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Formulas Flashcards

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1
Q

Sharpe Ratio

A

measures excess return per unit of risk

r_portfolio - r_free / sigma_portfolio

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2
Q

Roy’s safety first ratio

A

r_portfolio - r_target / sigma portfolio

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3
Q

Correlation and covariance

A

corr(a,b) = cov(a,b) / (sigma_a*sigmab)

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4
Q

Normal distribution, percentage:

68%, 90%, 95%, 99%

A

1 sigma, 1.65 sigma, 1.96 sigma, 2.58 sigma

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5
Q

Standard error

A

sigma_x = sigma / sqrt(n)

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6
Q

Confidence interval

A

x+- z * sigma/sqrt(n)

z = 1.645 for 90% conf int
z = 1.96 for 95% conf int
z = 2.58 for 99% conf int
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7
Q

Type I and Type II error

A

Type I: rejection of null hypothesis when it’s actually true

Type II: failure to reject null hypothesis when it’s actually false

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8
Q

Reversal patterns

A

Head and shoulders, double/triple top or bottom

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9
Q

Continuation patterns

A

Triangle, rectangles, pennants, flags

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10
Q

Own price elasticity

A

% quantity demand change / % price change
> 1, elastic
< 1, inelastic

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11
Q

Income elasticity, normal good, inferior good

A

% quantity demand change/ % income
positive, normal good
negative, inferior good (as income increase, demand decrease)

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12
Q

Cross price elasticity

A

% quantity demand change / % price of related good
positive, substitute (increase in relative good price increase own price, since people choose the substitute over the more expensive)
negative, complement

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13
Q

Sealed bid

A

Highest bid wins, pays amount bid, bids are unknown to other bidders

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14
Q

Vickery bid

A

(second price sealed bid)

Highest bid wins, pays second high bid price

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15
Q

Dutch bid

A

(descending price)

Price decline until all units can be sold, each bidder pays price bid

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16
Q

Modified dutch

A

Price declines until all units can be sold, each bidder pays last price (lowest)

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17
Q

Fiscal budget deficit, saving and trade balance equation

A

G - T = (S - I) - (X - M)

Fiscal budget deficit = Excess saving - trade balance

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18
Q

Frictional unemployment

A

Time lag in matching qualified workers with job openings

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19
Q

Structural unemployment

A

Unemployed workers do not have the skills to match newly created job

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20
Q

Cyclical unemployment

A

Economy producing at less than capacity during contraction phase of business cycle

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21
Q

Money multiplier

A

Money multiplier = 1 / Reserve requirement

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22
Q

Fiscal multiplier

A

Fiscal multiplier = 1 / (1 - MPC * (1-t))

MPC - Marginal propensity to consume
t = tax rate

Increase in aggregae demand = gov spending * fiscal multiplier.

Ex: Gov spending = $100, tax is 25%, 75 is received by other, MPC = 80%, thus additional spending by who receives gov spending = 75* 0.8 = 60.
Then this 60 is again spent at 60 0.750.8, etc..

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23
Q

Expansionary and contractionary monetary policy

A

If policy rate < neutral interest rate, is expansionary

If policy rate > neutral interest rate, is contractionary

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24
Q

Expansionary and contractionary fiscal policy

A

When budget deficit is increasing or surplus is decreasing, it is expansionary
When budget deficit is decreasing or surplus is increasing, it is contractionary

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25
Q

Real exchange rate (domestic/ foreign)

A

= nominal exchange rate * (foreign CPI) / (domestic CPI)

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26
Q

CFO calculation

A
  1. Start from net income
  2. Add noncash charge (depreciation), subtract noncash components
  3. Subtract gain (add back loss) from sales of assets (since they are CFI)
  4. Subtract gains or add loss from CFF
  5. Adjust for change in balance sheet
    Accounts receivables went up -> sales sales during the period were greater than cash collected -> subtract account receivables increase
    Basically:
    - Increase in operating asset accounts (use of cash) are subtracted
    - Increase in operating liability accounts (source of cash) are added

Need to subtract tax

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27
Q

Free Cash Flow

A

= Operating cash flow - net capital expenditures

= NI + NCC + [Int * (1 - t)] - FCInv - WCinv
NI = net income
NCC = non cash charges
Int = interest expense
t = tax rate
FCInv = fixed capital investment
WCInv = working capital investment
* Interest expense(net of tax) is added back to net income since FCFF is the cash flow available to stockholders and debt holders, interest expense are available to those people.
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28
Q

Common size balance sheet, income statement, and cash flow ratio?

