Formulas Flashcards
Sharpe Ratio
measures excess return per unit of risk
r_portfolio - r_free / sigma_portfolio
Roy’s safety first ratio
r_portfolio - r_target / sigma portfolio
Correlation and covariance
corr(a,b) = cov(a,b) / (sigma_a*sigmab)
Normal distribution, percentage:
68%, 90%, 95%, 99%
1 sigma, 1.65 sigma, 1.96 sigma, 2.58 sigma
Standard error
sigma_x = sigma / sqrt(n)
Confidence interval
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
Type I and Type II error
Type I: rejection of null hypothesis when it’s actually true
Type II: failure to reject null hypothesis when it’s actually false
Reversal patterns
Head and shoulders, double/triple top or bottom
Continuation patterns
Triangle, rectangles, pennants, flags
Own price elasticity
% quantity demand change / % price change
> 1, elastic
< 1, inelastic
Income elasticity, normal good, inferior good
% quantity demand change/ % income
positive, normal good
negative, inferior good (as income increase, demand decrease)
Cross price elasticity
% 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
Sealed bid
Highest bid wins, pays amount bid, bids are unknown to other bidders
Vickery bid
(second price sealed bid)
Highest bid wins, pays second high bid price
Dutch bid
(descending price)
Price decline until all units can be sold, each bidder pays price bid
Modified dutch
Price declines until all units can be sold, each bidder pays last price (lowest)
Fiscal budget deficit, saving and trade balance equation
G - T = (S - I) - (X - M)
Fiscal budget deficit = Excess saving - trade balance
Frictional unemployment
Time lag in matching qualified workers with job openings
Structural unemployment
Unemployed workers do not have the skills to match newly created job
Cyclical unemployment
Economy producing at less than capacity during contraction phase of business cycle
Money multiplier
Money multiplier = 1 / Reserve requirement
Fiscal multiplier
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..
Expansionary and contractionary monetary policy
If policy rate < neutral interest rate, is expansionary
If policy rate > neutral interest rate, is contractionary
Expansionary and contractionary fiscal policy
When budget deficit is increasing or surplus is decreasing, it is expansionary
When budget deficit is decreasing or surplus is increasing, it is contractionary
Real exchange rate (domestic/ foreign)
= nominal exchange rate * (foreign CPI) / (domestic CPI)
CFO calculation
- Start from net income
- Add noncash charge (depreciation), subtract noncash components
- Subtract gain (add back loss) from sales of assets (since they are CFI)
- Subtract gains or add loss from CFF
- 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
Free Cash Flow
= 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.
Common size balance sheet, income statement, and cash flow ratio?
Balance sheet: total asset
Income statement: sales
Cash flow: net revenue
Growth rate
g = RR * ROE
RR = retention rate= 1 - dividend payout ratio = 1 - dividend declared/operating income after taxes
DuPont analysis and extended form
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
Double declining method
2 * (cost - accum. depreciation) / useful life
Note no salvage value
Revaluation of long-lived assets
IFRS: gain is recognized to the extent it reverse previously recognized impairment loss. Further gains recognized in equity as revaluation surplus
GAAP: not allowed
Pure play method
- Delever asset beta for comparable company (divided by 1 + (1-t) * D/E)
- Relever project beta for subject firm (multiply 1 + (1-t) * D/E)
Working capital
Current Asset - Current Liability
Security Market line (SML) and stock pricing
Return plot over the SML is underpriced
Return plot under the line is overpriced
Measure of excess return per unity of total risk
Sharpe ratio and M-Squared
Measure of excess return per unit of systematic risk
Treynor measure and Jensen’s alpha
Security market operational efficiency
Lowest possible transaction cost
Security market informational efficiency
Price rapidly adjust to new information
Leveraged factor
1 / margin percentage
Levered return
HPR * leverage factor
Quote-driven market
Investor trade with dealers
Order driven markets
buyers and sellers matched by rules
Brokered markets
bnroker find counterparties
Dividend Discount Model assumptions
- Stock pays dividends, constant growth rates
- Constant growth rate never changes
- Required rate of return (k) must be greater than growth (g)
Bullet cash flow structure (bond)
All principal is repaid at maturity
Fully amortizing cash flow structure (bond)
Equal periodic payments include both interest and principal
Partially amortizing cash flow structure (bond)
Periodic payments including interest and principal, baloon payment at the end
Sinking fund cash flow structure (bond)
Schedule for early redemption of bonds
Floating rate cash flow structure (bond)
Coupon payments based on reference rate plus margin
Bond matrix pricing
For illiquid bonds, use yields of bonds with same credit quality to estimate yield
Adjust for maturity differences with linear interpolation
Issuer and currency for foreign bonds?
Foreign issuer, domestic currency
Eurobond market
Outside any one country.
Bond is denominated in currency other than those of countries in which bonds are sold
Underwritten offering
Investment banks buy entire issue, sell to public
Best efforts offering
Investment bank acts like broker
Embedded bond warrants
Bondholder may buy issuer’s common stock at exercise price
Current yield (bond)
annual coupon / price
Put-call parity
Portfolios with identical payoffs must sell for same price to prevent arbitrage
C + X / (1 + RFR)^t =
S + P
Discontinued operations, where is it reported
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
Unusual or infrequent items, where is it reported
- Gains of losses from sales of asset
- Impairments, write-offs, write downs and restructuring costs
Included in income from continuing operations and reported before tax.
Extraordinary items
Not allowed in IFRS
In GAAP, it is a material transaction that is both unusual and infrequent.
