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Nominal vs. Real
Real = Nominal  Inflation

70 Rule
years to double = 70 / Real GDP growth

Sources of economic growth (5)
aggregate hours, labor productivity, physical capital growth, human capital growth, technological advance

institutions critical to the development of incentives that promote economic growth (3)
markets, property rights, and monetary exchange

COGS equation
cost of goods sold = beginning inventory + purchases  ending inventory

Cost method allowed in IFRS
FIFO, Weighted Average cost


Periodic vs. Perpetual Inventory System
 periodic: inventory value/ COGS determined at end of accounting period
 Perpetual system: inventory values and COGS updated continuously

LIFO Reserve (equ)
FIFO Inventory = LIFO Inventory + LIFO Reserve

LIFO Liquidation
occurs when a LIFO firm's inventory quantities are declining. older, lower costs are included in COGS, so > higher profit margins and higher income taxes. (not sustainable)

Relative to FIFO, LIFO results in...(Profitability)
assuming inflation and increasing quantities (4)
 Higher COGS
 Lower taxes
 lower net income
 lower profit margins

Relative to FIFO, LIFO results in...(Liquidity)
assuming inflation and increasing quantities (4)
 lower inventory value, current asset is lower under LIFO
 Lower current ratio (CA/CL)
 lower working capital (CA  CL)
 quick ratio is unaffected

Relative to FIFO, LIFO results in...(Activity)
assuming inflation and increasing quantities (2)
 Higher inventory TO (COGS up /avg inventory down)
 Lower days of inventory on hand (365 / inventory TO)

Relative to FIFO, LIFO results in...(solvency)
assuming inflation and increasing quantities (3)
 Lower total assets since inventory is lower
 lower total assets => lower shareholder's equity
 debt ratio and debttoequity ratio are higher

Inventory Valuation IFRS vs. GAAP
 IFRS valued at lower of cost or net realizable value.
 inventory "writeups" are allowed, but only to the extent that a previous writedown to net realizable value was recorded
GAAP: lower of cost or market. market usually equal to replacement cost (or upper NRV: sale price  selling costs), no subsequeent "writeup" allowed

FIFO net income = (in terms of LIFO)
 IFO net income = LIFO Net income + (Ending
 reserve  begininning reserve) * (1tax rate)

When to capitalize vs. expense?
An expenditure that is expected to provide future economic benefit over multiple accounting periods should be capitalized. Unlikely or uncertain? expensed

Effect of capitalizing expense on net income: (short term)
delays expense recognition > higher net income
overtime: total net income is identical

Effect of capitalizing expense on shareholder's equity: (short term)
higher SE (since Net income is higher/RE)

Effect of capitalizing expense on CFO: (short term)
 Capitalized: CFI (higher CFO)
 Expensed: CFO (Higher CFI)
total cash flow is the same

Effect of capitalizing expense on Financial Ratios: (short term)
Capitalizing: debttoassets ratios and debttoequity are lower (A and E are higher)
Initially result in higher Return on Assets (ROA) and Return on Equity (ROE) due to higher net income

Effect of capitalizing expense on Capitalized interest: (short term)
interest is capitalized as part of the asset's cost. interest is then allocated to the income statement through depreciation expense and reported as an CFI, other interest goes as CFO

Effect of capitalizing expense on Interest Coverage Ratio: (short term)
EBIT/interest expense, measures a firm's ability to make required interest payments on its debt
higher ratio (smaller denom) as capitalizing lower interest expense and higher net income


depreciation types (3)
 straightline
 accelerated
 unitsofproduction methods

straightline and accelerated depreciation equations
1) depreciation = (original cost  salvage value)/ depreciable life
2) DDB in year x = 2 / asset life in years x book value at beginning of year x

IFRS asset impairment:
 carry/book value > recoverable amount
 carry/book value = original cost less accum. deprec.
 recoverable amount = fair value less selling costs
if impaired, asset is written down on BS and impariment loss recognized on IS