A

Balance sheet: total asset
Income statement: sales
Cash flow: net revenue

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29
Q

Growth rate

A

g = RR * ROE

RR = retention rate= 1 - dividend payout ratio = 1 - dividend declared/operating income after taxes

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30
Q

DuPont analysis and extended form

A

Traditional
ROE = net profit margin * asset turnover * equity multiplier

Extended 
ROE = tax burden * interest burden * EBIT margin * asset turn over* equity multiplier
tax burden = net income / EBT
interest burden = EBT / EBIT
EBIT margin = EBIT / revenue
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31
Q

Double declining method

A

2 * (cost - accum. depreciation) / useful life

Note no salvage value

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32
Q

Revaluation of long-lived assets

A

IFRS: gain is recognized to the extent it reverse previously recognized impairment loss. Further gains recognized in equity as revaluation surplus

GAAP: not allowed

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33
Q

Pure play method

A
  1. Delever asset beta for comparable company (divided by 1 + (1-t) * D/E)
  2. Relever project beta for subject firm (multiply 1 + (1-t) * D/E)
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34
Q

Working capital

A

Current Asset - Current Liability

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35
Q

Security Market line (SML) and stock pricing

A

Return plot over the SML is underpriced

Return plot under the line is overpriced

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36
Q

Measure of excess return per unity of total risk

A

Sharpe ratio and M-Squared

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37
Q

Measure of excess return per unit of systematic risk

A

Treynor measure and Jensen’s alpha

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38
Q

Security market operational efficiency

A

Lowest possible transaction cost

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39
Q

Security market informational efficiency

A

Price rapidly adjust to new information

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40
Q

Leveraged factor

A

1 / margin percentage

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41
Q

Levered return

A

HPR * leverage factor

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42
Q

Quote-driven market

A

Investor trade with dealers

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43
Q

Order driven markets

A

buyers and sellers matched by rules

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44
Q

Brokered markets

A

bnroker find counterparties

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45
Q

Dividend Discount Model assumptions

A
  1. Stock pays dividends, constant growth rates
  2. Constant growth rate never changes
  3. Required rate of return (k) must be greater than growth (g)
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46
Q

Bullet cash flow structure (bond)

A

All principal is repaid at maturity

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47
Q

Fully amortizing cash flow structure (bond)

A

Equal periodic payments include both interest and principal

48
Q

Partially amortizing cash flow structure (bond)

A

Periodic payments including interest and principal, baloon payment at the end

49
Q

Sinking fund cash flow structure (bond)

A

Schedule for early redemption of bonds

50
Q

Floating rate cash flow structure (bond)

A

Coupon payments based on reference rate plus margin

51
Q

Bond matrix pricing

A

For illiquid bonds, use yields of bonds with same credit quality to estimate yield
Adjust for maturity differences with linear interpolation

52
Q

Issuer and currency for foreign bonds?

A

Foreign issuer, domestic currency

53
Q

Eurobond market

A

Outside any one country.

Bond is denominated in currency other than those of countries in which bonds are sold

54
Q

Underwritten offering

A

Investment banks buy entire issue, sell to public

55
Q

Best efforts offering

A

Investment bank acts like broker

56
Q

Embedded bond warrants

A

Bondholder may buy issuer’s common stock at exercise price

57
Q

Current yield (bond)

A

annual coupon / price

58
Q

Put-call parity

A

Portfolios with identical payoffs must sell for same price to prevent arbitrage

C + X / (1 + RFR)^t =
S + P

59
Q

Discontinued operations, where is it reported

A

One that management has decided to dispose of, but either has not yet done so, or has disposed in the current year after operation had generated income or loss.

Reported separately in income statement

60
Q

Unusual or infrequent items, where is it reported

A
  1. Gains of losses from sales of asset
  2. Impairments, write-offs, write downs and restructuring costs

Included in income from continuing operations and reported before tax.

61
Q

Extraordinary items

A

Not allowed in IFRS
In GAAP, it is a material transaction that is both unusual and infrequent.

