FINAL REVIEW DECK Flashcards
What are the adjustments to convert LIFO inventory to FIFO inventory?
BALANCE SHEET Inventory = Inventory + LR Cash = Cash - (LR x tax rate) Equity = Equity + [LR x (1-t)] i.e. Adjusting assets = add LR net of tax
Income Statement
COGS = COGS - change in LR
Tax Expense = Taxes + (change in LR x tax rate)
Net Income = NI + [change in reserve x (1-t)]
*adjusting equity and net income are the same, just using the LR vs the change in LR
Impact of adjusting LIFO to FIFO in rising price environment?
Current Ratio = Higher
Gross and Net Profit = Higher
Inventory Turnover= Lower
LT Debt / Equity = Lower
LIFO vs FIFO which is better for the Balance Sheet? Income Statement? Why?
LIFO for Income Statement: better representation of current margin environment
FIFO for Balance Sheet: better representation of economic cost
Capitalizing Interest Costs - implications
- report as CFI, depreciate when the project is complete
2. Capitalizing usually results in higher interest coverage
Analyst Adjustments - Capitalizing Interest Costs
- Add Capitalized Interest (CI) to interest expense
- Remove depreciation of CI from earnings
- Deduct CI net of related depreciation from fixed assets
- Add CI to CFI
- Deduct CI from CFO
- Recalculate interest coverage and profitability ratios
Key differences between capitalizing R & D and Software
Research and Development (R & D)
IFRS: R = expense D = capitalize
GAAP: R & D = expense
Software developed for sale:
IFRS & GAAP: expensed until feasibility is reached
Software developed for internal use
IFRS: expensed until feasibility is reached
GAAP: capitalized all software development cost
Impairment
IFRS: BV > Recoverable Amount (write down to greater of FV - selling cost or PV of future cash flows) & allow loss reversal
GAAP: BV > undercounted cash flows (write down to fair value - or discounted future cash flows) only assets not held for use are allowed to reverse impairment
*DO NOT AFFECT CASH FLOW (non cash charge)
**Impairment means an asset was not depreciated fast enough
Fixed Asset Disclosure applications:
Estimated Useful Life: Historical Cost / Annual Depreciation
Estimated Age: Accum. Depr / Annual Depreciation
Estimated Remaining Life: Net PPE (NBV) / Annual Depreciation
Adjusting an operating lease into a financing (capital) lease:
- Lower of fair value or PV of future lease payments is reported as an asset and liability
- Asset is depreciated
- Interest expense is recognized on liabilty
- Lease payments like amortizing debt - each payment is part interest (CFO) and part principal (CFF).
Calculate IRR to determine implicit rate (us PV of future minimums as the outflow, and then use the payments as inflows)
SIMPLIFIED
- Increase A & L’s by PV of remaining lease payments
- Remove rent expense from I/S and replace with depreciation and interest expense
Calculating a change in an Equity Method investment:
- %share of company x change in RE
2. %share of company x (Earnings - Dividends)
Steps in the Acquisition Method
BALANCE SHEET
- Eliminate investment account of parent and equity accounts of subsidiary
- Create minority (non controlling) interest = share not owned
- Combine assets and liabilities of both firms (net of intercom any transactions)
INCOME STATEMENT
- Eliminate subsidiary earnings from parents (dividends)
- Subtract minority share of earnings
- Combine revenues and expenses net of inter company transactions
GOODWILL
GAPP: requires full goodwill
IFRS: permits partial also
Full goodwill = total fair value of subsidiary minus FV of net identifiable assets and
Minority interest = % not owned times total fair value of subsidiary
_______________________________
Partial goodwill = purchase price of partial interest minus the % owned times FV of net identifiable assets
Minority interest = % not owned times fair value of net identifiable assets
COMPONENTS OF PBO
BEGINNING PBO \+ Service Cost \+ Interest Cost \+/- Actuarial (gains) losses \+/- Past service cost - Benefits Paid =ENDING PBO
Fair Value of Plan Assets
BEGINNING FAIR VALUE OF PLAN ASSETS \+/- Actual return on plan assets \+ Employer contributions -Benefits paid to retirees =ENDING FAIR VALUE OF PLAN ASSETS
TOTAL PERIODIC PENSION COST
TPPC = Contributions - change in funded status
Components = Current and past service cost + Net Interest + Remeasurement (actuarial gain / loss and difference in actual vs expected return)
PENSION EXPENSE
GAAP Pension Expense= \+ Service cost (actual) \+ Interest cost (actual) - Expected return \+/- Amortization of actuarial (gain) and loss \+/- Amortization of past service costs = GAAP Pension expense on I.S.
