CFA Level 2, June, 2017 - Formula Sheet

FinQuiz Formula Sheet Level II 2017fgg Reading 9: Correlation & Regression • H1: b1 ≠ 0 (linear relationship does bcd ( h ) 10. F-Statistic or F-Test = = ggi exist) bce ( ) - ! jkhk/ *./ )* +) ,* +, b1 − b1 (df numerator = k = 1) 1. Sample Cov X, Y = 0+1 • Test statistic = t = (df denominator = n – k – 1 = n – 2) s b1 34567 2. Correlation Coefficient = r), = or b1 ± t c s b1 11. Prediction Intervals = Y ± t 3 sm (96 )(97 ) • Confidence Interval = 345(),,) 1 ()+))? r= ?ℎ??? sm> = s > 1 + + and 5;<()) 5;<(,) 0 0+1 9? 6 9. ANOVA (Analysis of variance) = 3. t-test (for normally distributed variables) = ANOVA SS MSS F s f = s 2f < 0+> ??? t= t distribution with n − 1+<? [ ??? Regression ??? ? 2 deg. of freedom = ?Z ??? Reading 10: Multiple Regression & Issues in df = k ? Z\1 ?−?−1 Regression Analysis > −? 4. Linear Regression = Yi = b0 + b1Xi + εi, ??? 1. Yi = b0 + b1X1i + b2X2i + … + bkXki + εi,i = Intercept (b0) = b0 = y − b1 x = [ • Error ??? = ?Z 1, 2, … n df = n-k-1 ?−?−1 • Slope or regression coefficient = b1 = Z\1 > −? 345(O,P) O+O P+P 2. Prediction equation = ?Z = ?u + ?1 ?1Z + or = 5;<(O) O+O ? ??? [ ?> ?>Z +. . . +?w ?wZ + εy , ? Total = ?Z 5. Standard Error of Estimate SEE = SR = df = n-1 Z\1 [+1 - (P +P)? −? > 3. Adjusted R2 = ? > = 1 − 1 − ?> SSR *./ * [+w+1 = 0+T+1 0+T+1 4. Breusch–Pagan test Source of Sum of Mean Sum 6. Coefficient of Determination (R2) = DoF • H0 = No conditional Variability Squares of Squares SSU+SSR VSS = = where, 0 ≤ R2≤ 1 Heteroskedasticity exists SSU SSU (for single independent variable R2 = r2) Regression MSR = • HA = Conditional Heteroskedasticity 1 RSS (Explained) RSS/1 exists 7. SST = SSE + SSR(or RSS) • Test statistic = n × R2residuals Error MSE = n-2 SSE (Unexplained) SSE/n-2 8. Hypothesis Testing: 5. Durbin-Waston Test = ?? = SST= • ? ~.? }~ +}~k/ • Null and Alternative hypotheses • } ? Total n-1 RSS + ~./ ~ • H0: b1 = 0 (no linear relationship) SSE • For Large Sample size DW Statistic (d) = d ≈ 2 (1 – r) FinQuiz Formula Sheet Level II 2017 • Random walk with a drift = xt = b0 + x Reading 13: Currency Exchange Rates t-1 + εt where, b0 ≠ 0 and b1 = 1 • By taking first difference yt = xt - x t-1 1. Bid-offer Spread = Offer price – Bid price = b0 + εt 2. Fwd rate = Spot Exchange rate + Reading 11: Time Series Analysis †4<‡;<ˆ ‰4y0Š9 7. Using Dickey-Fuller Test = xt - x t-1 = b0 + 1u,uuu (b1 -1) x t-1 + εt 3. Forward premium/discount (in %) = 1. Linear Trend Models = yt = b0 + b1t+ εt 9‰4Š •O3Ž;0•• <;Š•+(m4<‡;<ˆ ‰4y0Š9/1u,uuu) −1 • Predicted/fitted value of yt in period 9‰4Š •O3Ž;0•• <;Š• 8. Smoothing Past Values with n-Period (T + 1) = yˆ t +1 = bˆ0 + bˆ1 (T + 1) Moving Average = 4. To convert spot rate into forward quote: 2. Log-Linear Trend Models = yt = e b0 +b1t xt + xt −1 + xt −2 + ..... + xt −( n −1) • Spot exchange rate × (1 + % premium) • Spot exchange rate × (1 - % discount) n 3. Autoregressive Time-Series Models: 9. Correcting Seasonality in Time Series • First order autoregressive AR (1) = xt Models: 5. Covered interest rate parity: 1 = b0 + b1 x t-1 + εt • 1 + iˆ = S ∫ 1 + i∫ †∫ /‘ • pth-order autoregressive AR (p) = xt ˆ • For quarterly data = xt = b0 + b1x t-1 + 1’y∫ = b0 + b1 x t-1 + b2 x t-2 + …..+ bp x t-p b2x t-4 + εt • F∫ /ˆ = S∫ 1’y‘ ˆ +εt • For monthly data = xt = b0 + b1x t-1 + • Using day count convention: b0 b2x t-12 + εt ' ! Actual $* 4. Mean reverting level of xt = 10. ARCH model = 1 − b1 )1+ id # ,= εˆ 2 t = α 0 + α1εˆ 2 t −1 + µ t where µt is ( " 360 &%+ 5. Chain Rule of Forecasting: an error term ' ! Actual $*' 1 * S f /d )1+ i f # ,) , • One-period ahead forecast = • Predicting variance of errors in period ( " 360 &%+)( Ff /d ,+ xˆt+1 = bˆ0 + bˆ1 xt t+1 = σˆ t2+1 = αˆ 0 + α1εˆt2 • Two-period ahead forecast= ⎛ ⎡ Actual ⎤ ⎞ Reading 12: Excerpt from ‘Probabilistic ⎜ 1 + i f ⎢ ⎟ xˆt+2 = bˆ0 + bˆ1 xt+1 • ⎜ ⎣ 360 ⎥⎦ ⎟ Approaches , Scenario Analysis, Decision Tree Ff / d = S f /d ⎜ ⎡ Actual ⎤ ⎟ 6. Random Walks and Unit Roots: & Simulations’ ⎜ 1 + id ⎢ ⎟ • Random Walk without drift = xt = x t- ⎝ ⎣ 360 ⎥⎦ ⎠ 1 + εt where, b0 = 0 and b1 = 1. • Correcting Random Walk = yt = xt - x 6. Uncovered Interest Rate Parity : t-1 i f − %ΔS e f / d = id • FinQuiz Formula Sheet Level II 2017 %ΔS e f / d = i f − id ⎛ S f / d Pd ?– − ?— − ?– − ?— ⎟ = S f / d ⎜ Pd ⎞ ⎛ ⎞ • ⎜ ⎟ • Forward premium or discount: ⎜ P ⎟ ⎜ P ⎟ qf/d = ⎝ f ⎠ ⎝ f ⎠ 16. Interest Rate Differentials, Carry Trades • For one year horizon = and Exchange Rates Ff /d − S f /d = ⎛ CPI d ⎞ q f / d = S f / d ⎜ ⎟ "i −i % or ⎜ CPI ⎝ f ⎟ ⎠ qL/H = qL/H +(iH −i L )−(π Hε − π Lε )−(φH − φL ) S f /d $ f d ' ≅ S f /d (i f − id ) # 1+ id & 12. Fisher effect: • id = rd + πεd 17. Policy Rate under Taylor rule: • Using day count convention: ( " Actual % + • if = rf + πεf • i = rn + π + α (π − π *) + β (y − y*) * $ - • if – id = (rf – rd) + (πεf- πεd) # 360 '& - Ff /d − S f /d = S f /d * (i f − id ) • (rf – rd) = (if – id) - (πεf- πεd) • Neutral real policy rate + Current inf * 1+ i " Actual % - * d$ - ) # 360 '& , rate + α (Inf gap) + β (Output gap) 13. When both uncovered interest rate parity and ex-ante PPP hold: 18. Exchange rates using the Taylor Rule = 7. Forward discount or premium as % of spot • (rf – rd) = %∆ Sεf/d - %∆ Sεf/d = 0 q šS›/RšV = q šS›/RšV + r0Rš − r0šS + rate: • International Fisher Effect: if – id = πεf- Ff / d − S f / d π εd α πRš – π ∗Rš − πšS − π ∗šS + ≅ (i f − id ) S f /d β yRš − y ∗Rš − yšS − y ∗šS − 14. When all the key international parity ∅Rš − ∅šS If uncovered interest rate parity holds conditions are held at all times: • Ff /d − S f /d BOP = Current A/C + Capital A/C + = = %ΔS ef /d ≅ (i f − id ) Reading 14: Economic Growth & The S f /d Official Reserve A/C = 0 Investment Decision 8. Purchasing Power parity (PPP) 15. Real exchange rate = ?” = ?” + 1. Economic growth = Annual % ∆ in real • • • Pf = S f/d × Pd GDP or in real per capita GDP • S f/d = Pf / Pd R ¤ 2. P = GDP £›¤ R 9. Relative version of PPP = %∆S f/d = πf – πd 3. Expressing in terms of logarithmic rates: 10. Ex ante version of PPP = %∆Sef/d = πef – • (1/T) % ∆P = (1/T) % ∆GDP + (1/T) π ed %∆ (E / GDP) + (1/T) % ∆(P / E) 11. Real Exchange Rate • % ∆ in stock MV = % ∆ in GDP + % ∆ in share of earnings (profit) in GDP A two-factor aggregate production • Growth rate in potential GDP = LT g + ?? (y/k – Ψ) 1+¨ function: Y = AF (K. Under the Cobb-Douglas production • Growth in physical capital stock = ∆K 15. L) = Kα L1 . L) rate of labor force + LT g rate in labor • Capital-to-labor ratio = ∆k / k = productivity © ª © + ? − ? = +s 5. income / Output or GDP / k = ∆y / y = ∆A / A + α ∆k / k = knew " K %new . ¥¦§ =) è Steady state growth rate of • kold )!Y $ . FinQuiz Formula Sheet Level II 2017 + % ∆ in the price-to-earnings • Growth rates of output per capita = ∆y multiple 11. Contribution of Capital Deepening = Labor • Steady state Output-to-capital ratio = 16. Output per worker or Average labor labor productivity productivity (Y/L or y): • Growth rate of Total output = ∆Y / Y α • GDP/Labor input = TFP × capital-to- = Growth rate of TFP scaled by labor y new ⎡ k new ⎤ labor ratio × share of capital in GDP = ⎢ ⎥ force share + Growth rate in the labor • Or y = Y/L = Akα © • y old ⎣ k old ⎦ force = +n 1+ ¨ 8. In the steady state: ' ! Y $ *α −1 • α Y/K = r èα = r (K) / Y = Capital • Growth rate of capital per worker = ∆k )# & . Production function in the endogenous ª 1 © productivity growth rate – TFP = + ? + ? = ? growth model = ye = f (ke) = cke « ¬ 1+ ¨ • Gross investment per worker = • Growth rate of output per capita = 9. Growth Accounting based on Solow 14. Contribution of Improvement in © ∆ye/ye = ∆ke/ke = sc – δ – n technology = Labor productivity growth + ? + ? ? 1+ ¨ rate – Capital Deepening • Slope of straight line = [δ + n + θ / (1 Reading 15: Economics of Regulation – α)] 10. Proportional impact of the saving rate function: change on the capital-to-labor ratio and per = sY – δK • Marginal product of capital = MPK = capita income over time: 1 α AK α-1 L 1-α = α Y/K 13. Cobb-Douglas Production Function = F 1+ ¨ « 1+¨ (K. During the transition to the steady state Approach = ∆Y /Y = ∆A / A + α ∆K/K + growth path: (1 – α) ∆L/ L .α 12. Balanced or Steady State Rate of Growth (y/k – Ψ) in Neoclassical Growth Theory: 6. )( #" K &%old . Labor productivity growth accounting /y= © + ?? ª − ? = 1+ ¨ « equation © 4.+ 1+ ¨ 7. S= SP – Recorded FV Available § i income = Market rate at purchase × Initial Fv § Reported at FV at the end of Yr t Unrealized g/l (net -for-sale If debt security is sold: § Subsequently. of Yr t – Amort Cost recognized in P&l statement.S If debt security is sold: § Realized g/l reported on I.S) Balance Sheet (B. at FV at the subsequent reporting of tax) = FV at end § Cumulative unrealized g/l is removed from OCI and entire g/l date on the B. security § Realized g/l reported on I. at FV at subsequent reporting date trading If debt security is sold: on B.S = SP – CV or Amort cost Held § i income = Market rate × Initial FV § Initially. Amort = i pmt – i income § If debt security is sold: Realized g/l reported on I. Summary of Accounting Treatment of Investments Income Statement (I.S. for § Unrealized g/l = FV at the end of Yr t – Amort Cost at end of Yr t § Subsequently. FinQuiz Formula Sheet Level II 2017 Reading 16: Interoperate Investments 1.S.S.S= SP – Recorded FV Designated § i income = Market rate at purchase × Initial FV § Reported at FV at the end of Yr t at § Unrealized g/l = FV at the end of Yr t – Amortized Cost at end of § Subsequently. at FV. at end of Yr t Where. Realized g/l in I.S) Statement ofSH’sEq uity Held-to.S = (SP – Recorded FV) + Unrealized g/l • Unrealized g/l (net of tax) is reported as OCI . § i income = Market rate at purchase × Initial fair value (FV) of a § Initially. at FV (IFRS) or initial price paid (US N/A maturity debt security GAAP) Ori income = i pmt – Amort § Subsequently. reported at amort cost at the i pmt = (Coupon rate × Par value) subsequent reporting date on B. at FV at the subsequent reporting fair value Yr t date on B. of excess purchase price (xxx) -Land (% of Ownership Interest × difference b/wBV & FV) (xxx) Less: Unrealized profit (% of Ownership Interest × Profit from (xxx) = Residual Amount (Treated as Goodwill) Xxx upstream sale in Associate’s NI) 3. paid Investor’s proportionate share of Investee’s recorded net assets Xxx by the associate)] (% of Ownership Interest × Ending net assets) Add: Unamortized excess PP (Excess PP – Amort. of excess PP) xxx . paid (xxx) Ownership Interest × (beg BV of net assets) + (Reported NI of = Ending net assets Xxx associate – Profit from upstream sale in Associate’s NI) – Div.S* xxx Investment in associate: PP Xxx Balance in the investment in Associate to be reported at the end of • Add: Investor’s share of Investee’s NI (% of Ownership Xxx year: Interest × Investee’s NI) PP xxx Less: Div. FinQuiz Formula Sheet Level II 2017 2. received (% of Ownership Interest × Div. received (% of Ownership Interest × Div paid) (xxx) (Amount attributable to PP&E* ÷ Remaining life of PP&E) = Balance in investment in Investee Xxx = Value of Investment in Associate’s company at the end of year xxx Where. *Amount attributable to Plant & Equipment = % of Ownership Interest of investor × (FV of P&E – BV of P&E) Beg net assets Xxx • Composition of Investment account: Add: NI Xxx Investor’s proportionate share of Associate’s net equity = [% of xxx Less: Div. of excess PP attributable to plant & equipment (xxx) Less: Div. Upstream Transactions: Less: Attributable to Net Assets: Investor’s share of Associate’s reported NI (% of Ownership xxx -Plant & Equipment (% of Ownership Interest × difference (xxx) Interest × Reported net income) b/wBV & FV) Less: Amort. Amort. of Excess PP: = Equity Income to be reported as a line item on Investor’s I. Goodwill = Cost of acquisition – investor’s share of the FV of the net Add: Unamortized excess PP (Excess PP – Amount attributable xxx identifiable assets to PP&E) PP Xxx = Investment in Investee xxx Less: (% of Ownership Interest × BV of Investee’s Net (xxx) Assets) Transactions with Associates: = Excess Purchase Price Xxx 4. paid) (xxx) Add: Equity income (as calculated above)* xxx Less: Amort. S assets. Downstream Transactions Goodwill under acquisition method = BV for A&L Investor’s share of Associate’s xxx 9. Merger = Company X + Company Y = Goodwill xxx • Impaired when CA of the Cash-generating = Company X Unit > RA of the Cash-generating Unit 12. Goodwill Impairment Test under IFRS: Business Combinations 6. the allocation × Reported NI) of PP: 17. Acquisition = Company X + Company Y = Sum of diff b/w FV and BV of identifiable • Impairment loss = CA of Cash-generating (Company X + Company Y) assets + Goodwill Unit . Full Goodwill = Total FV of the of Investor + FV for A&L acquired from reported NI (% of Ownership Interest Subsidiary – FV of subsidiary’s Acquiree × Reported NI) identifiable net assets Less: Amort of excess PP (xxx) 14. RA = Higher of Net SP and its VIU 8.S cash-generating unit .RA of Cash-generating Unit where. Under Acquisition method. Combined Assets & Liabilities (A&L) Net SP = FV – costs to sell Y = Company Z reported on Consolidated B. Value of non-controlling interest under Less: Amort of excess PP (xxx) FV of the stock issued xxx partial goodwill method = Non-controlling Add: Realized profit (% of goods xxx Add: BV of Investee’s net assets xxx interest’s proportionate interest in unsold × Unrealized profit) = Excess PP xxx subsidiary × FVof the subsidiary’s = Equity Income to be reported as a xxx identifiable net assets on acquisition date line item on Investor’s I. Partial Goodwill Method: the stock issued to effect the transaction – Ownership Interest × Profit from the • Goodwill = FV of acquisition – Par value of the stock issued) + Additional downstream sale in Associate’s NI) Acquirer’s share of FV of all PIC of investor = Equity Income to be reported as a xxx identifiable tangible and intangible line item on Investor’s I. Combined Paid-in Capital (PIC) = (FV of Less: Unrealized profit (% of (xxx) 10. Allocation of excess PP: Excess PPP = 7.S FV of the stock issued xxx Less: FV allocated to identifiable net (xxx) Goodwill Impairment: assets 18. subsidiary × FV of subsidiary on Investor’s share of associate’s xxx acquisition date reported NI (% of Ownership Interest 11. Value of non-controlling interest under full Investor’s share of the unrealized profit = (acquirer’s) proportionate share of the goodwill method = Non-controlling Unrealized profit × % of goods unsold FV of subsidiary’s identifiable net interest’s proportionate interest in assets.S under VIU = PV of expected future CF of acquisition method: Consolidated B. FinQuiz Formula Sheet Level II 2017 5. Minority Interest = % of subsidiary not liabilities acquired owned by the Parent × Subsidiary’s Equity Unrealized profit = % of goods unsold × Profit Or on the sale to investee • Goodwill = Purchase price – parent’s 16. Consolidation = Company X + Company 13. liabilities and contingent 15. Adjusted i and investment Income in yr-end accruals where *Pension liability is treated as a =Reported i and investment income + negative Actual return on plan assets 2.’s Funded Status* – Beg Funded Status*) annual contribution to plans adjusted for ∆ – Employer Contribution 13. 7.y0y0• 5•9Šy0• ‰•<y4ˆ 4. Goodwill Impairment Test under U.Implied FV of Reporting cost + Actual return on plan assets unit’s Goodwill 8.Current service loss = CV of Reporting unit’s costs . 5. Compensation exp.i exp component of pension Goodwill . • Total Net periodic pension cost (End component of pension cost 1.Šy40 •O‰ (+) Actual return (loss) on plan assets V•´. = Reported i exp. + i exp. Under DC Plans: Pension exp = Co. Adjusted i Exp. Actuarial g/l = Actual return – (Plan assets reported pension and other post- • Step 2: Measurement of Impairment × Expected return) retirement benefits . Adjusted Net Operating Exp=Reported Net Goodwill = FV of Reporting Unit – operating exp – Total reported pension and FV of Reporting unit’s net assets • Total periodic pension cost in a given other post-retirement benefits + Current period = ∆in Net pension liability or service costs Reading 17: Employee Compensation: Post asset adjusted for employer Employment & Share-Based contributions 12. Total Periodic Pension Costs =Sum of • Where Implied FV of Reporting unit’s components of periodic pension costs 11. FinQuiz Formula Sheet Level II 2017 19.S. = FV of stock on the Grant Date 3.’s DB pension • = Current service costs + i costs + (-) plan = ∆ in Net pension liability or asset actuarial losses (actuarial gains) + past 16. Compensation exp recognized = š0<•34•0y³•ˆ 040+ adjusted for employer’s contributions service costs (or plan amendments) – 5•9Š•ˆ 34´‰•09. Adjusted Total P&L pension exp (income) 14. Adjusted Pre-tax Income: GAAP (Two Step Approach) Pension asset • = Reported Pre-tax income + (Actual return on plan assets – Expected return • Step 1: Goodwill Impairment Test 6. Net return on plan assets = Actual return on plan assets) • Impaired when CV of Reporting Unit on plan assets – (Plan assets × i rate) Or (including Goodwill) > FV of • = Reported Pre-tax income + Total Reporting Unit (including Goodwill). Net i exp = Discount rate × Net Pension Or liability • = Reported Total P&L pension exp where Discount Rate = rate used to (income) + Expected return on plan calculate PV of future pension benefits assets – Actual return on plan assets . Period pension cost of a Co. Funded Status = PV of DB obligations – FV of plan assets 9. Net i income = Discount rate × Net 10. E) translated NI – div.Ss separate component i) Measured at current value of equity i.S. rate & historical rate) ASSETS Monetary assets: Cash. div. Re-measurement Loss = NI − NI before Re-measurement loss EQUITY Other than R. deferred revenue Current rate Historical rate 3. Dep. Re-measurement Gain = NI − NI before re-measurement gain 4. a/c Current rate Current rate Exposure Net Assets or Net Net monetary assets or Net receivables Liabilities monetary liabilities Treatment of translation adj. accrued Net Asset B.E + translated NI – Statements (F. LT debt.S Exposure Strengthens Weakens Monetary liabilities: a/c Current rate Current rate When assets translated at +ve -ve payable. marketable securities & .E + Beg R.e. FinQuiz Formula Sheet Level II 2017 Reading 18: Multinational Operations Foreign Subsidiary’s Functional Currency FC Parent’s Presentation Currency 1.g. etc.S i) measured at current value Current rate Current rate current X rate > assets translation translation exposure ii) not measured at current translated at current X rate adj Adj (X = exchange) value i.e. Common Historical rates Historical rates 5.e. When liabilities translated at -ve +ve Nonmonetary liabilities: Net Liability B. subsidiary’s bookkeeping & Amort. ii) Measured at historical Current rate Historical rate 2. Cumulative Translation Adjustment = CTA = Assets – Liabilities – inventories measured at Common Stock – Retained Earnings market value under the lower of cost or market rule. GAAP translated at rate historical rate Foreign Subsidiary’s Functional Currency Revenues Average rate Average rate FC Parent’s Presentation Currency Translation Method: Current Rate Temporal Method EXPENSES method Most Expenses Average rate Average rate Expenses related to assets X rate at which F. Rules For Translation Of A Foreign Subsidiary’s FC Financial Stock Beg R. PP&E Foreign Currency (FC) LIABILITIES B. and deferred income exposure translated at current X rate adj adj taxes..Ss) Into Parent’s Presentation Currency Under IFRS & Retained Earnings (R. Balance Sheet Exposure: costs e. COGS..g.E i.S current X rate > liabilities translation translation exp.Ss are translated at historical X rate Average rate Historical rate translated from foreign e. translated at historical U. currency to parent’s NI Average rate Mixed (a mix of average presentation currency. Accumulated as a Included as g/l in NI Nonmonetary Assets: Current rate Current rate in parent’s consolidated F. » ‰<y3• y0ˆ•O 6.