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CFA Level II > Focus Formulas > Flashcards

Focus Formulas Flashcards

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1
Q

Basel III Requirements and Their Goals

A
  • Minimum Capital Requirement
    • specifies ratio of assets to risk-weighted assets
    • to ensure BS strong enough to cope with loan losses
  • Stable Funding Requirements
    • specify amount of stable funding relative to liquidity needs over one year
  • Minimum Liquidity Requirement
    • specifies minimum level liquidity to cover a partial loss of funding sources, or outflow due to off-BS commitments
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2
Q

Receivables Turnover

A

Sales

___________________

AR

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3
Q

DSO

A

365

____________________

Receivables Turnover

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4
Q

Asset Turnover

A

Revenue

__________________

Assets

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5
Q

Cash Conversion Cycle

A

DSO + Days Inventory on Hand - Days of Payables

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6
Q

Days of Payables

A

365

_______________________

Payables Turnover

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7
Q

Payables Turnover

A

Purchases

_________________

Avg. Payables

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8
Q

Days Inventory on Hand

A

365

____________________

Inventory Turnover

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9
Q

Inventory Turnover

A

COGS

___________________

Avg Inventory

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10
Q

Quick Ratio (2 ways)

A

Current Assets - Inventory

____________________________

Current Liabilities

OR

Cash + AR

__________________________

Current Liabilities

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11
Q

Cash Ratio

A

Cash + Marketable Securities

________________________

Current Liabilities

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12
Q

Inflation and BEI

A

Inflation:

1 + Nominal Rate

___________________

1+ Real Rate

BEI:

Expected Inflation + premium for inflation uncertainty

(the difference between the nominal and risk free rates)

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13
Q

Interest Coverage Ratio

A

EBIT

_____________________

Interest Expense

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14
Q

Fixed Charge Coverage Ratio

A

EBIT + Lease Payments

____________________________

Interest + Lease Payments

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15
Q

Debt to Capital Ratio

A

Total Debt

_________________________

Debt + Shareholders Equity

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16
Q

Debt to Equity Ratio

A

Total Debt

_________________

Shareholders Equity

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17
Q

Financial Leverage

A

Avg Total Assets

_________________________

Avg total Equity

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18
Q

Net Operating Assets

A

Operating Assets - Operating Liabilities

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19
Q

Operating Assets

A

Total Assets - Cash & Equiv - Marketable Securities

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20
Q

Operating Liabilities

A

Total Liabilities - Total Debt

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21
Q

Accruals

A

Ending NOA - Beginning NOA

NI - CFO - CFI

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22
Q

Accruals Ratio

A

Change in NOA

______________________

Avg NOA

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23
Q

Gross Margin

A

Rev - Cogs

___________________

Revenue

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24
Q

Operating Margin

A

Operating Income

_____________________

Revenue

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25
Q

Adjusted Operating Profit

A

Reported Operating Profit

+ Reported Pension Expense

  • Service Cost

_______________________________

= Adjusted Operating Profit

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26
Q

Partial Goodwill

A

IFRS ONLY

Proceeds - pro rata identifiable FMV of Net Assets

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27
Q

Full Goodwill

A

IFRS AND GAAP

FMV (acquisition cost / % purchased) - identifiable FMV of Net Assets

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28
Q

Goodwill Impairment: IFRS

A

If carrying value > recoverable amount

recoverable amount = higher of net selling price or PV of future CF

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29
Q

Goodwill Impairment: GAAP

A

2-step:

1) identify: if carrying value of reporting unit + goodwill > FV of reporting unit
2) Measure: carrying value of goodwill > Implied FV of goodwill

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30
Q

VIE Criteria

A

1) Equity interest <10% of total assets
2) Equity Investor lacks decision-making, obligation to absorb losses (guarantee), right to receive residual returns

VIE mustb e conslidated under parent if the company is the primary beneficiary

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31
Q

PBO

A

BGN POBO

+ Service Cost

+Interest Cost

+/- Actuarial G/L

+/- Prior Service Cost

-Benefits Paid

_______________________

= Ending PBO

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32
Q

FVPA

A

BGN FVPA

+ /- ARPA

+ Contributions

  • Benefits Paid

___________________

END FVPA

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33
Q

IFRS vs. GAAP Treatment of Prior Service Costs

A

IFRS: Expensed immediately: pension expense up 100

GAAP: Reported in comprehensive Income, amortized over employee service life

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34
Q

GAAP Pension Expense

A

CSC

+ Interest Expense

  • ERPA

+/- Amort PSC

+/- Actuarial

_______________

= Pension Expense

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35
Q

IFRS Pension Expense

A

CSC

+/- Net Interest

+/- PSC

___________________

= Pension Expense

Net Interest = discount rate x BGN Funded status -> if negative, interest is positive

