 6

Current Ratio

Answer 6

Current Assets / Current Liabilities

Question 7

Quick Ratio

Answer 7

(Current Assets - Inventories) / Current Liabilities

Question 8

Working Capital

Answer 8

Current Assets - Current Liabilities

Question 9

Inventory Turnover

Answer 9

COGS / Avg. Inventory

Question 10

Days to Sell Inventory

Answer 10

365 / Inventory Turnover

Question 11

Acct’s Receivable Turnover

Answer 11

Sales (credit) / Avg. Accounts Rec.

Question 12

Receivable Collection Period

Answer 12

365 / Accounts Rec. Turnover

Question 13

Gross Profit Margin

Answer 13

Gross Profit / Sales

Question 14

Operating Profit Margin

Answer 14

Operating Income / Revenue

Question 15

ROA

Answer 15

Return on Assets = EAT / Total Assets

Question 16

EAT

Answer 16

Earnings after tax

Question 17

ROE

Answer 17

Return on Equity = EAT / Equity

Question 18

Debt to Equity

Answer 18

(Total long - term debt) / Equity

Question 19

Times Interest Earned

Answer 19

EBIT / Interest Expense

Question 20

EBIT

Answer 20

Earnings before interest and tax

Question 21

Debt Ratio

Answer 21

Total Debt / Total Assets

Question 22

Liquidity Ratio

Answer 22

Used to determine the ability to meet short-term obligations

Question 23

Activity Ratio

Answer 23

Used to determine the relative efficiency of financial management

Question 24

Profitability Ratio

Answer 24

Used to measure relative profitability, how much money is output compared to inputs

Question 25

Debt Raio

Answer 25

Used to determine the ability to meet long-term obligations

Question 26

σr = √[(∑(rt−rbar)^2) / n]

Answer 26

σr = standard deviation (population) of results from the expected return
Σ = summation of all terms
n = number of periods being considered
rt = actual return
rbar = average return

Question 27

Sr = √ [(∑(rt−rbar)^2) / (n−1)]

Answer 27

Sr = standard deviation (sample) of results from the expected return
Σ = summation of all terms
n = number of periods being considered
rt = actual return
rbar = average return

Question 28

ri = rf + (rm−rf)βi

Answer 28

ri = CAPM - Capital Asset Pricing Model, used to determine a theoretically appropriate required rate of return of an asset
rf = risk-free rate (T-Bill)
rm = return of the market
βi = beta of the security

Question 29

αp = rp − [rf + (rm−rf)βp]

Answer 29

αp = Jensen’s Performance Index, Alpha, measures the difference of return from the amount required by investors
rp = return of the portfolio
rf = risk-free rate of return
rm = return of the market
βp = Beta of the portfolio

Question 30

Tp = (rp − rf) / βp

Answer 30

Tp = Treynor Index
rp = return of the portfolio
rf = risk free rate of return
βp = beta of the portfolio

Question 31

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

Answer 31

Duration = the length of time the discounted cash flow of a bond remains outstanding
c = rate of interest paid on the coupon
t = number of periods to maturity
y = Yield to Maturity (as a %)

Question 32

ΔP/P = −D[Δy/(1+y)]

Answer 32

ΔP = the dollar change in price
P = price of a bond
ΔP/P= % 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

Question 33

IR = (Rp−RB) / σA

Answer 33

IR = Information Ratio, which measures the return above a benchmark divided by std. dev.
RP = return of a portfolio
RB = return of a benchmark
σA = tracking error of active return

Question 34

EAR = (1 + i/n)^n − 1

Answer 34

EAR = Effective Annual Rate
i = interest rate
n = number of periods

Question 35

TEY = r / (1−t)

Answer 35

TEY = Tax Equivalent Yield, which provides the return that is required on a taxable investment to make it equal to the return on a tax-exempt investment
r = nominal rate of return
t = investor’s marginal tax rate (as a decimal)

Question 36

AM = (a1+a2+a3+…+an) / n

Answer 36

AM = Arithmetic Mean, or the average
a = rate of return for given period
n = number of periods

Question 37

SP = (rp−rf) / σp

Answer 37

Sp = Sharpe Index / Ratio, which measures the risk-adjusted performance of a portfolio in terms of std dev
rp = return of the portfolio
rf = risk free rate of return
σp = standard deviation of the portfolio being measured

Question 38

HPR = [(1+r1)×(1+r2)×…(1+rn)]−1

Answer 38

HPR = Holding period return, which provides the total return from holding an asset over a period of time
r = rate of return for given period
n = number of periods

Question 39

√[(1+r1) × (1+r2) × …(1+rn)] − 1

Answer 39

Geometric Mean = the central number in a geometric progression, also calculable as the nth root of a product of n number
r = rate of return for given period
n = rate of return for given period

Question 40

Front End PITI

Answer 40

PITI / Gross Income
28%

Question 41

Back End PITI

Answer 41

(PITI + Other Debt) / Gross Income
36%