CFA Level 2: Formula Sheet (2024)

CFA® Program Level II FORMULA SHEET (2024) Version 1.0 Prepared by: Fabian Moa, CFA, FRM, CTP, FMVA, AFM, FSA Credential FOR REFERENCE ONLY (Note: Formula Sheet is not provided in the CFA exam) Follow us on: YouTube LinkedIn Facebook Instagram NOESIS EXED SDN BHD Block VO2, Level 5, Unit 8, Lingkaran SV, Sunway Velocity, 55100 Kuala Lumpur, Malaysia Website: www.noesis.edu.sg CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by Noesis Exed. CFA Institute, CFA® and Chartered Financial Analyst® are trademarks owned by CFA Institute. CFA Level 2 (2024) Formula Sheet – Noesis Exed CFA Level 2 – Formula Sheet (2024) Setting Up the Texas BA II Plus Financial Calculator Video: https://youtu.be/0MS8d8QOFmc QUANTITATIVE METHODS Learning Module 1 | Basics of Multiple Regression and Underlying Assumptions + + ⋯+ + " si − oe = ! = 1, 2, 3, … , s where: = dependent variable = independent variable = intercept , , … , = slope coefficients = error term = number of observations = number of independent variables , , , … , = regression coefficients + d + Ex e = Learning Module 2 | Evaluating Regression Model Fit and Interpreting Model Results N Coefficient of determination, # # = $%& $%& $%& $'% $'% $'% () + $%& $'% () #(* ()) $%& $'% () + , ,, () #(* ()) () - , $$+ = , ! " $$# = $$- = ! " − ! " = $$# $$= 1− $$+ $$+ ./ − 0 . − /0 $$- ⁄ − − 1 −1 123%) (2 # , # = 1 − 4 6=1−7 8 1−# $$+⁄ − 1 − −1 2 CFA Level 2 (2024) Formula Sheet – Noesis Exed Akaike’s information criterion (AIC) $%& 19: = ln 7 )'% () ( where: = Sample size = Number of independent variables in the model 8+2 +1 Schwarz’s Bayesian information criterion (BIC of SBC) $%& ln 7 =9: = )'% () ( 8 + ln +1 F-distributed test statistic for jointly omitted variables $%& )'% () ( $%& () ? (2 & 2(, − $%& )'% () % () )'% () % () ? (2 & 2(,⁄ − − 1 d >= ? (2 ⁄' Ex e where: ' = Number of restrictions (i.e., number of variables omitted in the restricted model compared to the unrestricted model) si s @ : B = BC = ⋯ = BCDE = 0 @G : At least one of the ' slopes ≠ 0 oe F-test for joint test of slope coefficients ANOVA − N Regression df Residual Total >) ) ?= SS $$# ⁄ $$# − 1 $$- $$- ⁄ −1 $$+ J( $'% ( #(* ()) J( $'% ( - @: = =⋯= =0 @G : At least one K ≠ 0 MS = − −1 $$# ⁄ $$- ⁄ − − 1 3 I $$# ⁄ $$- ⁄ − − 1 CFA Level 2 (2024) Formula Sheet – Noesis Exed t-test statistic for slope coefficient where: /K = Regression estimate of K =K = Hypothesized value of coefficient 3 )L/M = Estimated standard error of /K = /K − =K )L/M Video (Simple Linear Regression): https://youtu.be/uR_9im2JP18 Learning Module 3 | Model Misspecification +() $ Breusch-Pagan Test ) ?, χOP, = # Ex e Variance Inflation Factor (VIF) 1 1 − #K explained by the other − 1 independent variables s K 9>K = si where: #K = Variation in d where: # = #-squared between squared residuals