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36
Q

TPPC

A

calculated the same IFRS and GAAP

1) Contributions - Change in Funded Status
2) Service Cost + Interest + Plan amendments +/- current period actuarial G/L
- ARPA
3) Reported Pension Cost + change in OCI items

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37
Q

Analyst Adjustments for PBO / Pension

A

Replace I/S Expense with TPPC

Split Pension Expense up within I/S:

Service Cost = Operating

Interest Cost = interest expense

ARPA = non-operating income

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38
Q

Analyst Adjustments to Cash Flow Statement for Pension Stuff

A

If contributions > TPPC, it’s like pre-paying a loan –> the delta is the prepayment of principal

eg contributions = 50

TPPC = 25

—> 50-25 = 25

principal amount goes to CFF - CFF down by 25

CFO up by TPPC

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39
Q

COGS on I/S for Temporal Method

A

COGS = BGN Inventory + Purchases - Ending Inventory

Separate and translate each separately, then add back together for COGS

BGN Inventory = Historical

Purchases = Average

END Inventory = Historical

NOTE: BGN & END historical rates can be different

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40
Q

GAAP Vs. IFRS Hyperinflation

A

GAAP: NO adjusting for hyperinflation -> requires temporal method NO MATTER WHAT

IFRS: DOES allow adjustment –> re-state for inflation using price index under the CURRENT rate

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41
Q

Liquidity Coverage Ratio

A

High Quality Liquid Assets (Easy convert to cash)

____________________________________________

Expected Cash Outflows (in stress scenario)

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42
Q

NSFR

A

Available Stable Funding

_________________________________

Required Stable Funding

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43
Q

Days of Stress Level Cash

A

= LCR x # of days (given)

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44
Q

Total Capital Ratio

A

Tier 1 + Tier 2

_________________________________

Total RISK WEIGHTED Capital

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45
Q

Net Premium Written

A

Premiums Earned over Coverage Period (less reinsurance)

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46
Q

Net Premium Earned

A

Premiums earned over Accounting Period

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47
Q

Expense Ratio

A

Underwriting Expenses (incl. Commissions)

________________________________________

Net Premium WRITTEN

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48
Q

UW Loss Ratio

A

Incurred Losses + Loss adjustment expenses

_______________________________________

Net Premium EARNED

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49
Q

Combined Ratio

A

Expense Ratio + UW Loss Ratio

>100% = loss

High = Soft Market (can raise premiums )

Low = Hard market (can’t raise premiums much)

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50
Q

Dividends to Policyholders

A

Dividends to Policyholders

_____________________________

Net Premium Earned

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51
Q

CRAD

A

Combined Ratio after Dividends

Combined Ratio + Divs to policyholders ratio

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52
Q

For CVA:

Recovery Rate

LGD

Hazard Rate

Probability of Survival

Probability of Default

Discount Factor

A

Recovery Rate= percent recovered = 1 - Loss Severity

LGD = exposure x loss severity

Hazard Rate = Initial Prob of Default

Probability of Survival = (1 - Hazard Rate)T

Probability of Default = (Hazard Rate x PSt-1)

Discount Factor = PV of $1. so for y3 = 1 / (1+r)3

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53
Q

Required Return

A

Rf + ERP

build-up:

RfR + ERP + size premium + company-specific premium

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54
Q

Blume Method of adjusting beta

A

Beta tends to revert to 1.0 over time -> adjusts for beta drift

adjusted beta = (2/3 x regression beta) + (1/3 x 1.0)

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55
Q

ERP

A

(1y fwd forecased dividend yield) + (consensus growth rate) - (current LT gov bond yield)

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56
Q

Bond Yield Plus

A

Expected Return = ( YTM on Long Term Debt ) + ( risk premium)

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57
Q

Find Weights for WACC

A

We = Mkt Value Equity / (mkt value debt + mkt value equity)

same for Wd

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58
Q

Pastor-Stambaugh Model

A

Finds required return, adds a liquidity factor to the Fama french, making it more useful for pvt / thinly traded firms