Š•< relative to § Liabilities ↑ § Liabilities ↑ § Liabilities ↑ ºy9Š4<y3.‡Žy3Ž•5•< y9 ». FinQuiz Formula Sheet Level II 2017 TEMPORAL METHOD: CURRENT ·¸<<•0Š P<¹ 9 ‰<y3• y0ˆ•O RATE 7. Gain from holding note payable = Notes payable × ·¸<<•0Š P<¹ 9 ‰<y3• y0ˆ•O+ºy9Š4<y3.‰<y3• y0ˆ•O loss gain § +ve Translation adj. Loss from holding beg balance in cash = -Beg balance in cash × FC weakens § Rev ↓ § Rev ↓ § Rev ↓ ·¸<<•0Š P<¹ 9 ‰<y3• y0ˆ•O –ºy9Š4<y3. Net Monetary Assets Gain Loss Net Monetary Liabilities Loss Gain Hyperinflationary Economy .» ‰<y3• y0ˆ•O Net Monetary Net Monetary METHOD Liability Exposure Asset Exposure FC § Rev ↑ § Rev ↑ § Rev ↑ 8. Restated Capital Stock = Capital stock original value × strengthens § Assets ↑ § Assets ↑ § Assets ↑ ·¸<<•0Š P<¹ 9 ‰<y3• y0ˆ•O 4< ˆ.O ½334¸0Šy0• ¤<4myŠ9 Strengthens Weakens CURRENT RATE METHOD: Net Assets Gain Loss 14. 12. 10. Impact of Changing Exchange Rates on Exposure U. effective tax rate = ¤<•Š. Organic sales growth = Net sales growth + Foreign X impact + Net Liabilities Loss Gain TEMPORAL METHOD: Acquisition/Divestiture impact.» ‰<y3• y0ˆ•O parent’s presentation § NI ↓ § NI ↑ § NI ↑ ·¸<<•0Š P<¹ 9 ‰<y3• y0ˆ•O currency § SH’ equity ↓ § SH’ equity ↑ § SH’ equity 9.» ‰<y3• y0ˆ•O ºy9Š4<y3.» ‰<y3• y0ˆ•O relative to § Assets ↓ § Assets ↓ § Assets ↓ ºy9Š4<y3. Loss from increase in cash during the yr = -Increase in cash × § SH’ equity ↑ § SH’ equity ↓ ↓ ·¸<<•0Š P<¹ 9 ‰<y3• y0ˆ•O+½5• ‰<y3• y0ˆ•O § Translation § Translation § SH’ equity ↓ ½5• ‰<y3• y0ˆ•O gain loss § -ve Translation adj.Š• 4m 340Š<y¼¸Šy40. Avg. Restatement Factor = ºy9Š4<y3.» ‰<y3• y0ˆ•O parent’s § Liabilities ↓ § Liabilities ↓ § Liabilities ↓ presentation currency § NI ↑ § NI ↓ § Net Income 11.O RO‰ Foreign Currency 13. Restated Revenue = Revenue original value × § Translation § Translation ↑ ½5•. Cash Flow to Reinvestment = 7.Ø-ÑÙÚÛ-Ú Assets > 7. Capacity to pay debt (in years) 9.·† ¼•m4<• y0Š•<•9Š & áâãä¬ Leveraget–1 where.S based aggregate accruals 10.0 × • U.·† items – Cash from operations)/TA • Adjusted Tax Burden = 3. DuPont Analysis: CFI t) • ROE = Tax Burden × Interest • CF based Accruals Ratio = 3. CF before interest and taxes = Op.R (Cash t + ST invstmnt. B.È 4m »y.¼y»yŠy•9 S. 4. SGAI (sales. FinQuiz Formula Sheet Level II 2017 ¿•Š À· V. Leverage = Debt / ÏÐÑ U. SGI (sales growth index) = Salest/Salest–1 EBIT/Sales × Sales/Assets × CF + cash i paid + cash taxes paid Assets/Equity • Op income adjusted for accounting ∆ 5.È 4m RÉ¸yŠP t – (Total LT debt t + Debt in current 3. Accruals = (Income before extraordinary Associates ß‰.» RO‰•0ˆyŠ¸<•9 2.› = ß‰. of 1/Dep ratet where. and admin exp 4. Earnings t+1 = α + (β1 × Earnings t) + ε Accruals and Earnings Quality U.»•9 B.‰yŠ. CF based aggregate accruals: 2.ÜÖ-‘ ÔÕkÖ-‘ Ö×. Account receivable turnover = (365/DSO) • Aggregate Accrualst = NOAt – NOAt-1 ß‰. DSR (days sales receivable index) = 1.·†+·.6 × + liab. Cash Flow to Total Debt = • Adjusted TATO = ß‰. GMI (gross margin index) = Gross margint–1 / Gross margint • Aggregate Accruals = NI t – (CFO t + 1.‰yŠ. CF Interest Coverage = Z ¤. Z-score = 1. LEVI (leverage index) = Leveraget / 6.·† 6. DEPI (depreciation index) = Dep ratet– • ROE = Net profit margin × asset = Profit before i& taxes + amort.½ ¿ß½~ +¿ß½~k/ (Receivablest/Salest) / (Receivablest– ¿ß½~ ’¿ß½~k/ > 1/Salest–1) Reading 20: Integration of Financial Statement Analysis 3.3 × + 0.2 × + 1. AQI (asset quality index) = [1 – (PP&Et+ Burden × EBIT margin × TATO × ¿ÄÚ +(·†ßÚ ’·†ÄÚ ) CAt)/TAt ] / [1 – (PP&Et–1+ CAt-1)/TAt-1] (¿ß½Ú ’¿ß½Úk/ ) Financial Leverage > • ROE = NI/EBT × EBT/EBIT × • Op.½ index) = (SGAt/Salest) / (SGAt–1/Salest–1) – Investments in Associates • Adjusted NI = NI of Co – NI from 5.› ÒÐÓ ÔÕkÒÐÓ Ö×.» •O‰•0ˆyŠ¸<•9 ¿Ä+RÉ¸yŠP y034´• RÃU 8.)}] U½ Ã. t)} – {Total liab Reading 19: Evaluating Quality of Financial 11. Dep rate = Dep/(Dep + PP&E) turnover × leverage goodwill • Adjusted Asset base = Adjusted Total Assets = Total Assets of the company ß‰.4 × + U½ U½ Reports RÃÄU Ç. S based Accruals Ratio = 1. Cash Return on Assets = ½5• U.·† ¼•m4<• Z& áâãä¬ where. NOAt = Net operating Assets t 8. general.yˆ = Op Assets t – Op Liab t = [{TA t – .Ø-ÑÙÚÛ-Ú. Value of subsidiary/affiliate holdings 3. Depreciable Basis = Purchase price + any when PI > 1.<•0Š ·4. total market Expansion Project 10.¤/R EBIT = earnings before interest and taxes Ö Ã•03Ž´.R (∆Sal T – ∆B T) NPV 16. Dep Implied Value of Parent Co.P´•0Š9 14. Terminal year after-tax non-operating cash = AT CF from invstmnt. pro-rata share of 1.P´•0Š9 flow = TNOCF = ∆Sal T + NWCInv – T 15. = original investment + 15. Adj. (excl.9• ‰. i-coverage Ratio = 8. Profitability index = PI = 1 + (NPV/Initial Valuation: investment) 9. × X. Total value of Co. = flow = TNOCF = Sal T + NWCInv – T (Sal MV)= AT CF from invstmnt.<T¹ 9 + ¤. (1 + Nominal rate) = (1 + Real rate) (1 + RÃÄU+›•‰ •O‰’V•0Š RO‰ 16. ∆non-debt current liabilities= ∆NWC 11. Residual income (RI) = NI – Equity Z •O‰’½99¸´•ˆ Z •O‰ 40 »•. Adj. D-to-E ratio = U. invest and when PI < 1. Initial Outlay = FCInv + NWCInv NWCInv = ∆non-cash current assets – Economic and Accounting Income 10.’s Mkt Cap . – Eco. CAPM = ri = R F + βi [E (R M) – R F] capitalization 2. Economic Profit (EP) = NOPAT– $WACC subsidiary/affiliates Replacement Project where.›’¤È 4m »•. MVA or NPV = Š\1 (1’À½··)Ú U. Accounting income = Rev – Exp subsidiary/affiliates) = Parent Co.’9 ´TŠ ·. 5.rate)/Parent Co.<T¹ 9 ¤/R 6.9•9 Inf rate) Charge • RI t = NI t – (re × B t-1) . Parent Co. Discount to Benchmark = T (Sal 0 – B0) i. Implied Value of Parent Co. FinQuiz Formula Sheet Level II 2017 Decomposition and Analysis of the Co’s Reading 21: Capital Budgeting 9.9• ‰. price in FC× Shares held by Parent Co.½ ’ ¤È 4m »•.R ì R¤Ú 7. Annual after-tax operating cash flow = CF 12. do subsidiary/affiliates = (Subsidiary’s share Shipping or handling or installation costs not invest. Adj. (excluding subsidiary/affiliates) T – B T) NI of Parent Co. −Equity Income from 13. EBIT (1 – Tax rate) ê Ã•03Ž´.<•0Š ·4. Implied P/E ratio of Parent Co.e. Economic Income = AT CF from = (S – C – D) (1 – T) + D or CF = (S – C) investment + ∆ in MV = AT CF from ¤.<•0Š ·4. Initial Outlay = FCInv + NWCInv – Sal 0 + NOPAT = net operating profit after tax 13.‰ investment + (End MV – Beg MV) 11. Annual after-tax operating cash flow $WACC= dollar cost of capital = WACC (incremental) × capital Off-Balance Sheet Leverage from Operating • CF = (∆S – ∆C – ∆D) (1 – T) + ∆D or Capital (after Year 1) = investment = Leases • CF = (∆S – ∆C) (1 – T) + T∆D Initial Investment – depreciation U. OR 4. – (Beg MV – End 12. P/E ratio of Parent Co = (1 – T) + TD ¿Ä 4m ¤. Terminal year after-tax non-operating cash 14. Fin Lev = U. MM Proposition I with Taxes: Co. FinQuiz Formula Sheet Level II 2017 where.’s value Share is sold (after share goes ex-div. Total value of Co. tax ·49Š 4m ˆ•¼Š (RÃÄU – y0Š•<•9Š ‰. Total value of Co. = value of liabilities + where. tax rate on div. CF from Sale = Sale price – cap gains tax • V L = V U + (t ×D) R ×r• (owed on sale) + AT amount of div. AT cost of debt = BT cost of debt × (1 – Pb = purchase price where b is for buy Marginal tax rate) TCG = marginal tax rate on capital gains Reading 22: Capital Structure 10. tax rate) (Indiv.P´•0Š9 40 ˆ•¼Š) *(r0.P´•0Š9 40 ˆ•¼Š • MVA = Š\1 1’< Ú + Analysis Ð ·49Š 4m ˆ•¼Š • Total value of Co. MM Proposition II with Taxes: WACC is goes from with div to ex-div › 4.) • Cost of Equity = r• = ru + (ru − distress) (personal tax rate)} › rˆ ) R . Pw = price with the right to receive value of equity dividend 9. tax Ä0Š•<•9Š ‰. Cash flow from Sale = Sale price – capital › R gains tax owned on the sale = Pw – (Pw – 8. = (Px– Pb) (TCG) + D (1 – TD) RÃÄU 1 – Š VU = 2. Dividend imputation tax system: ETR = R 6.P´•0Š9 40 ˆ•¼Š)(1 – Š) 1+Uò 1+Uò › R ·49Š 4m •É¸yŠP P‡ − PO = D or ∆P = D ×rˆ + ×r• 1+Uñó 1+Uñó È È where. According to MM proposition II: VL = V U + tD – PV(Costs of financial div + {(1 – Corp. = Px– È • Value of Unlevered all equity Co. When Px = Pw then Pw – (Pw – Pb) (TCG) = • V=D+E= + ·49Š 4m ˆ•¼Š Px– (Px– Pb) (TCG) + D (1 – TD) 3. WACC = rÀ½·· = › ×rˆ × 1 − t + is maximized at 100% Debt È 2. ∆P = ∆ in price when the stock 11.r d) rate)} › ·49Š 4m •É¸yŠP • WACC with taxes: rWACC = ×rd× (1 – È 5.) 1. Systematic Risk = βa = βd + βe È È Claims Valuation Pb)(TCG) • βe = βa + (βa – βd) (D/E) 17. According to MM proposition I: V L = V U t)+ ×re SH’s Marginal Tax Rate È and E = V – D 12.P´•0Š9 40 ˆ•¼Š 3. Split tax system: ETR = Corp. tax rate on 7.P´•0Š9 40 ˆ•¼Š R 5. Cost of Equity = r• = ru + (ru − rˆ ) minimized at 100% Debt R › • re = r0 + (r0 –rd)(1 – t) 4. V = D + E = + (r0 –rd)(1-t) = Slope coefficient * rate + {(1 – Corp. = V = D + E <ðÕññ Ä0Š•<•9Š ‰.P´•0Š9 40 ˆ•¼Š) Share is sold just before it goes ex-dividend: ·49Š 4m •É¸yŠP + Original Equity investment + Original Debt investment 1. • V=D+E= Reading 23: Dividends & Share Repurchases ì VÄÚ Ä0Š•<•9Š ‰. WACC without taxes = rÀ½·· = (RÃÄU – y0Š•<•9Š ‰. = NPV (PV of RI) (RÃÄU – y0Š•<•9Š ‰. Static trade-off theory of capital structure 6.r d)(1 – t) < (r 0 . Double Taxation Method: ETR= Corp. <0y0•9 ¤ ›y5.» 04. Policy • Div. Payout Ratio = ›y5.<•9 <•‰<•9•0Š•ˆ ¼P ŠŽ• ß‰Šy409 • Net interest after-tax = (i exp – i • When takeover premium is given in U4Š. EV =MV of debt + MV of equity – cash & [›y5. X + Co. = ↑ in Earnings × 1. of acquirer shares received by each per share (of target Co. in div.’SŽ. Div. Coverage Ratio = ½3É¸y<•<¹ 9 ‰<• ´•<••< R. New shares issued by Acquirer = deferred taxes + net noncash charges – ∆ in ÇTŠ 3. Post-merger no. of shares outstanding = Equity % in capital structure) or Acquirer’s pre-merger total shares 13. of yrs.