GAAP asset impairment test:
 Tested only when events and circumstances indicate need
 1)test for impairment: Carrying value > asset's future undiscounted cash flow
 2) measure loss: writtendown to fair value on BS and discounted value of future cash flows or fair value is recognized on IS

impairment effect on financial statements and:
ROA, ROE, Asset turnover
 lower assets and SE (net income)
 ROA, ROE > lower immediately (higher later as deprec expense is lower)
 asset TO > igher

IFRS vs. GAAP rules on revaluation of Fair Value after impairment
 GAAP: not allowed excepct during sale of longlived asset
 IFRS: can choose fiarvalue or depreciated costs
 Gain would be recognized in the IS
 Gain beyond initial loss would bypass the IS and be recognized in other comprehensive income (SE)

average age equ
accumulated depreciation/annual depreciation expense

average depreciable life equ
ending gross investment / annual depreciation expense
gross investment = orignial cost of the asset

remaining useful life equ
ending net investment / annual depreciation expense

finance (or capital) lease vs. operating
finance: purchase of an asset financed with debt. lessee will add equal amounts to both A and L on BS and recognize depreciation expense on the asset and interest expense on the liability
Operating Lease: rental agreement, rental expense on IS

Benefits to leasing over buying: (5)
 less costly financing: no down payment
 reduced risk of obsolescence: asset returned
 less restrictive provisions: more flexible
 offbalance shee financing: no liability, better leverage ratios
 tax reporting advantages: synthetic lease where treated as ownership for tax reporting purposes

Lease classification under IFRS and GAAP
IFRS: if substantially all rights and risks of ownership are transferred to the lessee the lease is treasted as a finance lease
 GAAP: finance lease if any of the following are met:
 title is transferred
 bargain purchase option exists: provision that permits the lessee to purchase leased asset for a lower price than FMV
 >75% of asset's ecnomic life
 PB of lease payments >90% of FMV

Finance vs. Operating lease ACCOUNTING

Finance vs. Operating lease RATIOs
 ALL LOWER except Debt RATIOS HIGHER

Salestype lease:
description
when
how
treated as if the lessor sold the asset and provided the financing to the buyer
used if the PV of lease payments exceeds the carrying value of the asset (typically of lessor is manufacturer, since cost of leased asset will be less than fair value)
lessor recognize a sale equal to the present value of lease payments and COGs equal to carrying value. also gets interest revenue over term of lease as CFO and principal reduction is inflow from CFI

Direct financing lease
description
when
how
no gross profit is recognized by the lessor at the inception, lessor is simply providing financing
if PV of lease payments is equal to the carrying value of the leased asset (lessor is third party) no gross profit recognized
lessor removes asset and a lease receivable is created for the same amount. principal portion reduces the lease receivable and as CFI. interest portion as CFO

Operating lease as lessor
lessor recognizes lease payment as rental income. keep the leased asset on balance sheet and revognize depreciation expense
total CF the same. all money as CFO

Accounting for Investments

Summary of Classification of Financial Assets

Transactions with Investee (upstream)
Investee to the investor, profit that is unconfirmed bust be eliminated proportionately:
Must reduce equity income by $2250: (15,000 profit x 50% unconfirmed) x 30% ownership interest
investor owns 30% of investee, investee sold to investor and recognized $15K profit

Transactions with Investee (downstream)
 must eliminate the proportionate share of the profit that is unconfirmed.
 $300: ($10,000 profit x 10% unconfirmed amount x 30% ownership interest)
 investor sold $40K of oods to investee for $50K, investee sold 90% of the goods

Business Combinations:
Merger
Acquisition
Consolidation
Special Purpose Entities
 Merger: acquiring firm absorbs all the A/L of the firm which ceases to exist.
 Acquisition: both entities continue to exist in a parentsubsidiary relationship
 Consolidation: a new entity is formed that absorbs both
 SPE: created for a single purpose by a sponsoring company


