CFA

Real = Nominal - Inflation

years to double = 70 / Real GDP growth

aggregate hours, labor productivity, physical capital growth, human capital growth, technological advance

markets, property rights, and monetary exchange

cost of goods sold = beginning inventory + purchases - ending inventory

FIFO, Weighted Average cost

• periodic: inventory value/ COGS determined at end of accounting period
• Perpetual system: inventory values and COGS updated continuously

FIFO Inventory = LIFO Inventory + LIFO Reserve

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)

• Higher COGS
• Lower taxes
• lower net income
• lower profit margins

• lower inventory value, current asset is lower under LIFO
• -Lower current ratio (CA/CL)
• -lower working capital (CA - CL)
• quick ratio is unaffected

• Higher inventory TO (COGS up /avg inventory down)
• Lower days of inventory on hand (365 / inventory TO)

• Lower total assets since inventory is lower
• lower total assets => lower shareholder's equity
• debt ratio and debt-to-equity ratio are higher

• IFRS valued at lower of cost or net realizable value.
• inventory "write-ups" are allowed, but only to the extent that a previous write-down 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 "write-up" allowed

• IFO net income = LIFO Net income + (Ending
• reserve - begininning reserve) * (1-tax rate)

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

delays expense recognition -> higher net income

overtime: total net income is identical

higher SE (since Net income is higher/RE)

• Capitalized: CFI (higher CFO)
• Expensed: CFO (Higher CFI)

total cash flow is the same

Capitalizing: debt-to-assets ratios and debt-to-equity 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

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

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

• straight-line
• accelerated
• units-of-production methods

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

• 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

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

• lower assets and SE (net income)
• ROA, ROE -> lower immediately (higher later as deprec expense is lower)
• asset TO -> igher

• GAAP: not allowed excepct during sale of long-lived 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)

accumulated depreciation/annual depreciation expense

ending gross investment / annual depreciation expense

gross investment = orignial cost of the asset

ending net investment / annual depreciation expense

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

• less costly financing: no down payment
• reduced risk of obsolescence: asset returned
• less restrictive provisions: more flexible
• off-balance shee financing: no liability, better leverage ratios
• tax reporting advantages: synthetic lease where treated as ownership for tax reporting purposes

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

• 
• ALL LOWER except Debt RATIOS HIGHER

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

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

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

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

• 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

• Merger: acquiring firm absorbs all the A/L of the firm which ceases to exist.
• Acquisition: both entities continue to exist in a parent-subsidiary relationship
• Consolidation: a new entity is formed that absorbs both
• SPE: created for a single purpose by a sponsoring company



Current ratio = current assets / current liabilities

quick ratio = (cash + short term investments + receivables) / current current liabilities

cash ratio = (cash + short term investments) / current liabilities

Inventory turnover = COGS / avg inventory

avg inventory processing period = 365 / inventory inventory

receivables turnover = revenue / avg receivables

avg receivables collection period = 365 receivables TO

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

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

gross profit margin = gross profit / revenue

operating profit margin = operating income / revenue

• Operating income = groww profit - operating costs
• approximation = EBIT

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

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

• total debt-to-equity ratio = total deby / total SE
• debt = all interest bearing liabilities

financial leverage ratio: average total assets / average total equity

interest coverage = EBIT / interest payments

payout ratio = dividends paid / net income

Basic EPS = NI - Pref Div / weighted avg # of ordinary shares

Diluted EPS = income available adjusted for dilutive securities / weighted avg # ajusted for dilutive securities

• FCF is cash available for discretionary uses
• frequently used to value firms

• FCFF = CFO + Int (1-T) - FCInv
• FCFE = CFO - FCInv + Net debt increase



average FX rate over reporting period

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

Local currency translation to function currency and presentation currency (gain/loss goes on income statement)

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

• 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

• 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

• 
• 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

• 
• mean-reverting level of beta = 1

macroeconomic factors: business cycle, interest rates, inflation

microeconomic factors: market cap, P/E ratio, firm factors

statistical factors: principal components, factor analysis

• 
• describes the equilibrium relationship between expected returns for well-diversified portfolios and their multiple sources of systematic risk

pretty much a multi-factor model of the CAPM

• difference between the portfolio return (P) and its benchmark (B) (Tracking error)
• Rp-Rb

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

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)

• 
• active return unit of active risk

measures manager's consistency in generating actie returns

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)

constructed to have the same set of factor exposures to match a predetermind benchmark

same set of factors as benchmark (s&P 500)

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

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 risk-free rate and unlimited short-selling is allowed

there are no frictions to trading (taxes or transaction costs)

1) psychological barriers

2) legal restrictions

3) transaction costs

4) discriminatory taxes

5) political risk

6) foreign currency risk

all investors hold the risk-free asset and the domestic market portfolio

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

~Return in foreign currency + %change in S

Rdc ~ Rfc +%change in S

S = spot rate

hedged Rdc ~ Rfc + (F-S0)/S0

S = spot rate

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

realized returns given interest rate / price evolution

• 1) exchange rate changes
• 2) asset value sensitivity to changes in exchange rates

• 1) investors can hedge real FX risk with forward contracts
• 2) investors can borrow/lend at the risk-free rate in every currency

• investors hold combination of
• 1) risk-free asset of own country in DC
• 2) world market portfolio optimally hedged against currency risk

(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

depreciation of its own domestic currency helps exporters

appreciation of its own domestic currency helps importers (imported goods are cheaper)

