1. Nominal vs. Real
    Real = Nominal - Inflation
  2. 70 Rule
    years to double = 70 / Real GDP growth
  3. Sources of economic growth (5)
    aggregate hours, labor productivity, physical capital growth, human capital growth, technological advance
  4. institutions critical to the development of incentives that promote economic growth (3)
    markets, property rights, and monetary exchange
  5. COGS equation
    cost of goods sold = beginning inventory + purchases - ending inventory
  6. Cost method allowed in IFRS
    FIFO, Weighted Average cost
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  8. Periodic vs. Perpetual Inventory System
    • periodic: inventory value/ COGS determined at end of accounting period
    • Perpetual system: inventory values and COGS updated continuously
  9. LIFO Reserve (equ)
    FIFO Inventory = LIFO Inventory + LIFO Reserve
  10. 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)
  11. Relative to FIFO, LIFO results in...(Profitability)
    assuming inflation and increasing quantities (4)
    • Higher COGS
    • Lower taxes
    • lower net income
    • lower profit margins
  12. 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
  13. 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)
  14. 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 debt-to-equity ratio are higher
  15. Inventory Valuation IFRS vs. GAAP
    • 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
  16. FIFO net income = (in terms of LIFO)
    • IFO net income = LIFO Net income + (Ending
    • reserve - begininning reserve) * (1-tax rate)
  17. 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
  18. Effect of capitalizing expense on net income: (short term)
    delays expense recognition -> higher net income

    overtime: total net income is identical
  19. Effect of capitalizing expense on shareholder's equity: (short term)
    higher SE (since Net income is higher/RE)
  20. Effect of capitalizing expense on CFO: (short term)
    • Capitalized: CFI (higher CFO)
    • Expensed: CFO (Higher CFI)

    total cash flow is the same
  21. Effect of capitalizing expense on Financial Ratios: (short term)
    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
  22. 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
  23. 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
  24. R&D costs; GAAP vs. IFRS
    Image Upload 3
  25. depreciation types (3)
    • straight-line
    • accelerated
    • units-of-production methods
  26. 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
  27. 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
  28. 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: written-down to fair value on BS and discounted value of future cash flows or fair value is recognized on IS
  29. 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
  30. IFRS vs. GAAP rules on revaluation of Fair Value after impairment
    • 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)
  31. average age equ
    accumulated depreciation/annual depreciation expense
  32. average depreciable life equ
    ending gross investment / annual depreciation expense

    gross investment = orignial cost of the asset
  33. remaining useful life equ
    ending net investment / annual depreciation expense
  34. 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
  35. Benefits to leasing over buying: (5)
    • 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
  36. 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
  37. Finance vs. Operating lease ACCOUNTING
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  38. Finance vs. Operating lease RATIOs
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  39. Sales-type lease:
    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
  40. Direct financing lease
    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
  41. 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
  42. Accounting for InvestmentsImage Upload 6
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  43. Summary of Classification of Financial Assets
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  44. 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
  45. 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
  46. Business Combinations:
    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 parent-subsidiary relationship
    • Consolidation: a new entity is formed that absorbs both
    • SPE: created for a single purpose by a sponsoring company
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  48. Liquidity Ratios
    Current ratio = current assets / current liabilities

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

    cash ratio = (cash + short term investments) / current liabilities
  49. 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
  50. 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
  51. 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
  52. 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
  53. 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
  54. 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
  55. Solvency ratios :Debt ratios
    total debt-to-equity ratio

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

    financial leverage ratio: average total assets / average total equity
  56. Solvency Ratios: coverage ratios
    interest coverage
    payout ratio
    interest coverage = EBIT / interest payments

    payout ratio = dividends paid / net income
  57. 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
  58. Free Cash Flow (FC)

    (2 points, 2 equ)
    • FCF is cash available for discretionary uses
    • frequently used to value firms

    • FCFF = CFO + Int (1-T) - FCInv
    • FCFE = CFO - FCInv + Net debt increase
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  60. Current rate
  61. FX rate as of balance sheet date
  62. Average Rate
    average FX rate over reporting period
  63. Historical Rate
    FX rate that existed when a transaction occurred (not fixed in time)
  64. Temporal Method (aka Remeasurement) definition
    Local currency translation to function currency and presentation currency (gain/loss goes on income statement)
  65. Current Rate definition (aka translation)
    Local Currency and Functional Currency translation to presentation currency (gain/loss shows on B.S.)
  66. Temporal Method ( 3
    • 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
  67. 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
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  69. market model (def, equ and 3 assumptions)
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    • 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
  70. expected return, variance and covariance (equs x 3)
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  71. adjusted beta (def and equ)
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    • mean-reverting level of beta = 1
  72. 3 types of multi-factor models
    macroeconomic factors: business cycle, interest rates, inflation