*Unamortized past service cost and actuarial gain goes to OCI
IFRS Pension Expense = \+ Service cost \+/- Net interest expense (income) - use same rate \+/- Past service costs = Pension expense on I.S.
*Remeasurements are reflected in OCI unamortized
Analyst adjustments for Pensions
- Full pension expense is taken through operating expenses (SG&A)
- Only service cost is operating
- Remove pension expense from operating expenses and include service cost
- Add interest cost to interest expense
- Add actual return on plan assets to non operating income
- Amortization is ignored
**TOTAL I/S EFECT = Service + Interest - Actual Return
CASH FLOW ADJUSTMENT
Adjust CFO and CFF for the after-tax difference in economic pension expense and cash contributions.
When you contribute positive after tax it is like paying off debt, which increases CFO and decreases CFF
FX adjustments
Temporal: when functional currency does not equal reporting currency
Current Rate: when functional currency does equal reporting currency
TEMPORAL METHOD
- Produce top of balance sheet (total assets)
- Produce SH Equity and Liabilities (plug RE)
- Derive NI from reconciliation of RE
- Produce the Income Statement
* The difference between the income in RE and in the I.S. is the adjustment
TEMPORAL METHOD RATES
Current Rate
1. Monetary Assets & Liabilities
Historical rate
- All other assets and liabilities
- Capital Stock
- COGS, D & A
- Dividends
Average Rate
6. Income Statement
Monetary assets: cash, AR, AP, STD, LTD
CURRENT RATE METHOD RATES
Current Rate
1. All assets and liabilities
Historical rate
- Capital stock
- Dividends
Average Rate
4. All I.S. Accounts
CURRENT RATE METHOD
- Convert the I.S @ Average rate
- Derive closing RE (plug)
- Convert the B.S. @ Current rate (will not balance) as difference is currency gain/loss
CALCULATING CURRENCY EXPOSURE
Temporal Method
= Net Monetary Assets [(cash + A/R) - (A/P + current debt + LTD)]
Current Rate Method
= Assets - Liabilites = SH Equity
HYPERINFLATION
GAAP: Temporal method is required
IFRS: foreign currency financial statements are restated for inflation and then translated at current rate (marked to market)
KEY: monetary assets and liabilities are not restated & purchasing power gain or loss is recognized based on net monetary position (net monetary asset = loss)
MEASURING EARNINGS QUALITY
Aggregate Accruals = Accrual based earnings - cash based earnings
B.S. Based: Change in NOA / avg NOA
NOA = (Total Assets - Cash) - (Total Liabilities - Total Debt)
______________
CF Based: NI - (CFO + CFI) / avg NOA
*issue is different treatment of finance costs and dividends under IAS and US GAAP
**Lower the ratio, higher the quality of earnings
DUPONT
ROE = Interest Burden x EBIT Margin x Asset Turnover x Leverage
(NI / EBT) x (EBT / EBIT) x (Tot Rev / Avg Assets) x (Avg Assets / Avg Equity)
*to adjust remove the equity method income and the investment asset from extended DuPont equation
CASH FLOW ANALYSIS
Adjusted operating cash flow = OCF = add back cash interest and cash taxes
Cash flow return on assets = OCF / Avg Total Assets
Cash flow to reinvestment = OCF / Capex
Cash flow interest coverage = OCF / Cash interest
Capital Budgeting Steps
- Outlay = Capex + NWC Invest