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59
Q

PVGO

A

V0 = (E1 / r) + PVGO

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60
Q

Forecast FCFE

A

FCFE = NI - [(1-DR) x (FCInv - Depr)] - [(1-DR) x WCInv]

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61
Q

WCInv

A

∆(Current Assets - Cash & Investments) - (Current L’s - ST debt & Div’s payable)

Note: CHANGE

BGN WC - END WC

Change in WC

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62
Q

FCInv

A

END Net PPE

  • BGN Net PPE

+ Depreciation

  • Gain (loss) on sale of PPE
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63
Q

Leading P/E

A

1-b

__________________

r-g

Payout Ratio

_____________

r-g

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64
Q

Trailing P/E

A

(1-b)(1+g)

____________________

r-g

Leading P/E times 1+g

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65
Q

Justified P/B Ratio

A

ROE - g

_________________

r - g

AKA trailing P/E X ROE

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66
Q

Justified P/S Multiple

A

(Net Margin)( 1 - b )( 1 + g )

________________________________

r-g

AKA trailing PE x Net Margin

67
Q

Enterprise Value

A

MVEquity (INCL preferred) + MVDebt + MI(not important) - Cash & Liquid investments

68
Q

Normalized Earnings

A

ROE x BVPS

69
Q

DLOC + total discount

A

DLOC

1 - [1 / (1 + Ctrl PREMIUM)]

Total Discount

1 - (1-DLOC)(1-DLOM)

70
Q

Wtd Harmonic Mean for Portfolio P/E

A

Add prices & EPOS to find portfolio P/E

Price: $12 + $15

EPS 1 + 2

27/3 = Portfolio P/E

OR

1

_____________________

sum of (weights/PE ratios)

71
Q

EVA

A

NOPAT - $WACC

EBIT(1-T) - (WACC x IC)

IC = S/HEquity + Total Debt (PREVIOUS PERIOD ENDING OR CURRNT PERIOD BGN)

72
Q

MVA

A

End of year market value - Total Capital

73
Q

Reasons Why Residual Income Approach Doesn’t Work

A

1) Off-BS Items -> Equity charge is wrong
2) non-recurring items or aggressive accounting
3) Differing international standards
4) VIOLATION OF CLEAN SURPLUS**

Clean surplus = New R/E = Old R/E + NI - Dividends

-> says these are the only changes in retained earnings -> accounting info is availabl,e but easily manipulated, and need many adjustments - > clean surplus is violated when items skip and go right to equity

74
Q

Swap Spread

A

Swap Fixed Rate - Treasury yield of same maturity

-> indicates liquidity, but not time value

75
Q

I-Spread

A

Bond rate - interpolated swap fixed rate of same maturity

-> lquidity AND credit risk - > use for risky bonds

76
Q

Z-spread

A

Constant plug spread added to ENTIRE spot rate curve to force PV of CF to equal market price of bond

  • > assumes zero volatility (ZO, so NOT appropriate for bonds with options of prepayment
  • > eg works for ABS, which have no prepayment option
77
Q

TED spread

A

LIBOR - T-bill of same maturity

  • > reflects risk of interbank loans
  • > not used for individual bonds, but rather as an indicator of perceived risk in the general economy
78
Q

LIBOR-OIS Spread

A

LIBOR - Overnigh indexed swap rate (can be fe funds rate)

  • > useful for credit risk and overall wellbeing of the banking system
  • > low = high mkt liquidity
  • > high = banks unwilling to lend
79
Q

of paths in int rate tree

A

2 (n-1)

n = # of periods

80
Q

Callable and Putable Bonds vs. one sided down duration

A

Callable = lower one sided down duration

putables = lower one sided up duration

81
Q

What risks do OAS and Z spreads incorporate?

A

OAS = liquidity and credit

Z = liquidty, credit, AND option risks (incl vol)

82
Q

Effective Duration Formula

A

BV-∆y - BV+∆y

____________________

2 x BV0 x ∆y

83
Q

How will Convertible perform:

stock price low?

sotck price flat?

Stock price high?

