2018 level 3 finquiz quicksheet

FinQuiz Formula Sheet Reading 5: The Behavioral Finance Perspective   Expected utility (U) = Σ (U values of outcomes × Respective Prob)   Subjective expected U of an individual =Σ [u (xi) × Prob (xi)]   Bayes’ formula = P (A|B) = [P (B|A) / P (B)]× P (A)   Risk premium = Certainty equivalent – Expected value   Perceived value of each outcome = = U = w (p1) v (x1) + w (p2) v (x2) + … + w (pn) v (xn)   After-tax (AT)Real required return (RR) % = 2$&  3%4$(&15"$  6(($&( 7*89$:&$-  %$$-(  #%  0$1*  % = 2$&  3%4$(&15"$  6(($&(   ATNominal RR % =   Total Investable assets = Current Portfolio -Current year cash outflows + Current year cash inflows   Pre-tax income needed = AT income needed / (1-tax rate)   Pre-tax Nominal RR = (Pre-tax income needed / Total investable assets) + Inf% If Portfolio returns are tax-deferred:   Pre-tax projected expenditure $ = AT projected expenditure $ / (1 – tax rate) ì wt of Tax-exempt Invst)] ì (1 – tax rate) + (Expected total R of Taxexempt Invst × wt of Tax-exempt Invst) – Inf rate Or Real AT R =[(Taxable R of asset class × wt of asset class 1) + (Taxable R of asset class × wt of asset class 2) + …+ (Taxable return of asset class n × wt of asset class n)] × (1 – tax rate) + (Expected total R of Tax-exempt Invst × wt of Tax-exempt Invst) – Infrate Reading 9: Taxes and Private Wealth Management in a Global Context   Average tax rate = Total tax liability / Total taxable income   AT Return = r × (1 – ti) Reading 8: Managing Individual Investor Portfolios !"#$%&' (  *$+,#*$-  $./$%-#&,*$(  #%  0$1*  % ATNominal RR% = +  AT  Real  RR% × (1 + Current Ann Inf %) –   Pre-tax real RR % = Pre-tax projected expenditures $ / Total investable assets   Abnormal return (R) = Actual R – Expected R CFA Level III 2018   Pre-tax nominal RR = (1 + Pre-tax real RR %) × (1 + Inflation rate%) – If Portfolio returns are NOT tax-deferred:   AT real RR% = AT projected expenditures $ / Total Investable assets 10   AT nominal RR% = (1 + AT real RR%) × (1 + Inf%) – 7*89$:&$-  %$$-(  #%  0$1*  % 2$&  3%4$(&15"$  6(($&( + Current Annual (Ann) Inflation (Inf) % = AT real RR% + Current Ann Inf% Or 11   Procedure of converting nominal, pre-tax figures into real, after-tax return: •   Real AT R = [Expected total R – (Expected total R of Tax-exempt Invst   AT Future Accumulations after n years = FVIFi= Initial Invst × [1 + r (1 – ti)]n   Tax drag ($) on capital accumulation = Acc capital without tax – Acc capital with tax   Tax drag (%) on capital accumulation = (Acc capital without tax – Acccapital with tax) / (Acc capital without tax – Initial investment) FinQuiz   Returns-Based Taxes: Deferred Capital Gains: •   AT Future Accumulations after n years = FVIFcg= InitialInvst × [(1 + r) n (1 – tcg) + tcg] •   Value of a capital gain tax deferral = AT future accumulations in deferred taxes – AT future accumulations in accrued annually taxes   Cost Basis •   Capital gain/loss = Selling price – Cost basis •   AT Future Accumulation = FVIFcgb= Initial Invst × [(1 + r) n (1 – tcg) + tcg – (1 – B) tcg] =Initial Invst × [(1 + r) n (1 – tcg) + (tcg × B)] Where, B = Cost basis tcg × B = Return of basis at the end of the Invst.horizon When cost basis = initial InvstèB=1, FVIFcg=Initial investment × [(1 + r) n (1 – tcg) + tcg] Formula Sheet b)  % of total return from Interest income (pi), taxed at a rate of ti pi = Interest ($) / Total dollar return c)   % of total return from Realized capital gain (pcg), taxed at a rate of tcg pcg = Realized Capital gain ($) / Total dollar return d)  Unrealized capital gain return: Total Dollar Return = Dividends + Interest income + Realized Capital gain + Unrealized capital