Liquidity Ratios
Current
Quick
Cash
Current ratio = current assets / current liabilities
quick ratio = (cash + short term investments + receivables) / current current liabilities
cash ratio = (cash + short term investments) / current liabilities

Activity ratios
Inventory turnover
avg inventory processing period
receivables turnover
avg receivables collection period
Inventory turnover = COGS / avg inventory
avg inventory processing period = 365 / inventory inventory
receivables turnover = revenue / avg receivables
avg receivables collection period = 365 receivables TO

activity ratios 2
Payables TO
Avg payables payment period
working capital turnover
working capital
Payables TO = purchases / avg trade payables
Avg payables payment period = 365 payables t/o
working capital turnover = revenue / avg working capital
working capital: current assets  current liabilities

activity ratios 3
fixed asset turnover
total asset turnover
equity turnover ratio
fixed asset turnover = revenue / average net fixed assets (aka net of accumulated depreciation)
total asset turnover = revenue / average total assets
equity turnover ratio = revenue / average total equity

profitabiilty ratios
gross profit margin
operating profit margin
gross profit margin = gross profit / revenue
operating profit margin = operating income / revenue
 Operating income = groww profit  operating costs
 approximation = EBIT

Profitabilility ratios
return on sales (2)
pretax margin = earnings before tax but after interest / revenue
net profit margin  net income / revenue
note: most of the return on sales ratois are on the common size income statement

profitability ratios: return on investment (3)
return on assets (ROA)
return on total invested capital
return on total equity
return on assets (ROA) = net income / avg total assets
return on total invested capital = net income + interest expense / equity + interest bearing debt
return on total equity = net income / avg total equity

Solvency ratios :Debt ratios
total debttoequity ratio
financial leverage ratio
 total debttoequity ratio = total deby / total SE
 debt = all interest bearing liabilities
financial leverage ratio: average total assets / average total equity

Solvency Ratios: coverage ratios
interest coverage
payout ratio
interest coverage = EBIT / interest payments
payout ratio = dividends paid / net income

Per share quantities
basic EPS
Diluted EPS
Basic EPS = NI  Pref Div / weighted avg # of ordinary shares
Diluted EPS = income available adjusted for dilutive securities / weighted avg # ajusted for dilutive securities

Free Cash Flow (FC)
(2 points, 2 equ)
FCFF
FCFE
 FCF is cash available for discretionary uses
 frequently used to value firms
 FCFF = CFO + Int (1T)  FCInv
 FCFE = CFO  FCInv + Net debt increase



FX rate as of balance sheet date

Average Rate
average FX rate over reporting period

Historical Rate
FX rate that existed when a transaction occurred (not fixed in time)

Temporal Method (aka Remeasurement) definition
Local currency translation to function currency and presentation currency (gain/loss goes on income statement)

Current Rate definition (aka translation)
Local Currency and Functional Currency translation to presentation currency (gain/loss shows on B.S.)

Temporal Method ( 3
steps)
 1) convert balance sheet and solve for Retained Earnings
 2) Reconcile retained earnings to find Net Income
 3) Product the IS. Net income in the income statemtn will be different from NI in RE. The difference is the exchange gain/loss which is taken to the IS

Current Rate (steps) 3
 1) convert income statement to find net income
 2) plug into reconciliation of Retained Earnings to find closing RE
 3) plug into BS to find difference between A and L+SE, exchange rate loss


market model (def, equ and 3 assumptions)
 regression of an asset's returns against an observable index's returns
Expected value of the error term = 0
return on the market portfolio (Rm) is not correlated with the error term
the error terms are uncorrelated across securities

expected return, variance and covariance (equs x 3)

adjusted beta (def and equ)
 meanreverting level of beta = 1

3 types of multifactor models
macroeconomic factors: business cycle, interest rates, inflation
microeconomic factors: market cap, P/E ratio, firm factors
statistical factors: principal components, factor analysis