<•9 4¸Š9Š. Policy • NOPLAT = Unlevered NI + ∆ in • Expected ↑ in Div. factor) 4. No. Share Overhang = 10. factor = 1/no.0ˆy0• †·† 11. FCF = NI + net interest after-tax + ∆ in Adj. HHI = Z ¥÷áâö câöä¬ ÷ø ÷ùáúùá ÷— ûâøwäá × Estimated stock price of Target based on 2 Comparables + Estimated takeover Reading 25: Corporate Governance 100 premium 1. = Earnings – (Capital budget × Terminal Value: 5. Stable Div.<••Š NWC – Capex 9Š43T ‰<y3• 4m ½3É¸y<•< 8. Subsidiary Merger = Co. Takeover Premium = takeover (deal price) 8. of target ›¤ + S¤ Reading 24: Corporate Performance. Terminal ValueU = FCFU × ¤49Š ´•<••< 0¸´¼•< 4m 9Ž. X deferred taxes Target payout ratio × Adj. Statutory Merger = Co. = shares he/she owns × X ratio c§ Governance & Business Ethics [ câöä¬ ÷ø ÷ùáúùá ÷— ¦Zøû Z 17. • Adj. Using constant growth formula • Div. Unlevered NI = NI + Net Interest after-tax ¿4. outstanding + new shares issued by †·†Ô (1’•) Terminal ValueU = 9.) = No. Acquirer (À½··ü‘ýþÙÚÐ‘ +•) ¿Ä ¿Ä 6. factor 2. FinQuiz Formula Sheet Level II 2017 Payout Policies: Reading 26: Mergers & Acquisitions • Unlevered NI = EBIT × (1. Using Market Multiple 10. Estimated takeover price of Target income) × (1 – Tax rate) Or .0ˆy0• %. FCF = NOPLAT + NCC – ∆ in Net WC – adj.) – current stock shareholder (in target Co. Div. Y=(Co. price of target Co.4m 9Ž.<• V•‰¸<3Ž. Y= Co.tax rate) 7. Residual Div. Y = Co. + (Expected 3. Consolidation = Co. = Zero.4m 9Ž.<••Š¹ 9 ‰<• ´•<••< R. Post merger P/E (if market is efficient) 15. Estimated takeover price of Target = 9.<•9 4¸Š9Š. over which X + Co. FCFE Coverage Ratio = †·†R 7. X + Co. Y) 11.<0y0•9’U. whichever is greater. X +Co. Z ↑ in earnings × Target payout ratio × 12.‰ 4m U.9•9] ¤<• ´•<••< 9Š43T ‰<y3• 4m ½3É¸y<•< cash equivalents = ¤49Š ´•<••< R¤S FCFE = CFO – FCInv + Net Borrowings 16. will take place Capex • Expected Div = Last div. Post-Merger EPS = 14. • VE–P: Mispricing . R) real EPS. Residual Income Model = NI – (cost of intrinsic value: k = (D1 / P0) + g P T = price paid for target company equity × Beg value Equity) V T = pre-merger value of target 8. Expected Alpha = Exp. Post-merger value of the combined 2. IRR: 18. Mispricing = VE – P = (V. R bonds) / (1+YTM of 20-yr TIPS)} – of shares outstanding of target co. V) where.e. cash paid = forecasted as) {(1+YTM of 20-yr T- cash price paid per share of target co.VE = estimated value P = market price 7. 3. the investor expects to after merger announcement Labor supply growth rate = population earn = RR + return from the convergence of price to value growth rate + increase in labor force Reading 27: Equity Valuation: Applications & • When an asset’s intrinsic value = participation rate Processes price. • Real GDP growth rate = labor P T = price paid for target co. × no. 1.rT = periodic required RoR. GGM Intrinsic value = D1/ (k-g) 19. Dividend yield or investment income = S – (P T – V T) (DH/P0) Macroeconomic Model Estimates (Supply side models): 20. 5. where. of new shares target receives growth rate • When an asset’s intrinsic value ≠ P AT = price per share of combined firm market price.P) + (VE – • E (RT) ≈ rT + {(V0 – P0) / P0} = 1+0 = 1. 2. Target Shareholders’ gain = Premium = P T V = intrinsic value • Intrinsic value= D1 / (k-g) –VT • If asset (fairly priced). In Stock offer = P T = (N × P AT) HPR) – (Contemporaneous Req. ratio. Acquirer’s gain = Synergies – Premium = 1. Price appreciation R = (PH-P0)/P0 company = V A* = V A + V T + S – C 10. 4.( C = cash paid to target SH i. (For efficient markets 1+EGPE 1. FinQuiz Formula Sheet Level II 2017 = (Estimated stock price of Target • V–P: True Mispricing • {(V0 – P0)/P0} = estimate of return based on Comparables) × (1 + • VE–V: Valuation Error from convergence over period Takeover premium in %) where. 6. Realized Alpha (Ex-post alpha) = (Actual • EGREPS = expected growth rate in 21. ERP = [{(1+EINFL) (1+EGREPS) where. R – Req. the investor expects to earn RR • EGPE = expected growth rate in P/E only. Expected HPR: productivity growth + labor supply N = No. Req ROE = Rf + ERP company Reading 28: Return Concepts 9. HPR = r = {(DH + PH) / P0} – 1 OR r = (1+EGPE)-1} +EINC]-Expected Rf R V A = pre-merger value of the acquirer {(P1 – P0+CF1) / P0 • where EINFL= expected inf. market price = where. % of sales (specific geographic region) = Sales of a particular region / Total sales of 11. Co. govt. Build-Up Approaches for Private Business 5. The Fama-French Model (FFM): ri =Rf + 20. Multifactor Models = r = Rf+ (RP)1 + (RP)2 + … + (RP)k 19. Beta Estimation for Thinly Traded Stocks timing risk × mkt. Finance costs = (Fixed i rate on debt × • Be’ ≈ [1+ (D’/E’)] ×Bu Valuation: ri = rf + ERP + Size premi Gross debt at beg. bonds small-cap portfolios – avg. 4. FinQuiz Formula Sheet Level II 2017 • EINC = expected income component • HML (high minus low) = Avg. COGS =Raw materials + Direct labor + 13. growth = Projected portfolio – RF R mkt. Pastor-Stambaugh Model (PSM): ri = Rf + a co. i rate on avg cash position =i income / Avg • RMRF = RM –Rf of developed market) – yield on cash position • SMB(small minus big) = Avg. reinvestment R) R on 2 low book-to-market portfolios. = yield on emerging mkt bonds (denominated in currency 9. large-cap portfolios. of period) – (i income +Specific Co.0) RP) + (sensitivity to business cycle risk × business cycle RP) + (sensitivity to mkt. premi rate × cash position at beg of period) 14. R on 3 10. Adjusted Beta = (2/3) (Unadjusted beta) + horizon RP) – (sensitivity to inf. portfolio var. 8. Net debt = Gross debt – Cash and cash 15. Forecasted variable costs = % of rev. R on 3 developed mkt. ERP estimate = ERP for a developed mkt equivalents Bimarket × RMRF + Bisize× SMB + Bivalue × + Country prem. Current expected Rf R + Bi (ERP) Bimarket×RMRF + Bisize× SMB + Bivalue × • where ERP = Expected R on mkt HML+ BiLiq× LIQ 2. Cost of Capital = WACC = {D/(D+E)}rd net debt (1-Tax rate) + {E / (D+E)}rE . timing RP) Overhead (in producing the goods) and Nonpublic Companies • Bu ≈ [1/ {1+ (D/E)}] ×Be 18. Bond yield Plus RP (BYPRP) cost of 6. i rate on avg. share × Projected sales of a given • Beta = Cov of returns with mkt R /mkt 17. 5-factor BIRR Model: ri = T-bill rate + product mkt.’s projected Rev. risk × inf. CAPM: Required Return on share i = 16. Or = 12. Unit volume × Unit variable costs (1/3) (1. Effective i rate = i exp / Avg gross debt HML • Country Prem. 21.’s LT debt + RP financial debt + Accrued interest RP)i. net debt = Net i exp / Avg. (sensitivity to confidence risk × confidence RP)–(sensitivity to time horizon × time 3. Country Spread Model 7. 1. Gross debt = LT financial debt + ST • RPi = (Factor sensitivity)i × (Factor equity = YTM on the co. R on 2 Reading 29: Industry & Company Analysis (includes dividend yield & high Book-to-market portfolios – avg. Rev. = Profit from continuing Add: Investment in associates ·4´‰.e. Projected inventory = Assumed COGS / 20. ROCE = Op. growth = [(1 + Add: annual sales (assuming all credit sales) × volume growth) (1 + % of price/mix dep. & amort. from cannibalization NI (profit after taxes) Adj. consumer & non-consumer) × = Owners of the co. due to cannibalization of (exp. loss for co. Add: Cash & cash equivalents Cannibalization factor for the category Add: Other current assets 21.g. Forecasted CF Statement loss (reported) tax amount – Cash tax cannibalization revenue – Estimated CF from operating activities: amount impact on rev. Deferred tax asset/liability = Profit and 18. of product shipments × = Net profit for the year Inventories % representation of each category Less: Non-controlling interests Add: Trade and other receivables (e. Projected A/C receivable = Forecasted 19.Š•ˆ 9Žy‰´•0Š9 4m ‰<4ˆ¸3Š operations Add: Other financial assets • No of units of a product cannibalized Add (Less): Profit (loss) from Add: Deferred tax assets by the new substitute product = discontinued operations = Total non-current assets Expected no. Add: Other income from operation CF from financing activities: debt and equity capital) = EBIT ↑ in notes payable Add (Less): Other operating income ↑ in LTD 16.5•. Exp. of units of product Less: Finance costs & other financial Net CF from financing activities cannibalized by the new substitute product exp. Forecasted ↑ in cash × Estimated ASP = Profit before tax Where. Overall organic rev. FinQuiz Formula Sheet Level II 2017 11. growth)] -1 ↓ in a/c receivable ↓ in inventory 13.S: ↑ in a/c payable Assumed Inventory TO ratio Sales Total adjustments Less: COGS Net CF from operating activities 14. Post cannibalization revenue =Pre. Post cannibalization shipments =Pre- Total assets = Total non-current + cannibalization shipments – Expected Total current assets cannibalization Share capital . Construction of Pro Forma I. Net CF from investing activities 15. =Total current assets 17.0P¹ 9 •9Šy´. EBITDA = EBIT + Dep. (Assumed DSO/ 365) contribution to rev. exp. 22. <•5. Less: Income Tax 23.) Less: Admin. Forecasted B.0P¹ 9 •9Šy´. to determine CF: 12. ???: ↓ in plant and equipment Less: Distrib.S • Average selling price (ASP) = Add: Income from associates PP&E ·4´‰. profit / Capital employed (i. ROIC= NOPLAT / Invested Capital = EBI = Gross profit CF from investing activities: / (Operating assets – Operating liab.Š•ˆ .) Less: Dividends paid demand = Projected no. exp. In RI Model: Value of stock = BVPS at t = + PVGO < LT financial debt 0 + PV of expected future residual where. Trailing P/E ratio = = = ì ›Ú R# (<+•) profit after tax future: Vu = Š\1 (1’<)Ú (1+¼)(1’•) Add: Dep. GGM can be used to derive required RoR or = = FCFF <+• <+• ›# (1’•) ›/ =r= +g= +g ¤# ¤# . Add: derivative financial instruments Selling Price at the end of year one = ›/ ¤/ PVGO/E1 = component of P/E value Add: Liabilities held for sale Vu = + (1’<)/ (1’<)/ that represents growth opportunities. Actual value of a company’s share = Vu = Plus: Non-controlling interest R/ = Equity 3. FCFF: + + ¤ ¤# R/ 1+¼ (1’<)/ (1’<)? (1’<)? 