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CFA Level 1 - Secret Sauce
Here is my version of Schweser's secret sauce. This set contains formulas and key concepts
Terms in this set (247)
What are financial statement notes (footnotes)?
1) details about the information summarized in the financial statements
2) summarize accounting methods and assumptions, estimates, contingencies, acquisitions and disposals.
3) *They are audited.*
4) discuss the fiscal period covered by the statements and the inclusion of consolidated entities
5) additional information on items such as business acquisitions or disposals, legal actions, employee benefit plans, contingencies and commitments, significant customers, sales to related parties, and segments of the firm
What is management's commentary (MD&A)?
*required to discuss *
1) trends, significant events and uncertainties that affect the firm's liquidity, capital resources and results of operations
2) effects of inflation
3) impact of off-balance-sheet obligations and contractual obligations
4) accounting policies that require significant judgement by management
5) forward-looking expenditures and divestitures
*not required to discuss*
1) discontinued operations
2) extraordinary items, and other unusual or infrequent events
*some parts may be unaudited; one of the most useful sections of the annual report*
What is "other comprehensive income"?
changes which result from *foreign currency translation, minimum pension liability adjustments, or unrealized gains and losses on investments (securities held-for-trading)*; flows to accumulated other comprehensive income on balance sheet
What is the super duper expanded accounting equation?
assets = liabilities
+ contributed capital
+ beginning retained earnings
+ revenue - expenses - dividends
What are the 4 owner's equity accounts?
1) capital (par value of common stock)
2) additional paid-in capital
3) retained earnings
4) *accumulated other comprehensive income (OCI)*
What are the
qualitative characteristics that make financial information
2) faithful representation
What are the three characteristics of
1) predictive value
2) confirmatory value
What are the three characteristics of
2) neutral (absence of bias)
3) free from error
What are the three aspects of a
coherent financial reporting framework
What are the 4
that enhance relevance and faithful representation under IFRS?
What are the major differences between GAAP and IFRS?
1) IASB: performance elements are income and expenses
*FASB: performance elements are revenues, expenses, gains, losses, and comprehensive income*
2) *FASB*: an asset as a future economic benefit
*IASB*: an asset is a resource from which a future economic benefit is expected
3) The word *probable* is used by the FASB to define assets and liabilities
4) *FASB does not allow the values of most assets to be adjusted upward*
What is the net income formula?
- ordinary expenses
+ other income
- other expense
+ gains - losses
= ending equity
- stockholder investments
- beginning equity
What is the percentage of completion method?
outcome of long-term contract *CAN BE* reliably measured; same for IFRS and GAAP; *more aggressive*; income and balance sheet will differ from completed contract - cash flows are not different
net income = [(total cost incurred / total cost) x total revenue] - total cost incurred
What is the "under completed contract method"?
when outcome of a long-term contract *CANNOT* be reliably measured
*IFRS*: pairs revenue and expense together, costs are expensed when incurred and profit is recognized only at completion.
*GAAP*: revenue, expense and profit are recognized ONLY when the contract is completed
What is the formula for straight-line depreciation?
= (orig cost - *salvage value*) / depreciable life
What is the formula for double-declining balance?
= *2 / depreciable life in years x book value at beg of year*; *does not use salvage value but depreciation stops when residual value has been reached*
Where are discontinued operations reported?
same for both US GAAP and IFRS; must be physically and operationally distinct from the rest of the firm; management has decided to dispose of but either hasn't done so or did dispose of in the current period after the operation had generated income or losses; reported separately in the income statement, net of tax, after income from continuing operations; should be excluded by the analyst when forecasting future earnings
What are extraordinary items?
US GAAP: *unusual AND infrequent items*; reported separately net of tax and appears on the income statement below discontinued operations
IFRS: *does not allow extraordinary treatment in the income statement
What are unusual or infrequent items?
events which are either unusual in nature or infrequent in occurrence but not both; included in income from continuing ops & reported before tax.
1) G/L from from sale of assets or part of business
2) Provisions for environmental remediation, impairments, write-offs, write-downs, restructuring.
3) Integration expense for recently acquired business
What is the basic EPS formula?
net income - preferred dividends
weighted avg of common shares out
What is the diluted EPS formula?
= net income
- [preferred dividends]
+ [*convertible* prf.dividends]
+ [*convertible* debt int.] (1-t)
(weighted avg. of c/s o/s)
+ (shares from conversion of conv. pfd. shares)
+ (shares from conversion of conv. debt)
+ (shares issuable from stock options)
only income from continuing operations is considered
What is the treasury stock method?
new shares = [(avg mkt price − exercise price) / avg mkt price] x [# of options out]
What is the statement of comprehensive income?