Macro vs. fundamental models (sensitivities, factors, number of factors, intercept term) table
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Arbitrage Pricing Model (APT) def + equ
 describes the equilibrium relationship between expected returns for welldiversified portfolios and their multiple sources of systematic risk
pretty much a multifactor model of the CAPM

active return (def and equ)
 difference between the portfolio return (P) and its benchmark (B) (Tracking error)
 RpRb

Active risk
 (Tracking risk) is the standard dviation of the active return

active risk squared (equ)
active risk squared = active factor risk + active specific risk
active factor risk: caused by deviations of portfolio's factor sensitivities versus benchmark's sensitivities to same set of factors (overweight airline sector)
active specific risk: caused by deviations of portfolio's individual asset weightings versus benchmark's individual asset weightings, after controlling for portfolio's factor sensitivities (overweight delta)

information ratio
 active return unit of active risk
measures manager's consistency in generating actie returns

factor portfolio (def)
constructed to have sensitivity equal to 1.0 to only one risk ractor and zero sensitivities to the remaining factors
(big firms will outperform small firms)

tracking portfolio (def)
constructed to have the same set of factor exposures to match a predetermind benchmark
same set of factors as benchmark (s&P 500)

CAPM (2) vs. APT (3)
CAPM: makes many implausable assumptions
considers one factor: market risk
APT: assumes returns derived from multifactor process
unsystematic risk can be diversified
no arbitrage opportunities

CAPM assumptions (6)
investors only need to know expected returns, variances, and covariances in order to create optimal portfolios
all investors have same forecasts of risky assets' returns, variances, and covariances
all assets are marketable, and the market for assets is perfectly competitive
investors are price takers whose individual buy and sell decisions have no affect on prices
investors can borrow and lend at the riskfree rate and unlimited shortselling is allowed
there are no frictions to trading (taxes or transaction costs)

6 impediments to capitla flow (across barriers)
1) psychological barriers
2) legal restrictions
3) transaction costs
4) discriminatory taxes
5) political risk
6) foreign currency risk

separation theorem (def)
all investors hold the riskfree asset and the domestic market portfolio

extended CAPM (2 assumptions)
1) all investors have same consumption basket
2) PPP holds exactly at any points in time
these two means no real exchange rate risk
CAPM can be extended internationally

unhedged return in domestic currency (equ)
~Return in foreign currency + %change in S
Rdc ~ Rfc +%change in S
S = spot rate

hedged Return on domestic equity (equ)
hedged Rdc ~ Rfc + (FS0)/S0
S = spot rate

real exchange rate (equ) and def
possibility that the change in the nominal exchange rate is not explained by inflation differentials
real S = S x (Pfc / Pdc)
real S = real exchange rate

expost returns (def)
realized returns given interest rate / price evolution

foreign currency risk premium (equ x 2 + def)

ICAPM accounts for 2 things (relative to CAPM)
 1) exchange rate changes
 2) asset value sensitivity to changes in exchange rates

additional ICAPM assumptions
 1) investors can hedge real FX risk with forward contracts
 2) investors can borrow/lend at the riskfree rate in every currency

ICAPM separation theorem
 investors hold combination of
 1) riskfree asset of own country in DC
 2) world market portfolio optimally hedged against currency risk


domestic currency exposure (def, equ)
(the gammas in the ICAPM formula)
sensitivity of asset return to exchange rate movements
depends on local currency sensitivity (correlation between LC value of an asset and the exchange rate)
gamma = gamma (LC) + 1
LC = local currency
point: sign of gamma can be determind intuitively

currency exposure of firms (apprec vs. deprec for domestic currency firm)
depreciation of its own domestic currency helps exporters
appreciation of its own domestic currency helps importers (imported goods are cheaper)

2 models of National Economies of Equity Markets
 Traditional model:
 effect of currency deprec/apprec on economic activity: currency value affects econmy
 Money Demand Model:
 effect of economic activity on currency values: economy affects currency value