gain Total realized tax rate = [(pi× ti) + (pd× td)+ (pcg× tcg)] 10   Effective Ann AT R = r* = r (1 – piti – pdtd – pcgtcg) = r (1 – total realized tax rate) Where, r = Pre-tax overall return on the portfolio and r*= Effective ann AT R 11   Effective Capital Gains Tax = T* = tcg (1 – pi – pd – pcg) / (1 – piti – pdtd – pcgtcg) 12   Future AT acc = FVIF Taxable = Initial Invst [(1 + r*)n (1 – T*) + T* – (1 – B) tcg]   Wealth-Based Taxes •   AT Future Acc = FVIF w = Initial Invst [(1 + r) (1 – tw)] n Where, tw = Ann wealth tax rate 13   Initial Invst (1 + Accrual Equivalent R)n = Future AT Acc   Blended Taxing Environments a)   Proportion of total return from Dividends (pd), taxed at a rate of td pd = Dividends ($) / Total dollar return 15   Accrual Equivalent Tax Rates = r (1 – TAE) 14   Accrual Equivalent R = (Future AT Acc / Initial Invst) 1/n– = RAE = TAE = 1− EFG E CFA Level III 2018 16   In Tax Deferred accounts (TDAs) Future AT Acc = FVIF TDA = Initial Invst[(1 + r) n (1 – Tn)] 17   In Tax-exempt accounts FVIF taxEx = Initial Invst (1 + r) n •   FVIF TDA = FVIF taxEx (1 – Tn) 18   AT asset wt of an asset class (%) = AT MV of asset class ($) / Total AT value of Portfolio ($) 19   AT Initial invst in tax-exempt accounts = (1 – T0) 20   FV of a pretax $ invested in a tax-exempt account = (1 – T0) (1 + r) n 21   FV of a pretax $ invested in a TDA = (1 + r) n (1 – Tn) 22   Investors AT risk = S.D of pre-tax R (1 – Tax rate) = σ(1 – T) 23   Tax alpha from tax-loss harvesting (or Tax savings) =Capital gain tax with unrealized losses – Capital gain tax with realized losses Or Tax alpha from tax-loss harvesting = Capital loss × Tax rate 24   Pretax R taxed as a short-term gain needed to generate the AT R equal to long-term AT R = Long-term gain after-tax return / (1 –short-term gains tax rate) FinQuiz Reading 10: Estate Planning in a Global Context   Estate =Financial assets + Tangible personal assets + Immoveable property + Intellectual property   Discretionary wealth or Excess capital = Assets – Core capital Formula Sheet   Value of a taxable gift (if gift & asset (bequeathed) have equal AT R ) = (1 – Tg) / (1 – Te) 10   The relative after-tax value of gift the when the donor pays gift tax and when the recipient’s estate will not be taxable (assuming rg = re and tig = tie): 𝑅𝑉JKLK\]OPQRS   Core Capital (CC) Spending Needs = p(Survival j ) × Spending j ∑ (1+ r) j j−1   CC needed to maintain given spending pattern = Annual Spending needs / Sustainable Spending rate = 12   Relative value of generation skipping = / (1 – T1) 13   Charitable Gratuitous Transfers = RVCharitableGift = Z UVN[ UXSY[ Z UXJ[   Relative value of the tax-free gift = / (1 – Te)   Taxable Gifts = 𝑅𝑉JKLK\]OPQRS = Z UXJW Z UVN[ UXSY[ UXJ[ UVNW UXSYW + 𝑟d − 𝑡Qd − 𝑇d + 𝑇d 𝑇O + 𝑟O − 𝑡QO f − 𝑇O 11   Size of the partial gift credit = Size of the gift × TgTe   Tax-Free Gifts = 𝑅𝑉JKLMNOOPQRS = UVNW UXSYW 𝐹𝑉PQRS = 𝐹𝑉_O`aObS f N   Expected Real spending = Real annual spending × Combined probability CFA Level III 2018 FVCharitableGift FVBequest n = (1+ rg )n + Toi [1+ re (1− tie )] (1− Te ) n [1+ re (1− tie )] (1− Te ) 14   Credit method = TC = Max [TR, TS] 15   Exemption method = TE = TS 16   Deduction method = TD = TR + TS– TRTS Reading 12: Risk Management for Individuals kl m SnU UVN l m o(ql )  klst (UVdl ) SnU (UVN Vv)l   Human Capital  𝐻𝐶j = extended model  𝐻𝐶j = u   Income yield (payout) = SwSK]  wfdwQfd  KffaK]  QfxwyO QfQSQK]  oaNxzKbO  oNQxO       Mortality wghtd NPV = mNPV0 = = m o(bl )  \l SnU (UVN)l   Reading 13: Managing Institutional Investor Portfolio Defined-Benefit Plans:   Funded Status of Pension Plan (PP) = MV of PP assets – PV of PP liabilities   Min