*net income + other comprehensive income*; includes all changes in equity except for owner contributions and distributions (e.g. issuing stock, repurchasing stock, and paying dividends)
What is accumulated other comprehensive income (OCI)?
*subsection in equity* where "other comprehensive income" is accumulated (summed or "aggregated"); difference between net income and comprehensive income; *represents certain gains and losses not recognized in the P&L account.*
How do you calculate ending stockholder's equity?
=beginning stockholder's equity + contributed capital + net income - dividends
What are treasury shares (stock)?
stock that has been reacquired by the issuing firm but not yet retired; *reduces stockholder's equity*; has no voting rights; does not receive dividends
How do you calculate ending cash balances?
Operating cash flow
+ Investing cash flow
+ Financing cash flow
= Chg in cash balance
+ Beg cash balance
= Ending cash balance
How do you calculate FCFF
+ non-cash charges
+ interest expense x (1 - tax rate)
- capex (net capital expenditure)
- working capital investment
What is receivables turnover?
annual sales / average receivables
What is days sales outstanding (DSO)?
365 / receivables turnover
What is inventory turnover?
COGS / average inventory
What is days of inventory on hand?
365 / inventory turnover
What is payables turnover?
purchases / average payables
purchases = ending inventory - beginning inventory + COGS
What is number of days of payables?
365 / payables turnover
What is total asset turnover?
revenue / average total assets
What is fixed asset turnover?
revenue / average net fixed assets
What is working capital turnover?
revenue / average working capital
What is the quick ratio?
cash + marketable securities + receivables / current liabilities
What is the cash ratio?
cash + marketable securities / current liabilities
What is the cash conversion cycle (CCC)?
DSO + DOH - DPO
How do you calculate income available to common?
= Gross Profit
- Operating expenses
= Operating Profit (EBIT)
= Earnings before taxes (EBT)
= Earnings after taxes (EAT)
+/- Below the line items adjusted for tax
= Net Income
= Income available to common
What is the original three-part ROE DuPont formula?
= Net Profit Margin
x Asset TO
x Leverage Ratio
What is the extended five-part ROE DuPont formula?
[NI / EBT]
x [EBT / EBIT]
x [EBIT / revenue]
x [revenue / total assets]
x [total assets / total equity]
x interest burden
x EBIT margin
x asset turnover
x financial leverage
What is the sustainable growth rate formula?
=RR x ROE
RR = (1 - dividend payout ratio)
FIFO results in (assuming inflationary period)
1) big inventory
2) current ratio = big
3) working capital = big
4) COGS = small
5) net income = big
6) higher taxes
7) lower cash flows
LIFO results in (assuming inflationary period)
1) small inventory
2) current ratio = small
3) working capital = small
4) COGS = big
5) net income = small
6) lower taxes
7) higher cash flows
= LIFO inventory + LIFO reserve
= LIFO COGS - ∆ LIFO reserve
FIFO after-tax profit?
= LIFO after-tax profit
+ [(∆ LIFO reserve) (1 − t)]
How is CFO/CFI affected when expenditures are capitalized?
CFI: lower; *capitalized expenditure is reported as an outflow*
How is CFO/CFI affected when expenditures are expensed?
CFI: higher; the expense flowed through the income statement & CFO statement. CFI is higher than normal because there is *no outflow for investing activities*
Under IFRS where can interest
as either an *operating expense OR an investing activity*
What is the units-of-production method?
[original cost - salvage value / life in output units] x output units in the period
What is a revaluation surplus account?
*a component of shareholder's equity* that reports the revaluation upward of an asset's value above its historical cost; this is not reported on the income statement and is only allowed under IFRS
How are impairments recognized under GAAP?
if carrying value > *undiscounted CF* from asset's use and disposal
What is the income tax expense equation?
= taxes payable + ∆DTL - ∆DTA
if taxes paid > income tax expense
if taxes paid < income tax expense
How do you calculate a DTL?
= (pretax income − taxable income) × tax rate
How is interest expense calculated for a discount or premium bond?
beginning bond value x *market rate of interest*
How do you calculate the ending book value of a bond liability?
*beginning book value + interest expense - coupon*
According to SAS No. 99 what are the three conditions that are usually present when fraud occurs?
1) *incentive/pressure* (the motive to commit fraud)
2) *opportunity* (weak internal controls)
3) *attitude/rationalization* (mindset that fraud is justified)
What are some examples of aggressive recognition of revenue?
1) *bill-and-hold arrangements* whereby revenue is recognized before the goods are shipped
2) *holding the accounting period open* past year-end
3) *sales-type leases* whereby the lessor recognizes a sale, and profit, at the inception of the lease, especially when the lessee does not capitalize the lease
4) *early revenue recognition*: IE before fulfilling all of the terms and conditions of sale
5) *recognizing revenue from swaps* and barter transactions with third parties
What are some indications of low quality earnings?