A

Low = CV behaves like bond, outperforms stock

Flat = CV outperforms because of favorable income (coupon vs, dividend) and downside protection

High = stock outperforms

84
Q

Structural Model Characteristics and Equivalencies

A
  • uses BS -> assumes asset strade
  • tells us WHY
  • disadvatage: they don’t actually trade - > cant use historical estimation -> implied that RF is better
  • Value of Equity = call on assets = MAX(0,Asset value - Face value of Debt)
  • Value of Debt = value of assets - value of equity
    • = value of assets - Max (0,A-K)
    • = Risk-free bond + SHORT European put option
85
Q

CDS Up front premium

A

(CDS Spread - CDS Coupon) X Duration

premium FROM protection buyer

CDS coupon is always 1% or 5%

if spread > coupon, buyer pays - > coupon > spread, seller pays

86
Q
A
87
Q

CDS Profit for PRotection Buyer

A

Change in spread (bps) x Duration X notional principal

AKA up-front premium X principal

88
Q

What does ISDA define as credit events for CDS?

A
  1. BK
  2. Failure to Pay
  3. Restructuring
89
Q

RF Model Characteristics

A
  • Do NOT rely on BS
  • Models intensity and PROBABILITY of default, NOT why
  • advantage: does not assume assets trade
  • uses regression models
90
Q

Price of CDS (per $100 of NP)

A

$100 - up-front premium %

91
Q

FFO and AFFO

A

FFO:

Accounting NI

+ D&A

  • Gains (losses) from property sales

AFFO:

FFO

  • non-cash rent
  • maintenance capex
  • LCs
92
Q

Demand Drivers for:

Storage

Office

Industrial

Retail

Resi/Multi

Hotel

Healthcare

A

Storage: population growth

Office: Job growth

Industrial: overall economy (retail sales frowth), import / export activity

Retail: consumer spending + sales growth -> overall economy: job growth, pop growth, savings rates

Resi/ Multi: population growth

Hotel: job growth

Healthcare: Population growth

93
Q

NOI

A

Gross potential Rent

+ Other income

______________________________________

Potential Gross Income

  • Vacancy & Collection loss

______________________________________

Eff. Gross Income

  • Opex

______________________________________

NOI

94
Q

RE Cost Approach

A

1) estimate land value
2) estimate replacement cost
3) deduct obsolescence & depreciation

Replacement Cost (incl builder profit)

  • Curable detrioration

______________________________________

Replacement Cost after Curable (new repl cost)

  • Incurable deterioration AKA depreciation (new replacement cost X (effective age / total life))
  • Functional Obsolescence (incurable) -> annual loss in rent/NOI capped at cap rate
  • Locational obsolsecence (Same as functional)
  • Economic obsolsecence

+ Mkt value of land

_________________________________________

= Estimated value using cost approach

95
Q

RE Appraisal-based vs. Transaction-based Indices

A
  1. Appraisal-based
    1. eg NCREIF
    2. -> lag transaction-based because transactions happen before appraisals
      1. not reflected until next quarter or later
      2. lag = lowe volatility of index, also results in lower correlation with other asset classes
  2. Transaction-based
    1. Repeat-sales: repeat sales of same property
    2. Hedonic: requires only one sale, uses regression. accounts for differences in property characteristics
96
Q

NAVPS Build

A

Y1 NOI capped = RE value

+ cash & equivalents

+ land held for development

+ AR

+ prepaid / other assets (excluding intangibles)

________________________________________

= Gross asset value

  • Ttoal Debt
  • other Liabilities

________________________________________

= NAV (divide by shares outstanding)

97
Q

Equity Dividend Rate

A

cash on cash return

NOI after debt service

______________________

Equity basis

98
Q

VC Discount Rate Adjusted for Risk of Failure

A

[(1+ normal discount rate) / (1 - probability of failure )] - 1

99
Q

DPI

A

Distributions to Paid-in Capital -> realized return -> cash on cash return

Cumulative distributions paid to LP’s / cumulative committed capital

net of mgmt fees and carry

100
Q

RVPI

A

Residual Value to Paid in Capital -> how much vlaue is stil out there -> unrealized return

= Value of LP’s holdings in fund / Cumulative committed (invested) capital

101
Q

Initial Outlay (expansion project)

A

Price (incl S&H) + Installation + NWCInv

102
Q

Categories of Merger

A
  • Statutory: target ceases to exist and all A&L become part of acquirer
  • Subsidiary: target becomes sub of acquirer
  • Conslidation: both companies cease to exist in their prior form and come together to form a new company

Types:

  • Horizontal: firms in similar lines of biz combine
  • Vertical: combine either further up or down the supply chain
  • Conglomerate: combine firms in unrelated businesses
103
Q

Pre and Post Offer Defense Mechanisms

A
  • PRE
    • Poison Pill
    • Poison Put
    • Reincorporating in a state with restrictive takeover laws
    • Staggered board
    • Restricted voting righrts
    • Supermajority voting
    • Fair price amendments
    • Golden parachutes
  • POST
    • “Just say no” defense
    • Litigation, greenmail
    • Share repurchases
    • Leveraged recapitalizations
    • “Crown jewel” defense
    • “Pac-Man” defense
    • Finding a white knight or white squire
104
Q

Types of Restructuring

A
  • Cash Divestitures - direct sale of division to an outside party for cash
  • Equity Carve-outs: create new independent company by giving a proportionate equity interest in a sub to outside S/H through a public offering of stock
  • Spin-offs: create new independent company by distributing SHARES to existing shareholders of the parent
  • Split-offs: allow S/H to receive new shares of a division of the parent company by exchanging a portion of their parent shares
  • Liquidations: break up firm and sell assets piece by piece. most associated with bakruptcy.
105
Q

Depreciable Basis

A

PP + ( Shipping / handling / installation )

106
Q

Initial Outlay (Expansion)

A

Price Including S&H & Installation + NWCInv

NWCInv is inventories needed to support the new project

107
Q

NWCInv

A

( ∆ non-cash current assets) - ( ∆ non-debt current liabilities)

108
Q

After-Tax Operating Cash Flow (Expansion Project)

A

(sales - cash operating costs - depreciation)(1-T) + depreciation

OR

(S-C)(1-T) + DT

109
Q

TNOCF (Expansion Project)

A

SalT + NWCInv - T(SalT - BVT)

SalT = pre-tax proceeds from sale

BVT = book value of fixed capital sold

110
Q

Initial Outlay (Replacement)

A

Price (incl S&H&installation) + NWCInv - SalOld + T( SalOld - BVOld )

111
Q

After-Tax Operating Cash Flow (Replacement Project)

A

INCREMENTAL cash flow

( ∆Sales - ∆Opex )( 1 - T) + ∆DT

112
Q

TNOCF (Replacement Project)

A

INCREMENTAL

∆Sal(<span>New - Old)</span> + NWCInv - T( ∆Sal<span>New</span> - ∆BV<span>Old</span> )

∆Sal(<span>New - Old)</span> = Salvage Value of New Minus Salvage Value of Old

∆Sal<span>New</span> = SalNew - BVNew

∆BV<span>Old</span> = SalOld - BVOld

113
Q

Economic Income

A

Cash Flow + Economic Depreciation

Economic Depreciation = END Mkt Value - BGN Mkt Value

Make decisions based on Economic Income, NOT accounting income

Economic ignores interest expense

114
Q

MM Propositions With and Without Taxes

A

WITHOUT TAXES - capital structure doesnt matter.

  1. Capital Structure doesn’t matter. Doesn’t affect market value.
  2. Cost of Equity Goes up Linearly as D/E goes up

WITH TAXES - Highest at 100% debt

  1. Value is maximized at 100% debt -> Interest is tax-deductible -> tax shield
  2. WACC is minimized at 100% debt.
115
Q

Pecking Order Theory

A

Based on asymmetric info

Management wnats to choose financing source that sends lowest signals

Order:

1. Internally generated equity (R/E)

2. Debt -> mgmt confident the firm can meet obligations

3. External Equity -> negative -> signals maybe stock overvalued

116
Q

Share Repurchase Plans

Open Mkt Transactions

Fixed Price Tender Offer

Dutch Auction

Driect Negotiation

A

NOTE: main reason for share repurchase is signaling

  1. OMT: buy in open market
    1. flexible
    2. no obligation to complete
    3. no S/H approval needed
  2. Fixed Price Tender Offer
    1. predetermined # of shares @ predetermined price (typically premium)
    2. less flexible but quick
  3. Dutch Auction
    1. firm gies range of prices; min clearing price for a certain # of shares
    2. bids suggested at lowest price first, but the last offer accepted (the highest price) is the price for all shares
    3. quick, but not as quick as tender offer
  4. Direct Negotiation
    1. purchase @ prem from one major S/H
    2. often greenmail, back when that was a thing
117
Q