RR for a fully-funded PP = Discount rate used to calculate the PV of plan liabilities   Desired R for a fully-funded PP = Discount rate used to calculate the PV of plan liabilities + Excess Target return   Net cash outflow = Benefit payments – Pension contributions Foundations   Min R requirement (req) = Min Ann spending rate + InvstMgmtExp+ Expected Inf rate   FinQuiz Or Min Rreq = [(1 + Min Ann spending rate) × (1 + Invst Mgmt Exp) × (1 + Expected Inf rate)] -1   Foundation’s liquidity req = Anticipated cash needs (captured in a foundation’s distributions prescribed by minimum spending rate*) + Unanticipated cash needs (not captured in a foundation’s distributions prescribed) – Contributions made to the foundation * It includes Minimum annual spending rate (including “overhead” expenses e.g salaries) + Investment management expenses Endowments   Ann Spending ($) = % of an endowment’s current MV Or AnnSpending ($) = % of an endowment’s avg trailing MV   Simple spending rule = Spending t = Spending rate × Endowment’s End MVt-1   Rolling 3-yr Avg spending rule =Spendingt = Spending rate × Endowment’s Avg MV of the last fiscal yr-ends i.e è Spending t = Spending rate × (1/3) [Endowment’s End MVt-1+ Endowment’s End MVt-2 + Endowment’s End MVt-3] Formula Sheet 10   Geometric smoothing rule = Spendingt = WghtAvg of the prior yr’s spending adjusted for Inf + Spending rate × Beg MV of the prior fiscal yr i.e è Spending t = Smoothing rate × [Spendingt-1 × (1 + Inft-1)] + (1 – Smoothing rate) × (Spending rate × Beg MVt-1 of the endowment) 11   Min ReqRoR = Spending rate + Cost of generating Invst R + Expected Infrate Or Min ReqRoR = [(1 + Spending rate) × (1 + Cost of generating Invst R) × (1 + Expected Inf rate)] -1 12   Liquidity needs = Ann spending needs + Capital commitments + Portfolio rebalancing expenses – Contributions by donor 13   Neutrality Spending Rate = Real expected R = Expected total R – Inf Life Insurance Companies 14   Cash value = Initial premium paid + Any accrued interest on that premium 15   Policy reserve = PV of future benefits - PV of future net premiums 16   Surplus = Total assets of an insurance company - Total liabilities of an insurance company CFA Level III 2018 Non-Life Insurance Companies 17   Combined Ratio = (Total amount of claims paid out + Insurer's operating costs) / Premium income Banks 18   Net interest margin = ({fSONObS  {fxwyOX{fSONObS  |LoOfbO) }~d  |KNfQfd  }bbOSb mOS  {fSONObS  {fxwyO = }~d  |KNfQfd  }bbOSb 19   Interest spread = Avg yield on earning assets – Average percent cost of interestbearing liabilities 20   Leverage-adjusted duration gap (LADG) = DA – (k ×DL) Where, k= MV of liabilities / MV of assets = L/A 21   Change in MV of net worth of a bank (resulting from interest rate shock) ≈ - LADG × Size of bank × Size of interest rate shock FinQuiz Formula Sheet Reading 14: Capital Market Expectations CFA Level III 2018 10   Nominal GDP = Real g rate in GDP + Expected long-run Inf rate   Precision of the estimate of the population 11   Earnings g rate = Nominal GDP g rate + Excess Corp g (for the index companies) mean ≈ / no  of  obvs   Multiple-regression analysis: A = β0 + β1 B + β2 C + ε   Time series analysis: A = β0 + β1 Lagged values of A + β2 Lagged values of B + β2 Lagged values of C + ε   Shrinkage Estimator = (Wt of historical estimate × Historical parameter estimate) + (Wt of Target parameter estimate × Target parameter estimate)   Shrinkage estimator of Cov matrix = (Wt of historical Cov × Historical Cov) + (Wt of Target Cov × Target Cov)   Vol in Period t =σ2t = βσ2t-1 + (1 – β) ε2t   Multifactor Model: R on Asset i = Ri = + bi1F1 + bi2F2 + … + biK FK + εi   Value of asset