* NWC = change in non cash current assets - change in non debt current assets - CF = (Sales - Cash Opex - Depreciation) x ( 1 - tax ) + Depreciation
- TV = Salvage Value + NWC - tax ( Salvage - BV )
ECONOMIC INCOME
EI = after-tax operating cash flow minus economic depreciation
economic depreciation = decline in investment’s market value (calculate by using discounting with the cost of capital)
ALTERNATIVE VALUATION METHODS
Economic Profit = EBIT ( 1 - t ) - $ WACC
MVA = NPV based on economic profit
Residual Income = NI - equity charge
Double taxation formula
effective tax rate = tax corporate + ( 1 - tax corporate) x (tax individual )
Target Dividend payout adjustment factor
Expected dividend = Do + [ ( E1 - Eo) x target payout x adjustment factor ]
adjustment factor = 1 / n (n = # of years to adjust)
Business cycle phases and mergers
- Horizontal mergers are common in all life cycle stages
- Tend to see vertical mergers primarily in mature growth stage
- Conglomerate mergers only common at beginning and end of industry life cycle
HHI - merger index
HHI = Market share (decimal form x 100)^2
Post Merger < 1000 = not concentrated
Post merger between 1000 & 1800 with change of 100 or more, antitrust action is possible
Post merger > 1800 with change of 50 or more virtually certain
Valuing a Merger
- DCF (do not fret)
- Comparable Company Analysis (Valuation relative to minority prices) + takeover premium
- Comparable Transaction Analysis: no need to calculate takeover premium (it is embedded) takes a control perspective
Evaluating a merger bid
- Post-merger value of an acquirer = pre merger value of acquirer + pre merger value of target + synergies - cash
- Gains accrued to the target = takeover premium = price paid for target - pre merger value of target
Ibbotson-Chen Model
ERP = Dividend Yield
{
\+ (1 + expected inflation)
\+ (1+ real growth rate)
\+ (1+ PE growth due to market correction)
-1
}
- risk free
Strength: uses consensus of experts
Weakness - wide disparity of opinions
Build up method for equity models
Expected Return = Risk free + ERP + size premium + company specific premium
DOES NOT USE BETAs
Beta Estimation
- Identify a publicly traded firm with similar industry characteristics
- Estimate the beta of the publicly traded firm using regression = Be
- Unlever the beta = Bu = [1/(1+(D/Ecomp))] x Be
- Relever beta = Bnonpublic = [1 + D/E nonpublic] x Bu
Strategy Styles
Less Malleable + Less Predictable = Adaptive
Less Malleable + More Predictable = Classical
More Malleable + Less Predictable = Shaping
More Malleable + More Predictable = Visionary
EXAMPLES
Classical: Consumer finance, household products, autos
Adaptive: Office electronics, Construction Materials, Biotech
Shaping: Heathcare tech, automobile components, internet software
Visionary: healthcare provider, media, insurance
ECONOMIES OF SCALE
Defined: average cost of production decreases as industry sales increase
Evidence: larger companies will have higher margins
Tax Rates
Changes in deferred tax items account for the difference between income tax expense and cash taxes due.
Watch out for companies who consistently report an effective tax rate that is less than the statutory rate.