Share Repurchase Effects on:

EPS

BVPS

Leverage

A
  1. EPS:
    1. always goes down if using internal funds
      1. Net Income goes down and shares outstanding go down
  2. BVPS
    1. If share price > BVPS, BVPS goes DOWN post purchase
    2. If share price < BVPS, BVPS goes UP post purchase
  3. Leverage:
    1. if using internal funds, leverage goes UP
      1. cash goes down, as does shareholders equity
      2. therefore debt to asset and Debt to equity ratios go up -> higher leverage
118
Q

Dividend Coverage Ratio

A

Net Income

_________________________

Dividends

119
Q

Value of Acquirer Post-Merger

A

VCombined = VAcquirer + VTarget + Synergies - Cash pmt to target S/H

NOTE: Iif all stock deal, Cash pmt = 0

120
Q

Gain To Target

A

Takeover premium

Deal price - target price (pre-takeover)

NOTE: can be per share. divide by target price pre takeover for percentage.

121
Q

Gain to Acquirer

A

Synergies - Takeover Premium

122
Q

Pre-offer defenses:

Poison Pill (flip-in and Flip-over)

Poison Put

Restrictive Takeover Laws

Staggered Board

Restricted Voting Rights

Supermajority

Fair Price Amendment

Golden Parachute

A

Poison Pill (flip-in and Flip-over) = Current Shareholders can buy stock at discount -> dilution -> higher acquisition price for acquirer

  • Flip-in = target shareholders buy target’s shares

Flip-over = targe shareholders buy ACQUIRER shares

Poison Put = gives bondholders option to demand immediate payment if there’s a hostile takeover

Restrictive Takeover Laws = some states more target-friendly as it relates to hostile takeovers

Staggered Board overlapping terms: in a given year, a bidder can only win a portion of board seats

Restricted Voting Rights = over a certain % ownership, you don’t get more voting rights unless approved by board -> neuters tender offer, b/c you can’t just buy more voting rights, have to negotiate directly with board

Supermajority = require for mergers

Fair Price Amendment = must offer fair price to shareholders, usually determined by formula or appraisal

Golden Parachute = comp agreements that give target’s management a big payout in cashe if they leave the firm post-merger

123
Q

Post-offer Defenses:

Just say no

Litigation

Greenmail

Share repurchase

Lever Up

Crown Jewel Defense

Pac-Man Defense

White Knight

White Squire

A

Just say no = convince shareholders it’s not in their best interest

Litigation = anti-trust or securities law -> time-consuming and expensive -> can give time to find a white Knight / squire

Greenmail = not used any mrore b/c taxes, but target reupruchases shares from acquirer at premium

Share repurchase = company submits tender offer for its own shares -> more control to target, and higher premium for buyer

Lever Up = recap company, assume lots of debt to finance share repurchases, and firm is less atractive target if highly levered

Crown Jewel Defense = sell a major asset or sub to a netural 3rd party -> could be illegal

Pac-Man Defense = counteroffer -> rare

White Knight = friendly 3rd party rescues target -> can get synergies and also start a bidding war leading to good price for target

White Squire = friendly third party buys minority stake big enough to stop hostile acquirer

124
Q

HHI

A

Sum of (mkt share of firm x 100)2

< 1000: industry concentration low, ANY change in HHI, no antitrust action

1000-1800: moderate concentration, 100+ change in HHI -> possible

> 1800: High, 50+, virtually certain

125
Q

Calculate VaR

A

% VaR = Expected Return - (StdDev x 1.65)

multiply by AUM to get $VaR

StDev of returns = SqRt of Variance

NOTE: convert Er and StDDev to rght timing first (annual -> daily = /250)

NOTE: StdDev can be expressed as “daily expected volatility”

NOTE: 1.65 is for 95% confidence

126
Q

Per Share Effective Spread Transaction Cost

and

Effective Spread

A

Trans cost:

= (Side +1 purchase / -1 Sale)(transaction price - Mid-quote Price)

Effective Spread

= / share effective spread transaction cost x 2

127
Q

Incremental VaR

A

how VaR will change with position size change, relative to remaining positions

128
Q

Relative VaR

A

AKA Ex-ante Tracking Error

measure of how much performance deviates from benchmark -> used to estimate tracking risk