9. BV of growth rate – LT govt. GGM ERP = 1-yr. yield on Plus: Translation reserve market index + consensus LT earnings +/-: Profit or loss recorded in equity 2. RI = NI – (cost of equity × Beg. BVPS = common SHs’ equity / profitable opportunities of reinvesting charges no. bond yield = Equity attributable to shareholders common equity) 8. BV t = BVt-1 + R/ = Total non-current liabilities • When P0 = V0 then.e. 1/r = value of P/E for no- charges PV of expected Div. (<+•) ∆ in WC 5. owners 0 ·†Ú CFs i. Asset’s value is PV of its expected future to co. PVGO = Pu − < ST financial debt and accrued interest NIt – Divt È# ¤# ¤ • Can be restated as or or = Add: Trade and other payables R/ R/ R 4.e. DDM 1 ¤È£ß Add: Income tax payable + < R/ Add: ST provisions for liabilities and • With Single HP = Value of Stock = where. GGM for Preferred stock (fixed rate Less: Treasury shares › perpetual preferred stock) = Vu = < Add: Consolidated reserves+Net profit 1. FinQuiz Formula Sheet Level II 2017 Add: Share premium Reading 30: Discounted Dividend Valuation 6. Vu = Š\1 1’< Ú 7. Gordon Growth Model (GGM) = Vu = Less: Capital expenditures ›# × 1’• ›/ 11. forecasted div. Add: Deferred tax liabilities • RI model (assumes Clean Surplus E1/r = no-growth value per share Accounting holds) i. = Current liabilities • Value of stock for 2 years HP = Vu = ›/ ›? ¤? ›/ 24. Leading ratio = = = R R/ <+• <+• Normalized operating profit 0 ›Ú ¤- • For n-HPs = Vu = Š\1 1’< Ú + 1’< - Less: Taxes ›# (1’•) • When HP is extended into indefinite ¤# R# = Normalized operating 10. + PV of expected growth company. Add: Provision for employee benefits earnings • PVGO =Sum of PV of expected Add: LT provisions for liabilities and • where. & amort. of common shares outstanding the earnings. cash 1’< .» ½99•Š9 PPE 0 ›Ú È.» ½99•Š9 proceeds from sale of LT assets or ›# × 1’•& . growth rate Borrowing + issuance of preferred H = half-life in years of the high. gross <+•' SŽ.e. Constant-Growth FCFE valuation Model = ¿Ä S.(<+•' ) Reading 31: Free Cash Flow Valuation & cash equivalents – ∆ in Current liab.» ½99•Š9 Borrowing + issuance of preferred U4Š.<•Ž4»ˆ•<¹ 9 •É¸yŠP (1’<)- = ¿Ä × S. gross PPE – Beg. Computing FCFE from FCFF gL= normal LT div. ROE = = × SŽ.e. Estimating Sustainable Growth Rate = g = Firm Value = Vu = = À½··+• À½··+• preferred stock b × ROE ¿Ä+›y5yˆ•0ˆ9 ¿Ä S. Two-Stage Div Discount Model = Vu = U4Š. Finding FCFF and FCFE from EBIT or a) When no LT assets are sold during the EBITDA yr: • FCFF = EBIT (1 – Tax rate) + Dep – FCInv – WCInv . WACC = × rˆ × 1 − 8.<•Ž4»ˆ•<9¹ •É¸yŠP U4Š. H-Model • Vu = ›# × 1’•' › ×º× •& +•' + # or 1. b) When LT assets are sold during the yr: Š\1 (1’<)Ú + SŽ. gross 15.Proceeds from sale of LT • Vu = Š\1 + (1’<)Ú Turnover × Leverage assets ›# ×(1’•& ). (<+•' ) where. PV of FCFE = Equity value = Š\1 (1’<)Ú stocks – redemption of preferred stock growth period i. ST debt 13. PV of FCFF = Firm Value = <+•' <+•' ì †·††Ú 7.»•9 • FCFE = CFO – FCInv + Net • g= × × × 5. 6. growth rate after ÇÈ 4m ›’ÇÈ 4m R ÇÈ4m R • FCFE = FCFF – Int ×(1 – Tax rate) – year 2H Tax rate + × r• ÇÈ4m ›’ÇÈ4m R preferred stock dividends + Net gS= initial ST div. high growth period • FCFE = NI + NCC – FCInv – WCInv = 2H years 4.» ½99•Š9 12.» ½99•Š9 †·†R/ †·†R# ×(1’•) Equity Value = Vu = = stocks – redemption of preferred stock SŽ. ÇÈ 4m › 2.»•9 U4Š.»•9 U4Š. FinQuiz Formula Sheet Level II 2017 ¿Ä ¿Ä FCInv = End gross PPE – Beg.. – FCInv – WCInv 9. ì †·†RÚ 3.<•Ž4»ˆ•<9¹ •É¸yŠP 0 ›# (1’•& )Ú = Net profit margin × Asset PPE) . S. excl.<•Ž4»ˆ•<9¹ RÉ¸yŠP <+• <+• • Total value of Equity (common) = • g = PRAT i. Constant-Growth FCFF valuation Model = + Net Borrowing + issuance of †·††/ †·††# ×(1’•) preferred stocks – redemption of 14.1’•' U4Š.»•9 × FCInv = Capital expenditures – where.» ½99•Š9 • V0 = = FCInv = (End. Computing FCFF from NI = FCFF = NI + Total Firm value – Market value of • g = profit margin (P) × retention rate NCC + Int × (1 – Tax rate) + Preferred Debt – Preferred stock (R) × asset turnover (A) × financial leverage (T) stock div. CF from operating activities = CFO = NI + ›# × 1’•' ’ ›# ×º×(•& +•' ) Š\1 (1’À½··)Ú • Vu = NCC – WCInv.×(1’•' ) WCInv = ∆ in Current assets excl. y0 34´´40 9Š43T 13. E = earnings. PEG ratio = discount rate: Ç•ˆy. Justified Trailing P/E = P0/E0 = <+• FCFE = NI – (FCInv – Dep) – WCInv equation = Equity Value = 1+¼ ×(1’•) + (DR) ×(FCInv – Dep) + (DR) 0 †·†RÚ †·†R-Ü/ 1 = where + × <+• Š\1 (1’<)Ú (<+•) (1’<)- ×(WCInv) Or P = price.(1-DR) ×(FCInv – Dep) required rate of return. and g = dividend – (1 – DR) ×(WCInv) 17.<0y0•9 Ä03<•.» − g <•. Justified Forward P/E = P0/E1 = = (À½··+•) (1’À½··).» – Tax rate) – FCInv – WCInv] FCFF1 = 2.»•9 = 3. Two-stage FCFF valuation model equation ¿4.9• y0 9.•.» as a proportion of sales increases = 4.<0y0•9 FCFE1 À•ŽŠˆ ½5• 04.<T•Š ¤<y3• ‰•< 9Ž.0 »•5•» 4 m Ä0ˆ¸9Š<P 3.Industry Adjustment [in %] 8.9• y0 9.9• y0 À· U4Š.» ·¸<<•0Š Ç.9Ž SŠ43T¹ 9 ¤/R 7.4m 9Ž. Yardeni Model CEY = CBY – (b × LTEG) +/ .<• 11.» − g <•.» ½99•Š RO‰•3Š•ˆ R. .» •O‰+›•‰ •O‰ FCFEu ×(1 + g <•.<Š•<9¹ R¤S 10.‰yŠ.Leverage Adjustment [in %] where.<¹ 9 RO‰•3Š•ˆ R.» ) ·¸<<•0Š ÇTŠ ¤<y3• ‰•< 9Ž.<• Value of firm = Vu = ´49Š <•3•0Š ) *¸.» U4Š. Basic EPS = r<•. Forecasted FCFF = Forecasted [EBIT ×(1 WACC<•. D = dividends. Incremental fixed capital expenditures as a P/E = ¿•OŠ . Excess Cash = Total Cash Available − growth rate Total Assets of Firm× 14.Size Adjustment [in %] + Residual +/ . FinQuiz Formula Sheet Level II 2017 • FCFF = EBITDA (1 – Tax rate) + Dep Required rate of return (real) [in %] Reading 32: Market based Valuation: Price & (Tax rate) – FCInv – WCInv Enterprise Value Multiples • FCFE = FCFF – Int (1 – Tax rate) + 15. Forward P/E or Leading P/E or Prospective WACC<•. r = FCFE = NI .» R.»•9 16.3Š¸. Single-Stage FCFF and FCFE Model for Net borrowing + issuance of preferred International Valuation: 1.» − g <•. × 5.0 »•5•» 4m Ä0ˆ¸9Š<P U4Š. FCFE = NI – (FCInv – Dep) – WCInv + 0 †·††Ú • Firm Value = Š\1 (1’À½··)Ú + ò/ Net borrowing †·††-Ü/ 1 Ö/ 1+¼ where. <+• <+• Net borrowing = DR×(FCInv – Dep) + DR×(WCInv) Or ›# (1’•)/R# • Two-stage FCFE valuation model 6.» R.<0y0•9 £<4‡ŠŽ V.<•9 4/9 ‡Ž•0 Ž4»ˆ•<9 4m is: •O3•<3y9•ˆ ŠŽ•y< 4‰Šy409 Š4 4¼Š.Š• y0 % Country return (Real) [in %] +/ . Diluted EPS = Ä03<•.» ) Ä03<•.»»P 4/9 ˆ¸<y0• ŠŽ• ‰•<y4ˆ 12.<•9 . Incremental working capital expenditures = r<•. Modified Build-Up method to estimate real Ç•ˆy. Trailing P/E or Current P/E = stocks – redemption of preferred stock FCFFu ×(1 + g <•.4m 9Ž.<0y0•9 proportion of sales increases = Value of Stock = Vu ·.» − g <•. <• Common equity + MV of preferred stock + • = Or R. Terminal Value (T.<•9 4/9 • = Or ·.V in yr n = (Benchmark leading g = b × PM0 × × added back. ¤<y3• ‰•< 9Ž. the mkt 13.<• • BVPS for equity shareholders = ¤<y3• ‰•< 9Ž. ¤<y3• ‰•< 9Ž. ·¸<<•0Š ´TŠ. cash × (forecasted earnings in year n+1) where.0ˆy0• ·¸<<•0Š ´TŠ ¤<y3• ‰•< 9Ž. Justified P/B = P0/B0 = †4<•3. g = Retention rate (b) × ROE included elsewhere.V in year n = (justified leading P/E) ¤# &# 1+¼ (1’•) shares o/s × Price per share Justified P/S = = S# (<+•) • Cash & Investments = cash.<• ¤ 1 • By taking inverse: = 14.» ½99•Š9 SŽ.<•Ž4»ˆ•<9¹ RÉ¸yŠP ß‰•<.9Ž 3Ž.V in yr n = (justified trailing P/E) × (forecasted earnings in year n) 16.Šy0• ‰<4myŠ .<• ŠŽ.» »y.4m 34´´40 9Š43T 9Ž.<• 12. FinQuiz Formula Sheet Level II 2017 CEY = current earnings yield on the mkt. index i. Terminal Value based on Comparables: margin etc. Own Historical P/E: Justified price = 1+ ›u <+• Ãu Yield = = Benchmark value of own historical P/Es × ¤u 1’• Most recent EPS ¤<y3• ‰•< 9Ž.<• 19.Š .» •.<0y0•9 ‰»¸9 0403. Dividend Yield = = ¤ ¤<y3• ‰•< 9Ž. of Ö# • T. E0/S0 = Business’s profit equivalents.»•9 • T.Šy409 Sº¹ 9¹ •É¸yŠP – Š4Š.9Š•ˆ ›y5 ‰•< 9Ž.Š• LTEG = consensus 5-year earnings growth 0¸´¼•< 4m 9Ž. Earnings surprise UEt = EPS t – E (EPS t) ¤<y3• ‰•< 9Ž. EV = MV of Common equity + MV of ½00¸. • Leading Div Yield = VßR+• b = coefficient (measures weight.S 9Ž.+¼ × +UR£ 20.<• • = UEt= unexpected earnings for quarter t RÃÄU›½ .<0y0•9 9. • T. ROIC = where.» .y´9 24.O n+1) 22.» •É¸yŠP 5.<• 04.V in yr n = (Benchmark trailing *If minority interest exists and it is not P/E) × (forecasted earnings in year n) 17. Total Invested Capital = TIC = MV of Ã44T È. * It includes preferred stock and div.<• 45•< ŠŽ• 0•OŠ P< <+• gives to 5-year earnings projections). P/B = where 18.<• rate forecast for the mkt index. short term investments 11.<• 9•0y4< Š4 34´´40 9Š43T∗ • = Or # 4m ·.<•9 4/9 †·†R where. E/P.¼y»yŠy•9 ›y5yˆ•0ˆ V.»¸• 3».<• CBY = current Moody’s Investors Service • BVPS for whole company = • Trailing Div Yield = A-rated corporate bond yield.» ½99•Š9 P/E) × (forecasted earnings in year U4Š. P/S ( in terms of Gordon Growth Model = • MV of Common equity = No. Š4Š.» y05•9Š•ˆ ·. Price To Cash Flow 23.V) based on where Net Sales = Total Sales – preferred stock* + MV of debt – Cash & Fundamentals: returns– customer discounts Short-term Investments • T.99•Š9 – Š4Š. Justified P/B based on RI model = P0/B0 = R ·Ã.S = ¤<y3• ‰•< 9Ž.9Ž m»4‡ m<4´ ß‰•<.» ¤<y3• ‰•< SŽ.<• 10.<••9 MV of debt U½ – U+ – ¤.e. U4Š.»•9 ‰•< 9Ž.mŠ•< Š.» 0•Š 9. in arrears on preferred stock. PM0 = Profit Margin at t = 0 U4Š.<•9 4¸Š9Š. › ›y5 ‰•< 9Ž. Div Yield (by using GGM) = Justified Div ¤È 4m •O‰•3Š•ˆ m¸Š¸<• <•9yˆ¸.<• 15.‰yŠ.»¸• ‰•< SŽ. then it should be S. P/S = 21. 03• 4m .e. RI Model (general) = Vu = Bu + S. ω= (1’<)/ 1’<+2 1’< Ôk/ 2. • PV of continuing RI in year T–1 VÄ/ VÄÔ ii. Capital ì VßRÚ +< ×ÃÚk/ Š\1 1’< Ú 25. PV of expected future RI + = where. Justified = = = 1 + Ã Ã# <+• <+• where. MVA = MV of Co.»P9Š9- •.B t i.3•´•0Š 349Š 4m U4Š.