CFA Level II Without Review and Secret Sauce Flashcards
All areas
What is R2?
SST-SSE/SST or RSS/SST
Adjusted R2
1- [((n-1)/(n-k-1)) x (1-R2)]
What is the difference between AIC and BIC
AID is for a forecast and BIC is goodness of fit a lower number is better
What is the F statsitic
(SSER - SSEu)/q / (SSEu)/(n - k - 1) with q and (n-k-1) degrees of freedom q = number of excluded variables in the restricted model and k = independent variables in the full model
What is the BP Chi-square test statistic
n x R2resid with k degrees of freedom where n is the number of observations, and R2 from a second egression on the independent variables and k is the number of independent variables.
What is the BG test
The BG test regresses the regression residuals against the original set of independent variables plus one more additional variables representing lagged residuals.
What is the Variance Inflation Factor?
It is used to quantify multicollinearity where VIF - 1 / (1-R2J) high VIF is what we are looking for
What is Cook’s Distance
It is a composite metric to evaluate if an observation is influential. It is D = ei2/(k+1) x MSE [hii/(1 - hii)^2]
What is the logistic regression
ln(p/1-p) = b0 + b1X1 + b2X2
What are odds?
Odds = e^y and P = odds/(1 + odds) = 1/(1 + e^-y)
What is an autoregressive model?
An AR is when the dependent variable is regressed against one or more lagged values of itself
What is the Durbin Watson or DW statistic?
It is used to detect autocorrelation and if the timeseries does not have autocorrelation it should be 2.0
How to forecast with AR models?
First start with the first orderAR model and then you find the autocorrelation of the residuals. After that you see if they are different from zero.
What is the formula for mean reversion for a linear regression?
xt = b0 / (1-b1)
What is a random walk with a drift?
It is when in addition to a random error the time series is expected to increase or decrease by a constant amount each period where xt = b0 + b1xt-1 + et where b0 = the constant drift and b1= 1
How do we test for random walk and when do we have unit root?
If the value of the lag coefficient is equal to one the time series is said to have unit root and follow a random walk
What is the Dickey Fuller aka Engle Granger test?
Used to test for unit root and it tests is an AR times series is equal to 1.
What is Autoregressive conditional heteroskedasticity (ARCH)
It exists if the variance of the residuals in one period is dependent on the variance of the residuals in a previous period and is used to test for AR conditional heteroskedasticity where et^2 = a0 + a1e^2t-1 + meant
What is cointegration?
It is when two time series are economically linked (related to the same macro variable) or follow the same trend and that relationship is not expected to change.
What is the difference between supervised and unsupervised learning?
Supervised uses labeled training data while unsupervised are not given labeled training data.
What is bias and variance error and how do they change with model complexity?
Bias error is the in-sample error resulting from a model with poor fit while variance is the out of sample error resulting from overfitting models that do not generalize well. Variance increases with model complexity and bias decreases.
What are eigen vectors?
They are uncorrelated factors which are a combinations of the original features and it the proportion of total variance in the data set explained. This is key in Principal component analysis
What is the difference between trimming and winorizing
Trimming is where the highest and lowest x% of observations are removed and winorizing is where extreme values are placed by the maximum value
What is normalization and how do you calculate it?
Normalization scales the variable between 0 and 1. Normalized X = (Xi - Xmin)/(Xmax - Xmin)
What is tokenization
It is the process of splitting sentences into individual words
What is document term matrix
Convert the unstructured data to structured data
What is a N-gram
It is used to represent words in a sentence one or two words
What is document frequency
It is the number of documents containing that token divided by the total number of documents
What is the Mutual Information?
It is used to determine if a token is a useful discriminant if it is then the MF should be close to 1
What is precision
Precision is the ratio of true positives to all predicted positives or TP/ (TP +FP)
What is recall
Recall is the ratio of True positives to actual positives or TP/ TP+FN
What is accuracy
(TP + TN) / (TP + TN + FP + FN) number of correct forecasts
What is F1 score (Quant)
It is the harmonic mean of precision and Recall (2PR)/ (P+R)
What are hyperparameters?
They are the number of hidden layers in a neural network of the pthreshold in logistic regression
What is a pip
it is 1/10000
How to calculate a bid and ask offer for cross rates?
(B/C)bid = 1/(C/B)offer
Forward premiums and discounts are based on which currency?
Base currency
What is the mark to market value of a currency contract and what is the value of r?
VT = (FPt - FP) (contract size)/[1 + R(days/360)] where r is the interest rate of the price currency
What is the covered interest rate parity?
It is when F = [1 + Ra(days/360)]/[1 + RB(days/360)] * S0
What is the international fisher relations
RnominalA - RnominalB = E(inflationA) - E(inflationB)
What is the formula for FX Carry Trade
Return = Interest earned on investment - funding cost - currency depreciation
What is the difference between the current account, financial account or capital account
CA - exchange of goods, services, investment income and unilateral transfers
FA - Flow of funds for debt and equity investment
What happens when monetary and fiscal policy are both expansionary and both restrictive in high and low capital mobility environments?
In EE and RR with high capital mobility it is uncertain and for low ee will lead to depreciation and rr will lead to appreciation
What happens when monetary policy is expansionary and fiscal policy is restrictive in high and low capital mobility
In High it will lead to depreciation and in low it will be uncertain
What happens when monetary policy is restrictive and fiscal policy is expansive in high and low capital mobility
In High it will lead to appreciation and in low it will be uncertain
What is the Expected Return of the country or Grinold-Kromer function
E(R) = Dividend Yield + change in EPS + inflation - change in shares outstanding + changeP/E (expected repricing)
What is the cobb douglas function
Y = TK^alphaL^(1-Alpha) where alpha is the share of labor and capital and T is the technological factor progress
What two things make up the labor growth rate?
It is growth due to capital change + growth due to capital deepening
What is the growth account relation?
changeY/Y = changeT/T + alphax(changeK/K) + (1-alpha)(changeL/L) or long term growth rate of technology + alpha(long-term growth rate of capital + (1-alpha)long term growth rate of labore where alpha is the elasticity of output with respect to capital
What is the simple formula for growth rate in potential GDP
It is long-term growth rate of labor force + long-term growth rate in labor productivity
What is the sustainable growth ratio of output per capita?
It is the growth rate of technology / labor’s share of GDP
What is the sustainable growth rate of output
It is the growth rate of technology / labor’s share of GDP + Growth of Labor
What are self-regulatory bodies
They are private organizations that represent as well as regulate their members
What is the regulatory competition and regulatory arbitrage
Regulatory competition is where regulators compete to provide the most business-friendly environment and arbitrage is where you shop for country that allows a specific behavior
What is considered a controlling interest?
It is either when the ownership interest is above 50% or is between 20 and 50 percent and has a significant influence on the target company and that uses either the equity method or acquisition method
What is considered at fair value through profit and loss and which is through OCI
Equity and Debt held for training is considered through PL while everything else is OCI for debt and equity
How are dividends and earnings treated in investments in associates?
They reduce the carrying value while earnings increase net income
How do you treaty upstream sales?
The investee recognized all profit but for unconfirmed profit the investor must eliminate its proportionate share of the profit from the equity income of the investee
What happens under the pooling of interests method
It combined the ownership interest of the two firms and viewed the participants as equal
What is the formula for full goodwill considering percent owned?
Full goodwill = (purchase price / % owned) - (fair value of net identifiable assets of the subsidiary)
What is the formula for partial goodwill
Purchase price - (% owned x FV of net identifiable assets of the subsidiary) or % owned x full goodwill
What is the accounting treatment for joint ventures
Equity method in rare instances proportionate consolidation is allowed which results in higher assets and liabilities but stockholder’s equity is the same
What is Variable Interest Entity (VIE)
- an at-risk equity that is insufficient to finance the entity’s activities without additional financial support
- Equity investors that lack any one of the following:
- Decision making rights
- The obligation to absorb expected losses
- The right to receive expected residual returns
Out of equity method, proprotionate consolidation and acquisition method which has the higher Net Profit Margin, ROE and ROA
Equity method for all and proportionate consolidation and Equity for ROE. Proportionate is between for all others
How is compensation expense used for stock options?
It is based on the fair value of the options on the grant date then allocated in a straight line over the vesting period. It will decrease NI and RE
What is the tax deduction formula for stock grants
Share price on settlement date x number of shares vested
What is the tax deduction for options
Intrinsic value on settlement date x number of options vested or
(stock price on settlement date - strike price) x number of options
What is the number of treasury shares
Assumed proceeds / average share price during the reporting period
where assumed proceeds = cash proceeds + average unrecognized share-based compensation expense and
cash proceeds = number of options x exercise price (cash proceeds is zero for stock grants) and average unrecognized share-based compensation expense = average of the last two period-end values of unamortized amounts of share-based expense
How do you estimate future grants
Discounting the estimated value of equity by a dilution factor or by an increase in the number of shares outstanding
What is the funded status of a pension plan
Fair value of plan assets - PBO
What is the interest cost of pension plan under US GAAP vs IFRS?