Traditional Model (effect of domestic currency depreciation on economic activity (long run) 4
Long run
competitiveness improves
exports increase
trade deficit decreases
economic activity increases
implies negative domestic currency exposure: currency down; equities/economy up

Money demand model
effect of real economic growth:
higher demand for currency leads to…
 increaes in real currency value, leads to…
increase in real stock returns
intuition: booming economy drives up currency values
implies positive exposure: currency up; equities/economy up

Free Market Theory (def +4)
regarding bond markets and currency exposure
increases in real interest rate leads to:
higher rates (bad for bondholders)
higher currency values (good for foreign bond holders)
Negative currency exposure
rate and currency effects tend to offset

Government intervention theory (def + 4)
Regarding bond markets and currency exposure
increases in currency value leads to:
government intervention to reduce interest rates
falling rates are good for bondholders
appreciating currency
 good for foreign bondholders
positive domestic currency exposure

Argument for efficient markets: Economic
As asset values diverge from equilibrium because everyone is indexed, some active managers will add value

Argument for efficient markets: Empirical
some active managers beat the benchmark, earn excess returns

treynorblack security selection
(def + 3 steps)
asset allocation framework
combines some degree of market inefficiency with modern portfolio theory
create two portfolios
1) passive portfolio (index, M)
2) active portfolio A (assts with nonzero alpha)
combine M and A optimally


TreynorBlack: Step 1
develop expectations for M and Rf
expected return for passive market index
variance for passive market index
Rf: riskfree rate (zero standard deviation)




picture of TreynorBlack model: optimal risky portfolio

solution for imperfect forecasts of alpha (2)
1) impose an imprecision penalty on alpha; force alpha to revert towards zero for inferior analysts
2) this decreases the allocation to A
adjusted alpha equals unadjusted alpha times the analyst's Rsquare
RSquare is from regression of analyst's historical and realized alphas

portfolio perspective
analyze portfolio risk/return, NOT risk/return of individual securities

Steps of PM process (7 out of 3 steps)
1) Planning
analyzing objectives and constraints
Developing IPS
Determining investment strategy
asset allocation
2) Execution
3) feedback

investment objectives: Risk
Risk objectives:
investors willingness to take risk
investor's ability to take risk

factors affecting ability to take risk (4)
1) required spending needs
2) longterm wealth target
3) financial strength
4) liabilities

investment objectives: return (2)
Return objectives
desired return (stated by client)
required return (determind by longterm goals)
Must be consistent with risk objective
consider from a total return perspective

investment contraints (5) + def
factors that limity available investment choices
1) liquidity: cash outflows > income
2) time horizon: time period over which portfolio is expected to generate returns
3) tax: government takes a cut of returns
4) legal/regulatory: external contraints
5) unique circumstances: catchall category

investment policy statement: def + 3 purposes
IPS: formal document that governs investment process: contraints/objectives
easily transportable
promote longterm discipline
prevent shortterm strategy shifts

strategic asset allocation
approaches to investing
passive, active, or semiactive (riskcontrolled, or enhanced index strategies)

noarbitrage principle
there should be no riskless profit from combining forward contracts with other instruments

forward price
price of underlying that would not permit profitable riskless arbitrage, so value equals zero

Cost of carry model
FP = S0 x (1+Rf)^T
FP: Forward Price
S0= spot price of underlying
Rf: risk free rate
T: maturity

value of long forward contract during the life of the contracct (Vt) is: (equ)

value of a long position at initiation and at maturity

how to compensate for interim cash flows in pricing forward contracts
reduce spot price by present value of dividends, or reduce FP by future value

Pricing equity forwards (equ)
(S0  PVD) x (1+Rf)^t
or
[S0 x (1+Rf)^T]  FVD
P/FVD: present/future value of dividend
both reduce forward price by value of dividends
# of days / 365
or #of months /12

Pricing index forward contracts (equ)
 Equity index = basket of many stocks

Valuing index forwards (equ)