at time t0 = …M  KS  SQyO  S ‡ SnU UV†QbxwafS  NKSO l   Expected RoR on Equity = ˆ#4  /$*  (‰1*$  1&  &#Š$  ‹  (UVŒ•  Ž  *1&$) !,**$%&  (‰1*$  /*#:$ + LT g rate = Div Yield + Capital Gains Yield 12   Expected RoR on Equity ≈ † • - ∆S + i + g + ∆PE -∆S = Positive repurchase yield +∆S = Negative repurchase yield ∆PE = Expected Repricing Return 13   Labor supply g = Pop g rate + Labor force participation g rate 14   Expected income R = D/P - ∆S 15   Expected nominal earnings g R = i + g 16   Expected Capital gains R = Expected nominal earnings grate + Expected repricing R 17   Asset’s expected return E (Ri) = Rf + (RP) + (RP) + …+ (RP) K 18   Expected bond R [E (Rb)] = Real Rf + Inf premium + Default RP + Illiquidity P + Maturity P+ Tax P 19   Inf P = AvgInf rate expected over the maturity of the debt + P (or discount) for the prob attached to higher Inf than expected (or greater disinflation) 20   Inf P = Yield of conventional Govt bonds (at a given maturity) – Yield on Infindexed bonds of the same maturity 21   Default RP = Expected default loss in yield terms + P for the non-diversifiable risk of default 22   Maturity P = Interest rate on longermaturity, liquid Treasury debt - Interest rate on short-term Treasury debt 23   Equity RP = Expected ROE (e.g expected return on the S&P 500) – YTM on a longterm Govt bond (e.g 10-year U.S Treasury bond R) 24   Expected ROE using Bond-yield-plus-RP method = YTM on a LT Govt bond + Equity RP 25   Expected ROA E (Ri) = Domestic Rf R + (βi) × [Expected R on the world market portfolio – Domestic Rf rate of R] Where,βi = The asset’s sensitivity to R on the world mktportf = Cov (Ri, RM) / Var (RM) 26   Asset class RPi= Sharpe ratio of the world market portfolio × Asset’s own volatility (σi) × Asset class’s correlation with the world mktportf (ρi,M) RPi = (RPM / σM) × σi × ρi,M Where, Sharpe Ratio of the world market portfolio = Expected excess R / S.D of the FinQuiz Formula Sheet world mktportfà represents systematic or nondiversifiable risk = RPM / σM 35   Neutral Level of Interest Rate = Target Inf Rate + Eco g 27   RP for a completely segmented market (RPi) = Asset’s own volatility (σi) × Sharpe ratio of the world mktportf 36   Taylor rule equation: Roptimal =Rneutral + [0.5 × (GDPgforecast – GDPgtrend)] + [0.5 × (Iforecast – Itarget)] 28   RP of the asset class, assuming partial segmentation = (Degree of integration × RP under perfectly integrated markets) + ({1 - Degree of integration} × RP under completely segmented markets) 37   Trend g in GDP = g from labor inputs + g from Δ in labor productivity 29   Illiquidity P = Required RoR on an illiquid asset at which its Sharpe ratio = mkt’s Sharpe ratio – ICAPM required RoR 30   Cov b/w any two assets = Asset beta × Asset beta × Var of the mkt ⎛ σ × ρ (1, m) ⎞ ⎟⎟ 31   Beta of asset = ⎜ ⎜ σm ⎝ ⎠ ⎛ σ × ρ (2, m) ⎞ ⎟⎟ 32   Beta of asset = ⎜ ⎜ σ m ⎝ ⎠ 33   GDP (using expenditure approach) = Consumption + Invst + Δ in Inventories + Govt spending + (Expo- Impo) 34   Output Gap = Potential value of GDP – Actual value of GDP 38   g from labor inputs = g in potential labor force size + g in actual labor force participation 39   g from Δ in labor productivity = g from capital inputs + TFP g* •   TFP g = g associated with increased efficiency in using capital inputs 40   GDP g = α + β1Consumer spending g + β2Investment g 41   Consumer spending g = α + β1Lagged consumer income g + β2Interest rate 42   Investment g = α + β1Lagged GDP g+ β2Interest rate 43   Consumer Income g = Consumer spending growth lagged one period CFA Level III 2018 Reading 15: Equity Market Valuation   Cobb-Douglas Production Function Y = A× Kα× Lβ Where,Y = Total real economic