Reported separately in the income statement

62
Q

Angel investing stage

A

Very early in firm’s life, often the idea stage. Funding source usually individuals rather than VC funds

63
Q

Seed stage

A

Investment made for product development, marketing, and market research

64
Q

Early stage (PE)

A

Investments made to fund initial commercial production and sales

65
Q

Later stage (PE)

A

Company already has product and sales and is operating as a commercial entity. Investment provided to expand production, increase sales

66
Q

Mezzanine-stage financing

A

Capital provided to prepare the firm for an IPO

67
Q

Significance level

A

5% significance level: 5% chance of rejecting a true null hypothesis. 95% chance of correctly rejecting the null hypothesis

68
Q

Power of test

A

Probability of rejecting the null when it is false.

Power of test = 1 - P(Type II error)

69
Q

LM Curve, X and Y axis

A

LM (Liquidity Preference/Money supply) curve illustrates a positive relationship between real income and the real interest rate, holding the real money supply constant.
X - income
Y - interest rate

70
Q

IS Curve, X and Y axis

A

IS(Investment/Saving) curve illustrates a negative relationship between real income and the real interest rate, holding the marginal propensity to save constant.
X - income
Y - interest rate

71
Q

Marginal propensity to consume

Marginal propensity to save

A

MPC: proportion of additional income spent on consumption
MPS: proportion of additional income saved

72
Q

Veblen good

A

Demand increase when price increases (such as luxury goods)

73
Q

Comprehensive income

A

= net income + other comprehensive income

It include all changes in equity except for owner contributions and distributions

74
Q

Other comprehensive income

A

Transactions that are not included in net income.

  1. Foreign currency translation gain/loss
  2. Adjustment for minimum pension liability
  3. Unrealized gain/loss from cash flow hedging derivatives
  4. Unrealized gain/loss from available-for-sale securities
75
Q

Business risk

A

Risk associated with a firm’s operating income

  1. Sales risk
  2. Operating risk
76
Q

Financial risk

A

The possibility that shareholders will lose money when they invest in a company that has debt, if the company’s cash flow proves inadequate to meet its financial obligations.

77
Q

Drags on liquidity

A

Delay or reduce cash inflows, or increase borrowing costs.

Ex: uncollected receivables, bad debts, obsolete inventory

78
Q

Pulls on liquidity

A

Accelerate on cash outflows.

Ex: paying vendor sooner.

79
Q

Dividend discount model approach (Cost of capital, k_ce)

A

P = D1/ (K - g) -> K = D1/P0 + g

where g = RR * ROE

80
Q

Bond yield plusRisk premium approach (cost of capital)

A

k_ce = bond yield + risk premium

Note YTM + Premium, do not consider tax rate

81
Q 
Bank
Risk tolerance
Investment Horizon
Liquidity needs
Income needs
A

Risk tolerance: Low
Investment Horizon: Short
Liquidity needs: High
Income needs: Pay interest

82
Q 
Endowments
Risk tolerance
Investment Horizon
Liquidity needs
Income needs
A

Risk tolerance: High
Investment Horizon: Long
Liquidity needs: Low
Income needs: Spending level

83
Q 
Insurance
Risk tolerance
Investment Horizon
Liquidity needs
Income needs
A

Risk tolerance: Low
Investment Horizon: Long (life), short - (Property&Casualty)
Liquidity needs: High
Income needs: Low

84
Q 
Mutual funds
Risk tolerance
Investment Horizon
Liquidity needs
Income needs
A

Risk tolerance: Depends
Investment Horizon: Depends
Liquidity needs: High
Income needs: Depends

85
Q 
Defined benefit pensions
Risk tolerance
Investment Horizon
Liquidity needs
Income needs
A

Risk tolerance: high
Investment Horizon: long
Liquidity needs: low
Income needs: depends

86
Q

Calculate stock covariance using beta

A

beta = covariance of asset return with market return / variance of market return
= cov_im / (sigma_m)^2

87
Q

price weighted index calculation

A

Index = sum of stock price / (number of stocks adjusted for splits)

Note, denominator must satisfy such that after split, index value remains same

88
Q

Market capitalization weighting index

A

current index value = current total market value of index stock / base year total market value of index stock * base year index

Ex, total market val change from 80 to 95, new index = 95/80*100 = 118.75

89
Q

Equal weighting index

A
  1. Calculate percent change of stock price for each stock
  2. Take average of those percent change
  3. Apply averaged change on stock index
90
Q

Stop buy/sell order

A

Stop buy: order will execute if price goes above a threshold
Stop sell: order will execute if price falls below a threshold

