Focus Formulas Flashcards
Basel III Requirements and Their Goals
- 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
Receivables Turnover
Sales
___________________
AR
DSO
365
____________________
Receivables Turnover
Asset Turnover
Revenue
__________________
Assets
Cash Conversion Cycle
DSO + Days Inventory on Hand - Days of Payables
Days of Payables
365
_______________________
Payables Turnover
Payables Turnover
Purchases
_________________
Avg. Payables
Days Inventory on Hand
365
____________________
Inventory Turnover
Inventory Turnover
COGS
___________________
Avg Inventory
Quick Ratio (2 ways)
Current Assets - Inventory
____________________________
Current Liabilities
OR
Cash + AR
__________________________
Current Liabilities
Cash Ratio
Cash + Marketable Securities
________________________
Current Liabilities
Inflation and BEI
Inflation:
1 + Nominal Rate
___________________
1+ Real Rate
BEI:
Expected Inflation + premium for inflation uncertainty
(the difference between the nominal and risk free rates)
Interest Coverage Ratio
EBIT
_____________________
Interest Expense
Fixed Charge Coverage Ratio
EBIT + Lease Payments
____________________________
Interest + Lease Payments
Debt to Capital Ratio
Total Debt
_________________________
Debt + Shareholders Equity
Debt to Equity Ratio
Total Debt
_________________
Shareholders Equity
Financial Leverage
Avg Total Assets
_________________________
Avg total Equity
Net Operating Assets
Operating Assets - Operating Liabilities
Operating Assets
Total Assets - Cash & Equiv - Marketable Securities
Operating Liabilities
Total Liabilities - Total Debt
Accruals
Ending NOA - Beginning NOA
NI - CFO - CFI
Accruals Ratio
Change in NOA
______________________
Avg NOA
Gross Margin
Rev - Cogs
___________________
Revenue
Operating Margin
Operating Income
_____________________
Revenue
Adjusted Operating Profit
Reported Operating Profit
+ Reported Pension Expense
- Service Cost
_______________________________
= Adjusted Operating Profit
Partial Goodwill
IFRS ONLY
Proceeds - pro rata identifiable FMV of Net Assets
Full Goodwill
IFRS AND GAAP
FMV (acquisition cost / % purchased) - identifiable FMV of Net Assets
Goodwill Impairment: IFRS
If carrying value > recoverable amount
recoverable amount = higher of net selling price or PV of future CF
Goodwill Impairment: GAAP
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
VIE Criteria
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
PBO
BGN POBO
+ Service Cost
+Interest Cost
+/- Actuarial G/L
+/- Prior Service Cost
-Benefits Paid
_______________________
= Ending PBO
FVPA
BGN FVPA
+ /- ARPA
+ Contributions
- Benefits Paid
___________________
END FVPA
IFRS vs. GAAP Treatment of Prior Service Costs
IFRS: Expensed immediately: pension expense up 100
GAAP: Reported in comprehensive Income, amortized over employee service life
GAAP Pension Expense
CSC
+ Interest Expense
- ERPA
+/- Amort PSC
+/- Actuarial
_______________
= Pension Expense
IFRS Pension Expense
CSC
+/- Net Interest
+/- PSC
___________________
= Pension Expense
Net Interest = discount rate x BGN Funded status -> if negative, interest is positive
TPPC
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
Analyst Adjustments for PBO / Pension
Replace I/S Expense with TPPC
Split Pension Expense up within I/S:
Service Cost = Operating
Interest Cost = interest expense
ARPA = non-operating income
Analyst Adjustments to Cash Flow Statement for Pension Stuff
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
COGS on I/S for Temporal Method
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
GAAP Vs. IFRS Hyperinflation
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
Liquidity Coverage Ratio
High Quality Liquid Assets (Easy convert to cash)
____________________________________________
Expected Cash Outflows (in stress scenario)
NSFR
Available Stable Funding
_________________________________
Required Stable Funding
Days of Stress Level Cash
= LCR x # of days (given)
Total Capital Ratio
Tier 1 + Tier 2
_________________________________
Total RISK WEIGHTED Capital