1) boosting revenue w/non-operating income and nonrecurring gains
2) delaying expense recognition
3) abnormal use of operating leases by lessees
4) *hiding expenses by classifying them as extraordinary or nonrecurring*
5) LIFO liquidations - used to boost earnings when more inventory is moved but that cannot go on forever, only so much inventory can be sold
6) abnormal gross margins and operating margin as compared to industry peers
7) extending useful lives of long-term assets
8) aggressive pension assumptions
9) year-end surprises
10) equity method investments and off-balance sheet special purpose entities
11) other off-balance-sheet financing arrangements including debt guarantees
What are the 3 C's for credit analysis?
1) *Character*: management's reputation and history of repayment
2) *Collateral*: ability to pledge specific collateral reduces lender risk
3) *Capacity*: ability to repay debt. requires LT view of firms prospect.
What are 4 way to terminate a
1) Mutual termination
2) Offsetting contract
What are the 4 major characteristics of futures contracts?
1) delivery time
2) quality/qty of the goods
3) manner of delivery
*what is not included is delivery price*
What is a Eurodollar deposit?
USD time-deposits outside of the US. Banks borrow dollars from other banks by issuing Eurodollar time deposits (*certificates of deposit*), which are essentially unsecured loans. The rate of the loans is LIBOR (London Interbank Offer Rate)
What is Euribor?
Europe Interbank Offer Rate; a daily reference rate based on the averaged interest rates at which Eurozone banks offer to lend unsecured funds to other banks in the euro wholesale money market (or interbank market)
What is a forward rate agreement (FRA)?
A forward rate agreement can be viewed as a forward contract to borrow/lend money at a certain rate at some future date. FRAs:
1) settle in cash
2) no actual loan is made
3) *creditworthiness of the parties involved need not be considered.*
Considering forward rates, if floating rate > fixed rate
long has right to borrow at below market rates and short has obligation to lend. *The long will receive a payment.*
Considering forward rates, if floating rate < fixed rate
short will receive cash payment from the long (right to lend at higher than market rates)
What is the FRA formula?
Why do we discount the future payout from a forward rate agreement (FRA)?
since the interest savings would come at the end of the loan period, the cash payment at settlement of the forward is the present value of the interest savings
What are the methods of settlement for a forward contract?
*Delivery*: seller delivers the good to the buyer
*Cash*: buyer and seller exchange the net cash value at the settlement date. This method is much more common.
How does the concept of margin in the futures market differ from the concept of margin in the stock market?
in the futures market no funds are loaned to the buyer of the futures and consequently there are no interest charges
What are the four ways to terminate a futures contract?
1) *short can deliver the goods* and the long can accept the delivery and pay the contract price
2) *cash-settlement*, delivery is not an option
3) make an *offsetting trade* (*most common*)
4) *exchange for physicals* (find a trader with an opposite position to your own and deliver the goods and settle up off the floor of the exchange. ex-pit transaction)
How do you solve futures contract margin problems?
1) *identify all the important elements in the question*
a) how many contracts are long/short?
b) what is the contract price?
c) how many units does each contract represent?
d) what is the initial margin per contract
e) what is the maintenance margin per contract
2) *start solving the problem*
a) take difference between initial price and next day's price
b) multiply: (a) x (units in contract) x (number of contracts)
c) next day's account value = initial margin - b
What are four synthetic portfolios illustrating put-call parity?
1) c = S + p - (X / (1+RFR) ^ T)
2) p = c - S + (X / (1+RFR) ^ T)
3) S = c - p + (X / (1+RFR) ^ T)
4) S + p - c = (X / (1+RFR) ^ T)
What are the maximum and minimum values for a European call option?
Min: c ≥ MAX[0, S - [X / (1+RFR)^T-t]]
What are the maximum and minimum values of a European put option?
Min: p ≥ MAX[0, [X / (1+RFR)^T-t] - S]
Max: X / (1+RFR)^T-t
What are the maximum and minimum values for a American call option?
Min: C ≥ MAX[0, S - [X / (1+RFR)^T-t]]
What are the maximum and minimum values of a American put option?
Min: P ≥ MAX[0, X-S]
What is the general formula for interest rate swaps?
(fixed rate - floating rate) x (days/360) x notional
If the net-fixed payment is positive ...
the fixed pays, floating receives
If the net-fixed payment is negative ...
the floating pays, fixed receives
What is the cost method?
value is determined by the *replacement cost* of improvements plus an estimate for the value of the land
What is the sales comparison method?
value is determined by the price of a *similar property* or properties from recent transactions
What is the income method?
uses a discounted cash flow model to estimate the present value of the future income produced by the property; this method uses NOI (net operating income) divided by estimated market required rate of return (or cap rate). Ignores changes to NOI and does not take in to account an investors income tax implications
How do you calculate NOI?