GAAP It is [beginning PBO + Past Service Cost] x discount rate
IFRS [beginning funded status - past service costs] x discount rate
When is amortization for pensions required under us gap corridor approach
It is when the beginning balance of actuarial gains and losses exceeds 10% of the greater of the beginning PBO or plan assets
Which two components of pension costs differ in their treatment under US GAAP and IFRS
It is Past service costs, which under GAAP is OCI, amortized over subsequent years while IFRS is under the income statement while for Actuarial gains and losses it is amortized portion in income, unamortized in OCI while in IFRS all in OCI and it is not amortized
What is the pension cost in P&L for GAAP and what is the difference between GAAP and IFRS?
It is current service costs + Interest cost - Expected return on plan assets while IFRS does not include expected return
When is the current rate method or remeasurement used?
It is when the local currency and functional currency are the same or different which is being translated to the presentation currency
When is the translation method used?
It is when the functional and presentation currency are the same or different and the local currency is being translated into the functional currency
Using the current rate method, when is the value of the net assets and net liabilities gaining
The net assets gain when the local currency appreciates and the net liabilities when the currency is depreciating
Using the temporal rate method, when is the value of the net monetary assets and net monetary liabilities gaining?
The net monetary assets gain when the local currency appreciates, and net monetary liabilities when the currency depreciates
How are monetary assets and liabilities measured using the temporal method and current rate method?
Temporal method - current rate
Current Rate method - current rate
How are nonmonetary assets and liabilities measured using the temporal method and current rate method?
Temporal method - historical rate
Current Rate method - current rate
How is common stock measured using the temporal method and current rate method?
Temporal method - historical rate
Current Rate method - historical rate
How is equity measured using the temporal method and current rate method?
Temporal method - Mix (average and historical)
Current Rate method - current rate
How are Revenues and SG&A measured using the temporal method and current rate method?
Temporal method - Average Rate
Current Rate method - Average Rate
How is the cost of goods sold measured using the temporal method and current rate method?
Temporal method - Historical Rate
Current Rate method - Average Rate
How are depreciation and amortization measured using the temporal method and current rate method?
Temporal method - Historical Rate
Current Rate method - Average Rate
How are net income measured using the temporal method and current rate method?
Temporal method - Mixed rate (average and historical rate
Current Rate method - Average Rate
Where is exposure measured using the temporal method and current rate method?
Temporal method - Net Monetary assets
Current Rate method - Net Assets
Where is exchange rate gain or loss measured using the temporal method and current rate method?
Temporal method - Income Statement
Current Rate method - Equity
What results if the parent has net monetary exposure when foreign currency is appreciating?
The result is a loss
When the currency is depreciating, the translation ratio is
Larger than the original ratio
How are nonmonetary assets and liabilities affected by hyperinflation?
They are not affected usually because GAAP does not allow for adjustment
What is the definition of hyperinflation
It is where cumulative inflation exceeds 100% over a 3-year period
What is the difference between clean-surplus account and dirty-surplus accounting
Clean-surplus is includes gains and losses in net income, and dirty surplus is used to describe gains and losses that are reported in shareholder’s equity
What is the difference between effective and statutory tax rate?
The effective tax rate is the tax expense in the income statement divided by the pretax profit
Statutory tax rate is provided by the tax code in the home country
What does CAMELS stand for?
It stands for Capital adequacy, asset quality, management, earnings, liquidity, and sensitivity
What are the percentage levels for RWA for Common Equity Tier 1 capital, Total Tier 1 Capital, and Total Capital
Common Equity Tier 1 capital - 4.5%
Total Tier 1 Capital - 6%
Total Capital - 8%
What is the allowance for loan losses
It is the result of provision for loan losses which is an expense at the discretion of management which is a contra assets
What is the liquidity coverage ratio?
LCR = Highly liquid assets/expected cash outflows where cash outflows are the estimated one-month liquidity needs in a stress scenario min recommended 100%
What is Net Stable Funding Ratio?
NSFR = Available stable funding/required stable funding - Needs of a bank’s assets to the liquidity provided by the bank’s liabilities
What is the underwriting loss ratio?
(Claimes paid + change loss reserve)/net premium earned
What is the expense ratio for insurers?
Underwriting expenses including commissions/net premium writted
What is the loss and loss adjustment expense ratio?
(loss expense + loss adjustment expense)/ net premiums earned
What is the dividends to policyholders ratio for insurers?
Dividends to policyholders (shareholders)/ net premiums earned
What is the combined ratio
Loss and loss adjustment expense ratio + underwriting expense ratio
What is the Combined ratio after dividends?
CRAD = combined ratio + dividends to policyholders ratio
What is the total investment return ratio?
Total investment income / invested assets
What is the difference between earnings quality and reporting quality
Reporting quality is the assessment of the information disclosed in the report while earnings quality is the sustainability of the earnings
Rank the financial reportings quality from high to low
- GAAP compliant and decision-useful, high-quality earnings
- GAAP compliant and decision-useful, low-quality earnings
- GAAAP compliant but not decision-useful (biased choices)
- Non-compliant accounting
- Fraudulent accounting
What is a method that firms in multiple lines of business or international firms use to mask bad profits
Moving profits to a specific part of the business they want to highlight while consolidated financials show negative or zero growth
What is considered a bad M-score under Beneish model?
If M-score > -1.78 indicates a higher than acceptable probability of earnings manipulation
What is the Altman model
It relies on discriminant analysis to generate a Z-score using five variables where a higher z-score means the firm is less likely to file for bankruptcy
What are the two major contributors to earnings manipulations?
- Revenue recognition issues
- Expense recognition issues (capitalization)
What is a coupled problematic sign for mature firms?
Negative operating cash flows couples with positive financing cash flow
A high-quality financial balance sheet reporting is evidenced by what three things
- Completeness
- Unbiased measurement
- Clarity of presentation
What is the framework for analysis?
- Establish the objectives
- Collect data
- Process data
- Analyze data
- Develop and communicate conclusions
- Follow up
What is Extended ROE?
Tax Burden x Interest Burden x EBIT Margin x Total Asset Turnover x Financial Leverage
(NI/EBT) (EBT/EBIT) (EBIT/revenue) (Revenue/Average assets) (Average assets/average equity)
What is the threshold for a business segment?
It is a portion of a larger company that accounts for more than 10% of the company’s revenue or assets and is distinguished from the company;s other lines of business in term of risk and return characteristics
What is NOA
NOA - Operating assets - operating liabilities
Accruals = NOAend - NOAbeg
What is the accruals formula for the balance sheet and for the cash flow
BS = NOAend - NOABeg
CF = NI - CFO- CFI
What is the accruals ratio with NI?
(NI - CFO - CFI)/ (NOAend + NOAbeg)/2
What is the formula for cash generated from operations from EBIT?
It is EBIT + non-cash charges - an increase in working capital
What is the difference between net debt (not net debt expense) and net interest expense?
Net debt is the gross debt minus cash, cash equivalents, and short-term securities.
Net interest expense - Gross interest expense minus interest income on cash and short-term debt securities
What is the difference between the effective tax rate and the cash tax rate?
Effective tax rate - income tax expense as a percentage of pretax income
Cash tax rate - cash taxes paid as a percentage of pretax income
What is the formula for projected accounts receivable?
(Days sales outstanding) x (forecasted sales/365)
What is ROIC?
Return on invested capital - net operating profit adjusted for taxes divided by invested capital (operating assets - operating liabilities)
What is the cannibalization rate?
New product sales that replace exisiting product sales/ total new product sales
What does a dividend payment do to cash and stockholder’s equity
It reduces both resulting in a lower quick ratio and current ratio and higher leverage
What is dividend irrelevance theory?
It is mart of the MM theory and mainaints that dividend policy has no effect on the price of a firm’s stock or it’s cost of capital
What is bird in hand theory?
When MM conclude that dividends are irrelevant they mean that investors don’t care about the firm’s dividend policy since they can create their own
What are agency costs?
They are between shareholders and managers and are due to a divergence of interests between managers and stockholders
What is effective tax rate for firms?
It is the corporate tax rate + (1- corporate tax rate)(individual tax rate)
What is the expected increase in dividends formula?
[(expected earnings x target payout ratio) - previous dividend] x adjustment factor
Adjustment factor = 1 / number of years over which the adjustment in dividends will take place
What is a fixed-price tender offer
Approach where the firm buys a predetermined number of shares at a fixed price, typically at a premium over the current market price
What is a Dutch auction
It is a tender offer in which the company specifies not a single price but rather a range of prices
What is the difference between cash dividend and share repurchase
Assuming the tax treatment of the two alternatives is the same, a share repurchase has the same impact on shareholder wealth as a cash dividend payment of an equal amount
What is the FCFE coverage ratio
FCFE / (dividends + share repurchase)
What is the dividend payout ratio?
Dividend/ NI
What is the dividend coverage ratio
NI / Dividend
What is the formula for FCFE from CFO
CFO - FCInv + net borrowing
What happens under dispersed ownership and concentrated voting power
Controlling shareholders do not own large positions rather they gather control using dual-class shares or pyramid structures
What happens under concentrated ownership and dispersed voting power
Usually enacted by governments, it is where voting rights of large share positions are restricted
What is a two-tier structure
It is sometimes required by countries it is where the management board is overseen by a supervisory board
What are say-on-pay rules
Stakeholders are given the opportunity to vote on executive compensation
What are the bottom-up factors that affect capital costs?