• 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

Long run

-competitiveness improves

-exports increase

-trade deficit decreases

-economic activity increases

implies negative domestic currency exposure: currency down; equities/economy up

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

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

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

As asset values diverge from equilibrium because everyone is indexed, some active managers will add value

some active managers beat the benchmark, earn excess returns

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 non-zero alpha)

combine M and A optimally

develop expectations for M and Rf

-expected return for passive market index

-variance for passive market index

-Rf: risk-free rate (zero standard deviation)

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 R-square

-R-Square is from regression of analyst's historical and realized alphas

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

1) Planning

-analyzing objectives and constraints

-Developing IPS

-Determining investment strategy

-asset allocation

2) Execution

3) feedback

Risk objectives:

-investors willingness to take risk

-investor's ability to take risk

1) required spending needs

2) long-term wealth target

3) financial strength

4) liabilities

Return objectives

-desired return (stated by client)

-required return (determind by long-term goals)

Must be consistent with risk objective

consider from a total return perspective

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: catch-all category

IPS: formal document that governs investment process: contraints/objectives

easily transportable

promote long-term discipline

prevent short-term strategy shifts

approaches to investing

passive, active, or semi-active (risk-controlled, or enhanced index strategies)

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

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

FP = S0 x (1+Rf)^T

FP: Forward Price

S0= spot price of underlying

Rf: risk free rate

T: maturity

reduce spot price by present value of dividends, or reduce FP by future value

(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

• Equity index = basket of many stocks
• 

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

1) de-annualize

R = .024 x 30/360 = .002

2) [(1+long)/(1+short)]-1

3) annualize

ex) times 360/60 = 3.3%

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

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

spot price = futures price

marked to market daily

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: mark-to-market feature of futures contract is valuable)

-gains on futures contract re-invested at high rates/losses financed at low rates



2) interest rate and underlying negatively correlated

futures price < forward price

-opposite as above

FP = S0 x (1+Rf)^T + FV (NC)

NC = storage costs - convenience yield

higher costs due to storage, insurance, etc.

Non-monetary benefits from holding asset will reduce the commodity futures price

-holding asset in short supply with seasonal/highly risky production process

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

U.S. dollar-denominated deposits outside the U.S.

based on 360 day year

important difference:

t-bills are discount instruments: buy for 98, get 100

eurodollars use add-on interest: buy 100, get 104

option that can only be exercised at expiration

exercised at any time prior to expiration (most common)

C0 + PV (X) = P0+S0

U = size of up-move

d= size of down move

Pie u: probability of up move

Pie d = probability of down-move

get value, use probability to get expected value

find expected value and discount back

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

value of a cap (floor) is the sume of the values of its component caplets (floorlets)

change in price of an option for a 1-unit change in the price of the underlying stock

(aka the slope of the prior-to-expiration curve)

Delta call = (C1-C0)/(S1-S0) = change in C / Change in S

delta call = N(d1)

change in C =~ N(d1) x change in S

Change in P =~ [N(d1)-1] x change in S

call deltas range from 0-1

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

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 = rate of change in delta, as stock price changes

(2nd derivative of black sholes, 1st is delta)

-largest when option is at-the-money and close to expiration

-small for deep in-the-money and deep out-of-the-money

use in-and-out-of-the-money options not close to expiration to reduct trading costs

standard deviation of continuously compounded returns on stock

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:

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 = (x-Ft)

cost of portfolio 1 = C0 + (x-Ft) / (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!

futures: america>europe because cash earned from mark-to-market, CFs can be invested if option is exercised

forwards: same, no mark to market on forward contracts

model for calculating value of european options on forwards

substitute discounted vlaue for Ft for S0

price = swap fixed rate

-the rate paid by the pay-fixed 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 non-zero after initiation

mimick: acts like th same CFs

Replicate: same cash flows

same as bonds, fras, or options

fixed-rate 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

swaps are approximated by a strip of FRAs

Swap rate is constants; FRAs have different rates for all forward rates

off-market FRAs have forward rates that do not yield a value at initiation

hence, a swap is a portfolio of off-market FRAs

swap fixed rate must be set so value at initiation is zero

method: value the swap as a combination of fixed-rate bond and floating rate bond

value of a payer swap = value of replicating floating rate bond - value of replicating fixed rate bond

Coupon = (1-Z4) / (Z1+Z2+Z3+Z4)

z: price of n-period $1 zero coupon bond = n-period discount factor

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

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

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

PV of cash flows and account for exchange rate changes

fixed-for-fixed example: value of receive euro fixed and pay $ fixed side =

PV (Euro fixed bond) - PV ($ fixed bond)

use yield curve for each currency

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

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 3-year swap

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)

hedge anticipated floating rate exposure in the future

speculate

terminate existing swap

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 rate - T-note rate

increases in times of more uncertainty

quality spread: swaps accrue default risk (swap rate is based on LIBOR, which is NOT risk-free)

t-note is risk free

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

marking-to-market: 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

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

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

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

determind by the spread between floor rate and LIBOR

PMT = [0, NP x (floor strike - index rate) x (actual days/360)]

long cap + short floor (or vice versa)

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

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

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

if CDS premium < bond't spread above benchmark

buy the bond and buy the CDS

ST instability and LT prospects sound

buy ST CDS and sell LT CDS

ST prospects OK but LT prospects poor

sell ST CDS and buy LT CDS

combine CDS with short or long position in credit index

receiver option gives buyer right to sell CDS

payer option gives buyer right to buy a CDS

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

trade baskets of CDS

first-to-default swap: seller provides protection for first default only

pricing: more CDS in basket -> higher premium; higher default correlation -> lower premium

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

weighted average of individual returns

E(Rp) = w1*E(R1) + w2*E(R2)

• 
• function of weights, variances and correlation

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)

also equals the slope of the CML line

E(R_M) - rf / σ_M

M = tangency portfolio

diversifiable = unsystemic