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

    statistical factors: principal components, factor analysis
  73. Macro vs. fundamental models (sensitivities, factors, number of factors, intercept term) table
    Image Upload 19
  74. Arbitrage Pricing Model (APT) def + equ
    • Image Upload 20
    • 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
  75. active return (def and equ)
    • difference between the portfolio return (P) and its benchmark (B) (Tracking error)
    • Rp-Rb
  76. Active risk
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    • (Tracking risk) is the standard dviation of the active return
  77. 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)
  78. information ratio
    • Image Upload 22
    • active return unit of active risk

    measures manager's consistency in generating actie returns
  79. 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)
  80. 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)
  81. 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
  82. 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 risk-free rate and unlimited short-selling is allowed

    there are no frictions to trading (taxes or transaction costs)
  83. 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
  84. separation theorem (def)
    all investors hold the risk-free asset and the domestic market portfolio
  85. 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
  86. unhedged return in domestic currency (equ)
    ~Return in foreign currency + %change in S

    Rdc ~ Rfc +%change in S

    S = spot rate
  87. hedged Return on domestic equity (equ)
    hedged Rdc ~ Rfc + (F-S0)/S0

    S = spot rate
  88. 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
  89. ex-post returns (def)
    realized returns given interest rate / price evolution
  90. foreign currency risk premium (equ x 2 + def)
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  91. ICAPM accounts for 2 things (relative to CAPM)
    • 1) exchange rate changes
    • 2) asset value sensitivity to changes in exchange rates
  92. additional ICAPM assumptions
    • 1) investors can hedge real FX risk with forward contracts
    • 2) investors can borrow/lend at the risk-free rate in every currency
  93. ICAPM separation theorem
    • investors hold combination of
    • 1) risk-free asset of own country in DC
    • 2) world market portfolio optimally hedged against currency risk
  94. ICAPM equ
    Image Upload 24
  95. 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
  96. 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)
  97. 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
  98. 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
  99. 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
  100. 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
  101. 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
  102. Argument for efficient markets: Economic
    As asset values diverge from equilibrium because everyone is indexed, some active managers will add value
  103. Argument for efficient markets: Empirical
    some active managers beat the benchmark, earn excess returns
  104. treynor-black 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 non-zero alpha)

    combine M and A optimally
  105. 5 Steps of treynor-black
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  106. Treynor-Black: Step 1
    develop expectations for M and Rf

    -expected return for passive market index

    -variance for passive market index

    -Rf: risk-free rate (zero standard deviation)
  107. Treynor-Black Step 2
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  108. Treynor-Black: Step 3
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  109. Treynor-Black: Step 4
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  110. picture of Treynor-Black model: optimal risky portfolio
    Image Upload 29
  111. 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 R-square

    -R-Square is from regression of analyst's historical and realized alphas
  112. portfolio perspective
    analyze portfolio risk/return, NOT risk/return of individual securities
  113. 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
  114. investment objectives: Risk
    Risk objectives:

    -investors willingness to take risk

    -investor's ability to take risk
  115. factors affecting ability to take risk (4)
    1) required spending needs

    2) long-term wealth target

    3) financial strength

    4) liabilities
  116. investment objectives: return (2)
    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
  117. 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: catch-all category
  118. investment policy statement: def + 3 purposes
    IPS: formal document that governs investment process: contraints/objectives

    easily transportable

    promote long-term discipline

    prevent short-term strategy shifts
  119. strategic asset allocation
    approaches to investing

    passive, active, or semi-active (risk-controlled, or enhanced index strategies)
  120. no-arbitrage principle
    there should be no riskless profit from combining forward contracts with other instruments
  121. forward price
    price of underlying that would not permit profitable riskless arbitrage, so value equals zero
  122. Cost of carry model
    FP = S0 x (1+Rf)^T

    FP: Forward Price

    S0= spot price of underlying

    Rf: risk free rate

    T: maturity
  123. value of long forward contract during the life of the contracct (Vt) is: (equ)
    Image Upload 30
  124. value of a long position at initiation and at maturity
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  125. 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
  126. Pricing equity forwards (equ)
    (S0 - PVD) x (1+Rf)^t


    [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
  127. Pricing index forward contracts (equ)
    • Equity index = basket of many stocks
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  128. Valuing index forwards (equ)
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  129. 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
  130. 3 steps to pricing an FRA
    1) de-annualize