- Business or operating risk
- Asset nature and liquidity
- Financial strength and stability
- Security features
What is the Implicit Formula in the lease of the IRR?
PV of lease payments + PV of residual value = Fair value of leased asset + Lessor’s initial direct cost
What are the benefits of an arithmetic mean
It is good estimate of a one-period return but does a poor job of estimating multiperiod return
What is the gordon growth model?
D1/V0 + g
What is Equity Return Premium (ERP) using dividend yield?
ERP = E(dividend yield) + g - rf
What is Capital Gains Yield (CGY)
change in P/E + expected inflation + real economic growth rate (G) - change ins shares outstanding
What is Grinold-Kroner model
It is used to express the expected market equity return = [DY + changeP/E + expected inflation + real economic growth rate - change shares outstanding] - rf
How to calculate i
(1+YTMtreas)/(1+YTMTips) -1
What is the Dividend Discount Model (DDM) that starts with re
re = DY + CGY
What is the bond yield plus risk premium model?
Add a risk premium to the yield to maturity of the company’s long-term debt
What is the CAPM
Required return on stock = risk-free rate + (equity risk premium x beta of stock)
What is the multifactor model form?
Required return = rf + (risk premium)…. where risk premium = factor sensitivity x factor risk premiium
What is the five factor fama french model
It is rf + BERP(Expected Return of Equity) + BSMB(Size premium) + BHML(value premium) + BRMW(profitability premium) + BCMA (investment premium)
What are the risk premiums for private companies?
They are size premium, industry risk premium, and specific company risk premium
What is the expanded CAPM for private companies
Required return = rf + Bpeer x ERP + Size Premium + Firm Specific Premium
What models do we need to consider for developing market security valuations? and how does this come together for the ERPemerging market
Need to include the country-spread model and the country-risk rating model which come together in the form of ERPemerging market = ERPdeveloped + exposure x country risk premium
Formula for calculating Country risk premium
Sovereign yield spread x (std devequity/std devbond)
What are three things that cause high security prices?
- Greater CEO confidence
- Lower cost of capital
- Overvalued stock
What is the difference between outsourcing and offshoring?
Outsourcing - contracting out standardized business process to thrid party vendors
Offshoring - Uses cheaper foreign labor while still keeping a business process in-house
What is a Leveraged Buyout
LBO - a private equity firm first purchases a company using a large amount of debt to finance the transaction This can also be known as a take-private transaction
What is best measure to value the whole company?
They use the Enterprise Value (EV) which is market value of firm’s debt and equity minus the value of cash and investments
What is the difference between Comparable Transaction Analysis and Comparable Company Analysis
Similar to each other but CTA instead uses actual takeover transaction prices where CCA uses relative valuation metrics and then adds a takeover premium
What is the premium ratio for the acquiring firm?
premium = (Deal price - unaffected price)/Unaffected price
What do you combine in the modeling phase to generate the pro forma financial statements
Combine revenues and make adjustments for synergies or dissynergies. Combine depreciation/amortization and other income and expenses
What two things are involved in the evaluation of divestment actions?
- Valuation of business segments
- Impact on ratios
What is R2 from RSS?
RSS/SST
What is adjusted R2
1 - [((n-1)/(n-k-1))x(1-R2)]
What is the F-statistic
F = (SSER-SSEU)/q/SSEu/(n-k-1)
If there isn’t an exact linear relationship among X variables what results
Multicollinearity
If the error terms are not correlated with each other what is the result?
Serial correlation (autocorrelation),
What is the formula for t-stat?
Estimate/standard error
What happens to SE, T-stats, and errors when there is multicollinearity?
Inflates SE, reduces T-stats, increase the chance of type II errors
What are signs of multicollinearity
- Significant F-stat
- High correlation between X variables
- Sign of coefficient is unexpected and we can drop one of the correlated variables
What type of errors occur when there is serial autocorrelation and how can we test for them?
Type I errors occur, can be tested through F-test
How do you correct for serial autocorrelation?
Use the Newey-West corrected standard errors
How can conditional heteroskedasticity be detected and what is the affect on coefficient values?
Unreliable hypothesis test: coefficient value isn’t consistent/unbiased and can be detected through the Breusch-Pagan chi-square test
How do we correct for conditional heteroskedastity?
We use the white-corrected standard errors
Is covariance stationarity good?
Yes where expected value, variance, and covariance is constant and infinite
What is the layman’s definition of Covered Interest Rate Parity (CIRP)?
The forward discount will just offset differences in interest rates
What is the domestic fisher relation
Nominal Interest rate = Real Interest rate + Inflation
What is the E(R) of a carry trade
(investment currency rate - funding currency rate) = E(%changefund/inv)
What is the growth accounting equation or growth rate in potential GDP for econ?
Growth Rate in potential GDP = change Y/Y + changeT/T + elasticity(change K/K) + (1 - elasticity)changeL/L
What is the labor productivity formula?
It is long-term growth rate of labor force + long-term growth rate in labor productivity
What is the classical growth theory
There is no permanent improvement in standard of living from new technologies and it leads to short term economic growth but will revert to subsistence levels
What is the neoclassical growth theory?
Sustainable growth rate is a function of
population growth, labor’s share of income, and the rate of technological advancement.
* Growth rate in labor productivity driven only by improvement in technology.
* Assumes diminishing returns to capital.
What is the main tenant of endogenous growth theory
Economy is perpetual motion machine,
Investment in capital can have constant returns.
* ↑ in savings rate → permanent ↑ in growth rate.
* R&D expenditures ↑ technological progress.
What is held at Fair Value Profit and Loss
Fair Value assets on the balance sheet, Dividends, Interest, Realized G/L, and Unrealized G/L
What is held at FVOCI
Fair Value and Unrealized G/L on the balance sheet and dividends and interest on the income statement
What is held at Amortized Cost
Amortized Cost on balance sheet and Interest and Realized G/L on Income statement
For unrealized gains and losses, what is the formula for debt and equity securities
Fair Value - Amortized Cost = Cumulative Unrealized Gain
Is reclassification under IFRS allowed for FVPL and FVOCI
Initial choice is irrevocable for equity
Reclassification of debt securities permitted only if the business model has change
What is the change in balance sheet investment for associates and joint ventures for equity method
%share in company x change in retained earnings
What happens in transactions with associates when the pro rata share of profit is not confirmed
If it is not through resale or use it is eliminated from equity income
What is Goodwill?
FVsub - FMVNA
What is Minority Interest
(Cash paid for majority interest/majority percentage) x minority interest
What is the classification of impairment and what happens to goodwill
It is reported as a line item on the income statement where goodwill impairment cannot be reversed
How is impairment of goodwill different between IFRS and US GAAP
IFRS - one step process if recognizable amount of cash generating unit < carrying value recognize difference as impairment
US GAAP - two step process if fair value of reporting unit < carrying value, goodwill is impaired amount of impairment is unti’s reported goodwill - current fair value of unit’s goodwill
When it come to sales expenses net income, assets & liabilities and SH equity which is higher equity method or acquisition method
For all the acquisition method is higher except for NI which is the same
When it comes to Net profit margin, ROA, and ROE under the equity method and acquisition which is higher
Equity method is higher for all but for ROE it is only in minoirty interests
For share based compensation what three things are we required to disclosures?
- Nature and extent of share-based compensation arrangement during the period
- How fair value was determined
- Impact on income for the period
What are the stock grants value aka compensation expense in the balance sheet?
Compensation expense equals market value at grant date and it is allocated over period benefited by employee’s service
How do you calculate the number of treasury shares with options?
( (number of options x exercise price) + average unrecognized compensation expense) / average share price
What is the formula for Funded Status
Fair Value of Plan Assets - Plan Benefit Obligations
What are PBO Components rather how do you get from Opening PBO to Closing PBO?
Opening PBO
+ Service Cost
+ Interest Cost
+/- Actuarial (gains) or losses
+/- Past Service Costs
- Benefits Paid
= Closing PBO
What is considered aggressive accounting for PBO
- Low rate of Growth
- High Discount Assumption
- High Expected Return on Assets
- Short Life Expectancy
What are the four assumptions of PBO
- Rate of Compound growth
- Discount Rate
- E(ROA) —> GAAP
- Life Expectancy
On the balance sheet for the current rate how is Assets & Liabilities, Capital Stock, RE, CFXgains/loss, and SH Equity measured?
Balance Sheet
For all assets and liabilities - the current rate
Capital Stock - Historical Rate
Retained Earnings - Accumulated Average Rates
Cumulative FX gain/loss - Plug Figure
Aggregate stockholder’s equity - current rate
When using the current rate method what are revenues and expenses and dividends recorded as?
Revenues and Expenses - Average
Dividends - historical rate when they are declared
What are the three key aspects of Basel III?
- Minimum capital requirements
- Minimum liquidity requirements
- Stability of funding
What does CAMELS stand for
- Capital adequacy
- Asset quality
- Management
- Earnings
- Liquidity
- Sensitivity
What is considered common equity or equity tier I under Basel III?
- Common equity - Common stock, APIC, retained earnings and OCI less intangibles and DTAs
What does asset quality include
It includes existing and potential risk
What is the provision for loan losses
Bad debt expense in the I/S = net charge-offs + change allowance for loan losses
What is an example of aggressive accounting for loan losses
- Possible underprovision
What five things makes high-quality earnings?