Net Premium Written
Premiums Earned over Coverage Period (less reinsurance)
Net Premium Earned
Premiums earned over Accounting Period
Expense Ratio
Underwriting Expenses (incl. Commissions)
________________________________________
Net Premium WRITTEN
UW Loss Ratio
Incurred Losses + Loss adjustment expenses
_______________________________________
Net Premium EARNED
Combined Ratio
Expense Ratio + UW Loss Ratio
>100% = loss
High = Soft Market (can raise premiums )
Low = Hard market (can’t raise premiums much)
Dividends to Policyholders
Dividends to Policyholders
_____________________________
Net Premium Earned
CRAD
Combined Ratio after Dividends
Combined Ratio + Divs to policyholders ratio
For CVA:
Recovery Rate
LGD
Hazard Rate
Probability of Survival
Probability of Default
Discount Factor
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
Required Return
Rf + ERP
build-up:
RfR + ERP + size premium + company-specific premium
Blume Method of adjusting beta
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)
ERP
(1y fwd forecased dividend yield) + (consensus growth rate) - (current LT gov bond yield)
Bond Yield Plus
Expected Return = ( YTM on Long Term Debt ) + ( risk premium)
Find Weights for WACC
We = Mkt Value Equity / (mkt value debt + mkt value equity)
same for Wd
Pastor-Stambaugh Model
Finds required return, adds a liquidity factor to the Fama french, making it more useful for pvt / thinly traded firms
PVGO
V0 = (E1 / r) + PVGO
Forecast FCFE
FCFE = NI - [(1-DR) x (FCInv - Depr)] - [(1-DR) x WCInv]
WCInv
∆(Current Assets - Cash & Investments) - (Current L’s - ST debt & Div’s payable)
Note: CHANGE
BGN WC - END WC
Change in WC
FCInv
END Net PPE
- BGN Net PPE
+ Depreciation
- Gain (loss) on sale of PPE
Leading P/E
1-b
__________________
r-g
Payout Ratio
_____________
r-g
Trailing P/E
(1-b)(1+g)
____________________
r-g
Leading P/E times 1+g
Justified P/B Ratio
ROE - g
_________________
r - g
AKA trailing P/E X ROE
Justified P/S Multiple
(Net Margin)( 1 - b )( 1 + g )
________________________________
r-g
AKA trailing PE x Net Margin
Enterprise Value
MVEquity (INCL preferred) + MVDebt + MI(not important) - Cash & Liquid investments
Normalized Earnings
ROE x BVPS
DLOC + total discount
DLOC
1 - [1 / (1 + Ctrl PREMIUM)]
Total Discount
1 - (1-DLOC)(1-DLOM)
Wtd Harmonic Mean for Portfolio P/E
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)
EVA
NOPAT - $WACC
EBIT(1-T) - (WACC x IC)
IC = S/HEquity + Total Debt (PREVIOUS PERIOD ENDING OR CURRNT PERIOD BGN)
MVA
End of year market value - Total Capital
Reasons Why Residual Income Approach Doesn’t Work
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
Swap Spread
Swap Fixed Rate - Treasury yield of same maturity
-> indicates liquidity, but not time value
I-Spread
Bond rate - interpolated swap fixed rate of same maturity
-> lquidity AND credit risk - > use for risky bonds
Z-spread
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
TED spread
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
LIBOR-OIS Spread
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
of paths in int rate tree
2 (n-1)
n = # of periods
Callable and Putable Bonds vs. one sided down duration
Callable = lower one sided down duration
putables = lower one sided up duration
What risks do OAS and Z spreads incorporate?
OAS = liquidity and credit
Z = liquidty, credit, AND option risks (incl vol)
Effective Duration Formula
BV-∆y - BV+∆y
____________________
2 x BV0 x ∆y
How will Convertible perform:
stock price low?
sotck price flat?
Stock price high?
Low = CV behaves like bond, outperforms stock
Flat = CV outperforms because of favorable income (coupon vs, dividend) and downside protection
High = stock outperforms
Structural Model Characteristics and Equivalencies
- 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
CDS Up front premium
(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
CDS Profit for PRotection Buyer
Change in spread (bps) x Duration X notional principal
AKA up-front premium X principal
What does ISDA define as credit events for CDS?