= rental income x (1 - vacancy rate)
- insurance costs
- property taxes
- utility expense
- repair / maintenance costs
*no financing cost or depreciation when calculating NOI*
What is the discounted after-tax cash flow method?
net present value of an investment equals the present value of after-tax cash flows, discounted at the investor's required rate of return, minus the equity portion of the investment. Only projects w/a NPV > 0 should be accepted.
What are the stages of venture capital investing?
1) *seed stage*: provide capital for r&d
2) *early stage*
a) start-up financing: complete product development
b) first stage financing: refers to the funding of the transition to commercial production and sales of the product
3) *formative stage*
4) *later stage*: company is still private, company needs second and third stage financing. Third stage financing would fund a major expansion of the company. *Mezzanine or bridge financing would enable a company to take the steps necessary to go public*
How do calculate whether to invest in a start-up?
1) estimate probability of failure for each year until a payment is expected
2) take each probability and subtract it from 1 and multiply them all together: this is the probability of success
3) discount the expected payout to the present and multiply that value by the probability of success (value from #2)
4) subtract probability of success from 1 to get the probability of failure and multiply that value by the initial cash outlay
5) add the two numbers together:
*[PV x P(success)] + [CF0 x P(failure)]*
How do you calculate after-tax cash flows?
- first mtge payment
= blah x (1 - marginal income tax rate)
= after-tax blah
- (mtge payment - (amt borrowed * mkt rate of interest))
What are the three sources of return for a commodity investment?
1) *Collateral yield*: the return on the cash used as margin
2) *Roll Yield*: the return from rolling forward the maturity
3) *Spot price*: changes to the price
What are the capital budgeting principals?
1) decisions are based on cash flows, not accounting income
2) Cash flows based on opportunity costs & taxes
3) timing of cash flows is important
4) Cash flows are analyzed on *after-tax basis*
5) *financing costs are reflected in the projects required rate of return and thus should not be included in incremental cash flows.*
What is the discounted payback period?
uses present values of the projects estimated cash flows. Number of years it takes a project to recover its initial investment in PV terms and must be greater than the payback period without discounting. This method ignores terminal values.
What are NPV profiles?
graph that show's a project's NPV for different discount rates; y-axis=NPV
x-axis=cost of capital/discount rate
*when profile touches x-axis NPV = 0*
What is the crossover rate?
*point where two project's NPV's are equal*. Usually need to find mystery initial cash outflow for a project.
1) Find NPV for project w/all known cash flows. 2) set initial cash outflow for unknown project to 0 and calculate NPV
3) subtract that value from other project's NPV
What is project sequencing?
an investment in a project today that creates the opportunity to invest in other projects in the future
What is capital rationing?
The situation where a firm has more positive NPV projects than its available budget can fund. It must choose a combination of those projects that maximizes shareholder wealth.
What is the WACC formula?
(Wd) [Kd (1-t)] + (Wps)(Kps) + (Wce)(Kce)
Wd = % of debt in cap structure
Wps = % preferred stock in cap structure
Wce = % C/S in cap structure
What are the three methods of determining cost of equity?
1) *CAPM*: Kcs = RFR +β [E(Rm) - RFR]
2) *(Div / P0) + growth rate* (sometimes you will have to add growth to the dividend if it's going to be paid in the future)
3) *Add-on yield* method (bond yield + add-on rate)
What is the CAPM formula?
Kcs = RFR +β [E(Rm) - RFR]
What is the CAPM with country risk premium (CRP)?
Kce = RFR + β [E (Rmkt) - (RFR + CRP)]
What are the two dividend discount model formulas?
1) Po = D1 / [Kce - g]
2) Kce = (D1 / Po) + g
D1 = next year's dividend
Kce = required rate of return
g = expected constant growth rate
What is asset beta?
D/E: % debt / (1 - %debt)
t : marginal tax rate
What is project beta?
measure of its systemic / market risk
D/E: % debt / (1 - %debt)
t : marginal tax rate
What is the break point formula?
amt of capital at which a component's cost of cap chgs
weight of component in capital structure
What is the marginal cost of capital schedule?
the WACC at different levels of capital investment. It is usually upward sloping and is a function of a firm's capital structure and its cost of capital at different levels of total capital investment.
What is business risk?
risk associated with *operating income* and is result of *uncertainty about a firms revenues and expenditures* necessary to produce those revenues; main factors are *demand variability, sales price variability, input price variability, ability to adjust output prices, and operating leverage*
What is operating risk?
uncertainty about operating *EARNINGS* caused by *FIXED* operating costs.
What is a DOL (using price and qty)?
What is a DOL (using sales and total variable cost)?