- greater than the required return
- Sustainable
- Positive trend
- Unbiased estimates
- Recurring sources
What is the combined ratio and what does it mean
Total incurred losses + expenses / net premium earned High = soft market Low = hard market >100% = underwriting loss
what is the underwriting ratio
[(claims + change of loss reserves) + cost of investigating claims]/net premium earned
What is the expense ratio for insurers?
Underwriting expenses (including commissions)/net premium written
What is the difference between net premium written and earned
Written - premums earned over the period of coverage (net or reinsurance)
Earned - premiums earned over a relevant accounting period
What is Dividend to Policyholders ratio for insurers?
Dividends to policyholders/net premium earned
What is CRAD
Combined ratio + dividends to policyholders
What are the two values in the beneish model that are negative
SGAI -Sales general and administrative expense over sales
LEVI - Leverage index (total debt/total assets)
What are we looking for in balance sheet quality
- Completeness
- Unbiased measurement
- Clear presentation
What is considered aggregate accruals?
Accrual based earnings - cash earnings
What is NOA
(Total Assets - Cash) - (Total Labilities - Total Debt)
What is aggregate accruals for NOA
NOAt - NOAt-1
What is the accruals ratio
Aggregate accruals / (NOAt + NOAt-1)/2
What is the aggregate accruals cfo formula
NI - (CFOt + CFIt)
For cash flow analysis what is the ratio used for operating earnings equality?
Cash generated from operations / EBIT
What is the ratio for cash flow return on assets?
Cash Generated from operations / Average total assets
What is the formula for market value decomposition?
Market capitalization of parent - parent’s share of associates’ market cap = implied value of parent and then put that over net income - parent’s share of associates earnings
What is the dividend irrelevance theory
Dividend policy is irrelevant assumes perfect markets no corporate taxes bankruptcy costs and transactions cost
What are the six factors affecting dividend payout policy?
- Investment opportunities
- Expected volatility of future earnings
- Financial Flexibility
- Tax considerations
- Flotation costs
- Contractual and legal restrictions
What is the effective tax rate for double taxation
tax corporate + (1 - tax corporate)(tax individual)
What is the imputation system for taxes?
Effective tax rate = shareholder’s tax rate
What are the rationales for share repurchases?
- Tax advantage to shareholders
- Signal to shareholders
- Added flexibility
- Offsetting Dilution
- Increase leverage
What is the FCFE coverage ratio?
It is Cash Distributable to shareholders/(dividends + share repurchases)
What is the formula for FCFE from CFO?
CFO - FCInv + Net Borrowing
What is the interpolated yield
Yieldshort + [(yieldlong - yieldshort)/(maturitylong - maturityshort)] x (maturityinterpolated-maturityshort)
What is the Grinold-Kroner Model
ERP = DY + change(P/E) + i + g - changeS] - E(Rf)
What is the formula for return in private companies with Beta?
It is required return = rf + BpeerERP + Size premium + Industry Risk premium + Specific Company risk premium
What can you use the sovereign yield spread for?
You can use it as an estimate of Country Risk Premium
What is the formula for CRP?
Soverign yield spread x (std devequity/std devbond)
What is the formula for extended CAPM or ICAPM?
E(re) = rf + B[E(rm) - rf] + Bc[Foreign Currency Risk Premium]
What are the motivations to investment in a company?
- Creating synergies
- Increasing growth
- Improving capabilities
- Improving access to resources
- Pursuing undervalued investments
What the top down drivers of corporate restructurings (there are 2)
- Industry shocks
- High security prices
What are the three commons valuation methods for corporate restructing?
- Comparable company - not good for minority steak
- Comparable transactions
- Discounted Cash flow
When is DDM appropriate?
For mature firms that are profitable but without fast growth
What is Residual Income
Earnings in excess of the investors’ required return on the beginning-of-period investment - think economic profit
What is the Gordon Growth Model
V0 = D0 x (1+g)/(r-g) or D1/(r-g)
What is the PV of Growth Opportunities
P0 = E1/r + PVGO
What is the H-model?
V0 = [(D0 x (1+gL))/(r-gl)] + (D0 x H x (gs-gl))/(r-gl)
where H is the transition period/2
where gl is low growth
What is the triangle for the H-model growth model
(D0 x H x (gs-gl))/(r-gl)
What is the formula for required return for H-model
r = [D0/P0 x {(1+gl) + [H x (gs - gl)]} } + gl
What is the formula to derive g for valuation purposes?
g = b x ROE or retention rate (b) x NI/SE
What is the short form of ROE
ROE = (net profit margin) x (asset turnover) x (equity multiplier)
What is the definition of FCFF
Cash available to shareholders and bondholders after taxes, FCinv and WCINV - pre-levered cash flow
What is the FCFE
Cash available to equity holders after payments to and inflows from bondholders: post-leveraged cash flow
How do we figure out firm value from FCFF and when do we use it?
We use FCFF discounted at WACC and we use it when high or changing debt levels because using FCFE will result in negative values
How do we figure out firm value from FCFE and when do we use it?
FCFE1 divided by the required return on equity (r) minus the growth rate and We use FCFE when the capital structure is stable
What is the formula for NI
Net Income + NCC + Int(1-t) + FCinv + WCInv
What do we do with Depreciation and Amortization when adjusting NI
We add it to NI and it can be found in I/S or CFO
What do we do with impairment/write-down when adjusting NI
We add it to NI and it can be found in I/S
What do we do with Gains (losses) on asset sale
We Subtract Gains and add losses it can be found in I/S
What do we do with provision for restructuring expenses and income?
We add for expenses and subtract for income which can be found in I/S
What do we do with deferred tax liability
Add if it is unlikely to reverse and it can be found in B/S
What is the formula for FCInv
end net PPE - beg. net PPE + depreciation +/- loss/(gain) on sale
What is the formula for investment in Working Capital
Change of Operating Current Assets - Operating Current Liabilities and it part of CFO
What does WCinv specifically excludes
It excludes cash and cash equivalents, short-term interest-bearing debt, notes payable, current portion of long-term debt
What happens as you increase or decrease working capital adjustments?
An increase in a liability account is a source of cash a decrease in a liability is a use
What is the major difference between FCFF and FCFE when it begins with Net Income
FCFF uses int(1-t) and FCFE is net borrowing
What is FCFF with NI
NI + NCC + [int(1-t)] - WCinv - FCinv
What is FCFF with CFO
CFO + [int(1-t)] - FCinv
What is FCFF for EBIT
FCFF = [EBIT(1-t)} + NCC - WCinv - FCinv
What is the FCFE for NI
NI + NCC - WCinv - FCinv + net borrowings
What is FCFE for CFO
CFO - FCinv + net borrowings
What is the formula that relates FCFE and FCFF
FCFE = FCFF - Int(1-t) + net borrowings
What is the relationship between justified trailing P/E and justified leading P/E?
Justified trailing P0/E0 = (justified leading P/E) (1+g)
What are the drawbacks of P/B ratio
It does not reflect value of intangible assets, off-B/S assets. It is misleading when comparing firms with significant differences in asset size, also different accounting standards obscure comparability
What is the justified P/B ratio
P0/B0 = (ROE-g)/(r-g)
What is the rationale for using P0/S0
P/S useful for mature, cyclical, and zero-income stocks
What is the justified P/S0 ratio
Justified P/S = ((E/S) x (1-b)(1+g))/(r-g)
What is the justified dividend yield D0/P0
D0/P0 = (r-g)/(1+g)
For RI what is the PVGo model
P = EPSt/r + PVGO
What is the P/B ratio using fundamentals
P/B = (ROE-g)/(r-g)
What are the two formulas for calculating RI using EPS and ROE?
RI = EPS - (r x BVt-1)
RIt = (ROEt - r) x BVt-1
What is the formula for the Intrinsic value of multistage residual income in layman terms?
V0 = B0 + (PV high-growth RI) + PV cont. RI
How do you calculate the PV of cont RI with a persistence factor?
RIT/1+r-w where w is the persistence factor
What are the strengths of the RI model
- Terminal value does not dominate intrinsic value estimate
- Accounting data is usually accessible
- Applicable event without dividends or positive cashflow
- Applicable even when cash flows are volatile or unpredictable
Discount for lack of marketability varies with what?
- Likelihood of IPO
- Contractual restricitions
- Pool of buyers
- Ownership concentration
What is the total discount value using DLOC and DLOM?
1 - [(1-DLOC)(1-DLOM)]
What is the IV formula for equity
IVanalyst - price = (IVprice - price) + (IVanalyst - IVactual)
What are porters five elements
- Threat of new entrants in the industry
- Threat of substitutes
- Bargaining power of buyers
- Bargaining power of suppliers
- Rivalry among existing competitors
What is the one-period DDM
V0 = Dividend after year 1 + price expected upon sale in year 1 / (1 +r)
What is the gordon growth model used for?
It is applicable to stable, mature, dividend-paying firms and is straightforward
What is the PRAT model?