129
Q

Conditional VaR

A

AKA “expected tail loss” or “ expected shortfall”

estimates how much loss is if VaR cutoff is exceeded

130
Q

credit spread for a bond

A

Bond Yield - BEI - RfR

131
Q

QM:

Bias Error

Variance Error

Base Error

A

Bias Error = in-sample error

Variance Error = out of sample error

Base Error = occurs due to randomness of the data

132
Q

Absolute Convergence

Conditional Convergence

Club Convergence

A

Absolute: all developing countries will catch up and meet per capita output of developed countries over time no matter their characteristics

Conditional: poorer country will converge to teh same steady growth rate and per capita output if it has the same pop growth rate, savings rate, and production function

Club Convergence: look for INSTITUTIONS - ones that have the right institutions will converge to the income level of the richest countries in the world. poor countries can join the club by making the right institutional changes.

133
Q

FI: expected future spot vs fwd rates over/under value

A

Fwd is inversely related to evolution of spot rates

if future spot rates are higher (lower) than current forwrad rates, then forward price will decrease (increase)

if your expected future spot rates are higher than current fwd rates for same maturity, bond is OVERvalued according to you

134
Q

Put-call Parity Relation

A

C - P = S - X

C = long call

P = long put

S = own stock

X = LEND - you OWN the bond

135
Q

Delta

A

How value of a call option changes when underlying changes

Calls: positive relation: Delta > 0

Puts: Negative relation: Delta <0

Long Calls: 0 to 1,

therefore

Short calls: 0 to -1

136
Q

Vega

A

How value of a call option changes as VOLATILITY changes

Calls: positive relation:: V> 0

Puts: Positive relation: V>0

137
Q

Rho

A

How value of an option changes as the RfR changes

Calls: positive relation: R > 0

Puts: negative relation: R<0

138
Q

Theta

A

How value of a call option changes as TIME to expiry changes:

Call: negative relation: T<0

Puts: negative relation: T<0

Because the value of the option approaches zero as it reaches maturity

139
Q

Information RAtio

A

Active return / Active Risk

AKA

Expected Active Return / Std Dev of Active return

140
Q

Assumptions of APT

A

1) Unsystematic risk can be diversified away
2) returns are generated using factor model (weakness: APT provides little practical help for identifying Risk factors)
3) no arbitrage opportunties exist

141
Q

Active Risk

A

AKA tracking error or tracking risk

it’s the stdDev of active return

SigmaRp-Rb

142
Q

Gamma

A

Sensitivity of option price to changes in Delta

143
Q

Change in a call price (using Greeks)

A

Change in Call price = delta (∆S) + 1/2gamma(∆S)2 + vega (∆v)

∆S = change in price of underlying asset

∆V = change in future volatility

144
Q

Change in price of a bond for change in duration and convexity

A

Just duration:

  • Duration (∆Y)
    incl. convexity:
  • Duration(∆Y) + 1/2Convexity(∆Y)2
145
Q

Inter-temporal Rate of substitution

A
  • marginal utility of consuming 1 unit in the future / marginal utility of current consumption of 1 unit
  • based on utility theory
  • investors always prefer current consumption, so the rate is <1
  • If GDP growth is high -> expect better times in future -> utiltiy of future consumption goes down -> save less, increases real int rates

Key Concepts:

  1. higher utility assigned to current consumption = higher real rate -> investors must be compensated more for forgoing current consumption
  2. diminishing marginal utility of wealtj: if you’re richer the marginal utility of consumption goes down bc you’re rich - marginal utility of consumption is HIGHER during periods of scarcity
  3. if investors have good expectations for future, expected marginal utility of future consumption is decreased relative to current consumption - > investors favor current consumption
146
Q

Sharpe Ratio of Optimal Portfolio

A

SQUARE ROOT OF ALL THE BELOW COMBINED:

(SRB)2 + (IR)2

147
Q

Sharpe Ratio

A

Rp - RF

_____________________

StDev

Excess return per unit of risk

148
Q

Information Coefficient

A

Measures manager skill

Ex-ante: EXPECTED correlation between active retrns and forecast active returns

Ex-post: ACTUAL correlation between active returns and forecast active returns

Ex-post is typicall a small postiive value

149
Q

Transfer Coefficient

A

Correlation between actual active weights and optimal active weights

TC = 1 for unconstrainted portfolios

TC< 1 with constraints

150
Q

Breadth

A

Number of independent bets (forecasts of active return)

bets taken per year - so if a mgr takes active positions in 10 securities each month, BR = 10x12 = 120