FRA, 2x3 FRA
Forward rate agreements
agreement to borrow (long) or lend (short) in the future
usually based on LIBOR with #ofdays/360 day count convention
ex) underlying in a 2x3 FRA is a 30 day loan 60 days from now
2 months from today at a fixed rate for a term that ends, 3 months from today

3 steps to pricing an FRA
1) deannualize
R = .024 x 30/360 = .002
2) [(1+long)/(1+short)]1
3) annualize
ex) times 360/60 = 3.3%

Valuing a FRA (4 steps)
1) deannualize
2) calc what the fixed rate would now be on a new FRA [(1+long)/(1+short)]1
3) compare the payoff on the original FRA to the fixed rate on a new FRA
4) discount the payoff back to today

3 keys to valuing an FRA
1) value is determined by rate changes
e.g. you contracted to borrow at 3.3% when rates increased to 4%
2) the long wins when rates go up
3) paid in arrears: the impact of rate changes won't be realized until the end of the loan


Valuing Currency Forwards (equ)

convergence
spot price = futures price
marked to market daily

Futures Price (on treasury bond futures)

2 situtations where futures vs. forwards prices different
1) interest rate and underlying positively correlated
futures prices > forward price
if rates increase and the underlying goes up, the long will receive cash (think: marktomarket feature of futures contract is valuable)
gains on futures contract reinvested at high rates/losses financed at low rates
2) interest rate and underlying negatively correlated
futures price < forward price
opposite as above

futures price with commodities
FP = S0 x (1+Rf)^T + FV (NC)
NC = storage costs  convenience yield
higher costs due to storage, insurance, etc.

convenience yield
Nonmonetary benefits from holding asset will reduce the commodity futures price
holding asset in short supply with seasonal/highly risky production process

normal backwardization
futures price < expected spot rate
this must be true for speculators to go Long on futures contract
they think they can gain money from buying future
normal contango is opposite: shorts need to be compensated for risk: futures price > expected spot price

Eurodollar deposits
U.S. dollardenominated deposits outside the U.S.
based on 360 day year
important difference:
tbills are discount instruments: buy for 98, get 100
eurodollars use addon interest: buy 100, get 104

European option
option that can only be exercised at expiration

american option
exercised at any time prior to expiration (most common)

European Putcall parity
C0 + PV (X) = P0+S0

Binomial stock option model
U = size of upmove
d= size of down move
Pie u: probability of up move
Pie d = probability of downmove
get value, use probability to get expected value
find expected value and discount back

value option on a fixed income security (3 steps)
1) price the bond at each ending node in the interest rate tree
2) calculate terminal value of option at each ending node in tree
3) discount expected terminal option values back through tree

valuing caps and floors
value of a cap (floor) is the sume of the values of its component caplets (floorlets)

BSM and "Greek Risks" (5)

What happens to option value? (positive or negative related, calls and puts (10)

Delta
change in price of an option for a 1unit change in the price of the underlying stock
(aka the slope of the priortoexpiration curve)

discrete time (equ)
Delta call = (C1C0)/(S1S0) = change in C / Change in S

Continuous time (equ)
delta call = N(d1)
change in C =~ N(d1) x change in S
Change in P =~ [N(d1)1] x change in S

Delta ranges (3)
call deltas range from 01
0 far out of the money
 1 far in the money
 put deltas range from 1 to 0
 far out of the money: 0
1 far in the money
put delta = call delta 1

Deltaneutral hedge (def and equ)
Combination of Long stock short calls so the portfolio value doesn't change as stock price changes
# of short calls needed = # of shares hedged / Delta call
hint: delta <1, so always need more calls than shares

gamma (def)
gamma = rate of change in delta, as stock price changes
(2nd derivative of black sholes, 1st is delta)
largest when option is atthemoney and close to expiration
small for deep inthemoney and deep outofthemoney
use inandoutofthemoney options not close to expiration to reduct trading costs