and independent variables oe Learning Module 4 | Extensions of Multiple Regression Detecting Influential Points Sum of individual leverages for all observations = N If observation’s leverage > 3 R C ! S ⇒ Potentially influential observation Studentized Deleted Residual, UV∗ ∗ +1 (∗ ( = = )X ∗ YJ$- 1 − ℎ [ − −1 $$- 1 − ℎ − ( where: ( ∗ = The residual with the th observation deleted )X ∗ = The standard deviation of the residuals = The number of independent variables J$- = Mean squared error of the regression model that deletes the th observation ℎ = The leverage value for the th observation 4 CFA Level 2 (2024) Formula Sheet – Noesis Exed Cook’s Distance ( ℎ ] + 1 J$- 1 − ℎ \ = ^ where: ( = Residual for observation = The number of independent variables J$- = Mean square error of the estimated regression model ℎ = The leverage value for the th observation If \ > _ ` , then th observation is highly likely to be an influential data point Logistic Regression (Logit) 1 + expe− + 1 + + + ⋯+ + +⋯+ + f 2% () Ex e a= + d a ln 7 8= 1−a a ln 7 8 = g * 22) 1−a = ( Li Likelihood ratio (LR) test 2 () ? (2 & 2(, − g * , (, ℎ N oe g# = −2 g * , (, ℎ si s h22) Learning Module 5 | Time-Series Analysis Linear Trend Models j = = time (independent variable) Log-Linear Trend Models Growth rate of = ( Ll − 1 j + + = ( LkCLlj ln j = 1,2, … , + j = + 5 = 1,2, … , + ? (2 & 2(, CFA Level 2 (2024) Formula Sheet – Noesis Exed p-th order autoregressive model, mn o pj = + pjE + pjE + ⋯ + q pjEq + j Test statistic for autocorrelation of residuals where: : u st, = #() 2% , % ? (, $ 2 2( j , jE vt = jw 2( −0 % ? #() 2% , % ? 1⁄√+ (, pj = Root Mean Squared Error #J$- = [ ℎ( () 2% , 1− $'% (2 ( + * pjE + si s Dickey and Fuller Unit-Root Test pj − pjE = oe where: * = −1 N ARCH(1): (, Ex e Mean reverting level for AR(1) model = d = vxjC = + j ŷj Learning Module 6 | Machine Learning Neural Networks {(| ( | |( *ℎ = h,2 |( *ℎ − g( * 6 (×~ a , 2( u u( ℎ( ,( | ℎ ()•(? € ℎ( ,2 |( *ℎ CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 7 | Big Data Projects Normalization of variable X !•‚BGƒ „X… − B! BG† − B ! = Standardization of variable X = ‡jG!…G‚… „X… + %( a ) u( + %( a ) u( + > ,)( {(* ?‰ = >1 $? (= > ,)( a ) + %( a ) u( + %( a ) u( + + %( {(* u( + > ,)( a ) u( + + %( {(* 2 × a (? ) × #(? ,, a (? ) + #(? ,, u( # (, >a# = > ,)( a ) u( + %( {(* u( + > ,)( a ) + %( a ) u( + %( a ) u( + > ,)( {(* u( # (, +a# = \ ?%&( > ('%( ?‰, \> = N oe + %( a ) 9 u( )( \ ?%&( $( ( ?( : % + , {%& ( > ('%( ?‰, 9\> = log 7 +>-9\> = +> × 9\> u( u( + > ,)( {(* d 1??% u( s #(? ,,, # = + %( a ) u( + %( a ) u( + > ,)( a ) Ex e ,a = si a (? ) −ˆ v | ℎŠ 2 $( ( ?