[S - TVC] / [S - TVC - TFC]
What is a DOL formula (using EPS and sales and knowing about the firm's use of debt)?
= [%∆EPS / %∆Sales] / [EBIT / (EBIT-interest)]
= DTL / DFL
What is the DFL formula?
[S - TVC - TFC] / [S - TVC - TFC - interest]
EBIT / [EBIT - interest]
What is the DTL formula?
= DOL x DFL
What is an alternative DTL formula?
= %∆EPS / %∆Sales
What is Qbe (break even quantity)?
fixed operating costs + fixed financing costs
Price - variable cost per unit
What is Qbe (operating breakeven quantity)?
fixed operating costs
Price - variable cost per unit
What is the proper dividend sequence?
DEHP (Department of Environment and Heritage Protection)
1) Declaration date
2) ex-dividend date (occurs TWO business days before the holder-of-record date)
3) holder-of-record date
4) payment date
= ([face value - price] / face value) x (360 / days)
= HPY x (360 / days)
= HPY x (365 / days)
most appropriate for comparing a company's investments in short-term securities
Good corporate governance practices seek to ensure that?
1) the board of directors protects shareholders interests
2) the firm acts lawfully and ethically in dealings w/shareholders
3) the rights of shareholders are protected and shareholders have a voice in governance
4) the board acts independently from management
5) proper procedures and controls cover management's day-to-day operations.
6) the firm's financial, operating and governance activities are reporting to shareholders in a fair, accurate and timely manner.
How do you calculate the margin call price?
P0 x (1 - initial / 1 - maintenance)
What are the 3 types of market structures?
QOB (Queen of Bobs)
1) *quote-driven*: investors trade w/dealers
2) *order-driven*: matches buyers and sellers based on price and time precedence
3) *brokered markets*: investors use brokers
What is the price-weighted index formula?
*= sum of stock prices / number of stocks in index*
simple to calculate; downward bias; divisor is adjusted for stock splits and changes in the composition of the index when securities are added or deleted (reconstituted); higher priced stocks have greater impact than lower priced stocks
What is the market capitalization-weighted index formula?
computed by adding up the collective market capitalizations of its members and dividing it by the number of securities in the index
What is the equal-weighted index formula?
arithmetic average *of the returns* of each component in the index; disadvantage: period rebalancing (similar to price-weighted); weights placed on returns of the securities of smaller cap firms are greater than their proportions of the overall market value of the index stocks
What is a total return index?
uses both price return and interim cash flows to calculate return; *always greater than price return index*
What is weak form market efficiency?
1) prices fully reflect all currently available security mkt data
2) price chgs are *independent* from one period to the next.
3) *TA will not work.*
What is semi-strong form market efficiency?
1) prices fully reflect all publically available security mkt data
2) prices do include past security mkt info plus non-mkt info available to the public
3) timing of *news announcements are independent* of each other
4) large # of profit maximizing participants
5) *FA will not work*
What is strong-form market efficiency?
1) prices fully reflect all *public and private sources* (perfect market)
2) *all info is reflected, past, public and private (inside)*
3) no group has a monopoly on info
4) noone should be able to consistently achieve abnormal returns
5) assumes cost *free availability* of all information
What does market efficiency assume?
it does not assume that individual market participants correctly estimate asset prices, but does assume that their *estimates are unbiased*. That is, some agents will over-estimate and some will under-estimate, but they will be correct, on average
What are the 5 most important external factors influencing industry growth?
1) *macro* - cyclical or structural; interest rates; credit availability; inflation; education leading to productivity
2) *technology* - increases in productivity
3) *demographic* - age distribution and size
4) *governments* - taxes and regulation
5) *social influences* - relate to how people work, play, spend money
What are the five phases of industry life cycle?
1) *embryonic*: slow growth, high prices, large investment needed, high risk of failure
2) *growth*: rapid growth, limited competition, falling prices
3) *shakeout*: growth has slowed, intense competition, industry overcapacity, declining profitability, cost cutting, increased failures
4) *mature*: slow growth, consolidation, high barriers to entry, stable pricing, superior firms gain market share
5) *decline*: negative growth, declining prices, consolidation
What is the one-year holding period DDM?
value of stock *TODAY* is PV of any dividends during the year plus the PV of the expected price of the stock at the end of the year (terminal value); *be sure to use the expected dividend*
What is the multi-period DDM?
discount all dividends to present as well as a "perpetuity" value; don't forget to discount the "perpetuity" value to the present as well. add dividends and perp value together; *appropriate for rapidly growing companies*
What is the earnings multiplier model (justified P/E formula)?
= [D1 / E1] / (k - g)
= payout / (k - g)
According to Markowitz, an investor's optimal portfolio is determined where the?
investor's highest utility curve is tangent to the efficient frontier
What are the 3 steps in the portfolio management process?