output A = Total factor productivity (TFP) K = capital stock α = Output elasticity of K L = Labor input β = Output elasticity of L   Cobb-Douglas Production Function Y (assuming constant R to Scale) = ln (Y) = ln (A) + αln (K) + (1 – α) ln (L) Or ∆0   ≈   ∆6 +α ∆“ “ +   −  α ∆Œ Œ   Solow Residual = %∆TFP = %∆Y – α (%∆K) – (1 – α) %∆L   H-Model: Value per share at time = ˆ‹ ˆ#(:8,%&  *1&$XŒ•  (,(&1#%5"$  ˆ#4  Ž  *1&$   × 1+  LT  sustainable  Div  g  rate +   ›,/$*  %8*Š1"  Ž  /$*#8œ  ×   ST  higher  Div  g  rate − LT  sustainable  Div  g  rate   Gordon g Div discount model: Value per share at time = ˆ × UVŽ *X  Ž   FinQuiz Formula Sheet CFA Level III 2018   Forward justified P/E =   After-tax Portfolio Return = rat = rpt(1-t) 3%&*#%(#:  41",$   12   10-year Moving Average Price/Earnings [P / 10-year MA (E)] = 0* 1$1- $./$:&$- Ă1*%#%( Ô$1" 8* 3%ƠX1-9,(&$- & ă NQxO {fâOL Fed Model: ê84#% 64 8Ơ /*$:$-#% U ô*( 8Ơ Ô$1" 8* 3%Ơ 1-9 Ă1*%#%( ÂÊ-  j/$*1&#%Ž  ¡1*%#%Ž(   ¡U 3%-$  Œ$4$"   7‹ =Long-term US Treasury securities   Yardeni Model: = E1 = yB − d × LTEG P0 Where,E1/P0=Justified (forward) earnings yield on equities yB=Moody’s A-rated corporate bond yield LTEG= Consensus 5-yr earnings g forecast for the S&P 500 d=Discount or Weighting factor that represents the weight assigned by the market to the earnings projections *The stock index and reported earnings are adjusted for Inflation using the CPI 13   Real Stock Price Index t = (Nominal SPIt × CPI base yr) / CPI t 14   Real Earnings t = (Nominal Earnings t × CPI base year) / CPI t+1 15 Tobins q = êơ8Ơ -$5&Vêơ 8Ơ $+,#&ô Ô$/"1:$$%& :8(& 8Ơ 1(($&( Ă+,#&ô ê& !1/ Equity q = 2$& -8*& 7*#:$ /$* (1*$ ì 28 8Ơ 1*$( j/ = Ô$/"1:$%& :8(& 8Ơ 1(($&(Xêơ 8Ơ "#15#"#&#$( Expected Equity Return (dividend income + Price Appreciation) = rat = pd rpt (1-td) + pa rpt (1-tcg) where, pd & pa are proportion attributed to dividend income & price appreciation respectively   𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑  𝑎𝑓𝑡𝑒𝑟  𝑡𝑎𝑥  𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 𝜎}J = 𝜎•J (1-t) Reading 19: Currency Management: An Introduction   Bid Fwd rate = Bid Spot exchange (X) rate + Ì#-  ¢£-  /8#%&( U‹,‹‹‹   Offer Fwd rate = Offer Spot X rate + jƠƠ$* ÂÊ /8#%&( U, Yardeni estimated fair value of P/E ratio = P0 = E1 yB − d × LTEG 10   Fair value of equity mkt under Yardeni Model (P0) = P0 = E1 yB − d × LTEG Reading 16: Introduction to Asset Allocation   Risky  Asset  Allocation =   U XNu = àả Reading 17: Principles of Asset Allocation   œ   𝑈y = 𝐸 𝑅y − 0.005𝜆𝜎y     U 11   Discount/weighting factor (d) = E yB − P0 d= LTEG Q ì Q , = 𝜎•œ   f Reading 18: Asset Allocation with Real-world Constraints   FwdPrem/Disc % = (/8&  Í  *1&$X( ỴÏÐ  ĐỊĨƠ ) t , (/8&  Í  *1&$ –1   To convert spot rate into a forward quote when points are represented as %, Spot X rate × (1 + % prem) Spot X rate × (1 - % disct) Mark-to-MV on dealers position = $&&"$$%& -1ô ! UV#(:&  *1&$∗   Ó Õ FinQuiz Formula Sheet   CF at settlement = Original contract size × (All-in-fwd rate for new, offsetting fwd position – Original fwd rate) 15   Long Straddle = Long atm put opt (with delta of -0.5) + Long atm call opt (with delta of +0.5)   Hedge Ratio = 16   Short Straddle = Short ATM put opt (with delta of -0.5) + Short ATM call opt (with delta of +0.5) ATM = at the money opt = option 28#%1" ơ1",$ 8Ơ -$*#41$( :8%&*1:& êơ 8Ơ &$ $-$- 1(($& RDC =(1 + RFC)(1 + RFX)–1   RDC (for multiple foreign assets) = n ∑ω (1+ R ) (1+ R ) −1 i FC,i FX,i i=1 17   Long Strangle: Long OTM put option + Long OTM call opt OTM = out of the money 10   Total risk of DC returns = = 𝜎 œ 𝑅†… ≈ 𝜎 œ 𝑅M… + 𝜎 œ 𝑅MÖ + 2𝜎 𝑅M… 𝜎 𝑅MÖ 𝜌 𝑅M… , 𝑅MÖ 11   % Δ in spot X rate (%∆SH/L) = Interest rate on high-yield currency (iH) – Interest rate on low-yield currency (iL) 12   Forward Rate Bias = ¢Ù/Ú X›Ù/Ú ›Ù/Ú = Ĩ ÛÜ Ĩ UV#Ú ÛÜ 18   Long Risk reversal = Long Call opt + Short Put opt 19   Short Risk reversal = Long Put opt + Short Call opt 20   Short seagull position = Long protective (ATM) put + Short deep OTM Call opt + Short deep OTM Put opt CFA Level III 2018 23   Min or Optimal hedge ratio = ρ (RDC; RFX) ! S.D (RDC ) $ & " S.D (RFX ) % ×# Reading 20: Market Indexes and Benchmarks   Periodic R (Factor model based) = Rp = ap + b1F1 + b2F2+…+ bKFK+ εp   For one factor model Rp = ap + βpRI + εp Where,RI = periodic R on mktindex ap = “zero factor” βp = beta = sensitivity εp = residual return   MV of stock = No of Shares Outstanding × Current Stock Mkt Price   Stock wgt(float-weighted index) = Mktcap wght × Free-float adjustment factor   Price-weighted index (PWI) = (P1+P2+…+Pn) /n #Ù X#Ú 13   Net delta of the combined position = Option delta + Delta hedge 21   Long seagull position = Short ATM call + Long deep-OTM Call opt + Long deepOTM Put opt 22   Hedge ratio = 14   Size of Delta hedge (that would set net delta of the overall position to 0) = Option’s delta × Nominal size of the contract 7*#%:#/1"  ¥1:$  41",$  8¥  &‰$  -$*#41$(   :8%&*1:&  ,($-  1(  1  ‰$-Ž$   7*#%:#/1"  ¥1:$    8¥  &‰$  ‰$-Ž$-  1(($& Reading 21: Introduction to Fixed-Income Portfolio Management   E(R)≈Yield income + Rolldown Return + 𝐸𝑥𝑝 ∆𝑃 − 𝐸𝑥𝑝 𝐶𝑟𝑒𝑑𝑖𝑡  𝐿𝑜𝑠𝑠𝑒𝑠 + 𝐸𝑥𝑝 𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦 dKQfb ]wbbOb FinQuiz Formula Sheet CFA Level III 2018   Roll Down return = Information Ratio = _wfâ NQxOGZỏ X_wfâ NQxOõ[W Asset BPV + ì _wfâ NQxOõ[W rp = wNSRw]Qw EOSaNf wNSRw]Qw O`aQSv N{ ì óG Vóõ X óõ ìN_ óG LeverageFuture = qốKo _ó U = 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦  𝐵𝑃𝑉 = = 𝑟{ +   ãâ ãG 𝑟{ − 𝑟_   Asset BPV ×  ∆𝐴𝑠𝑠𝑒𝑡  𝑦𝑖𝑒𝑙𝑑𝑠 + 𝐻𝑒𝑑𝑔𝑒  𝐵𝑃𝑉  ×  ∆𝐻𝑒𝑑𝑔𝑒  𝑦𝑖𝑒𝑙𝑑𝑠   ≈  𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦  𝐵𝑃𝑉  ×  ∆𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦  𝑦𝑖𝑒𝑙𝑑𝑠   mwSQwfK]  ãK]aOXäKNdQf Reading 23: Yield Curve Strategies äKNdQf   Dollar Interset = Principal ×  Repo  Rate  × (Days/360) Reading 22: Liability-driven and Index-based Strategies   Convexity = äKx.†aNKSQwf¶ VäKx.†aNKSQwfV†QboONbQwf   mwSQwfK]  owNSRw]Qw  ~K]aO •wNSRw]Qw  O`aQSv ×𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛   Total return  ≈ −1  ×  𝑒𝑛𝑑 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒  𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛  ×   𝑒𝑛𝑑 𝑌𝑇𝑀 − 𝑏𝑒𝑔 𝑌𝑇𝑀 + 𝑏𝑒𝑔 𝑌𝑇𝑀 Reading 24: Fixed Income Active Management: Credit Strategies   Future Contracts=Nf = éQK\Q]QSv  •wNSRw]Qw  _•ãX}bbOS  owNSRw]Qw  _•ã MaSaNOb  _•ã   ABO =   PBO = P×è UVN ë …Mêëì × U N − P×è × UVè ë UVN ë U N× UVN í × U Nì UVN = óX X óV ìaN~Oì ó Excess Return = XR = ( ì) ì _óờởỡ U N Passive investment using Equity Index futures = Long cash + Long futures on the underlying index   Passive investment using Equity total return swaps = Long cash + Long swap on the index   Effective Portfolio Duration ≈ UVKbz R]wố vQO]â ả Future BPV 6:$ Ô *1:ứ#% Ô#(ứ 8* 6:$ Ô#(ứ Expected XR = EXR = (𝑠  ×𝑡)− ∆𝑠× 𝑆𝐷 − 𝑡×𝑝×𝐿 where 𝑝×𝐿 = 𝑒𝑥𝑝 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦  𝑜𝑓  𝑙𝑜𝑠𝑠  ×  𝑒𝑥𝑝 𝑙𝑜𝑠𝑠   R on Portf = b0 + (b1 × R on Index style 1) + (b2 × R on Index style 2) +… (bn × R on Index style n) + ε   RoR of Equitized Mkt neutral strategy = (G/L on long & short securities positions + G/L on long futures position + Interest earned on cash from short sale) / Portfolio Equity   Active wgt = Stock’s wgt in actively managed portf – Stock’s wgt in B   Info Ratio ≈ Info Coefficient × Info  Breadth Reading 25: Equity Portfolio Management 10   Risk-adjusted Expected Active R= UA = rA–λA ×σ2A   Active R = Portf’s R – B’s return B = benchmark   Tracking Risk (active risk) = ann S.D of active R 11   Portfolio Active R = % #nU Wgt  assigned  to  ith  Mngr  (hAi)  × Active  R  of  the  ith  Mngr  (rAi) FinQuiz Formula Sheet CFA Level III 2018 12   Portfolio Active Risk = œ % Wgt  assigned  to  ith  Mnger × #nU œ Active  R  of  ith  Manager 13   Mngr’s “true” active R = Mngr’s R Mngr’s Normal B 14   Mnger’s “misfit” active R = Mnger’s normal B R - Investor’s B 15   Total Active Risk = 𝑇𝑟𝑢𝑒  𝐴𝑐𝑡𝑖𝑣𝑒  𝑅𝑖𝑠𝑘 œ + 𝑀𝑖𝑠𝑓𝑖𝑡  𝐴𝑐𝑡𝑖𝑣𝑒  𝑅𝑖𝑠𝑘 œ Where, True active risk = S.D of true active R Misfit risk = S.D of misfit active R 16 True Information Ratio = ê%*( *,$ 6:$ Ô ê%*( *,$ 6:$ *#(ứ Marketable minority interest ($) = Marketable controlling interest value ($) – minority interest discount ($) 12   Rolling R = RR n,t = (Rt + Rt-1 + Rt-2 + … + R t –(n-1) / n 13   Downside Deviation = =   Marketability discount ($) = Marketable minority interest ($) × marketability discount (%) Z yQf N XN ∗ ,‹ ¶ l Y!t fXU where, r* = threshold   Non-Marketable minority interest ($) = Marketable minority interest ($) marketability discount ($)   Total R on Commodity Index = Collateral R + Roll R + Spot R 14   Semi-deviation = =   Monthly Roll R = ∆ in futures contract price over the month - ∆ in spot price over the month   Compensation structure of Hedge Funds (comprises of ) Management fee (or AUM fee) + Incentive fee 16   Sortino Ratio = (Annualized RoR – Annualized Rf*) / Downside Deviation Z yQf N XK~d    ywfSz]v  NOSaNf,‹ ¶ l Y!t fXU 15   Sharpe ratio = (Annualized RoR – Annualized Rf rate) / Annualized S.D 17   Gain-to-loss Ratio = 28  8¥  Š8%&‰( Ê#&V4$ Ô 28 8Ơ 8%&( Ê#&X4$ Ô 64 ,/ 8%& Ô ì 64 -8Ê% 8%& Ô 17 Investors net of fees alpha = Gross of fees alpha (or mngr’s alpha) – Investment mgmt fees Reading 26: Alternative Investments Portfolio Management   Minority interest discount ($) = marketable controlling interest value ($) × minority interest(%) discount = (investor’s interest in equity × total equity value) × minority interest discount(%)   Management fee= % of NAV (net asset value generally ranges from 1-2%)   Incentive fee = % of profits (specified by the investment terms) 10   Incentive fee (when High Water mark Provision) = (positive difference between ending NAV and HWM NAV) × incentive fee % 11   Hedge Fund R = [(End value) – (Beg value)] / (Beg value) 18   Calmar ratio = Compound Annualized ROR / ABS* (Maximum Drawdown) 19   Sterling ratio= Compound Annualized ROR / ABS* (Average Drawdown - 10%) where, *ABS = Absolute Value FinQuiz Formula Sheet Reading 27: Risk Management   Delta Normal Method: VAR = E(R) – zvalue (S.D) •   Daily E(R) = Annual E(R) / 250 •   Daily S.D = Annual S.D / 250 •   Monthly E(R) = Annual E(R) / 12 •   Monthly S.D = Annual S.D / 12 •   Daily E(R) = Monthly E(R) / 22 •   Daily S.D = Monthly S.D / 22 •   Annual VAR = Daily VAR× 250   Diversification effect = Sum of individual VARs – Total VAR   Incremental VAR=Portf’s VAR inclu a specified asset – Portf’s VAR exclu that asset   Tail Value at Risk (TVAR) or Conditional Tail Expectation = VAR + expected loss in excess of VAR   Value Long = Spot t – [Forward / (1 + r) n]   Swap ValueLong = PV inflows – PV outflows   Fwd  contract  valueŒ8%Žn Mốâ EKSO UVEMỡ l ở%l&' lY([ qowS EKSOỡ/$ UVEM$ ì Sharpe Ratio = ê$1% /8*&Ơ ÔXÔƠ . 