It is where the sales growth rate is a function of Profit margin, retention rate, asset turnover, and financial leverage
If long-term assets were sold during the year what is the FCInv formula
Capital Expenditures - proceeds from sales of long-term assets
What is the FCFE for Target debt to asset ratio
FCFE = NI - [(1 - DR)(FCInv - Dep)] - [(1 - DR) x WC INV] where DR = target debt-to-asset ratio
What is the value of the firm using FCFF formula
FCFF1 or FCFF0 x (1+g)/WACC-g
What is the terminal value in year n using P/E
(trailing P/E) x (earnings in year N) or
(leading P/E) x (forecasted earning in year n+1)
What is the inflation pass-through rate and what is the telltale sign
It is the ability to pass some portion of higher costs on to customers and these firms should have a higher P/E ratio
What is the Yardent model?
Current earnings yield of the market = Current Moody’s A-rate corporate bond yield - constant assigned by the market to earnings growth rate x five year consensus earnings growth rate + error
CEY = CBY - k x LTEG + e
What is the formula for PEG are we looking for with PEGs
PEG ratio = (P/E)/g
Stocks with lower PEGs are more attractive than stocks with higher PEGs
What is the formula for earnings-plus-noncash charges
CF = net income + depreciation + amortization
What is the formula for EV
Market Value of Common Stock + market value of preferred equity + market value of debt + minority interest - cash and investment
What is the difference between Total Invested Capital and EV
It is the same except EV doesn’t include cash and short term investment
What is the formula for standardized unexpected earnings (SUE)
Earnings Surprise/Standard deviation of earnings surprie
What is the weighted harmonic mean
1/sumw1/Xi
What is the layman definition for residual income?
It is economic profit or net income of a firm less a charge that measures stockholders’ opportunity cost of capital
What is the formula for equity charge
Equity capital x cost of equity
What is the formula for EVA
NOPAT - (WACC x total capital)
Total capital = net working capital + net fixed assets
What is Tobin’s Q
Market Value of debt + market value of equity / replacement cost of total assets
What is the growth rate formula for residual income valuation model
g = r - [(B0 x (ROE-r)) / (V0-B0)]
What two factors lead to higher persistence factors?
- Low dividend payouts
- Historically high residual income persistence in the industry
What are clean surplus violations
- Foreign currency translation gains and losses
- Certain pension adjustments
- Gains/losses on certain hedging instruments
- Changes in revaluation surplus
- Certain liabilities due to change in credit risk
- Changes in market value of debt and equity
What are the adjustments made to operating income after tax for private firm
Plus depreciation and amortization
Minus capital expenditures
Minus increase in working capital
FCFF
How do we unleaver a beta
Bpublic / [1 + (1-t)(D/E)]
How do we calculate DLOC
1 - [1/ 1 + control premium]
What is the reinvestment rate or b for a private firm
b = g/WACC
What is the value of private firm using EBIT and WACC?
EBIT1(1-T)(1-b)/WACC-g
When is the excess earnings method useful
It is useful for small firms when their intangible assets are significant
For private firms using the EEM what is the formula for firm value?
Firm value = working capital + fixed assets + intangible assets
What is the formula for $1 notional
SumSFRT/(1+St)^t + 1/(1+St)^T = 1
What is the Z-spread
The spread that when added to each spot rate on the default-free spot curve, makes the present value of a bond’s cash flows equal to the bond’s market price. Therefore, the Z-spread is a spread over the entire spot rate curve.
What is the effective duration?
It measures price sensitivity to small parallel shifts in the yield curve
What is the formula for change in the value of fixed income portfolio?
changeP/P = -DLchange of level - Dschange in steepness - DcChange in curvatures
What is the relationship between parallel nodes on a binomial tree?
i1,U = i1,Le^2std dev
What is the CIR and Vasicek model for FI?
They are equilibrium term structure models
CIR is the original model that says that interest rates mean-revert to a normal level this is sped up by a volatility in the interest rate where it has been sqared
It is the same for Vasicek excek there is no sqrrt where it doesn’t matter what the interest rate.
What are equilibrium models and what are arbitrage-free models?
Equilibrium - fundamental models CIR models and Vasicek model
Arbitrage - begin with observed prices these are the Ho-Lee model and KWF model
What happens when the volatility increases for callable and putable bonds?
For callable bonds (where the investor is short the call) the value decreases and the value of the putable bond increases
How are callable and putable bonds related to interest rates?
Call options value is inversely related while put option vary directly
High coupon bonds are
More likely to be called and will tend to dominate the time-to-maturity rate
What is the value of a capped floater?
Value of a straight floater - value of the embedded cap
What is the value of a floored floater?
Value of a straight floater + value of the embedded floor
What is the minimum value of a convertible bond?
Max (straight value, conversion value)
What is the market conversion price
Market price of convertible bond/conversion ratio
What is the market conversion premium ratio?
Market conversion premium per share/market price of common stock
What is the callable convertible bond value
Straight value of bond + Value of call option on stock - value of call option on bond
What is the probability of survival?
PSt = (1 - hazard rate)^t
What is the Credit Valuation Adjustment CVA?
CVA = price of risk-free bond - price of risky bond
What is the formula for cheapest to deliver?
Payoff = notional principal - percentage of par the bond is trading at (notional principal)
where the bond chosen is the same seniority and is delivered at the lowest cost
What is the relationship between the swap seller and swap buyer during the swap?
The swap buyer send the reference obligation to the swap seller and the swap seller sends the par value to the buyer
What is the CDS spread
(1 - Recovery Rate) x Probability of Default
What is the upfront payment by the protection buyer? hint leg
PV(protection leg) - PV(premium leg)
What is the CDS spread from premium?
Upfront premium %/duration + CDS coupon
What is monetizing for the protection buyer?
The difference between the upfront premium paid and received should be equal to the profit for the protection buyer
What is the VT of the long position of the dividend-paying stock using PVD
[St - PVDt] - [FP/(1+Rf)^(T-t)]
What is VT using FP current
FPt-FP/(1+Rf)^(T-t)
What is the value of futures contract during the life of the contract?
Current futures price - previous mark-to-market price
What is the Swap Fixed Rate SFR periodic formula?
1 - final discount factor/sum of discount factor
What is the formula to calculate the discount factor
Z = 1/[1+(MRR x days/360]
What is the swap fixed rate (annual)
SFR(periodic) x number of settlement periods per year
What is the value to the payer of an interest rate swap?
Sum of discount factors x (SFRnew - SFRold) x (days/360) x notional principal
What is the Forward Price of an equity security
(Spot Price - Present Value of Expected Dividends) x (1 + Rf)^T
[S0 x (1+Rf)^T] - FVD
What is the value of a long position on a dividend paying stock
V(long position) = [(FPt-FP)/(1+Rf)^(T-t)]
What is the FP(on an equity index)
S0 x e^(Rcf-gammac)xT
What is the dirty or full price
Clean Price + Accrued interest
What is the value of futures contract during the life of the futures contract?
Current futures price - previous mark-to-market price
What is the probability of an up move in a binomial tree
(1 + Rf - D)/(U - D)
Rf = risk free
D = down move factor
U = Up move factor
What is the put-call parity
C - P = S - PV(X)
What do you do if an option is overpriced in the market
- Sell the option
- Buy a fractional share of the stock for each option we sold
What do you do if a call option is underpriced
- Purchase the option
- Short a fractional share of stock for each option purchased
What is the hedge ratio?
h = (C+ - C-)/(S+ - S-)
Call Payoffs/Stock Prices
What is the call payoff of an interest rate options?
Notional principal x [Max (0, reference rate - exercise rate)]
What is the formula for the black scholes model call?
S0N(d1) - e^(-rT)XN(d2)
What is N(d1) and N(d2)
N(d1) - cumulative standard normal probability where N(d1) stock units are purchased
N(d2) - Risk-neutral probability that a call option will expire in the money
What is the black model
C0 = e^(-Rcf x T) [Ft x N(d1) - X x N(d2)]
What are the interest rate option formula
(AP) e^-r(actual/365) [FRA(MxN)N(d1) - XN(d2)] x NP
AP = Accrual period
What constitutes an interest rate cap
A series of interest rate call options with different maturities and the same exercise price
What is the formula to find the change of a call or put option
Call or Put delta x change of stock price + 1/2 gamma x change in stock price^2
What is Rho
RHO - sensitivity to interest rate
What is theta
Sensitivity of an option to the passage of time
What is the number of short call options needed to detail the hedge
Number of short call options needed to delta hedge = Number of shares hedged/delta of call options
What is the number of long put options needed to delta hedge
Number of shares / delta of the put option
What is the basis of the futures contract
Spot price minus the futures price and can be positive or negative
What is insurance theory?
Those who own the commodity want to hedge future prices, and that drives down future prices. This results in backwardation
What is the hedging pressure hypothesis
Hedging behavior of commodity consumers. This will put upward pressure and result in contango
What is the theory of storage
The price depends on the benefits of holding physical inventory and the costs of storing the commodity. When costs of storage outweigh holding physical inventory then futures price will be higher and in contango
What is the formula for futures price from spot price?
Spot price + Storage costs - Convenience Yield
What is the collateral return
It is simply the holding period yield on T-bills
What is the formula for roll return
Price of expiring futures contract - price of new futures contract/ price of expiring futures contract
What happens when to the long in a notional amount?