Forecasting the balance sheet
Forecasted Inventory: Forecasted COGS / inventory turnover
Forecasted A/R: days of sales outstanding x forecasted sales / 365
Net PPE = Begin balance + Capex - Depr
ROIC
ROIC = NOPLAT / invested capital
*ROIC is preferred over ROE for companies with different capital structures
Forecasting Value with Dividends
Advantages
- Less volatile
- Theoretically justified
- Accounts for reinvested earnings
Disadvantages
- Non-dividend paying firms
- Dividends artificially small for tax reasons
- Dividends may not reflect the control perspective
When suitable
- Company has history of paying
- Board has a dividend policy that has an understandable and consistent relationship with profitability
- Minority shareholder takes non-control perspective
- Mature firms
Assumptions of the constant growth or Gordon Growth Model
Assumptions:
- Dividend expected in one year
- Dividends grow at constant rate forever
- Growth rate less than required rate of return
MOST USEFUL:
- Mature firms
- Broad-based equity index
- Terminal value in more complex models
- International valuation
- Can be used to calculate P/E (justified)
PV of Growth Opportunities
Po = (E1 / r) + PVGO
USING LEADING P/E
Po / P1 = ( 1 / r ) + (PVGO / E1)
Weakness of Gordon Growth
- Terminal value very sensitive to rate estimates
- Difficult to use with non dividend paying stocks
- Minority perspective only (not useful for M & A valuation)
Phases of Growth and correct model to use
Initial : 3 stage model
Transitional: 2 stage or H model
Mature : GGM
FCF Strengths / Limitations
Strengths
- Used for firms with no dividends
- Functional model for assessing alternative financing polices
- Rich framework that provides additional insight into company
- Other measures like EBIT, EBITDA and CFO either double count or omit important cash flows
Limitations
- If FCF<0 due to large capital demands
- Requires detailed understanding of accounting and FSA
- Information not readily available or published
FCFE vs FCFF
FCFE: use when capital structure is stable
FCFF: when high or changing debt levels or negative FCFE
FCFF Formulas
FCFF = NI + NCC + INT ( 1 - t ) - WC - Net Capex FCFF = CFO + INT ( 1 - t ) - Net Capex FCFF = EBIT ( 1 - t ) + NCC - WC - Net Capex FCFF = EBITA ( 1 - t ) + NCC ( 1 - t ) - WC - Capex
- ( 1 - t ) = pre leverage
FCFE Formulas
FCFE = NI + NCC - WC - Net Capex + Net Borrowings FCFE = CFO - Net Capex + Net Borrowings FCFE = EBIT ( 1 - t ) - Int ( 1 - t ) + NCC - WC - Net Capex + Net Borrowings FCFE = EBITDA ( 1 - t ) - Int ( 1 - t ) + NCC ( t ) - WC - Net Capex + Net Borrowings
- POST LEVERAGE
WHY Net Income is a poor estimator for FCFE
- NI is an accrual concept not cash flow
- NI recognizes noncash charges
- NI Fails to recognize cash flow impact of investments in working capital, capex, net borrowings
EBITDA is a poor estimate for FCFF
- does not reflect taxes paid
- ignores effect of depreciation tax shield
- does not account for needed investments in WC and net fixed assets
Calculating Underlying Earnings
- Remove gain/losses on asset sales
- Remove asset write-downs (impairments)
- Remove loss provisions
- Remove Changes in accounting estimates
Calculating Normalized Earnings
Remove cyclical component with either of two methods:
- historical average EPS
- average ROE (preferred)
Average ROE = take arithmetic average and multiply by latest BVPS (book value per share)
Problems with PEG ratios
DO NOT ACCOUNT FOR:
- differences in firm risk attributes
- differences in the duration of growth
- Nonlinear relationship between growth and P/E ratio
Drawbacks of a P/B ratio
- does not reflect value of intangibles
- misleading when comparing firms with significant differences in asset size
- Different accounting conventions make it difficult to compare
- Inflation and technological change can cause big differences between BV and MV
P/B Formulas
P/B = MV Equity / BV of Equity
Justified P/B = (ROE - g) / ( r - g )
P/S Drawbacks
- High sales growth does not translate to operating profit
- P/S does not capture different cost structures between firms
- Revenue recognition methods can distort reported sales and forecasts
P/S Formula
Is same as trailing P/E and simply is multiplied by current period profit margin
= Margin x payout x growth / cap rate
P/CF Drawbacks
- Ignores some NCC, WC, Capex, Net Borrow
- FCFE is preferable to CFO but FCFE is more volatile and difficult to compute
- FCFE can be negative with large capex
P/CF Justifed
Vo = FCFEo (1 + g) / r - g
then take Vo / CF
Will increase if required return decreases
EV / EBITDA
Pros:
- Comparing firms with different financial leverage since EBITDA is pre leverage
- Controls for D & A differences
- EBITDA usually positive when EPS is negative
Cons:
- Ignores changes in WC
- FCFF is more closely tied to value because it controls for CAPEX
Justified Dividend Yield
Do / Po = ( r - g ) / ( 1 + g )
*Factors affecting dividend yield are opposite of other ratios.