- BK
- Failure to Pay
- Restructuring
RF Model Characteristics
- Do NOT rely on BS
- Models intensity and PROBABILITY of default, NOT why
- advantage: does not assume assets trade
- uses regression models
Price of CDS (per $100 of NP)
$100 - up-front premium %
FFO and AFFO
FFO:
Accounting NI
+ D&A
- Gains (losses) from property sales
AFFO:
FFO
- non-cash rent
- maintenance capex
- LCs
Demand Drivers for:
Storage
Office
Industrial
Retail
Resi/Multi
Hotel
Healthcare
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
NOI
Gross potential Rent
+ Other income
______________________________________
Potential Gross Income
- Vacancy & Collection loss
______________________________________
Eff. Gross Income
- Opex
______________________________________
NOI
RE Cost Approach
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
RE Appraisal-based vs. Transaction-based Indices
- Appraisal-based
- eg NCREIF
- -> lag transaction-based because transactions happen before appraisals
- not reflected until next quarter or later
- lag = lowe volatility of index, also results in lower correlation with other asset classes
- Transaction-based
- Repeat-sales: repeat sales of same property
- Hedonic: requires only one sale, uses regression. accounts for differences in property characteristics
NAVPS Build
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)
Equity Dividend Rate
cash on cash return
NOI after debt service
______________________
Equity basis
VC Discount Rate Adjusted for Risk of Failure
[(1+ normal discount rate) / (1 - probability of failure )] - 1
DPI
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
RVPI
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
Initial Outlay (expansion project)
Price (incl S&H) + Installation + NWCInv
Categories of Merger
- 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
Pre and Post Offer Defense Mechanisms
- 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
Types of Restructuring
- 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.
Depreciable Basis
PP + ( Shipping / handling / installation )
Initial Outlay (Expansion)
Price Including S&H & Installation + NWCInv
NWCInv is inventories needed to support the new project
NWCInv
( ∆ non-cash current assets) - ( ∆ non-debt current liabilities)
After-Tax Operating Cash Flow (Expansion Project)
(sales - cash operating costs - depreciation)(1-T) + depreciation
OR
(S-C)(1-T) + DT
TNOCF (Expansion Project)
SalT + NWCInv - T(SalT - BVT)
SalT = pre-tax proceeds from sale
BVT = book value of fixed capital sold
Initial Outlay (Replacement)
Price (incl S&H&installation) + NWCInv - SalOld + T( SalOld - BVOld )
After-Tax Operating Cash Flow (Replacement Project)
INCREMENTAL cash flow
( ∆Sales - ∆Opex )( 1 - T) + ∆DT
TNOCF (Replacement Project)
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
Economic Income
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
MM Propositions With and Without Taxes
WITHOUT TAXES - capital structure doesnt matter.
- Capital Structure doesn’t matter. Doesn’t affect market value.
- Cost of Equity Goes up Linearly as D/E goes up
WITH TAXES - Highest at 100% debt
- Value is maximized at 100% debt -> Interest is tax-deductible -> tax shield
- WACC is minimized at 100% debt.
Pecking Order Theory
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
Share Repurchase Plans
Open Mkt Transactions
Fixed Price Tender Offer
Dutch Auction
Driect Negotiation
NOTE: main reason for share repurchase is signaling
- OMT: buy in open market
- flexible
- no obligation to complete
- no S/H approval needed
- Fixed Price Tender Offer
- predetermined # of shares @ predetermined price (typically premium)
- less flexible but quick
- Dutch Auction
- firm gies range of prices; min clearing price for a certain # of shares
- bids suggested at lowest price first, but the last offer accepted (the highest price) is the price for all shares
- quick, but not as quick as tender offer
- Direct Negotiation
- purchase @ prem from one major S/H
- often greenmail, back when that was a thing
Share Repurchase Effects on:
EPS
BVPS
Leverage
- EPS:
- always goes down if using internal funds
- Net Income goes down and shares outstanding go down
- always goes down if using internal funds
- BVPS
- If share price > BVPS, BVPS goes DOWN post purchase
- If share price < BVPS, BVPS goes UP post purchase
- Leverage:
- if using internal funds, leverage goes UP
- cash goes down, as does shareholders equity
- therefore debt to asset and Debt to equity ratios go up -> higher leverage
- if using internal funds, leverage goes UP
Dividend Coverage Ratio
Net Income
_________________________
Dividends
Value of Acquirer Post-Merger
VCombined = VAcquirer + VTarget + Synergies - Cash pmt to target S/H
NOTE: Iif all stock deal, Cash pmt = 0
Gain To Target
Takeover premium
Deal price - target price (pre-takeover)
NOTE: can be per share. divide by target price pre takeover for percentage.