(B t . Justified Price is the stock’s EPSt= reported/actual EPS for time t where. End. RI model • RIt = E t – (r × B t-1) = (ROE – r) × B t-1 10. BV of equity = Beg. Relative strength indicator Invested capital = net WC + net fixed V•‰».03• = assets = BV of LT debt + BV of equity ¤•<m4<´. – Accounting BV of ×Bu 27. Residual Income (RI) VÄ? VÄ/ persistence factor. Harmonic Mean = XH= . Multi-Stage RI Valuation = V0 = B0 + (PV 1.0ˆ RÉ¸yŠP 26. BV of equity + • Two components of intrinsic value of of interim high-growth RI) + (PV of Earnings – Div. capital) where.<0y0•9 S¸<‰<y9• • RI = (ROIC – Effective Capital 6. stock/equity continuing RI) B t = B t-1 + E t – Dt & D t = E t .9Š Charge) × Beg.<0y0•9 m4<•3. E (EPSŠ )] over some historical time period.<0y0•9 S¸<‰<y9• • RI (with preferred stock) = NI – ⋯ RO‰•3Š•ˆ R¤S Equity Charge – Preferred Stock Div • Scaled Earnings Surprise = R./ 6 * total capital = MV of Co – (BV of Debt + • Implied Growth rate in RI = g = r − BV of Equity) Ã# VßR+< È# +Ã# Reading 33: Residual Income Valuation 5. Single-Stage RI Valuation = Vu = Bu + VßR+< 0 4. FinQuiz Formula Sheet Level II 2017 EPSt= reported/actual EPS for quarter VÄÚ • =NOPAT – Total Capital Charge = • Vu = Bu + ì Š\1 1’< Ú = Bu + t NOPAT – Debt Charge – Equity RÚ +<ÃÚk/ ì E(EPSt) = expected EPS for the Charge = NOPAT – (AT cost of debt Š\1 (1’<)Ú quarter × Debt Capital) – (cost of equity × • Vu = Bu + VÄ/ + VÄ? + VÄ/ + (1’<)/ (1’<)? (1’<)/ • Percent Earning Surprise = Equity Capital) R. P0 = V0 E (EPSt) = expected EPS for the time t C% = cost of capital BV of equity = B0 = Total assets – σ [EPSŠ − E (EPSŠ )] = S.0. WACC × invested capital = dollar cost of capital 8. Tobin’s q = ÇÈ 4m ›•¼Š .D of [EPSŠ − TC = Total capital total liab. Intrinsic value i.› 4m . Standardized Unexpected Earnings = SUE R¤SÚ +R (R¤SÚ ) 3. Current BV of Equity that is B0.» ½99•Š9 SŠ43T¹ 9 ‰•<m4<´.(/) <+• *. [R¤SÚ +R (R¤SÚ )] Or = [EBIT (1 – t)] – (WACC × invested 7. 0 ≤ ω ≤ 1 + +⋯ • = NI – Equity Charge = NI – (Equity (1’<)? (1’<)/ • Assumptions about Continuing RI: Capital × Cost of Equity Capital) .0 RÉ¸yŠP Ä0ˆ•O 9. EVA = NOPAT – (C% × TC) t = ¤ ¤# VßR+• VßR+< .B t-1) = E t + B t-1 . T*. Forward rate model = [1 + r (T* + T)] (T* + T) 1 = [1 + r (T*)] T* × [1 + f (T*.Š–ŠŽ•–´40•P" ‰¸Š 4‰Šy40 • P* (T) = § §á ’á ¥ ≤1 DLOM = PV of continuing RI in year T-1= 5. Lack of Marketability Discount = become 0 eventually). 1-yr.»¸• 4m ". 0 ≤ ω È. F (T*. having maturity of À½··+•3 T > 1 • Value of Equity = Vf – MV of Debt . Forward pricing model: P (T* + T) = P P/B ratio) over 1-yr HP = (T*) × F (T*. Yield Curve Movement and the Forward = 1 1’<+u 1’< Ôk/ 1’< Ôk/ DLOC = 1 − Curve 1’·40Š<4» ¤<•´y¸´ o RI declines to 0 as ROE • F (T*. T*. T) = 6 (~Ü•∗ k~) = = (1 – DLOM in %)] § (¥∗) o RI declines to long-run mean 6 (~) level of mature industry. HPR = = 1 + ?(1) 1 1’— 1. Spot rate for a security. current 6.9• ‰<y3• 4m ¼40ˆ Reading 34: Private Company Valuation 3. Return of the 2-year zero-coupon bond 2.T) ¤<y3• 4m .1)]} (1/T) future indefinitely: -1 2. T) Reading 35: The Term Structure & Interest Where premium over book value is assumed at Rate Dynamics Active Bond Portfolio Management 1’ø ¥’1 •Ü/ the end of time horizon T (PT – Bt). ? VÄÔ = = 1’<+2 1’< Ôk/ VÄÔ VÄÔ 4. FinQuiz Formula Sheet Level II 2017 o RI is at +ve level currently and †·††/ r (T) = {[ 1 + r (1)] [1 + f (1.1)] [1 + f • To value Equity directly = V = <+• will persist at this level in the (2.1)] … [1 + f (T – 1. Excess Earnings or RI = Normalized PV of continuing RI in year T-1 VÄÔ VÄÔ VÄÔ earnings – [(RR on WC × value of WC) + = = = Forward rate model can be expressed as: 1’<+2 1’<+1 < (RR on fixed assets × value of fixed •∗ o RI will become 0 from the assets)] 1 + ? ?∗ + ? • 1 + ? ?∗ + ? terminal yr forward. Capitalized CF to the firm = Vm = 4. Discount Factor = P (T) = = 1’¬ú÷áøâáä • (when the spot curve one year from today B0 + ∑ (ROEt − r )Bt −1 + PT − BT T 1 is today’s forward curve) 1’ø (¥) • t =1 (1 + r )T (1 + r )T Where PT =BT × (forecasted 7. >+P< ³•<4+34¸‰40 ¼40ˆ 1 P< m<4´ Š4ˆ. T)] T †·††/ 1. 1 + ? ?∗ PV of continuing RI in year T-1 3.0P ›+ßÇ • F*(t. MVIC = MV of Debt + MV of Equity = 1 + ? ? ∗.e. T) = §∗ §∗ ¥∗ ¥∗ ’+¥+á á VÄÔ 6 (~Ü•∗ Ü•k~) 6.P − ¤¸<3Ž.»¸• 4m 9Š43T ¼•m4<• . Calculation of Lack of Control Discount = 5. T) = § §¥∗ ¥∗’¥ approaches r over time (& RI will 5. Total Discount = [1 – (1 – DLOC in %) × 6 (~) §∗ (¥∗ ’¥) 1’<+2 1’< Ôk/ • F*(t.1)] [1 + f (3. i.¥ • value (V0) = 1. TED spread = LIBOR . Value of putable bond = Value of straight bond + Value of investor put option 15.•) (1’¦9–øâáä—÷ø1:ø8÷[–1:ø—ø÷ûá÷–â:) maturity T at time t = σ (t. Market Conversion Price or Conversion 12. Value of a Convertible Security is § (á.T-bill rate of price of C. Swap Spread = Fixed-rate of an interest Reading 37: Valuation & Analysis: Bonds with 12. Value of floored floater = Value of straight (1’¦9–øâáä—÷øá9÷:ø8÷[–1:äâø—ø÷ûá÷–â:) Framework bond + Value of embedded floor §âø7âöùä÷—8÷[– Analysis of a Convertible Bond 1’— 1.¥) 5. FinQuiz Formula Sheet Level II 2017 • Price of a 2-yr zero-coupon bond 1 yr 9. ? 14. Interest rate volatility for a security with §âø7âöùä÷—8÷[– C ∆D (~. Conversion Ratio (CR) = No. Convexity = 18. Effective Duration = Price >× ∆·¸<5• × ¤ÈE . Duration = Ç.> 8. Cox–Ingersoll–Ross (CIR) Model = dr = a Parity Price = (b – r) dt + σ ??? Èk +ÈÜ 6.stock from exercising call option Govt. Straight Value or Investment Value = 10. The rate in the up state = Ru = Rd × e2σ ? (greater of conversion value or straight 1 + ? 1 1 + ? 1. T) = D (~. Rd = Rate in the down state value) ? 3.Overnight Market value of a security without indexed swap (OIS) rate 4.1 ] σ = Interest rate volatility t = Time in years between “time slices” 17. Conversion Value (or Parity) = Market 9. Effective Convexity = §Fk ’ §FÜ + >× §F# ∆Gùø7ä ? × §F# from today = 15.stock × CR matching maturity 3. Ho-Lee model = drt = θtdt + σdzt ¤Èk + ¤ÈÜ Market Conversion Price – Current Market 8. Value of issuer call option = Value of straight bond – Value of callable bond 14. Market Conversion Premium per share = >× È# × ∆.<T•Š ¤<y3• 4m ·405•<Šy¼»• S•3¸<yŠP >×È# × ∆. security ¥ ¬ (¥) + 1 1. Local expectations theory = = 16. Value of capped floater = Value of straight ∆á • Price of a 3-yr zero-coupon bond 1 yr bond – Value of embedded cap from today = Reading 36: The Arbitrage Free Valuation §âø7âöùä÷—8÷[– = 11. Min.1 1 + ? 2. Conversion Price (or stated conversion á\1 1’ø á Ú 1’ø ¥ • =1 bond – Value of issuer call option price) = Par value of convertible bond ÷ • ↓ ↓ ??????????????? CR ???????????? 2.1 … [1 + ? ? − 1. Value of investor put option = Value of conversion option putable bond – Value of straight bond 1 11.1 1+ where. Libor–OIS spread = Libor .•) 10. of shares of rate swap – Interest rate on “on-the-run” Embedded Options C. Value of callable bond = Value of straight 13. Vasicek Model = dr = a(b – r)dt + σdz ÈÜ ’Èk + >×È# 7. ·V 13. T) – D (t.’s asset R in CAPM (a static one-period 21.σ T − 1 4. Historical Estimation Expected recovery or = Loss given default • Probability of default over [t.T] = Prob = Straight value + Value of call option on stock – Value of call option on bond + At N (−d1 ) + Ke − r (T −1) N (d 2 ) ? ≤? =1− á IJ « Value of Put option on bond • where. FinQuiz Formula Sheet Level II 2017 19.54<. (Expected R per year on Mkt. Value of debt = D (t. Expected loss = Full amount owed – Where. Non-callable/Non-putable Convertible ln⎜⎜ t ⎟⎟ + r (T − t ) + σ 2 (T − t ) K 2 = Rf+ (β of co. (AT ≥ K) = P (t.<• K 2 • e1 = ⎝ ⎠ 3.<T•Š ¤<y3• 4m ·405•<Šy¼»• Ã40ˆ St = At N(d1 ) − ke−r(T −1) N(d2 ) –1 Co. Favorable Income Differential per share = ·4¸‰40 y0Š•<•9Š+ ·V ×·.’s debt if default occurs + PV of payoff model: 24. Premium over straight value = model): Ç. Value of Call Option – Value of Put defaulting á IJ « Option = PV (Forward price of bond on ¥+∆ ?á\u ?Z ∆ 1’K I# ∆ ’ 1’K I∆ … ? exercise date – Exercise price) 6.»¸• Where. portfolio – ⎛ A ⎞ 1 R f) 22. ? = « 23. Credit Risk Measures 1’K IJ ∆ • Probability of the debt defaulting = • Present value of the expected loss = K Reading 38: Credit Analysis Models Prob.’s debt if default does not occur = • Default probability over [0. Credit spread = Yield to maturity of a risky ⎛ A ⎞ 1 Ç. Premium Payback Period = 2.’s debt not • Expected loss = 25.¼»• Ä034´• ›ymm•<•0Šy.’s asset R = Rf + β of co. Callable & Putable Convertible bond value on co.‰•< 9Ž. 10. t+∆] = × Probability of default 1 Prob (t) = N −α − ∑ bi X i t 1+ e i =1 .<• bond – Yield to maturity of a Govt. bond ln⎜⎜ t ⎟⎟ + u (T − t ) + σ 2 (T − t ) †. Put option’s price = Value of risky debt – σ T −t 20. Black-Scholes Option pricing Formula = 7.y•ŽŠ È. Credit risk measures in reduced form co.T) 1 – N(e2) 1. N (d2) = Risk neutral ? 1’K I# ∆ ’ 1’K I∆ … 1’K I•k∆ ∆ probability of the co. Callable Convertible bond value = Straight d2 = d1 – σ T − 1 ? 1’ø/ ∆ 1’ø/Ü∆ … 1’ø•Ü∆ value + Value of call option on stock – Value of call option on bond 5.<• Value of riskless debt ·V • e2 = e1 .» ‰•< 9Ž. Price of debt? ?.’s asset × Mkt.<T•Š ·405•<9y40 ‰<•´y¸´ ‰•< 9Ž.9Š43T ›y5. Co.’s ERP) security value = Straight value + Value of d1 = ⎝ ⎠ Call option on stock σ T −1 8. (AT< K) = 1 – Prob. T) = PV of payoff on 9.’s asset SŠ<. % change in CDS price = ∆ in spread in 12.T)] XT Where. …. XT = Promised CF at T of a risky 8. T ) • Expected loss = Loss given default × spread in bps × D × NP i =1 Probability of default • Prob. Credit spread Pricing Conventions . Upfront premium = Credit spread – (Credit spread – Fixed coupon) × D of ⎝ 1 − dt ⎠ i =1 the CDS Standard rate dt = {1 if default. amount = Payout ratio × Notional amount of CDS in currency per 100 par • Price of CDS in currency per 100 par 11.Expected *Bond’s Credit spread = Yield on bond - bond – Average yields on riskless zero. Upfront pmt = PV of protection leg – PV securities + CDS holdings debt – PV of CF of risky debt = [P (t. Value of premium leg = PV of pmts. Credit spread ≈ Prob. N} are 3. made Credit spread = Expected % loss per year on the risky by the protection buyer to the protection where. Price of the coupon bond (assuming no 4. 