The long makes the promised fixed payment percentage plus the native return percentage on the commodity over the period, times the notional amount
What is the excess return swap
A party may make a single payment at the initiation of the swap and then receive periodic payments of any percentage by which the commodity price exceeds some fixed or benchmark value times the notional value
What is a triple net lease?
Requires tenants to pay their share of common area maintenance, repairs, property tax, and building insurance
What is the return of appraisal-based index
Return = [NOI - capital expenditures + (ending market value - beginning market value)]/beginning market value
A repeat-sales index
Relies on repeat sales of the same property
What is a hedonic index
It requires only one sale for the index
What are the two equity real estate securities
- Equity REITs (Real Estate Investment trusts)
- REOCs (real estate operating companies)
What are the two debt real estate securities
- Residential or commercial mortgage-backed securities (MBS)
- Mortgage REITs - primarily invest in mortgages
What is the cap rate
NOIcomps/transaction pricecomps
How do you calculate the FFO
NOI
+ depreciation, amortization, impairments, and write-downs
- Gains from sales of property
+ Losses from sales of property = FFO
What is AFFO
FFO (funds from operations)
- Non-cash (straight-line) rent adjustment
- Recurring maintenance-type capital expenditures and leasing commissions
= AFFO
What are the six hedge fund strategies
- Equity related
- Event driven
- Relative Value
- Opportunistic
- Specialist
- Multi-manager
For a step-wise regression, what are the four factors that avoid multicollinearity?
- Equity Risk (SNP500)
- Currency Risk (USD)
- Credit Risk (CREDIT)
- Volatility risk (VIX)
What are the in-kind creation/redemption process serve three purposes?
- Lower cost
- Tax efficiency
- Keeping market prices in line with NAV
What makes up the spread of an ETF?
Creation/redemption fees plus other trading costs
+ spread of the underlying securities
+ risk premium for carrying the trade until close of trading
+ AP’s normal profit margin
- discount based on probability of offsetting the trade in secondary market
What is the formula for ETF premiums and discounts
ETF premium (discount) % = (ETF price - NAV per share) / NAV per share
What are the sources of premiums or discounts of ETFs?
- Timing differences
- Stale pricing
What is the total cost of owning an ETF?
Total Cost = Round-trip commission + spread + management fees
What are the three portfolio uses of ETFs?
- Efficient portfolio management
- Asset class exposure management
- Active investing
What are the two factors of the macroeconomic factor models?
- Surprize in GDP rate
- Surprise in credit quality + firm-specific surprise
What are the two factors of a fundamental factor model?
- Return associated with the P/E factor
- Return associated with the SIZE (market capitalization) factor
What is the two part active return formula?
Factor return + Security selection return
What is the formula for active risk squared no calc
Active factor risk + active specific risk
What are the four factors of the Carhart model?
- RMRF - (Return of value=weighted equity index - risk free rate)
- SMB (difference between small cap and large cap stocks)
- HML (Difference between high and low Book-to-market stocks)
- WML - (average returns on past winners - average returns on pas losers)
What is the Information Ratio?
IR = (Rp - RB)/std dev(Rp-RB)
What standard deviation do we use for 5% Var and 2.5% vae
1.65 and 1.99
What is the marginal Var
It is the slope of a curve that plots VaR as a function of a security’s weight in the portfolio
What is the difference between scenario and sensitivity analysis
Sensitivity is based on the change of one factor while scenario is based on a whole set of changes
What is the change in price of the fixed income portfolio?
-Duration (change Y) + 1/2 convexity (change Y)^2
What is the formula for a change in call price for an options-based portfolio?
Change in call price = delta(change in price) + 1/2 gamma (change S)^2 + vega (change in future volatility)
What is the data mining trap?
Many different factors are considered and those that perform well in a backtest are incorporated into the strategy even if they don’t have a reason to be included
What is the difference between a benchmark portfolio and risk parity portfolio?
BM - weights factors equallys
Risk Parity - Combines factors so each contributes equally to risk
What is rolling window backtesting
The investor uses a wal-forward system rather than dividing the data into just two samples. The investor will calibrate the trade signals or factors based on the moving window, adjust the model and rebalance after each period. It does not account for randomness
What is look-ahead bias
It is when investors make use of data that would not have been available at the time an investment decision is made.
What is cross-validation
It is a technique that involves testing a hypothesis on a different set of data than the one that was initially used to form the inference or test hypothesis
When would a Risk-Parity portfolio perform well and when would a Benchmark portfolio perform well?
RP - performs well in both a low or high volatility environment
BM - may not perform well in a low-volatility environment
What is tail dependence
It measures the correlation between the tails of two random variables. Those that have high dependence will have tails that move together.
What is the risk premium of the bond given an E(p1)
P0 = E(P1)/(1+R) + cov(P1,m1)
where R = real risk-free rate
What is the inter-temporal rate of substitution?
(marginal utility of consuming 1 unit in the future at time t)/(marginal utility of current consumption of 1 unit)
the rate at which a consumer is willing to substitute consumption in the present for consumption in the future.
What is the price of the sales price?
P0 = E(P1)/(1+R) + cov(P1,m1)
What is the formula for the short-term risk free securities
Nominal = Real Risk-free rate + Expected inflation
What is the formula for the nominal long-term risk free securities? no calc
Nominal = Real Risk-free rate + Expected inflation + inflation uncertainty
What is the Taylor Rule?
Central Bank policy rate = neutral real policy interest rate + current inflation rate + 0.5(current inflation rate - central bank’s target inflation rate) + 0.5(log of current level of output - log of central bank’s target (sustainable) output)
What is the break-even inflation rate with bonds and not with bonds?
BEI = yield on non-inflation-indexed bond - yield on inflation-indexed bond
General BEI = expected inflation + uncertainty premium for inflation
What is the required rate of return for credit-risky bonds
Real interest rate + inflation rate + inflation uncertainty + credit spread
What is the nominal rate of return for equity?
Real interest rate + inflation rate + inflation uncertainty + credit spread + additional risk premium relative to risky debt for an investment in equity
What is the Sharpe Ratio?
Excess return per unit of risk is
SR = (Rp - RF)/std devp which is unaffected by cash or leverage
What is the information ratio?
Active return/active risk
(Rp-RB)/std dev(Rp-RB) - this is affected by cash or leverage
What is the optimal active risk?
std devA = (IR/SRb)std devb
The Sharpe ratio of portfolio with optimal level of active risk is?
SRp = sqr rt(SRB^2+IR^2)
What is the total risk of the portfolio or std devp?
std devp^2 = std devB^2 + std devA^2
What is the Information Ratio and Expected Return of an unconstrained portfolio?
IR = IC sqr rt(BR)
E(RA) = ICsqr rt(BR)std devA
What is the IR and value of a constrained portfolio?
IR = TC IC sqr rt(BR)
E(RA) = TC IC sqr rt(BR)std devA
What is the optimal level of active risk
std CA = TC (IR/SRB) std devB
What is the information coefficient of a market timer?
IC = 2(% correct) - 1
If individual decisions are correlated, then the breadth can be estimated as?
BR = Number of decisions / (1 - [(Number of decisions - 1) correlation between the decisions])
What are the seven standards of professional conduct?
I. Professionalism
II. Integrity of Capital Markets
III. Duties to Clients
IV. Duties to Employers
V. Investment Analysis, Recommendations, and Actions
VI. Conflict of Interest
VII. Responsibilities as a CFA Institute Member or CFA candidate
What are the two things needed to maintain CFA membership?
- Sign PCS annually
- Pay CFA institute membership dues annually
What is rolling down the yield curve?
Investors purchase bonds with the maturity higher than their holding period.
What is the unbiased expectations theory?
Investors expectations determine the shape of the interest rate term structure
What is preserved under local expectations theory?
Risk-neutrality is preserved for short term under local expectations
What is liquidity preference theory?
The longer dated cash flows are more sensitive to rate changes. the forward rates are biased estimates of future rates because of liquidity premium
What is preferred habitat theory and what would make investors leave?
People have preferred maturities that they prefer
Investors are willing to leave preferred maturity habitat to obtain a lower price
What is effective duration?
It measures price risk for small parallel shifts in the yield curve
What is key rate duration?
Key Rate duration is price sensitivity to 1% change in a single par rate
What are the three things the parallels curves risk are broken down into?
- Level
- Steepness
- Curvature
What are the equilibrium term structure models?
- The Vasicek Model
- The Cox-Ingersoll-Ross Model
These are both single-factor models
What are the arbitrage-free interest rate models?
- The Ho-Lee Model
- The Kalotay-Williams-Fabozzi Model
These are binomial models
How does volatility affect straight bond values and embedded options
Volatility does not impact straight bonds they do affect embedded options
What happen when the value of the volatility goes up to the Value of the callable bond and putable bond
Callable bond the value goes down
Putable bond the value goes up
When rates decline what happens to a callable bond
The upside on a callable bond is limited
When rates increase what happens to a putable bond
The downside of a putable bond is limited
What is OAS and where is it higher and where is it lower?
It is the constant interest rate spread added to all rates in the binomial tree it is lower for callable and higher for putable bonds
How is duration of callable or putable bonds related to duration of straight bonds?