() 1 8 \> 7 u( u( u( CFA Level 2 (2024) Formula Sheet – Noesis Exed ECONOMICS Learning Module 1 | Currency Exchange Rates: Understanding Equilibrium Value Cross Rates When given Ž and O, then O = Ž × O • Ž • • When given Ž and Ž , then O = Ž × • O • • Ž • R•S Bid Bid/Ask p ‰ ⁄ 1 ‰ 1⁄p Currency pair A/B B/A Ex e d Video: https://youtu.be/wyDKKPkPhzw Arbitrage Opportunities Between Dealers and Interbank Video: https://youtu.be/Lqo9UZ3yyEA si >‘⁄… 1? % , R 360 S = $‘⁄… ’ ” 1? % , 1+ …R S 360 1+ >‘⁄… − $‘⁄… ‘− = $‘⁄… 1+ oe N ‘ s Covered Interest Rate Parity 1? % , R 360 S 1? % , … R 360 S … Video: https://youtu.be/9jOzFA9GuHU Mark-to-Market Value of a Forward Contract Original position: Long base currency d forward at forward rate > ,%( g *> | 2= .>j,‘⁄… − > ,‘⁄… 0 × : #(& * 2 ‰) 1+ ‘7 360 >j,‘⁄… = Forward rate at valuation date, t (Bid side) Video: https://youtu.be/wLqyZRrutAc 8 ,‘⁄… (Offer side) ? $ •( & % ‰ 8 CFA Level 2 (2024) Formula Sheet – Noesis Exed Uncovered Interest Rate Parity - $‘⁄… %Δ$‘X⁄… 1? % , R 360 S = $‘⁄… ’ ” 1? % , 1 + … R 360 S 1+ ‘ 1? % , R 360 S = ≈ 1? % , 1 + … R 360 S ‘ − … ‘ − … 7 1? % , 8 360 Video (Carry Trade): https://youtu.be/_26fG3Zvzyg $‘⁄… = %Δ$‘⁄… 1? % , ™‘ − ™… R 360 S 1? % , = ≈ ™‘ − ™… 7 8 1? % , 360 1 + ™… R S 360 Ex ante PPP Ex e Relative PPP a‘ a… d Absolute PPP oe International Fisher Effect si s %Δ$‘X⁄… ≈ ™‘X − ™…X 7 − … = ™‘X − ™…X N where: ™ X = Expected inflation rate ™ = Actual inflation rate ‘ 1? % , 8 360 Mundell-Fleming Model Bonus Video: https://youtu.be/xNo3GpWYgKA 9 CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 2 | Economic Growth and the Investment Decision a a = š\a × 7 8×7 8 š\a Return on aggregate equity market %∆a = %∆š\a + %∆ 7 where: a = aggregate value of equities - = aggregate earnings a 8 + %∆ 7 8 š\a - Cobb-Douglas Production Function = +œ • g E• s œ • = +7 8 g g si Ÿ ¡¢ ¡ ¢£¤ ¥¦¤§£¤ = Ex e d where a < 1 where: Y = Output ž = Share of output allocated to capital (œ) 1 − ž = share of output allocated to labor (g) + = total factor productivity (+>a), represents technological progress of the economy oe Marginal product of capital, MPK Jaœ = ž 7 8 œ N Amount of output that is allocated to providers of capital, a œ ž= Growth Accounting equation: ∆ = ∆+ ∆œ ∆g +ž + 1−ž + œ g Growth rate in potential GDP = Long-term growth rate + Long-term growth rate of labor force in labor productivity g ?( • ?• = Š g ?( * *( • •%, 10 CFA Level 2 (2024) Formula Sheet – Noesis Exed Sustainable growth rate of output per capita ¨ *∗ = 1−ž Sustainable growth rate of output (Steady state growth rate) ¨ š∗ = + 1−ž Ex e d Equilibrium output-to-capital ratio (in steady state): 1 ¨ = ] + + ©^ œ ) 1−ž where: ¨ = growth rate of TFP ž = elasticity of output with respect to capital ) = fraction of income (Y) that is saved © = rate of depreciation of physical capital stock = labor supply growth = %∆g Endogeneous Growth Model ‰X = ? X s Production function: N oe si Growth rate of output per capita: Δ‰X Δ = = )? − © − ‰X X where: ‰X = output per worker X = capital per worker ? = marginal product of capital in the aggregate economy (constant) 11 CFA Level 2 (2024) Formula Sheet – Noesis Exed FINANCIAL STATEMENT ANALYSIS Learning Module 1 | Intercorporate Investments Investments in Associates (Equity Method) - 2 * u() &( )) ? () = =(* * $ℎ + u() &( ( )) ? () $ℎ ( 1& • (p?