Dividend yield increases when:
- required return increases
- High growth decreases payout
- high D/P strategy
Residual Income Models
= same as economic profit
POST LEVERED
RI = NI - (BVo x Ke)
PRE LEVERED
RI = EBIT ( 1 - t ) - (Total Capital x $WACC)
Alternative RI Measures
EVA = EBIT ( 1 - t ) - (Invested Capital x $WACC)
MVA = MV of Firm - invested Captial
Calculating Future RI
TWO METHODS for Calculating Future RI
- RI = EPS - (r x BVt-1)
- RI = (ROE - r) x BVt-1
OR
[(ROE - r ) / (1 + r)] x Bt-1
RI Valuation Models
SINGLE STAGE
Vo = Bo + [ ((ROE - r) x Bo) / (r - g) ]
Continuing Residual Income
IF:
w = 0, no competitive advantage
w = 1, perpetual competitive advantage (perpetuity)
0 < w < 1 = decline over time to zero
The w simply goes after the (1 - r) in the denominator of the formula
Adjustments to make when valuing a private company
- Nonrecurring and unusual items
- Discretionary expenses
- Non market compensation levels
- Personal expenses
- Real estate expenses
- Non-market lease rates
- Strategic vs non strategic buyers
Capitalized Cash Flow Method (valuing private companies)
Firm = FCFF / WACC-g
Equity = FCFE / r - g
Excess Earnings Method
EE = Normalized earnings - Return on WC - Return on Fixed Assets
Discount for Lack of Control (DLOC)
DLOC = 1 - [ 1 / ( 1 + Control Premium ) ]
Total Discount = 1 - [ (1 - DLOC) x ( 1 - DLOM)]
Calculating NOI
=Rental income if fully occupied \+ Other income = Potential gross income - Vacancy and collection loss = Effective Gross Income - Opex = NOI
*Income tax and interest expense are not operating expenses
Cost Approach to valuing real estate
Land cost + construction cost - economic depreciation
NCRIEF Property Index
Capital Return = [(change in mkt value - capex) / beg mkt value]
Return = [(NOI - capex + (end mkt value - beg mkt value)) / beg mkt value]
Holding Period Return = NOI / beg mkt value = Current yield = income yield = cap rate
Real Estate financial ratios
DSCR = first-year NOI / debt service
LTV = loan amount / appraisal value
Equity dividend rate = NOI - debt service / equity
Private Equity Calculations
NAV before distributions = previous year NAV after distribution + called capital - management fee + operating results
NAV after distributions = NAV before distributions - carried interest - distributions
Distributed to PIC (DPI) = LP realized return = cumulative distributions / paid in capital
Residual value to PIC (RVPI) = LPs unrealized return = NAV after distributions / paid in capital
Total Value to PIC (TVPI) = realized and unrealized returns = DPI + RVPI
VC Math
POST = FV / (1+r)
PRE = Post - INV
REQ f OWNERSHIP = INV / POST
Shares required for PE firm
Spe = Se [ f / ( 1 - f )]
P = INV / Spe
Hedge Fund Performance Biases
- Selection: choosing not to report
- Backfill: incubation
- Survivorship: bad ones fall out
Nonnormality in Return Distribution
Hedge funds have:
- Negative Skew
- High kurtosis
*Std Deviation is unsuitable
You PREFER THE OPPOSITE
Convenience Yield and Inventory Level
High inventory = lower CY and lower Futures Price
Forward price of a commodity
FPo = Soe^( r + U - Y ) t
r = Rf U = cost of storage (% of commodity price) Y = CY
Backwardation & Contango
Backwardation will result in a positive roll yield
Contango will result in a negative roll yield
Normal backwardation: occurs when producers hedge using futures
Make-up of Commodity Futures Portfolio Return
= spot \+ roll return \+ collateral return \+ rebalancing return = total return
Excess Return = spot + return returns
Total Return = collateral + futures
Theories of commodity returns
- Insurance: speculators earn premium from short hedgers
- Hedging pressure: depends on the balance of hedgers to short or long side
- Theory of storage: difficult to store = positive CY
Measures of Credit Risk
Loss Given Default (LGD): % of principal and interest lost if borrower defaults
Expected Loss (EL) = Probability Of Default (POD) x LGD
PV of EL = highest price investor would pay to an insurer to bear the credit risk of the investment
MAKES 2 ADJUSTMENTS
- Time value of money (duh)
- Uses Risk-Neutral Probability (RNP) instead of POD to account for the risk of the cash flows
STRUCTURAL MODEL BACKGROUND
Shareholders have a call option on the company’s assets with the Face Value of debt as the strike price.