Lower or equal
What is the duration of a floater
It is the time (years) to next reeset
The callable and putable bonds relationship to their upside and downside duration?
Callable have higher one-sided down duration
Putable bonds will have higher one-sided down duration
What is the formula for effective duration?
ED = V- - V+ / 2Vochange Y
What happens as the option moves into the money for time to exercise and key rate duration?
The time-to-exercise rate becomes more important. Key rate duration corresponding to the time-to-exercise will be highest
What is the value of a callable convertible
Straight bond + call on stock - call on bond
What is the formula for change in price for credit migration?
-(modified duration of the bond) x (change in spread)
What is the term structure of credit spreads
It represents the relationship of credit spreads to debt maturity
What are credit spreads?
It is the difference in yields for credit-risky bonds and risk-free bonds
How does quality impact term structure?
Higher-rate sectors have flatter term structures
How does financial conditions impact term structure
They are steeper when expecting recessions
What is the formula for upfront premium for CDS?
Upfront Premium % = (CDS spread - CDS coupon) x Duration
What is the formula for profit for protection buyer?
Change in spread (bps) x duration x notional principal
What is the formula for forward price of derivatives contract?
FP = S0 x (1+Rf)^T
What is the no-arbitrage value of a long forward contract during the life of the contract? hint using St
Vt(of long position during life of contract) = St - [FP/(1+Rf)^(T-t)]
What is the no-arbitrage value of a long forward contract during the life of the contract? hint using FPt
[ (FPt - FP)/ (1 + Rf)^(T-t) ]
What happens when interim cash flows (dividends and coupons) are incorporated into equity forward contracts?
Interim CFs offset cost of carry and reduce the no-arbitrage FP
What are formulas for pricing equity forwards with PVD and FVD?
- (S0 - PVD) x (1+Rf)^T
- [S0 x (1+Rf)^T] - FVD
Use #of days/365
What is the Future Price of an equity index
S0 x e^(Rfc-deltac) x T
What is the futures price for a bond contract?
FP = [ (full price) (1 + Rf)^T - [(days since last coupon/days between coupons)xcoupon payments] - FVC]
What is the quoted futures price of a bond future?
Futures Price/Conversion Factor
What does it mean to Long FRA?
Pay-fixed, receive floating
What does short FRA mean?
Pay-floating, receive-fixed
What is the formula for the swap fixed rate?
[ (1 - last discount factor)/sum of Discount Factors] x settlement periods per year
What is the value of the payer?
Sum of Discount Factors x [ (SFRNew - SFROld)/# settlements/year] x Notional Principal
What is the PV (equity side cash flows)
Current index level/index level at last settlement x notional
For the binomial model what is the probability of an up-move?
( 1 +Rf - D)/(U - D)
What is the relationship between up-move size and down-move size and probability of up-move and probability of down-move
D = 1/U
piu = 1 - pid
What is the formula for call value using binomial tree
It is (Value of upmove x probability of upmove) + (value of down move x probability of downmove)/risk free rate
What it the formula for the put call parity?
C - P = S -X
What is the hedge ratio?
We use it compute untis of long stock per short call
(C+1 - C-1)/(S+1 - S-1)
What is the risk-free rate of return formula using a hedge ratio?
P1/P0 - 1 = 0.07
What are the arbitrage rules for options? To put it differently what should you do if an option is overppriced or underpriced?
Option overpriced: sell option and buy fraction share of stock
Option Underpriced: Buy option and short sell fractional share of stock
What is an interest rate call?
Holder (long) receives payments if the reference rate > the strike (fixed rate)
What is the PMT formula for interest rate calls?
PMT = max [ 0,NPx(reference rate - strike) x actual days/360]
What is the PMT formula for interest rate puts?
PMT = max [ 0,NPx(strike - reference rate) x actual days/360]
For European bonds what is the MRR over
360 days
A Long FRA combines what two things?
Long call + short put
Interest rate caps and floors are a series of…?
Cap = Series of IR Calls
Floor = series of IR puts
What is the value of a call and a put when it nears time to expiration?
It approaches 0
How are calls and put impacted by the change in exercise price
- Negatively related to calls and positively related to puts
What is the relationship between put delta and call delta
Put delta = call delta - 1
What are the values of call deltas and what happens when they are out of and in the money?
The values range from 0 to 1 if no dividend
Out of the money delta approaches 0
In the money delta approaches 1
What are the values of put deltas and what happens when they are out of and in the money?
The values range from -1 to 0 if no dividend
Out of the money delta approaches 0
In the money delta approaches -1
What is the change of call price formula in relationship to delta?
Change of Call = deltacall x change in stock
In order to get delta neutral hedging how many short calls are needed
shares hedged/deltacall
What is the gamma and delta formula to figure out the change in call price
Change in call = call delta x change in S + 1/2 gamma x change in S^2
What is contango
Futures prices > spot prices
What is backwardation
futures price < spot price
What is the total return formula for a futures contract?
Total return = collateral return + price return + roll return
For markets in backwardation roll return is
positive long holder will buy longer-dated contracts that are priced lower than expiring contracts
For markets in contango roll return is
negative long-dated contract priced higher than expiring
What is the return of real estate formula?
Return = (NOI - capex + (end mkt value - beg mkt value) / beginning market value
How do you get to the Value per share for FFO?
FFO
divided shares
equals FFO/share
times office subsector multiple
this equals to value per share
What are the goals of short selling and short biased?
Produce negative correlation with conventional securities
What is the goal of equity market neutral strategy?
Generate alpha from mispricing but zero exposure to market where there is modes return given zero beta exposure
What is role of equity market neutral in the portfolio and when is it beneficial?
It is to produce alpha without taking market beta risk in especially beneficial in volatile and poorly performing markets
How do you implement an equity market neutral strategy for the undervalued security?
For the undervalued security you will short:
Total amount available/(undervalued beta/overvalued beta)
What are the overall characteristics of a merger arbitrage and what kind of risk does it have?
You earn a return from the uncertainty due to time between announcement and completion of an acquisition. There is significant left-tail risk
What are important aspects of fixed-income arbitrage? hint return and inital investment
It is overall low expected return, so much use of leverage (400% to 1500%) to magnify returns
What are the two kinds of opportunistic hedge fund strategies?
- Systematic implementation (computer algorithms)
- Discretionary process (instinct)
What is the purpose of managed futures?
Long/short derivatives and they have low correlation with traditional assets: diversifier
What is the goal of volatility trading?
To buy underpriced volatility, sell overpriced volatility, long position in volatility has + convexity
What is the role in the portfolio of volatility trading?
Strong diversification is due to the negative correlation of market volatility with market returns.
What are some risks of Fund-of-Funds?
It has potential netting risk; investors may need to make large incentive payments, even if FOF overall performance is poor
What is the difference between Sharpe Ratio and Sortino Ratio to evaluate hedge funds?
Sharpe uses SD so both downside and upside risk impact Sharpe while Sortino better reflects hedge fund risk because only uses downside deviation
What are the three factors of fama-french three-factor model
- Market risk factor - Market index - Rf
- SMB - (Small - big) returns
- HML - (High B/M - low B/M)
What is the purpose of scaling all factors in a fundamental factor model?
Scaling allows all factor sensitivities to be interpreted similarly, regardless of units of measure
For the Macro Factor model vs. Fundamental model what is the difference between what regression coefficients are and their intercepts?
Macro - Times series of surprises and intercept is expected return
Fundamental - Cross-sectional asset returns and intercept is undefined
For the Macro Factor model vs. Fundamental model what is the difference between factor sensitivity vs. Factor returns
Macros for Factor Sensitivity are regression based while for fundamentals are from computed from multiple regression
What are the z-values on both sides of a 5% var and 2.5% var?
5% (on both sides) - 1.645
2.5 (on both sides) - 1.96
What is incremental VAR
Estimated change in VaR from change in size of a portfolio position
What is ex-ante tracking error?
Var of difference between portfolio vs. benchmark returns
What is bootstrapping
It is a way of simulating where the samples are drawn with replacement
What is the Real risk-free rate portfolio or (1-P0)/P0?
(1 - P0) / P0 = [ (1/intertempoal rate of substitution) - 1]
What is the relationship between future incomes and real rates?
If investors expect higher incomes in future, utility of consumption in future relative to current consumption is lower and real rates will be higher
What is the price of a risk-free long-dated bond?
P0 = E(P1)/(1 + R) + cov(P1,m1)
What will happen to future consumption of GDP growth rates are forecast to be high?
Investors expect higher income in the future hence, they prefer current consumption
According to the Taylor rule how are short-term policy rates related to inflationary and output gap
Short-term policy rates are positively related to inflationary gap and output gap
If inf is high then running above
and output high the economy is overheating
What are the two formulas for BEI
Yield on default-free nominal bond (T-bond) - yield on default-free real bond (TIPS)
Expected inflation + Risk premium for inflation uncertainty
The equity risk premium is a function of what two things?
Volatility and hedging
Why is equity a poor hedge?
Equity provides a poor hedge against bad consumption outcomes and causes equity risk premium to be positive
General formula for value added of active return? hint add
Sum (change of weights x Expected Benchmark return) + Sum (Portfolio Weights x Active return within asset classes)
First part is for active return from asset allocation and then second part is active return from stock selection
What is the active return from stock selection (RAj)
Weight of the asset class in portfolio times the difference of the asset classes between the portfolio return and benchmark return
What is the active return from asset allocation?