0 if no default} • PV of credit spread = Upfront prem. of default × Loss Co. PV of expected loss = PV of CF of riskless 7. Rf + Funding spread = LIBOR zero-coupon bond + Liquidity Premium seller 13.) – Bond’s Or 5. given default (%) 9. of no default bps × D zero-coupon bond – Avg. FinQuiz Formula Sheet Level II 2017 • Parameters estimation: Reading 39: Credit Default Swaps • Upfront premium = PV of credit ⎛ dt ⎞ N spread – PV of fixed coupon Or = i ln⎜ ⎟ = α + ∑ bi X t Where 1. + • To estimate the loss given default: PV of fixed coupon 2. yields on risky T years) = 1 – Prob. Value of protection leg = Expected payoff credit spread* = [Average yields on the risky zero-coupon of bond/loan with credit risk . Profit for the buyer of protection ≈ ∆ in BG (t) = ∑ CP(t . i) + (C + F ) P(t. yields on riskless during T years zero-coupon bond 12. Expected Credit Loss (%) = Payout ratio = N 1 – Recovery rate (%) • Credit spread ≈ (Upfront prem. of default (at some point during 11. Loss Given Default: = 100 – Upfront premium % arbitrage and frictionless markets) • Expected loss = Full amount owed – T −1 Expected recovery 10. Synthetic CDO = Portfolio of default-free 13.T) – of premium leg D (t. Expected Credit Loss Amount or Payout • Upfront premium in % = 100 – Price constants./D) + t(Xt) = c 0 + ∑ ci X i t Fixed coupon i =1 Where {ci for i = 1. Basis = CDS spread (prem. Credit spread (t) = Avg. payoff of bond/loan with no credit risks Investor’s cost of funding coupon bond] + Liquidity premium Bond yield = Rf rate + Funding spread + or 6. Swap Pricing = j §F J.T (Park) 20.m)={[1+L0(h+m)th+m]/[1+L0(h) ¿U›RS•.t.m)−Lh(m)]tm}/[1+Dh(m)t 4.T} 13. (compounded continuously) Pricing & Valuing Swap Contracts: 15. for carry = L0(m)tm] .T[Ft(£/€. FV(S0) = S0(1 + r)T (compounded m] Floating Leg Cash Flow: annually) OPQRS•. 22.i=APFIX. Settlement amount at h for receive-fixed: Interest Rate Swap Contracts: NA{[FRA(0.i 16. Settlement amount at h for receive.T[B0(T+Y)+AI0]−AIT−FVCI0. NA{[Lh(m)−FRA(0.áZ (1)+PV0. Vt(T) = PVt. Interest Paid = TA – NA = NA[L0(m)tm] Pricing & Valuing of Forwards & Futures 1. ti conversion factor: 11. FV0.T(S0 + θ0 – γ0) Fixed Income Forward/Future Price including V=NA(FS0−FSt) [Z\1 PVt. Forward contract value (Long) VT(T) = ST Currency Forward & Fututre Contracts: FRAs – F0(T).T(S0) Fixed Income Forward & Future Contracts: [ 8. Vt (T)=PV£.T)] rcT m] 3. F0(T) = FV0. Forward Price (carry arbitrage): F0(T) = 25. F0(T) = FV0.irFIX.Š0(1) Periodic coupon amount 27. Future Value (adj.J 24. FinQuiz Formula Sheet Level II 2017 Reading 40: Pricing & Valuation of Forward QF0(T) = Commitments [1/CF(T)]{FV0.T[Ft(T)−F0(T)] Or AI = (NAD/NTD) × (C/n) 28. Value of fixed rate swap at time t = 10.T(1)/FV€.i=( OPQRTU. Si=CFFLT.h.h.T(S0+θ0−γ0) 18. Accrued interest = Accrual period × 1+¤Èu. FRA(0. FV adj.áZ.m)={[1+L0(h+m)th+m]/[1+L0(h) th]−1}/tm Value of Floating Rate Bond: 7.T(1) 2. PVt.i=( )rFLT. F0(T)=?u ? (<3’©-‐‑N)U (carry arbitrage: 19. FV(S0) = S0e .Š0. FRA Value at time g = Soe(rc−γ)T ¿U›RTU.h.T) =FV£. Value of fixed rate bond in currency k: continuous compounding) FBk=Ck [Z\1 ??u.~J (1)’ 9. F0(T)=QF0(T)CF(T) 29.w (1) + ??u.J FRA(0.tn(1) F0(T) =FV0.J 5.T]=B0(T+Y)+AI0−PVCI0. for carry cash flows) = 26. S0(£/€)FV£.i=APFLT.T(1)S0(€/£)]= 14. Terminal Amount = TA = NA[1 + 21./ #. Conversion factor adj.T[S0−PVCI0. FS=CFFIX.irFLT.T(1)/[FV€.m)]tm}/[1+Dh(m)t 23.T[Ft(T) – F0(T)] th]−1}/tm 6.J )rFIX 17. F0(£/€.T)−F0(£/€.h. Forward contract value (short)VT(T) = floating: F0(T) – ST.T] Interest Rate Forward & Future Contract: 12. FB=C Z\1 ??u. S+– – X) = Max(0. E(p2) = π2p++ + 2π(1 – π)p+– + (1 – π)2p– – Expected terminal option payoffs 31. nS = –N(–d1) < 0 for puts c+ For puts: 4. Up factor = u= 16. c+– = Max(0.0(rFIX.S – X) = Max(0. p– – = Max(0.â + 11. Two period Binomial Hedge Ratio h+= 7.8 + ? ) 25.X – S++) = Max(0.S++ – X) = Max(0. FinQuiz Formula Sheet Level II 2017 30. E(pT) = XN(–d2) – Se(r–γ)TN(–d1). c = Max(0. Call Value = cT = Max(0. c = PV[πc+ + (1 – π)c–] 22.d S – X) ¬ 29. E(c1) = πc+ + (1 – π)c BSM Model ??á. E(p1) = πp+ + (1 – π)p– 32. p+– = Max(0. Put Hedge ratio = ≥0 32.X – udS) c Ü +c k Carry Benefit-Adjusted BSM Model úÜ +úk 19. Call Hedge ratio h= ≥0 18.X – S+–) = Max(0. Replicating strategy cost = nSS + nBB 2.â )−StNAb. p = e–rTXN(–d2) – Se–γTN(–d1) c ÜÜ +c Ük 8. . c = Se–γTN(d1) – e–rTXN(d2) c Ü +c k 20. nB = N(–d2) > 0 for puts 5.~J. nS = N(d1) > 0 for calls One Period Binomial Model: c’ –– –– 2 3.b= §F#.á[.á[¹.ST – X) For calls: 14.X – u2S) Y Ü +Y k 31.0(rFIX. c = SN(d1) – e–rTXN(d2) 12. p = e–rTXN(–d2) – SN(–d1) NAE) 13.X – d2S) 6.áZ.b.X – ST) 15. Equilibrium Fixed Swap rate = where probability of an up move 23. E(c2) = π2c++ + 2π(1 – π)c+– + (1 – π)2c 1+§Fu.0 [- Z\1 ??á. p = PV[πp+ + (1 – π)p–] Expected terminal option payoffs: 36.áZ. c = PV[π2c++ + 2π(1 – π)c+– + (1 – π)2c– –] 34.u2S – X) 27.8(1) π = [FV(1) – d]/(u – d) rFIX. single-period call = c = hS + PV(–hS + c ) – – Y ÜÜ +Y Ük 33. p++ = Max(0.udS – X) 28. c++ = Max(0. Put Value pT = Max(0. single-period put= p = hS + PV(–hS– + p–) carry benefit-adjusted put–call parity: 21. Va=NAa.X – S– –) = Max(0.X (1) 24. E(cT) = Se(r–γ)TN(d1) – XN(d2) 10. p = PV[π2p++ + 2π(1 – π)p+– + (1 – π)2p– –] 35.a. nB = –N(d2) < 0 for calls ¬ 17. p + Se–γT = c + e–rTX 9.0 [- Z\1 ??á. Put Call Parity = S + p = PV(X) + c where Reading 41: Valuation of Contingent Claims Two Period Binomial Model: • d1 = ö[(c/I)’(ø’C>/>)¥ C ¥ • d2=d1− ? ? 1. Down factor = d= 30. Vt = FBt(C0) – (St/St–)NAE – PV(Par – 26. tm)N(d1)−RXN(d2)] Option Greeks & Implied Volatility Reading 43: Private Real Estate Investments 41. Rent of Net Lease = Gross rent – Op.T) = erTPAYSWN Reading 42: Derivative Strategies • E(RECSWN.T)] for calls 38. c = e–rT[F0(T)N(d1) – XN(d2)] Payer Swaption Model Value: 54.T) = erTRECSWN.Š• 42. above a certain Qäöáâ^ level × Tenant’s sales • d2=d1−σ ??-‐‑1 Change in option Price based on Delta Approximation: 3. Implied land value = Value after Swaptions construction – Cost to construct a building 50. ?−c ≅ Deltac(?−S) for calls PV of annuity matching Forward Swap 4. PVA= [\\1 ??u. Lease §÷øá—÷öZ÷–äöáâ C á\-‐‑1 =− Rent = % of sales rev. ?−p ≈ Deltap ( ? − ? ) + ( ?-‐‑? )> > rT [F0(T) – X] + p for puts where Price of Interest Rate call & Put options: • E(PAYSWN. p= (??)? -‐‑ø(á\-‐‑1’áû) 47.tj−1. PAYSWN = (AP)PVA[RFIXN(d1) – RXN(d2)] Gamma: • Gross potential income = Rental ä kaÔ income at full occupancy + Other Receiver swaption: 53.áû)/dI]’(C>/>)á\-‐‑1 49.Gemma Approximation: 37. C= ?? ? +ø á\+1’áû [FRA(0. RECSWN = PV[E(RECSWN. ?−p ≅ Deltap(?−S) for puts = ·.á\ (1) where. exp.‰yŠ.Šy40 <.tm)N(−d1)] 48.T)]. Optimal # of Hedging Units = NH • d1= • In case of natural break-point. rent + % of sales rev where. PAYSWN = PV[E(PAYSWN. [RXN(−d2)−FRA(0.á\-‐‑1. Lease Rent = Min. RECSWN = (AP)PVA[RXN(–d2) – RFIXN(– European Options on Futures d1)] Delta-plus. Gammac = Gammap = n(d1) SC ¥ income . above a certain level ö[[¦dP(u. ?=c+Deltac(?−S)  • NOI = Net operating income for the Payer Swaption: subject property 43. Appraised value of a property ¿ßÄ payment: 51. p = e–rT[XN(–d2) – F0(T)N(–d1)] Receiver swaption Model Value: bâûûâd 39. 52. 55.tj−1. ?−c ≈ Deltac ( ? − ? ) + bâûûâc ( ?-‐‑? )> > 45. 40. Call Deltac = e–δTN(d1) 1.»y³. Put Deltap = –e–δTN(–d1) 2. FinQuiz Formula Sheet Level II 2017 44. Futures option put–call parity: c = e– 46. < ¿ßÄ • Value of a property = {NOI of a (Replacement cost + Developer’s profit – 5. Post-renovation NOI of a property . Amount of locational obsolescence 8. no. When effective age of property < its collection losses – Insurance – value = Loss in income due to economic life.¼»• ‰<4‰•<ŠP in the value . FinQuiz Formula Sheet Level II 2017 • Effective gross income =Gross (Discount raVVVVVVVate – growth potential income – Vacancy and rate) 17.Repairs renovation / (1 + discount rate) worn out = Effective age / Economic life and maintenance exp. of months vacant 9. no. Capitalization rate = ¤<4‰•<ŠP 5. OR NOI of a property during renovation rent review • NOI = Gross potential income – time-period Estimated vacancy losses – Estimated • PV of the lost income è Loss in 18. Incurable depreciation deduction = †y<9Š+P•. of months vacant if not renewed S.¼»•9 renewed) deterioration + functional obsolescence + Locational V•0Š 15. Mkt. Discount rate = Cap rate + Growth rate property (1 + growth rate)] / (Discount rate – growth rate)]} / (1 + discount 20. Amount of functional obsolescence = 7. PV of expected incremental rent after the exp.mŠ•< 9.»• • Depreciated building value = 12. Capitalization rate = associated with building only = Total Loss ¿ßÄ × No. Cost Approach Calculations until the lease is renewed / (Lease term + 10. S. Avg. could be sold for at rent review (PV of value of the property = Depreciated renovation NOI of a property / estimated rental value or ERV) building value + Land value . value = ½V. Stabilized NOI i. of months vacant until the lease is renewed = Lease Non-renewal probability 21. (NOI of a non- (Replacement cost + Developer’s renovated property or post-renovated NOI 16. Reciprocal of the cap rate = ·¸<<•0Š ¿ßÄ 22. Under Layer Method Value of a property = collection loss • Loss in income due to renovation = PV of current contract rent in perpetuity + • NOI = Effective gross income – Op.<. All Risks Yield = ARY = • Total depreciation = Physical V•0Š Avg.»¸• curable depreciation costs) × Physical property during renovation time- period + [Post-renovation NOI of a deterioration 6.»•9 ‰<y3•9 4m 34´‰. • Value of a property = Post-renovation Value .e. of months vacant until the lease is V•3•0Š 9.»•9 ¤<y3• obsolescence RO‰•3Š•ˆ £. no.