Historical volatility
standard deviation of continuously compounded returns on stock

cash flows on underlying assets (dividends etc.)
cash flows on underlying asset affect options values
reduce call values
increase put values
for continuous dividents
fix by replacing S0 in BSM model with:

forward putcall parity (def and equ)
Derivation: create two portfolios
portfolio 1)
a call option on forward contract with exercise price of X and forward price of Ft that matures at time T
a discount bond with face = (xFt)
cost of portfolio 1 = C0 + (xFt) / (1+Rf)^T
Portfolio 2)
a put option on the forward contract with exercise price of X
a long position in the forward contract
cost of portfolio 2 = P0
the trick: we can show that the payoffs in all states are the same for both portfolios, same PRICE!

american options > or < value of european options (futures vs. forwards)
futures: america>europe because cash earned from marktomarket, CFs can be invested if option is exercised
forwards: same, no mark to market on forward contracts

black model (def)
model for calculating value of european options on forwards
substitute discounted vlaue for Ft for S0

Swap pricing/valuation defs
price = swap fixed rate
the rate paid by the payfixed side
Principle: PV fixed payments = PV floating payments
Swap value: difference in the value of the fixed payments and floating payments
zero at initiation
usually nonzero after initiation

mimick vs. replicate (with swaps)
mimick: acts like th same CFs
Replicate: same cash flows
same as bonds, fras, or options

replicating bonds with swaps
fixedrate payer side ( a payer swap) could be replicated by:
1) issuing fixed rate bonds (match maturity and payment dates)
2) using proceeds to purchase floating rate notes at LIBOR
replication with bonds is key to pricing and valuing swaps

replicating offmarket FRAs with swaps
swaps are approximated by a strip of FRAs
Swap rate is constants; FRAs have different rates for all forward rates
offmarket FRAs have forward rates that do not yield a value at initiation
hence, a swap is a portfolio of offmarket FRAs

replicating options with swaps

Swap fixed rate (def and method)
swap fixed rate must be set so value at initiation is zero
method: value the swap as a combination of fixedrate bond and floating rate bond
value of a payer swap = value of replicating floating rate bond  value of replicating fixed rate bond

Swap fixed rate cformula (to find annual swap rate) equ
Coupon = (1Z4) / (Z1+Z2+Z3+Z4)
z: price of nperiod $1 zero coupon bond = nperiod discount factor

valuing a swap (fixed rate payer side)
swap value: difference in PV of fixed and floating payments
to calc value, find:
PV of replicating fixed rate bond
PV of replicating floating rate bond
Fixed rate payer swap value = Pvfloat  PV fixed

Currency swaps (def)
interest rates used to price currency swaps are just the swap rates calculated from each currency's term structure
principal amounts are exchanged at initiation
valuation is similar, but you must adjust payments for the exchange rate

four possible structures of currency swaps
1) receive euros fixed, pay $ fixed
2) receive euro floating, pay $ fixed
3) receive euro fixed, pay $ floating
4) receive euro floating, pay $ floating
fixed rates are based on each currency's yield curve
notional principal amounts are based on current spot exchange rate

valuing a currency swap
PV of cash flows and account for exchange rate changes
fixedforfixed example: value of receive euro fixed and pay $ fixed side =
PV (Euro fixed bond)  PV ($ fixed bond)
use yield curve for each currency

Equity swaps (value equ and method) 4
value = PV payments received  PV payments made
index side is the return on the index times the notional principal since the last settlement date
equity return payer: pays any positive return on equity, receives fixed rate payment plus any negative equity return
betting index goes down
Fixed rate payer: pays fixed rate plus negative equity return, receives positive equity return

swaptions (def and notation) 2x5
options on swaps
right to enter a swap in the future with swap rate determined today
notation similar to FRA:
2x5 swaption: options expires in 2 years, underlying is 3year swap

payer swaption and receiver swaption
payer: right to enter swap as fixed rate payer (wins if rates increase)
receiver: right to enter swap as fixed rate receiver (wins if rates fall)

uses of swaptions (3)
hedge anticipated floating rate exposure in the future
speculate
terminate existing swap

valuing a swaption
PV of the difference between payments based on higher existing (market) swap rate and payments based on strike price
discount CFs based on "Spread" between contract and market

swap spread
swap spread = swap rate  Tnote rate
increases in times of more uncertainty
quality spread: swaps accrue default risk (swap rate is based on LIBOR, which is NOT riskfree)
tnote is risk free