This is for stopping loss

91
Q

Limit buy/sell order

A

Limit buy: order will execute if price falls below a threshold
Limit sell: order will execute if price rise above a threshold

92
Q

Effective annual yield

A

EAY = (1+HPY)^(365/5) - 1

93
Q

Money market yield (CD equivalent yield)

A

MMY = 360/(#days) * HPY

94
Q

Bank discount yield (BDY)

A

BDY = D/F * 360/t
D - Difference between the face value and purchase price
F - face value
t - # days remaining until maturity

95
Q

Bond equivalent yield

A

(Face - Purchase val) / Purchase val * 365/(Days to maturity)

96
Q

Modified duration calculation

A

D = (V- - V+) / (2 V0 * deltaY)

97
Q

Arbitrage free forward exchange rate calculation

A

Forward / Spot = (1 + interest_num) / (1 + interest_den)

Ex. 1.3382 USD/EUR,Spot
Forward = 1.3382 USD/EUR * (USD Inflation) / (EUR Inflation)

98
Q

Useful lives and salvage value

A
  1. Company typically do not disclose date about estimated salvage values
  2. They are chosen by management and allow for the possibility of income manipulation.
99
Q

Held-to-maturity securities

A

Debt acquired with the intent to be held to maturity.
Subsequent change in market value is ignored

Dividends, interest income and realized gain/losses are recognized in income statement.

100
Q

Trading securities

A

Debt and equity acquired with the intent to profit over the near term.
Reported on the balance sheet at fair value.
Unrealized gains and losses are recognized in income statements.

Dividends, interest income and realized gain/losses are recognized in income statement.

101
Q

Available-for-sale securities

A

Debt and equity that are not held to maturity or trade in near term.
Reported on balance sheet at fair value
Unrealized gain/loss recognized in other comprehensive income as part of equity

Dividends, interest income and realized gain/losses are recognized in income statement.

102
Q

Nine major sections of the GIPS standards

A 
Fundamentals of compliance
Input data
Calculation methodology
Composite construction
Disclosures
Presentations and reporting
Real estate
Private equity
Wrap fee/Separately Managed Account
103
Q

Defined contribution

A

Firm contributes a sum each period to employee’s account. No promise to employee regarding future value of plan assets.

Employer contribution expensed in period incurred.

104
Q

Defined benefit

A

Firm promise to make periodic payments to employee after retirement. Employer makes contributions to a fund established to provide the promised future benefits.

Overfunded plan recognized as asset, underfunded plan recognized as liability

105
Q

Embryonic stage

A

When the industry just started.
Slow growth, customer not familiar with the product
High prices, volume is not large enough to reach economies of scale
Large investment required
High risk of failure

106
Q

Growth stage

A

Industry growth is rapid.
Rapid growth
Limited competitive pressures
Falling prices, since reaching economies of scale
Increasing profitability, due to economies of sacle

107
Q

Shakeout stage

A

Growth and profitability are slowing due to competition.
Growth has slowed.
Intense competition
Increasing industry overcapacity
Declining profitability
Increased cost cutting, restructure to survive and attempt to build brand loyalty
Increased failures

108
Q

Mature stage

A 
Little industry growth and firm begin to consolidate
Slow growth, since market is saturated
Consolidation, evolving into oligopoly
High barriers to entry
Stable pricing
Superior firms gain market share
109
Q

Decline stage

A

Industry growth is negative
Declining prices
Consolidation, firm exit or merge

110
Q

Intrinsic value of an option

A

The amount by which the option is in-the-money

111
Q

Time value of an option

A

The amount by which the option premium exceeds the intrinsic value.
Option value = intrinsic value + time value

112
Q

Hedge fund’s trading NAV is higher or lower compared to NAV in accordance with accounting standards?

A

Lower

113
Q

Relationship between mean, mode and median for positive skewness?

A

Mean > median > mode.

Think lots of weight at tail, yet median is not affected

114
Q

Coefficient of variation

A

CV = standard deviation/mean

115
Q

Calculate price elasticity of demand

A

Elasticity = percent_change_Q/percent_change_P
= (deltaQ /Q0)/(deltaP/P0)
= (P0/Q0) * (deltaQ / deltaP)
- deltaQ / deltaP is the slope

*** P0, Q0 is the middle point

CFA (11 decks)

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