151
Q

Fundamental Law Formula

A

IR = (TC)(IC)(SqRt of Breadth

Er = (TC)(IC)(SqRt Breadth)sigma

For unconstrained portfolio, TC = 1

152
Q

Optimal Active Risk for UNconstrained portfolio

A

optimal active risk is the amount that maximizes sharpe ratio

153
Q

Optimal Active Risk for CONSTRAINED portfolio

A
154
Q

VWAP

A

volume weighted average price

Weighted avg price at which all trades were executed between when order was placed and executed

weights based on dollar volume per trade

INTERPRETATION: evaluates your execution price relative to other trades happening at same time -> compare your VWAP to benchmark VWAP

VWAP Transaction Cost = Trade size x (side) x (trade VWAP - benchmark VWAP)

155
Q

Electronic Arb

A

3 Types:

  1. Take liquidity on both sides
    1. least amount of risk of the three
    2. buy and sell same security in different markets to take advantage of mispricing; simultaneous buy and sell orders
  2. Offer liquidity on one side
    1. if two markets have the same bid-ask on one security, make an offer in just ONE market that’s lower than the lwoest bid: if it fills, really quickly sell in the other market that’s still at the same bid
  3. Offer liquidity on both sides
    1. post limit order inferior to the best bid and offer prices in different markets.
    2. Very risky; after one leg of the order is filled, if the other doesn’t fill, trader is exposed to adverse price movement
156
Q

Optimal Hedge Ratio

A

C+ - C-

_________________________

S+ - S-

C+ = call value if up-move: delta between up move stock price and original stock price

C- = call value with a down-move: if below strike price, zero

S+ = stock value x up factor

S- = stock value X down factor

157
Q

Stock Option Prob of up or down move

A

Up probability =

1 + r - down factor

_________________________

up factor - down factor

Down probability = 1 - Up probability

158
Q

Tier I and Tier II Capital

A
  • Tier I
    • Common Equity: common stock, APIC, Retained earnings and OC, less intangibles, and DTA’s
    • Subordinated instruments iwth no specified maturity and contractual dividends/interest
  • Tier II
    • subordinated insturments with original maturity >5 years
159
Q

Levered Equity Formula (To go to a levered capital structure from purely Equity)

A

re = r0 + (r0 - rd) (1-t) (D/E)

r0 = cost of capital as all equity

rd = before tax marginal cost of debt capital

t = tax rate

D/E = debt/ equity ratio

160
Q

QM Problems: What is it, detect, correct

Heteroskedasticity

Serial Correlation

Multicollinearity

A
  • Hetero
    • only conditional is bad
    • error terms non-cosntant, and ARE related to x’s; t-stats unreliable
    • DETECT: Scatter/Breusch Pagan Chi Squared
    • CORRECT: White Standard errors / robust standard errors
      • OR generalized least squares (modifies original equation)
  • Serial
    • each error term trends in same direction as previous one; t-stats too high; type 1 errors
    • DETECT: Durbin-Watson - if close to 2, NO autocorrelation. if close to 0, there is auto.
    • CORRECT: Hansen Method; adjusts std errors upwards
      • or improve model specification
  • Multicollinearity
    • two or more x’s correlated; inflates std errors and coefficients unreliable
    • DETECT: telltlale signs:
      • F stat is significant (high R2) but all T-stats are insignificant
      • high correlation of x’s
      • sign of coefficient is unexpected (eg high rates but low mortgage apps)
    • CORRECT: omit one or more x variable
161
Q

Commodity Portfolio Return

A

Price Return + Rolle Return + Collateral Return

+ rebalancing return (only for portfolios, not individual contracts)

Roll return is biggest component

162
Q

Profitability Index

A

1 + (NPV/outlay)

rank projects by it

163
Q

Valuing Real Options

A

1) find NPV of project WITHOUT options - if it’s positive, don’t need to consider options
2) work out NPV of options - add value to NPV of original

164
Q

M&A Types

Acquisition

Merger

Statutory Merger

Subsidiary Merger

Consolidation

A

Acquisition = Buy

Merger = absorb target entirely

Statutory Merger = target ceases to exist

Subsidiary Merger = target becomes sub of buyer

Consolidation = acquirer and target form completely new company

CFA Level II (9 decks)

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