Value of Risky Debt = Value of Rf Debt - Value of a put option on the company’s assets
STRUCTURAL MODEL ASSUMPTIONS
- Assets are traded in a frictionless and arbitrage free environment
- The Rf rate is constant
- Only zero-coupon bonds
STRUCTURAL Strengths / Weakness
STRENGTHS
- Uses option pricing theory to understand POD & LGD
- Inputs can be estimated using current market prices
WEAKNESSES
- Only uses zero coupon bonds
- Company assets are not actually traded, hence not directly observable
- Estimation procedures do not consider business cycle
REDUCED FORM ASSUMPTIONS
- Company has a zero-coupon bond liability that trades in a frictionless market
- the Rf rate, economy, POD, and recovery rate are non-constant
REDUCED FORM STRENGTHS & WEAKNESSES
STRENGTHS
- Model can be estimated using historical data
- Credit risk is allowed to fluctuate with the cycle
- No need to specify company’s B/S
WEAKNESSES
1. Past market conditions do not reflect future estimates
Formula for PVEL
= max amount an investor would pay an insurer to bear the credit risk of a risky bond
PVEL = Value of risk free bond - value of credit risky bond
KEY RATE DURATION
Change in Key Rate Duration = - D x Key rate
SPREAD MEASURES
- Z-spread: spread added to each rate on spot rate curve that makes PV of bond CFs equal to market price (difference between theoretical sport rate curve and the market)
- Option Removed Spread: spread added to each rate in binomial interest rate tree that makes bond value calculated from binomial equal to market price
* OAS = Z-Spread - cost of embedded option
** WANT OAS HIGH
Valuing Embedded Options
Value of Call = Vnoncallable - Vcallable
Value of Put = Vputable - Vnonputable
IF: Rate volatility incresases
THEN: Value of embedded call increases, value of callable bond falls
Effective Duration Formulas
ED = (BV-y - BV+y) / (2 x BVo x change in y
EC = [(BV-y - BV+y - (2 x BVo) / (2 x BVo x change in y^2)
CONVERTIBLE BONDS = call option on stock
Conversion Ratio (CR) = number of share per bond
Market conversion price (MCP) = Effective price per share when converting
Conversion Value (CV) = Market price of stock after conversion x CR
Favorable income difference = (ann $ coupons - [CV ratio x ann. divs]) / CV Ratio
Premium over straight value = (MV of bond / straight value) -1
Premium payback period = = market conversion premium / favorable income difference
Callable Convertible Bond
CCBV + call on bond = straight bond + call on stock
IF stock volatility increases = call on stock increases
IF rate volatility increases = CCBV goes down and call on bond goes up
IF rates increase CCBV and straight bond go down
Single Monthly Mortality Rate
SMM = 1 - (1-CPR)^(1/12)
100 PSA = 0.2% per month up to 6%
200 PSA = 2x CPR
Factors affecting Mortgage Prepayment
- Prevailing Mortgage Rates (most important)
- Housing turnover
- Characteristics of underlying mortgages (seasoning and locations)
Collateralized Mortgage Obligations (CMOs)
- Basic Sequential pay
- all tranches receive interest
- shortest tranche receives all principal until paid off
- Z-tranch or accrual tranche receives NO payments until sequential pay tranches are serviced BUT interest accrues as additional principal
- Z tranche bears the most extension risk and the lowest contraction risk