<. Value of property = NOI / (discount rate – Income loss due to the functional rate) Growth rate) obsolescence / cap rate 13. Vacancy rate = Avg. Gross income multiplier = GIM = obsolescence + Economic 11. Physical deterioration = % Property Taxes – Utilities .»• ‰<y3• 4m 34´‰.Ä 4m ‰<4•‰<ŠP y0 19Š P< . Total capital value = PV of income until profit) – Total depreciation of a property) the rent review + PV of what the property • Final Appraisal value èEstimated • Post-renovation Value = Post.Loss in value OR 19.Loss in land value ¤<y3• 14. CPT à I/Y èUnleveraged IRR. Appraised value = NOI / Cap rate 24.E Co. debt service based on DSCR / 2.debt service based on DSCR = 1. • Capital return = PV = – Initial investment R0ˆy0• ´ .»¸• Pro forma cash NOI + Expected • Total Index Return = Value-Weighted n = Holding period growth in NOI average return for individual FV = Cash flow received from sale • Estimated value of operating real properties CPTà I/Y è Leveraged IRR. FinQuiz Formula Sheet Level II 2017 • Principal payments=Part of the loan Reading 44: Publicly Traded Real Estate 23.<T•Š 5. costs of the mall (based on space leased) building / Cap rate or discount rate Max. payments on the mortgage. (but not deferred taxes) . for full impact of • Income return = Cap rate = NOI / acquisitions beginning value 27. Private market real estate debt NOI / Cap rate • Loan-to-value = Loan / value of the 28. NAVPS = (MV of R.’s liab. contractual • Amount of cash flows available each CF received by the equity investor from rent over the leases’ terms – Cash rent quarter = NOI – Capex the sale = Sale price – Mortgage balance actually paid. Valuation in an international context when payment that amortizes the loan over Securities land and building are valued separately: the loan term.‰•O’(R0ˆy0• ÇÈ+Ã••. estate =Estimated future expected cash 25.»¸• +·. The NCREIF Property Index (NPI): Cash flow / Equity • Total Return of individual Property = where.E Co. loan amount based on LTV ratio from the sale = Sale price + NOI in the 1st estate + BV of Cash & equivalents + = LTV ratio (in %) × Appraisal value year BV of Land held for future of property (in $) PV = – Initial investment development + BV of a/c receivables • Debt serve coverage ratio = NOI/Debt PMT = NOI in the 1st year + BV of Prepaid/other assets service n = Holding period • Net asset value = Estimated gross • Debt service=Interest + Principal FV = Sale price asset value – Total debt – Other liab.<T•Š 5.<T•Š 5. Cash flow = NOI – Debt 4. Estimating NAVPS: ¿ßÄ+·.) / # of shares outstanding approach) 26. Calculating Unleveraged IRR: • Estimated gross asset value = property Cash flow received by the equity investor Estimated value of operating real • Max.»¸•+Ã••y00y0• ´ . Equity dividend rate or Equity yield rate = 3. Calculating Leveraged IRR: • *Non-cash rent = Avg.loan amount based on DSCR= • Total value = PV for Building + Value Max. • Income to the building = NOI – • Max.‰•O • Estimated future expected cash NOI = PMT = Cash flow Ã••y00y0• ´ .ÇÈ) Service • Pro forma cash NOI = NOI – Non Ã••. Rent paid by Tenants = Net rent + assumed land lease payment NOI/DSCR Proportionate share of the common area • PV for building = Income to the • When the loan is interest-only.’s assets – MV of the land (from sales comparison Debt interest rate of R.ÇÈ Equity = Price – Mortgage cash rents* + Adj. Accounting for Risk in Venture Capital Venture Capital Method: . TVPI = DPI + RVPI Step 3: y = x [F / (1 – F)] Step 4: p1 = I / y 6.’s expected FFO in yr Step 5: PRE1 = POST1 –I1 carried interestt – distb. NAV after distbt = NAV before distb. CF for Net IRRt = – Capital called down at Reading 45: Private Equity Valuation Step 11: y2 = x2[F2/ (1 – F2)] the beg of periodt+1 + Op. resultt-1 yr N Step 9: p1 = I1/ y1 Step 10: x2 = x1 + y1 10. Estimated Value of a REIT Co. resultt-1– mgmt. ×x Recurring Maintenance type Capital –CC) in year when NAV before distb.e. / CC called down 12. NAV before distb. NPV Method with multiple (two) rounds expenditures – Leasing costs (i.t = NAV after distbt-1 + Step 2: POST2 = V / (1 + R2) called down capitalt– mgmt feest+ 7.’s expected AFFO in Step 8: y1 = x1[F1/ (1 – F1)] at the beg of periodt+1 + Op. CF for Gross IRRt= – Capital called down yr N) × REIT co. General Case: NPV Method outstanding down Step 1: POST = V / (1 + r) t • PIC Multiple = PIC / CC Step 2: PRE = POST – I 5.t N or Step 6: F2 = I2 / POST 2 = (P/AFFO of overall REIT group for Step 7: F1 = I1 / POST 1 9.E + Deferred tax charges – g/l from sales of property and debt 3. 7. Mgmt. P/FFO = Current stock prices / Yr-ahead Step 3: F = I / POST estimated FFO 2. on PIC) Step 5: p1 = I / y R. PIC: 14. • *Non-cash rent = Straight-line rent . RVPI = NAV after distb. Carried interest= % × (NAV before distb. / CC called down (or Step 4: y = x [F / (1 – F)] • FFO = Net earnings + Dep. • T1 and T2 = (1 + R1) Cash rent paid during the period • T2 and T3= = (1 + R2). DPI = Sum of distb. P/AFFO = Current stock prices / Yr-ahead 5. first > CC of financing: leasing agent’s commissions – Thereafter. FinQuiz Formula Sheet Level II 2017 • NAVPS = Net asset value / # of shares • PIC = Cumulative capital (CC) called 11. in yr N Step 3: PRE2 = POST2–I2 operating resultst = (P/FFO of overall REIT group for Step 4: POST1 = PRE2 / (1 + R1) 8. Exp. Alternative Method using IRR: restructuring + Losses on sales of (or PIC) Step 1: W = I (1 + r) t property and debt restructuring OR Step 2: F = W / V • FFO = EBITDA – Interest Expense 4.t– yr N) × REIT co.. Carried interest = % × ΔNAV Tenants’ improvement allowances) Step 1: Compound interest between dates: before distb. Is 13. fees = % fee × PIC Step 5: POST = I / F or p1 × (x + y) estimated AFFO Step 6: PRE = POST – I or PRE = p1 • AFFO = FFO – Non cash rent* – 6. Step 12: p2 = I2/ y2 feest– carried interestt 1. Delta = ?????? ? w + ???????? ????????? ∆ Z[ 7âöùä ÷— ù[–äøö:Z[g ∆ Z[ Qäöáâ 7. Vega = ∆ Z[ 7÷öâáZöZá: ÷— ù[–äøö:Z[g Models Vm +VÒ 10.Ù Ù Active specific risk .+ λk βp.)= C Derivatives: An Introduction i1 F1 + bi2 F2+ …. 2. Fixed Income Exposure Measure using 3. Information Ratio = = 9 Vm +VÒ Reading 50: Economics & Investment Markets 1. biK = 3. = Predicted Inf.2 + …. Carhart Four Factor Model = E (Rp) = RF+ 13. Theory of Storage states: Future Prices = Fâöùä ÷— w —÷ø â¬¬äá Z +P7äøägä 7âöùä ÷— w 5. scenario n × Reading 49: Measuring & Managing Market HML = high minus low expected E × expected P/E multiple) Risk WML = winners minus losers d+n Reading 46: Commodities & Commodity 4. Tracking Error TE = s(RP-RB) ∆ Z[ ÷úáZ÷[ 7âöùä Reading 48: An Introduction to Multifactor 8. Gemma = ∆ Z[ 7âöùä ÷— ù[–äøö:Z[g 9. FinQuiz Formula Sheet Level II 2017 [ • By adjusting Discount Rate = r = 3. Active R (decomposition)= 1 1 ∆: ? w ????????? ?????????? − ? Reading 47: The Portfolio Management > 1’: ? Process & the Investment Policy Statement ????ℎ???? ?????????? w × ∆ Z[ ÷úáZ÷[ 7âöùä 6. TV = (% prob.+ ℰ P Where 15.. Arbitrage Pricing Theory = E (R p) = RF + RÚ ·†qÚÜÙ ¿ λ1β p. Price Return = (Current Price – Previous ∆h ∆: Duration = = −? Price)/Previous Price h 1’: 7.k 12.Ù ’rÚ. To obtain a 5% VaR = ? d§ − 1.+ biKFK+ εi 2... scenario 1 × RMRF = Portfolio’s sensitivity to Mkt. scenario 2 × expected E × expected SMB = small minus big P/E multiple) + … + (% prob. ?}>J is ith asset’s residual risk expected E × expected P/E multiple) + (% Index prob. Multifactor Model = Ri = ai + b i1I1 + bi2I2+ …. Active risk squared = s2(RP-RB) 1.+ biK IK+ εi 11. (z-dist.65?§ (−1) Portfolio Value 1. Total Return = Price Return + Roll Return ∆h ∆: + Collateral Return Duration & Convexity = = −? + h 1’: 8.. Macroeconomic Factor Model = Ri =ai + b 1.1 + λ2β p. Present Value Model = 2. Std. + Surprise Inf. By adjusting terminal value using Scenario ?Zâ = ith asset’s active weight analysis = Adj. Active R = ?ú − ?h 5. Actual Inf. Active specific risk = Z\1 ?Zâ > ?}>J 1’ø – 1 βp1RMRF + + βp2SMB + + βp3HML ++ 1+e βp4WML…. Fixed Income Exposure Measure using 6. Normal Dist. Equity Exposure Measure = E(Ri) = RF + C (—÷ø 7âöùä¬ ÷— w ) Spot Price of the physical commodity + βi[E(RM) – RF] Direct Storage costs – Convenience Yiled 4. Active risk squared = Active factor risk + 9\1 1’»Ú.Ù ’s*Ú. ? 18. Expected Holding period return = ?á. ??§> = ??h> + ?? > ?? ∗ > RÚ ´Ú. ?\ Reading 52: Algorithmic Trading & High 6. ??§> = ??h> + ?? > 1 −1 16. Fundamental Law: E(RA) = 4. ∆?Z ?Z ) . Breadth BR = 1’(O+1)~ e~ §~Ü/./ + ???á ?á’1. Anticipated value added for Active portfolio = E(RA) = IC ???P O 2.9 = EŠ 1mŠ.Q d6 15. Information Ratio IR = = xd ∗ c. S. Active Security R as residual R in 4./ xd 7. Transfer Coefficient TC= 3.Q d6 off one unit of real consumption at time s = (TC)(IC) ???P PŠ.D(RA) = ×?.tk/ +§~.1 ?Z − w\\1 ?\. Sharpe Ratio SR = c.¬ = 9. Mean-var optimal security wghts for Frequency Trading e~ §~Ü/. One period Rf interest rate lŠ.t 10.¬ = 1’ö~.t active portfolio risk = ?Z ?P ∆?Z∗ = > 7. Relation b/w expected value and Cov. ?P = ?xG ??db 8.tk/ = ?á.9 d6 +du dv 5. ∆?Z∗ = CJ? xG hd O 1. Grinold Rule = ?Z = ???Z ?Z Reading 51: Analysis of Active Portfolio nJ Cv Management 11. Price of default-free bond certain to pay d6 +dR 14. ?(?P ) = ? • Single factor statistical model =?PZ = CT} P ?Z − ?h 5. Portfolio Return = ?§ = Z\1 ?§.9 = EŠ mŠ. FinQuiz Formula Sheet Level II 2017 2.1 = = ¤Ú. Pricing for real default free i rate =?áZ = ?Z O nJ ? J Z\1 C ? O G¦~Üt J ¬\1 t 1’ö~./ cdu 3. Alternate way to view the pricing relation O • Multi factor statistical model = ?PZ = 19.t uncorrelated active R subject to limit on §~. ?P = ?? ?h 1+¤Ú. ? ?h cdu Ex Ante Measurement of Skill Risk premium on risky assets: 17.Z . Benchmark Portfolio = ?h = Z\1 ?h. ?á.Z ?Z 13./ 6. = xG ?á ?? = ?á ? ?á ? + ??? ?.¬+1 .Z ?Z 12. Value added return = RP-RB Cor(?Z ?Z .Q d6 c.

CFA Level 2, June, 2017 - Formula Sheet

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