1) *Planning*: IPS
2) *Execution*: top-down or bottom up analysis, security selection
3) *Feedback*: monitor changes with client and rebalance portfolio, evaluate performance relative to benchmark portfolio identified in the IPS
How do you calculate covariance between two assets?
1) put return data into calculator using 2nd data func to find mean
2) find difference between each period's value and each sets mean
3) take period A's difference and multiply it by period B's
4) sum all the values up
5) *divide by n -1*
What is the formula for correlation coefficient?
(Cov of A, B)
(STD of A) x (STD of B)
be careful, sometimes the question will include the variance, which is the standard deviation squared.
What is the formula for the standard deviation of a portfolio of two risky assets?
What is the efficient frontier?
*plots expected return against standard deviation of returns for efficient portfolios*; the set of portfolios that gives investors the highest return for a given level of risk or the lowest risk for a given level of return; *the point at which there are no more benefits to diversification*; the efficient frontier line bends backwards due to less than perfect correlation between assets; a *portfolio to the left of the efficient frontier is not attainable*
The portfolio on the efficient frontier that has the least risk is the ...
global minimum-variance portfolio
What is the separation theorem?
think budget constraints and indifference curves from economics; this combines the CML (risk-free rate and efficient frontier) with an investor's indifference curve map; it separates out the decision to invest from what to invest in. The investment selection process is simplified from stock picking to efficient portfolio construction through diversification.
What is the capital allocation line (CAL)?
A line created in a graph of all possible combinations of risky and risk-free assets. Also known as the "reward-to-variability ratio"; as you increase the weight of the risky asset you get more risk but also a higher return
What is the capital markets line (CML)?
A line used in the capital asset pricing model to illustrate the rates of return for efficient portfolios depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio; represents all possible combinations of the market portfolio with the risk-free asset; *derived by drawing a tangent line from the intercept point on the efficient frontier to the point where the expected return equals the risk-free rate of return.*; considered to be superior to the efficient frontier since it takes into account the inclusion of a risk-free asset in the portfolio. The capital asset pricing model (CAPM) demonstrates that the market portfolio is essentially the efficient frontier.
What is the security market line (SML)?
positively sloped straight line showing relationship between expected return and beta (systemic risk)
=(COV stock,market) / (VAR mkt)
Alternate beta formula =
=correlation x [Std Stock / Std Market]
What does it mean to move rightward of the mkt portfolio?
you are borrowing funds and owning more than 100% of the market portfolio
What does it mean to move leftward of the mkt portfolio?
you are lending funds or *buying the risk-free asset* (IE lending to someone else for a return)
What are some assumptions of Capital Asset Pricing Model (CAPM)?
1) Aim to maximize economic utilities
2) Are *rational* and risk-averse
3) Are broadly diversified across a range of investments
4) Are *price takers*; they cannot influence prices
5) Can *lend and borrow* unlimited amounts under the risk free rate of interest
6) Trade *without transaction* or taxation costs
7) Deal with securities that are all *highly divisible* into small parcels
8) Assume *all information is available* at the same time to all investors
9) All investors have the *same one-period time horizon*
10) All investors have the *same risk/return expectations*
What is the Sharpe ratio?
calculated by subtracting the risk-free rate - such as that of the 10-year U.S. Treasury bond - from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns
What is Roy's Safety First Criteria?
calculated by subtracting the minimum desired return from the expected return of the portfolio and dividing the result by the standard deviation of portfolio returns. The optimal portfolio will be the one that minimizes the probability that the portfolio's return will fall below a threshold level.
If the RR < ER
stock is underpriced; buy it
If the RR > ER
stock is overpriced; short it
If a portfolio plots
the SML, the portfolio is ...
undervalued (RR < ER)
If a portfolio plots
the SML, the portfolio is ...
overvalued (RR > ER)
What are federally related institutions?
1) owned by the US govt and exempt from the SEC registration
2) *backed by full faith and credit of US govt*
3) free from credit risk
EX: Government National Mortgage Association (Ginnie Mae), TVA (Tennessee Valley Authority)
What are government sponsored enterprises?
1) privately owned but publicly chartered organizations
2) created by US Congress
3) securities issued directly in the marketplace
4) expose investors to some credit risk
What are the four tools the Fed uses to control interest rates?
1) discount rate
2) open market operations (most common)
3) bank reserve requirements
4) persuading banks to tighten or loosen their credit policies
coupon rate = current yield = yield to maturity
coupon rate < current yield < yield to maturity
coupon rate > current yield > yield to maturity
What are four characteristics of the zero-volatility spread measure?
1) Z-Spread is the credit spread that adjusts for the curvature of the spot rate yld curve.