Reported separately in the income statement
Angel investing stage
Very early in firm’s life, often the idea stage. Funding source usually individuals rather than VC funds
Seed stage
Investment made for product development, marketing, and market research
Early stage (PE)
Investments made to fund initial commercial production and sales
Later stage (PE)
Company already has product and sales and is operating as a commercial entity. Investment provided to expand production, increase sales
Mezzanine-stage financing
Capital provided to prepare the firm for an IPO
Significance level
5% significance level: 5% chance of rejecting a true null hypothesis. 95% chance of correctly rejecting the null hypothesis
Power of test
Probability of rejecting the null when it is false.
Power of test = 1 - P(Type II error)
LM Curve, X and Y axis
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
IS Curve, X and Y axis
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
Marginal propensity to consume
Marginal propensity to save
MPC: proportion of additional income spent on consumption
MPS: proportion of additional income saved
Veblen good
Demand increase when price increases (such as luxury goods)
Comprehensive income
= net income + other comprehensive income
It include all changes in equity except for owner contributions and distributions
Other comprehensive income
Transactions that are not included in net income.
- Foreign currency translation gain/loss
- Adjustment for minimum pension liability
- Unrealized gain/loss from cash flow hedging derivatives
- Unrealized gain/loss from available-for-sale securities
Business risk
Risk associated with a firm’s operating income
- Sales risk
- Operating risk
Financial risk
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.
Drags on liquidity
Delay or reduce cash inflows, or increase borrowing costs.
Ex: uncollected receivables, bad debts, obsolete inventory
Pulls on liquidity
Accelerate on cash outflows.
Ex: paying vendor sooner.
Dividend discount model approach (Cost of capital, k_ce)
P = D1/ (K - g) -> K = D1/P0 + g
where g = RR * ROE
Bond yield plusRisk premium approach (cost of capital)
k_ce = bond yield + risk premium
Note YTM + Premium, do not consider tax rate
Bank Risk tolerance Investment Horizon Liquidity needs Income needs
Risk tolerance: Low
Investment Horizon: Short
Liquidity needs: High
Income needs: Pay interest
Endowments Risk tolerance Investment Horizon Liquidity needs Income needs
Risk tolerance: High
Investment Horizon: Long
Liquidity needs: Low
Income needs: Spending level
Insurance Risk tolerance Investment Horizon Liquidity needs Income needs
Risk tolerance: Low
Investment Horizon: Long (life), short - (Property&Casualty)
Liquidity needs: High
Income needs: Low
Mutual funds Risk tolerance Investment Horizon Liquidity needs Income needs
Risk tolerance: Depends
Investment Horizon: Depends
Liquidity needs: High
Income needs: Depends
Defined benefit pensions Risk tolerance Investment Horizon Liquidity needs Income needs
Risk tolerance: high
Investment Horizon: long
Liquidity needs: low
Income needs: depends
Calculate stock covariance using beta
beta = covariance of asset return with market return / variance of market return
= cov_im / (sigma_m)^2
price weighted index calculation
Index = sum of stock price / (number of stocks adjusted for splits)
Note, denominator must satisfy such that after split, index value remains same
Market capitalization weighting index
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
Equal weighting index
- Calculate percent change of stock price for each stock
- Take average of those percent change
- Apply averaged change on stock index
Stop buy/sell order
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
Limit buy/sell order
Limit buy: order will execute if price falls below a threshold
Limit sell: order will execute if price rise above a threshold
Effective annual yield
EAY = (1+HPY)^(365/5) - 1
Money market yield (CD equivalent yield)
MMY = 360/(#days) * HPY
Bank discount yield (BDY)
BDY = D/F * 360/t
D - Difference between the face value and purchase price
F - face value
t - # days remaining until maturity
Bond equivalent yield
(Face - Purchase val) / Purchase val * 365/(Days to maturity)
Modified duration calculation
D = (V- - V+) / (2 V0 * deltaY)
Arbitrage free forward exchange rate calculation
Forward / Spot = (1 + interest_num) / (1 + interest_den)
Ex. 1.3382 USD/EUR,Spot
Forward = 1.3382 USD/EUR * (USD Inflation) / (EUR Inflation)
Useful lives and salvage value
- Company typically do not disclose date about estimated salvage values
- They are chosen by management and allow for the possibility of income manipulation.
Held-to-maturity securities
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.
Trading securities
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.
Available-for-sale securities
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.
Nine major sections of the GIPS standards
Fundamentals of compliance Input data Calculation methodology Composite construction Disclosures Presentations and reporting Real estate Private equity Wrap fee/Separately Managed Account
Defined contribution
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.
Defined benefit
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
Embryonic stage
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
Growth stage
Industry growth is rapid.
Rapid growth
Limited competitive pressures
Falling prices, since reaching economies of scale
Increasing profitability, due to economies of sacle
Shakeout stage
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
Mature stage
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
Decline stage
Industry growth is negative
Declining prices
Consolidation, firm exit or merge
Intrinsic value of an option
The amount by which the option is in-the-money
Time value of an option
The amount by which the option premium exceeds the intrinsic value.
Option value = intrinsic value + time value
Hedge fund’s trading NAV is higher or lower compared to NAV in accordance with accounting standards?
Lower
Relationship between mean, mode and median for positive skewness?
Mean > median > mode.
Think lots of weight at tail, yet median is not affected
Coefficient of variation
CV = standard deviation/mean
Calculate price elasticity of demand
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