Difference between the weight in the asset class between the portfolio and benchmark times the return of Benchmark return
What is the Sharpe ratio?
Access return per unit of risk
SR = Rp - RF / std devP
What is the information ratio?
Active return/Active risk
(RP - RB)/std dev(Rp - RB)
What is the difference between the Sharpe ratio and Information ratio?
The IR is affected by leverage and cash
What is the formula that relates SR and IR in an active portfolio and how does IR help with manager selection?
SRP^2 = SRB^2 + IR^2 Choosing the manager with the highest information ratio will produce the highest Sharpe ratio
What is the formula that relates SR and IR in an active portfolio stand dev
SD(Rp)^2 = SD(RB)^2 + SD(RA)^2
Total portfolio return volatility = benchmark return volatility
What is the formula for the optimal aggressiveness from total risk?
IR/SR x Total Risk
What does the information coefficient measure and what is a typical value?
It measures the manager skill typically post will be less than 0.2
What is the transfer coefficient?
It is the correlation between actual active weights and optimal active weights most of the time it will be 1 for unconstrained portfolios and less than one for constrained
What is the breadth
Number of independent bets
What is the E(RA) for a Return Alpha for both constrained and unconstrained portfolio?
E (RA) = TC IC sqrt(BR) std devA
TC is usually 1 for unconstrained portfolios
What is the IR for constrained portfolio?
IR = TC IC sqr rt(BR)
What is the SR for an active risk for a constrained portfolio?
SRp^2 = SRB^2 + (TC)^2 (IR)^2
What is the standard dev of Return of Alpha for a constrained portfolio?
SD (RA) = TC (IR/SRB) x SD(RB)
What is the IC for an active management
IC = 2 (% correct) - 1
Formula for actual P/FCFE and trailing P/FCFE
Actual = current market price of $15 divided by FCFE for that year
Trailing = value derived from the FCFE valuation model ($11.18) divided by FCFE for 2008:
What is the formula for adjusted CFO from Net Income?
It is Net Income + Depreciation - Increase in Net Working Capital + After-tax interest expense
How do you calculate Implied Growth rate for a residual income model?
Find shareholder equity/total shares
then g = r - [B0 x (ROE-R)/V0-B0]
Why does increasing financial leverage increases the value of the firm?
Value of the firm will increase due to tax shields and lower cost of equity
Payables formula ratio?
Accounts Payable/NI
Where are tax windfalls reported?
They are reported directly to equity and would reduce tax expense in the income statement
What is justified trailing P/E
Payout x required rate of return / required rate of return - growth or ((1-b)(1+g))/(r-g)
What is a floor on a floating rate considered
Owning a series of calls
How to get the value of a firm from FCFF1?
FCFF1/(WACC-g)
What is the impact of FVOCI on income statement
The only impact is to dividends so just increase the amount of dividend income
If a company exerts significant influence how do you account for it on the income statement?
You do not include the dividends and just a percentage of the NI
If a company changes to FVPL
The difference between fair market value and amoritized cost is shown in Net Income.
How to calculate a SFR?
SFRN(P1 + P2 + P3 + … + PN) + PN = 1 for prices of zero coupon $1 par bonds
What is the difference between a structural model and a reduced form model?
Structural models of corporate credit risk are based on the structure of a company’s balance sheet and rely on insights provided by option pricing theory. as opposed to Instead, they statistically model when default occurs. Default under the RF model is a randomly occurring exogenous variable. As such, the RF model imposes assumptions on the output of the structural model (asset values, recovery rates, etc.).
If you expect lower incomes in the future
The utility of future consumption relative to current consumption is higher and real rate will be lower
modified duration
change in spread x -modified duration
What is the difference between soft and hard catalyst trade? alternate investments
A soft-catalyst event-driven approach is an investment made before an event has been announced. A hard-catalyst event-driven approach is an investment made after a corporate event has been announced; this strategy seeks to take advantage of security prices that have not fully adjusted. Soft-catalyst investing is generally more volatile (and, thus, riskier) than a hard-catalyst approach.
What is the upfront payment for a protection buyer for a CDS?
= (CDS spread − CDS coupon) × duration × notional principal
How to test if at least one variable has explanatory power?
Use the anova table and Mean square regression/mean square error
then use the table for df1 as the numerator of the number of regressions and df2 at the number of observations
What is the difference between Breusch Pagan and Breusch Godfrey stats?
BP - heteroskedasticity tet
BG - for AR models and tests for serial correlation
What is the formula for MSR
SST - SSE/number of independent variables
What is the formula for MSE
SSE/n - k - 1
What is the justified leading P/E ratio?
(1-b)/(r-g) b - payout
What is the FI market conversion premium?
(market bond price/conversion ratio) - Price of the stock now
What is the conversion value of a convertible bond
Market price of stock x conversion ratio
What is the balance sheet accrual ratio?
Change in NOA/Average NOA
How do you get P/E from ROE
You get the average or given ROE and then multiply by BV of previous year. Then that becomes EPS and take P and divide by that number.
If you are looking for economic profit which would you use in real estate?
AFFO - current economic income
When the model needs to be split into two time periods it arises from
functional form model misspecification.
When a variable is omitted the estimates are
Biased and inconsistent
How do you calculate the Revenue growth rate
sqrt(Revenuet/Revenuet-1) - 1
Owning a company’s debt is the same as
Owning a riskless bond and selling a European put on the assets of the company
Under black scholes a call is valued as
the present value of the difference between the current futures price times N(d1) and the exercise price multiplied by N(d2).
How do you replicate a payer swap
zero-cost portfolio consisting of a long cap and a short floor with the same strike rate.
Under black scholes a put is valued as
the present value of the difference between the exercise price multiplied by N(-d2) and the current futures price times N(-d1)
What is the weight of the active portfolio it is:
The optimal level of risk/active return of the portfolio
The highest sharpe ratio of a portfolio?
SRp = sqrt(SRB^2+IR^2)
What happens when a country expects high levels of growth?
real rates will be high. Investors will be less concerned about the future, and the inter-temporal rate of substitution will be low.
What is the justified leading P/E
Payout ratio/required rate - growth
(1-b)/(r-g)
What is the P/CF ratio?
Justified P/CF = (FCFE0 x (1+g))/(r-g)
What is the formula for the single stage RI model?
V0 = B0 + [(ROE-r)xB0/(r-g)]
What is the breakdown of EVA breaking down NOPAT?
[EBIT x (1 - t)] - $WACC (dollar cost of capital) (Total Capital (LTD and SH Equity)
Capital Deepening Occurs in what situations?
When the capital-to-labor ratio is low
What is the formula for long-term GDP growth rate?
Total Factor Productivity + alpha (long term growth of capital) + (1-alpha) (long term growth of labor
What makes up pension expense?
Service Cost + Interest Cost - Expected Return on Assets
What is Operating Profit ratio?
EBIT/Sales
What is the difference between structural and reduced-form models in FI?
Structural - it explains why the default occurs and in what situations it occurs in
Reduced - it explains when the default occurs and does not assume it trades
What are the BSM assumptions?
- Price of the underlying has a normally distributed continuously compounded return
- Risk free rate is constant and known
- volatility of the return of the stock is constant and known
- frictionless markets
What is in equity tier 2 and additional tier 1?
This includes subordinate instruments with either no specific maturity or specific maturity
What is the number of days of stress volume of cash outflow?
Liquidity coverage ratio x number of days for the stress test
What happens under hyperinflation
You use the temporal rate method and you would recognize a gain in the income statement and equity and cash flow will remain the same
What happens under tax aversion theory?
Under tax aversion shareholders are acutely aware of their tax situation and taken to the extreme would prefer the firm to not issue dividends
What two factors is an ICAPM model based on?
- a global market index factor
- a foreign currency denominated, wealth-weighted market index
Callable bonds are most likely to have what kind of convexity?
Negative
What is a basis swap?
periodic payments are exchanged based on the prices of two commodities that are imperfectly correlated.
If both data series have a unit root and are cointegrated then the results are?
If both data series have unit root and are not cointegrated then the results are?
Valid
Invalid
What happens with a tax windfall under US GAAP and IFRS?
a tax windfall would reduce tax expense in the income statement and hence result in a higher net income. Tax windfalls would go directly into equity via OCI under IFRS. Either way, the stockholders’ equity would be the same.
The maximum amount an investor holding the bond would pay to a third party to remove the risk of default would be:
The Present Value of the expected loss
What is the Futures Price formula for bonds?
(1/Conversion Factor)[(Clean price + AI0)x(1+Rf)^T - AIC - FVC]
How do dividends impact the value of calls and puts?
It will decrease the value of calls and increase the value of puts
How do you get NAVPS?
Divide RE by cap rate then add Cash and AR and subtract debt and other liabilities
What is a support vector machine?
It can be applied to classify text from documents into useful categories for investors
What is considered a credit event?
- Bankruptcy
- Missing a payment
- Restructuring
What is the fundamental law of active management?
It is that active decisions should be independent of each other and should not suffer from cross or time series dependency