2) Z-Spread is the constant spread which must be added to each rate on the Treasury spot yield curve in order to make the present value of the risky bond's cash flows equal to its market price.
3) The steeper the benchmark spot rate curve, the greater the difference between the two spread measures.
4) The earlier bond principal is paid, the greater the difference between the two spread measures.
When the spot yield curve is upward sloping ...
z-spread > nominal spread
When the spot yield curve is downward sloping ...
z-spread < nominal spread
How do you calculate a forward rate from spot rates?
if given 3f3, this means you want to know the 3 year fwd rate, 3 years from now. what you need to calculate this is:
1) 3-year spot rate
2) 6-year spot rate
= [ (1 + z6)⁶ / (1 + z3)³ ] - 1
How do you calculate reinvestment income?
EX: how much reinvestment income would so-and-so need to earn over X years to achieve a compound rate of return of Y?
PV * (rate ^ periods)
- principal repayment
- [bond coupons x periods]
= reinvestment income
How do you calculate total interest expense?
(coupon payments x n periods) + bond FV - bond PV
How do think about duration
think sensitivity; when you get more cash now, the bond has less sensitivity to interest rate moves; when you have to wait longer to get the final payout, the bond has more sensitivity
What is the effective duration formula?
How do you apply the effective duration when given a change in yield and the effective duration?
-(effective duration) x Δ yield x original bond price
What is the combined duration/convexity formula?
= [-duration x Δ y] + [convexity x (Δ y) ²] x 100
What is the PVBP formula?
= duration x 0.0001 x bond value
What does r on your calculator when using the 2nd Data functions?
How do you calculate HPY from MMY?
MMY x [t / 360]
How do you calculate HPY from EAY?
[1 + EAY] ^ (t / 365)
How do you calculate the MMY from the BDY?
[360 × bank discount yield]
[360 − (t × bank discount yield)]
How do you calculate the BEY from the HPY?
2 x [[1+HPY] ^ (182.5 / t)]
What are the four measurement scales?
1) *nominal*: no particular order
2) *ordinal*: ordered w/respect to a specific characteristic
3) *interval*: provides relative rankings; differences between the scale values are equal
4) *ratio*: equal differences between scale values; also have true 0 as the origin
What is the formula for determining the position of an observation at a given percentile?
=(n + 1) x [y / 100]
What is Chebyshev's inequality?
=[1 - 1/k²]
What is the formula for the coefficient of variation?
standard deviation of x / mean of x
mode < median < mean
mean < median < mode
What are the 3 moments?
Moment 2 = variance (squared)
Moment 3 = skew (cubed)
Moment 4 = kurtosis (4ths)
What is the multiplication rule of probability?
=P(AB) = P(A|B) x P(B)
What is the addition rule of probability?
=P(A or B) = P(A) + P(B) - P(AB)
What is the total probability rule?
=P(X | Y) = P(X).
What are the "odds for" something happening?
= P(E) / [1 - P(E)] A probability of 20% would be "1 to 4"
What are the "odds against" something happening?
= [1 - P(E)] / P(E) A probability of 20% would be "4 to 1"
What is a confidence interval?
How do you calculate continuous compounding given a rate?
1) input the given rate in decimal format (IE: 10% = .10)
2) 2nd + LN
3) raise to power if doing for multiple periods
4) subtract 1 and multiply by 100
How do you calculate continuous compounding given a beginning and ending value?
1) divide ending value by beginning value
2) Hit the LN button
What is sampling error?
sample mean - population mean
What is the standard error of the sample mean?
What is the general confidence interval formula?
point estimate + reliability factor + standard error
Normal distribution with known variance?
1) small sample: z-stat
2) large sample: z-stat
Normal distribution with unknown variance?
1) small sample: t-stat
2) large sample: t-stat or z-stat
Non-normal distribution with known variance?
1) small sample: NA
2) large sample: z-stat
Non-normal distribution with unknown variance?
1) small sample: NA
2) large sample: t-stat
Type I & II Errors
If null is true & fail to reject = Correct!
if null is true and reject = Type 1 error! significance level, α
If null is false & fail to reject = Type 2 error!
if null is false and reject = Correct! (1- P)
When is a pooled variance used?
with the t-test for testing the hypothesis that the *means of two normally distributed populations are equal*, when the variances of the populations are unknown but assumed to be equal
What is a paired comparisons test?
a test of whether the average difference between monthly returns is significantly different from zero, based on the standard error of the differences in monthly terms
What is a chi-squared test?
used for hypothesis tests concerning the variance of a normally distributed population
How do you calculate a test chi-squared statistic?
(n-1) / hypothesized value
What is the F-statistic?
s₁² / s₂²; always put the larger variance in the numerator
concerned with the *equality of the variances of two populations*
What are parametric tests?
rely on assumptions regarding distribution of population and are specific to population parameters.