    R = .024 x 30/360 = .002

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

    3) annualize

    ex) times 360/60 = 3.3%
  131. 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
  132. 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
  133. pricing currency forward
    Image Upload 34
  134. Valuing Currency Forwards (equ)
    Image Upload 35
  135. convergence
    spot price = futures price

    marked to market daily
  136. Futures Price (on treasury bond futures)
    Image Upload 36
  137. 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: 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
  138. futures price with commodities
    FP = S0 x (1+Rf)^T + FV (NC)

    NC = storage costs - convenience yield

    higher costs due to storage, insurance, etc.
  139. convenience yield
    Non-monetary benefits from holding asset will reduce the commodity futures price

    -holding asset in short supply with seasonal/highly risky production process
  140. 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
  141. Eurodollar deposits
    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
  142. European option
    option that can only be exercised at expiration
  143. american option
    exercised at any time prior to expiration (most common)
  144. European Put-call parity
    C0 + PV (X) = P0+S0

    Image Upload 37
  145. Binomial stock option model
    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
  146. 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
  147. valuing caps and floors
    value of a cap (floor) is the sume of the values of its component caplets (floorlets)
  148. BSM and "Greek Risks" (5)
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  149. What happens to option value? (positive or negative related, calls and puts (10)
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  150. Delta
    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)
  151. discrete time (equ)
    Delta call = (C1-C0)/(S1-S0) = change in C / Change in S
  152. 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
  153. Delta ranges (3)
    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
  154. Delta-neutral 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
  155. gamma (def)
    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
  156. Historical volatility
    standard deviation of continuously compounded returns on stock
  157. 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:
  158. forward put-call 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 = (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!
  159. american options > or < value of european options (futures vs. forwards)
    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
  160. black model (def)
    model for calculating value of european options on forwards

    substitute discounted vlaue for Ft for S0
  161. Swap pricing/valuation defs
    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
  162. mimick vs. replicate (with swaps)
    mimick: acts like th same CFs

    Replicate: same cash flows

    same as bonds, fras, or options
  163. replicating bonds with swaps
    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
  164. replicating off-market FRAs with 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
  165. replicating options with swaps
    Image Upload 40
  166. 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 fixed-rate bond and floating rate bond

    value of a payer swap = value of replicating floating rate bond - value of replicating fixed rate bond
  167. Swap fixed rate c-formula (to find annual swap rate) equ
    Coupon = (1-Z4) / (Z1+Z2+Z3+Z4)

    z: price of n-period $1 zero coupon bond = n-period discount factor
  168. 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
  169. 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
  170. 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
  171. valuing a currency swap
    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
  172. 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
  173. 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 3-year swap
  174. 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)
  175. uses of swaptions (3)
    hedge anticipated floating rate exposure in the future


    terminate existing swap
  176. 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
  177. swap spread
    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
  178. 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
  179. 2 ways to reduce credit risk
    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
  180. 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
  181. 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
  182. 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
  183. 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)]
  184. interest rate collar
    long cap + short floor (or vice versa)
  185. 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
  186. 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
  187. 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
  188. CDS strategy: basis trade
    if CDS premium < bond't spread above benchmark

    buy the bond and buy the CDS
  189. CDS strategy: credit curve flattener
    ST instability and LT prospects sound

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

    sell ST CDS and buy LT CDS
  191. CDS strategy: Index trade
    combine CDS with short or long position in credit index
  192. CDS strategy: options trade
    receiver option gives buyer right to sell CDS

    payer option gives buyer right to buy a CDS
  193. 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
  194. CDS strategy: correlation trade
    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
  195. 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
  196. portfolio expected return equ
    weighted average of individual returns

    E(Rp) = w1*E(R1) + w2*E(R2)
  197. portfolio variance (def)
    • Image Upload 41
    • function of weights, variances and correlation
  198. minimum variance portfolio
    Image Upload 42
  199. 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)
  200. relation of correlation and diversification between 2 assets
    Image Upload 43
  201. variance for an equally-weighted portfolio (w = 1/n)
    Image Upload 44
  202. capital market line (def, graph and equ)
    Image Upload 45
  203. sharpe ratio
    also equals the slope of the CML line

    E(RM) - rf / σM

    M = tangency portfolio
  204. Capital Market Line vs. Capital allocation line (def and equs)
    Image Upload 46
  205. unsystemic risk vs systemic
    diversifiable = unsystemic
  206. total risk equ and picture
    Image Upload 47
Card Set
cfa book 1 level 1