Gain to Acquirer
Synergies - Takeover Premium
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
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
Post-offer Defenses:
Just say no
Litigation
Greenmail
Share repurchase
Lever Up
Crown Jewel Defense
Pac-Man Defense
White Knight
White Squire
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
HHI
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
Calculate VaR
% 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
Per Share Effective Spread Transaction Cost
and
Effective Spread
Trans cost:
= (Side +1 purchase / -1 Sale)(transaction price - Mid-quote Price)
Effective Spread
= / share effective spread transaction cost x 2
Incremental VaR
how VaR will change with position size change, relative to remaining positions
Relative VaR
AKA Ex-ante Tracking Error
measure of how much performance deviates from benchmark -> used to estimate tracking risk
Conditional VaR
AKA “expected tail loss” or “ expected shortfall”
estimates how much loss is if VaR cutoff is exceeded
credit spread for a bond
Bond Yield - BEI - RfR
QM:
Bias Error
Variance Error
Base Error
Bias Error = in-sample error
Variance Error = out of sample error
Base Error = occurs due to randomness of the data
Absolute Convergence
Conditional Convergence
Club Convergence
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.
FI: expected future spot vs fwd rates over/under value
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
Put-call Parity Relation
C - P = S - X
C = long call
P = long put
S = own stock
X = LEND - you OWN the bond
Delta
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
Vega
How value of a call option changes as VOLATILITY changes
Calls: positive relation:: V> 0
Puts: Positive relation: V>0
Rho
How value of an option changes as the RfR changes
Calls: positive relation: R > 0
Puts: negative relation: R<0
Theta
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
Information RAtio
Active return / Active Risk
AKA
Expected Active Return / Std Dev of Active return
Assumptions of APT
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
Active Risk
AKA tracking error or tracking risk
it’s the stdDev of active return
SigmaRp-Rb
Gamma
Sensitivity of option price to changes in Delta
Change in a call price (using Greeks)
Change in Call price = delta (∆S) + 1/2gamma(∆S)2 + vega (∆v)
∆S = change in price of underlying asset
∆V = change in future volatility
Change in price of a bond for change in duration and convexity
Just duration:
- Duration (∆Y)
incl. convexity: - Duration(∆Y) + 1/2Convexity(∆Y)2
Inter-temporal Rate of substitution
- 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:
- higher utility assigned to current consumption = higher real rate -> investors must be compensated more for forgoing current consumption
- 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
- if investors have good expectations for future, expected marginal utility of future consumption is decreased relative to current consumption - > investors favor current consumption
Sharpe Ratio of Optimal Portfolio
SQUARE ROOT OF ALL THE BELOW COMBINED:
(SRB)2 + (IR)2
Sharpe Ratio
Rp - RF
_____________________
StDev
Excess return per unit of risk
Information Coefficient
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
Transfer Coefficient
Correlation between actual active weights and optimal active weights
TC = 1 for unconstrainted portfolios
TC< 1 with constraints
Breadth
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
Fundamental Law Formula
IR = (TC)(IC)(SqRt of Breadth
Er = (TC)(IC)(SqRt Breadth)sigma
For unconstrained portfolio, TC = 1
Optimal Active Risk for UNconstrained portfolio
optimal active risk is the amount that maximizes sharpe ratio
Optimal Active Risk for CONSTRAINED portfolio
VWAP
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)
Electronic Arb
3 Types:
- Take liquidity on both sides
- least amount of risk of the three
- buy and sell same security in different markets to take advantage of mispricing; simultaneous buy and sell orders
- Offer liquidity on one side
- 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
- Offer liquidity on both sides
- post limit order inferior to the best bid and offer prices in different markets.
- Very risky; after one leg of the order is filled, if the other doesn’t fill, trader is exposed to adverse price movement
Optimal Hedge Ratio
C+ - C-
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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
Stock Option Prob of up or down move
Up probability =
1 + r - down factor
_________________________
up factor - down factor
Down probability = 1 - Up probability
Tier I and Tier II Capital
- 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
Levered Equity Formula (To go to a levered capital structure from purely Equity)
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
QM Problems: What is it, detect, correct
Heteroskedasticity
Serial Correlation
Multicollinearity
- 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
Commodity Portfolio Return
Price Return + Rolle Return + Collateral Return
+ rebalancing return (only for portfolios, not individual contracts)
Roll return is biggest component
Profitability Index
1 + (NPV/outlay)
rank projects by it
Valuing Real Options
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
M&A Types
Acquisition
Merger
Statutory Merger
Subsidiary Merger
Consolidation
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