8Ơ /8*&Ơ Ô l ở%l&' lY([ Sortino Ratio = ê$1% /8*&Ơ ÔXê#% 1::$/&15"$ Ô ˆ8£%(#-$  -$4#1%   10   Risk Adjusted R on Capital = Ă./$:&$- Ô 8% 1% #%4(& :1/#&1" 1& *#(ứ  Š$1(,*$ 11   R over Max Drawdown = ¡./$:&$-  64$*1Ž$ Ô 8% 1% #%4(& #% #4$% ô* CFA Level III 2018   Reducing β to zero: N¥ = Xè* èẻ Ơ and T =0 Effective β = Combined position R in % / Market R in %   Synthetic Cash: Long Stock + Short Futures = Long risk-free bond Š1  -*1£-8£%   Reading 28: Risk Management Applications of Forward and Futures Strategies   β = CovSI / σ2I •   CovSI= covariance b/w stock portf& index •   σ2I= var of index   $β of stock portf = β of stock portf × MV of stock portf = βs S   Future $ β = βf × f where, βf = Futures contract beta   Target level of beta exposure: βT S = βs S + N fβ f f B B S NƠ = BƠ F Nf = $(#*$- è$&1 !1%$ Â,&,*$( è$&1 78*&Ơ8"#8 ơ1",$ ì ¢,&,*$(  :8%&*1:&  7*#:$ *Actual futures price = Quoted futures price × Multiplier   Synthetic Stock: Long Stock = Long Rf bond + Long Futures   Creating a Synthetic Index Fund: •   No of futures contract = Nf* = {V ×(1 + r) T}/ (q×f) where, Nf* = No of futures contracts q = multiplier V = Portfolio value •   Amount needed to invest in bonds = V* = (Nf*ì qì f) / (1 + r)T   Equity purchased = (Nf* ×q) / (1 + δ) T where,δ = dividend yield •   Pay-off of Nf* futures contracts = Nf*× q ×(ST –f) where,ST = Index value at time T Reading 29: Risk Management Applications of Options Strategies   Covered Call = Long stock position + Short call position a)   Value at expiration = VT = ST – max (0, ST – X) FinQuiz b)   c)   d)   e)   Profit = VT – S0 + c0 Maximum Profit = X – S0 + c0 Max loss (when ST = 0) = S0 – c0 Breakeven =ST* = S0 – c0   Protective Put = Long stock position + Long Put position a)   Value at expiration: VT = ST + max (0, X - ST) b)   Profit = VT – S0 - p0 c)   Maximum Profit = ∞ d)   Maximum Loss = S0 + p0 – X e)   Breakeven =ST* = S0 + p0   Bull Call Spread = Long Call (lower exercise price) + Short Call (higher exercise price) a)   Initial value = V0 = c1 – c2 b)   Value at expiration: VT = value of long call – Value of short call = max (0, ST – X1) - max (0, ST – X2) c)   Profit = VT – c1 + c2 d)   Maximum Profit = X2 – X1 – c1 + c2 e)   Maximum Loss = c1 – c2 f)   Breakeven =ST* = X1 + c1 – c2   Bull Put spread = Long Put (lower XP) + Short Put (higher XP) Identical to the sale of Bear Put Spread XP = exercise price Formula Sheet   Bear Put Spread = Long Put (higher XP) + Short Put (lower XP) a)   Initial value = V0 = p2 – p1 b)   Value at expiration: VT = value of long put – value of short put = max (0, X2 - ST) - max (0, X1 - ST) c)   Profit = VT – p2 + p1 d)   Max Profit = X2 – X1 – p2 + p1 e)   MaxLoss = p2 – p1 f)   Breakeven =ST* = X2 – p2 + p1   Bear Call Spread = Short Call (lower XP) + Long Call (higher XP) Identical to the sale of Bull Call Spread   Long Butterfly Spread (Using Call) = Long Butterfly Spread = Long Bull call spread + Short Bull call spread (or Long Bear call spread) Long Butterfly Spread = (Buy the call with XP of X1 and sell the call with XP of X2) + (Buy the call with XP of X3 and sell the call with XP of X2) where, X1< X2 < X3 and Cost of X1 (c1) > Cost of X2 (c2) > Cost of X3 (c3) a)   Value at expiration: VT = max (0, ST – X1) – max (0, ST – X2) + max (0, ST – X 3) b)   Profit = VT – c1 + 2c2 - c3 c)   Max Profit = X2 – X1 – c1 + 2c2 – c3 d)   Maximum Loss = c1 – 2c2 + c3 CFA Level III 2018 e)   Two breakeven points i   Breakeven =ST* = X1 + net premium = X1 + c1 – 2c2 + c3 ii   Breakeven = ST* = 2X2 – X1 – Net premium = 2X2 – X1 – (c1 – 2c2 + c3 ) = 2X2 – X1 – c1 + 2c2 - c3   Short Butterfly Spread (Using Call) = Selling calls with XP of X1 and X3 and buying two calls with XP of X2 •   Max Profit = c1 + c3 – 2c2   Long Butterfly Spread (Using Puts) = (Buy put with XP of X3 and sell put with XP of X2) + (Buy the put with XP of X1 and sell the put with XP of X2) where,X1< X2 < X3 and Cost of X1 (p1) < Cost of X2 (p2)