- PAC CMO: guaranteed principal payments based on sinking fund schedule
- the Support Tranches bears the contraction and extension risk
CONTRACTION & EXTENSION RISK
CONTRACTION: avg life decreases as rates fall and prepayments increase
EXTENSION: avg life increases as rates rise and prepayments fall
Stripped Mortgage Back Securities
Principal Only (PO) win if rates fall
Interest Only (IO) win if rates rise
MBS SELECTION
BUY CHEAP: big OAS, low option cost
SELL RICH: small OAS, high option cost
Analyzing Interest Rate Risk
% Change in bond price = duration effect + convexity effect
= -ED x change in y x 100 + EC x change in y^2 x 100
Pricing a forward contract
FP = So x ( 1 + Rf)^T
Cash and Carry
IF forward price is too high:
- Borrow and buy bond today
- Short the forward and reap the reward
REVERSE
- Short the bond (receive proceeds)
- Invest proceeds at Rf rate
- Go long the forward
- Cover the short and reap the reward
Valuing a forward contract
V1 = St - [FP / ( 1 + r )^( T - t )]
Pricing an equity forward contract (same for fixed income)
FP = (So - PVD) x ( 1 + Rf)^T
Valuing an equity forward contract (same for fixed income)
Vt = (St - PVD) - [FP / ( 1 + Rf)^(T-t)
Pricing Index Forward Contracts
FP = So x e^((Rf - Div) x t)
Valuing Index Forwards
Vt = (St / e^(Div x (T-t)) - (FP / e^(Rf x (T-t))
Forward Rate Agreement (FRA)
FRA = agreement to borrow or lend in the future
i.e. “2 x 3” = FRA price = implied 30-day forward rate 60 days from now
- Can be replicated wit ha long interest rate call + a short interest rate put
Valuing currency forwards
Vt = [St / (1 + Rfc)^(T-t)] - [FT / (1 + Rdc)^(T-t)]
Treasury Bond Futures Contracts
FP = [bond price x (1 + Rf)^T - FVC] x 1 / CF
CF = cash flow of cheapest to deliver bond
European Put-Call Parity
C - P = S - PV(X)
OPTIONS AND BINOMIAL MODEL
Probablities are not 50/50
Probabilty of Up Move = 1 + Rf - size of down move / (size of up minus size of down)
Calculate the value of an option using an interest rate tree:
Step 1: Price the bond at teach ending node in the interest rate tree
Step 2: Calculate terminal value of option at each ending node in tree
Step 3: Discount expected terminal option values back through tree
BSM Model Assumptions
- Underlying asset price follows a lognormal distribution
- The risk-free rate is constant and known
- The volatility of the underlying asset is constant and known
- Markets are ‘frictionless’
- Underlying asset has no cash flow
- Options are European
BSM Limitations
- Not useful for pricing options on bond prices and interest rates
- Known and constant volatility assumption is unrealistic
- Less useful with taxes, transaction costs
- Doesn’t price American options
The Greek Risks
- S (asset price) = Delta
- volatility = Vega
- Rf = interest rate = (Rho)
- T = tie to expiration = (Theta)
- X = exercise price
GAMMA
rate of change in delta as stock price changes
- largest when option is at the money and close to expiration
- Use in and out of the money options not close to expiration to reduce trading costs
AFFECT OF CASH FLOWS ON UNDERLYING ASSETS
- Reduce call values
2. Increase put values
Assumption of the Market Model
- e = 0
- The return on the market portfolio is not correlated with the error term
- The error terms are uncorrelated across securities
* e = unsystematic risk or diversifiable risk