What are non-parametric tests
does not consider particular population parameter or have few assumptions about population that is sampled. Used when concerned about quantities other than the parameters of a distribution or when the assumptions of the parametric tests can't be supported.
What are non-parametric test situations?
1) hypothesis test of mean value for a variable that comes from a distribution
2) when data are ranks (an ordinal measurement scale) rather than values
3) hypo not involve parameters of distribution, such as testing whether a variable is normally distributed. Use run tests
Marginal cost =
∆ TC / ∆ in output
1) perfect competition: AR = ATC
2) imperfect competition: TR = TC
Short-run shutdown points
1) perfect competition: AR < AVC
2) imperfect competition: TR < TVC
Long-run shutdown points
TR < TC
P < AC
GDP deflator =
[nominal GDP in year t / value of year t output at base year prices] x 100
GDP equation =
C + I + G + (X - M)
Growth in potential GDP =
growth in technology + growth in labor + growth in capital
Money multiplier =
1 / reserve requirement
Equation of exchange =
MV = PY (money supply x velocity = price x real output)
Fisher effect =
nominal interest rate = real interest rate + *expected* inflation rate
What are the three categories of price elasticity?
Ep > 1; demand is elastic
Ep = 1; demand is unitary elastic
Ep < 1; demand is inelastic
Is there a well-defined supply function under
monopolistic competition, oligopoly and monopoly
no. why? bc all three face downward sloping demand curves; qty supplied is determined by the intersection of MC and MR; price charged is then determined by the demand curve. only perfect competition has a well-defined supply curve.
What is the N-firm concentration ratio?
1) measures the concentration of a market (usually in regards to determining if a merger should be allowed).
2) sum of the percentage mkt shares of the N firms in a mkt. *does not directly measure mkt power or elasticity of demand*.
3) *may be relatively insensitive to mergers of two firms w/large mkt shares.*
What is the Herfindahl-Hirschman Index?
1) measures concentration of a market (usually in regards to determining if a merger should be allowed).
2) *sum of the squares of the mkt shares of the largest firms in the mkt*.
3) *does not take possible entry into mkt into account; nor does it consider elasticity of demand*
What is the source of differences in production costs in the Ricardian model?
differences in labor productivity due to differences in technology
What are the two factors of production under the Heckscher/Ohlin model?
capital and labor
What are the 5 kinds of trading blocs?
1) *Free Trade area*: all barriers to flow of goods are eliminated between members
2) *Customs Union*: same as FTA & in addition creates a common trading policy with non-members
3) *Common Market*: same as customs union & allows free movement of factors of production; removes all barriers to movement of labor and capital among members
4) *Economic Union*: same as common market & coordination of economic policy
5) *Monetary Union*: same as economic policy + adopt a common currency
What are the three accounts which constitute the BOP (balance of payments)?
1) current account
2) capital account
3) financial account
What is the current account?
sum of the balance of trade (X - M); both government and private payments are included in the calculation; goods and services are generally consumed in the current period.
What is the capital account?
reflects net change in national ownership of assets. A surplus means money is flowing into the country; deficit means money is flowing out the country, but it also suggests the nation is increasing its claims on foreign assets.
What is the financial account of?
1) govt-owned assets abroad
2) foreign owned financial assets with the reporting country
What is the equation representing the relationship between trade deficit, saving and domestic investment?
X - M = private savings + government savings - investment
X - M = (T - G) + (S - I)
How do you calculate ending inventory?
ending inventory = beginning inventory + purchases - COGS
What is the base currency?
currency in the denominator
What is the price currency?
currency in the numerator
The foreign currency is the base currency for a?
direct quote (foreign currency in denominator)
The home currency is the base currency for a?
indirect quote (home currency in denominator)
What is the interest rate parity formula?
forward rate = spot rate x (1+domestic rate / 1+foreign rate)
If USD/EUR spot exchange rate is 1.3500 and 6-month forward points are −75, the 6-month forward exchange rate is:
1.3425, USD = forward premium, EUR = forward discount; in 6 months 1 Euro will only buy 1.3425 instead of 1.3500, so currently it is at a premium
If RFR goes up
puts: go down
calls: go up
If RFR goes down
puts: go up
calls: go down
How are lease payments accounted for?
whether a lease is an operating or a finance lease, both GAAP and IFRS require disclosure of the minimum lease payments *for each of the next five years and the sum of minimum lease payments more than five years in the future*
Recommended textbook explanations
Principles of Economics
N. Gregory Mankiw
Krugman's Economics for AP*
David Anderson, Margaret Ray
Principles of Microeconomics
Principles of Microeconomics
N. Gregory Mankiw
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