Credit risk (swaps) def, current , potential
def: probabilty that a counterparty will default
current credit risk: payment due
potential credit risk: future obligations
highest in the middle of the life of an interest rate swap
past middle of life currency swap

2 ways to reduce credit risk
markingtomarket: make payments equal to swap value and reprice the swap so new value is zero
payment netting: one party makes net payments to the other, rather than exchanging payments

interest rate caps
holder (the long) receives payments if market rates > the cap rate
big point: CFs mimic a strip of long call options on LIBOR
each individual call option is referred to as a caplet

interest rate cap formula
payoff: determined by spread between cap rate and LIBOR
PMT = max [ 0, NP x (index rate  cap strike) x (actual days/360)]
NP: notional principal

interest rate floors def
holder (the long) receives payments if rates fall below the floor rate
CFs mimic a strip of long put options on LIBOR
each individual put option is referred to as a floorlet

interest rate floor formula
determind by the spread between floor rate and LIBOR
PMT = [0, NP x (floor strike  index rate) x (actual days/360)]

interest rate collar
long cap + short floor (or vice versa)

credit default swap (CDS)
insurance contract on "reference obligations" (a specific bond or loan)
buyer pays seller default swap premium (default swap spread)
protects buyer from losses due to default
swap seller is "long the bond" except: only long the credit risk, not the interest rate risk

CDS advantages (5)
risk management: separate credit risk from interest rate risk
short positions: expensive in repo market
liquidity: more liquid than cash market
flexibility: greater ability to create unique positions
confidentiality: confidential OTC

CDS: participants
commercial banks: hedge loan portfolios, satisfy regulators
investment banks: dealers, liquidity, hedge bonds, trading desk
hedge funds: convertible arbitrage, distressed debt
insurance firms: long positions selling credit protection

CDS strategy: basis trade
if CDS premium < bond't spread above benchmark
buy the bond and buy the CDS

CDS strategy: credit curve flattener
ST instability and LT prospects sound
buy ST CDS and sell LT CDS

CDS strategy: credit curve steepener
ST prospects OK but LT prospects poor
sell ST CDS and buy LT CDS

CDS strategy: Index trade
combine CDS with short or long position in credit index

CDS strategy: options trade
receiver option gives buyer right to sell CDS
payer option gives buyer right to buy a CDS

CDS strategy: capital structure trade
exploit views on firm's securities (e.g. sub has less credit risk than parent) > buy parent CDS and sell sub CDS

CDS strategy: correlation trade
trade baskets of CDS
firsttodefault swap: seller provides protection for first default only
pricing: more CDS in basket > higher premium; higher default correlation > lower premium

mean variance analysis assumptions (4)
investors are risk averse
investors know expected returns, variances, and covariances for all assets
investors use Markowitz Framework
frictionless markets: no taxes or transactions costs

portfolio expected return equ
weighted average of individual returns
E(Rp) = w1*E(R1) + w2*E(R2)

portfolio variance (def)
 function of weights, variances and correlation

minimum variance portfolio

efficient frontier/portfolio
porftolio: no other portfolio offers higher return with same risk
efficient frontier: set of portfolios with highest return for each risk level (markowitz efficient frontier)

relation of correlation and diversification between 2 assets

variance for an equallyweighted portfolio (w = 1/n)

capital market line (def, graph and equ)

sharpe ratio
also equals the slope of the CML line
E(R_{M})  rf / σ_{M}
M = tangency portfolio

Capital Market Line vs. Capital allocation line (def and equs)

unsystemic risk vs systemic
diversifiable = unsystemic

total risk equ and picture