()) ( − 2 u 2( 2 − •% ?ℎ )( • ?( ? &( (?( u(2 Impact on Investor’s Income Statement 1& • (p?()) $ℎ ( ª ( , •(2 • & $ℎ ( = − − •% ?ℎ )( • ?( 2 | ) ( & %•) ( & ) ,( ( ? &( Ex e d Business Combinations (Acquisition Method) Excess purchase price = Acquisition price – %Ownership × Book value of net identifiable assets Partial Goodwill = Acquisition price – (%Ownership × Fair value of identifiable net assets) = Acquisition price – (%Ownership × Book value of identifiable net assets) – (%Ownership × Excess purchase price attributable to identifiable net assets) ,, * ( () = %{:9 × > u ,%( s ? si { 2( ? ,, * ( () = %{:9 × > u ,%( N { oe Full Goodwill = Fair value of entity – Fair value of net identifiable assets ( ‰ Video: https://youtu.be/RgxmPbx4-0o IFRS 9&• &( , )) = : ‰ * u ,%( ? )ℎ *( ( *% US GAAP 9&•, (2 > u ,%( = (• *% * 2| ,, 9&• &( , )) = : − > − #(? u( ,( & % ? )ℎ *( ( *% u ,%( 2( ‰ * u ,%( 9&•, (2 − * 2| ,, * 2| ,, 12 (• ,( ( * % ′) ))( ) ,( ( ))( ) CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 2 | Employee Compensation - Post-Employment and Share-Based Share-Based Compensation Accounting : &•( ) (p•( )( = > u ,%( | 2 () * •( * 2 2 ( Treasury Stock Method a ?((2) & u( ) (p( ? )( = )? $ℎ () ))%(2 & \ ,% (2 )ℎ ( )(2 | 2) )ℎ () )ℎ () (p( ? )( − = + ? u( ) 1u( *( )ℎ ( • ?( %) 2 * %) 2 * )ℎ ( )(2 | 2) ℎ( (• * •( 2 1u( *( % (? * •(2 )ℎ (- )(2 ? &•( ) (p•( )( Ex e 1))%&(2 : )ℎ • ?((2) = + • ?((2) & (p( ? )( d ¬? Forecasting Shares Outstanding With Share-Based Awards = ) ? )ℎ () = ) ? )ℎ () %) 2 *, = %) 2 *, ( 2 •( 2 (* * •( si s 2 + #$ª) u() (2 + $ℎ () ))%(2 & $ℎ ( )(? 2 (), − (•% ?ℎ )() ?'% ) ), ( ?. oe + $ℎ ( • ) (p( ? )(2 >% 2(2 ) - 2 * •, N Financial Reporting for Defined Benefit Pension Plans %) = > u ,%( u ,%( =(* = ))( ) - 2 * •( ) ,* = 9 ( () ? ) = =(* =(* IFRS Only =(* {( ( () =7 ? ) ⁄ ? &( •, * •, ))( ) − a( ) u ,%( +: ))( ) * •( ) ,* * •( ) ,* * •( ) ,* + × − % ,* )+ =( ( ) 1? % , ( % − •, ))( ) • 2 1? % $( u ?( 9 ( () + + , ))⁄ * ? )) ? ) (,2 =(* u() &( * • ( 2 ? •, 13 * , 2( u ,%( (,2 8× * 2( ? ))( ) − =( ( ) • 2 • u() &( ( 2 CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 3 | Multinational Operations Net assets = Total assets – Total liabilities Net monetary assets = Monetary assets – Monetary liabilities Current Rate Method Currency translation adjustment = Total assets of foreign subsidiary in parent currency terms − Total liabilities of foreign subsidiary in parent currency terms − Shareholder capital of foreign subsidiary in parent currency terms − Other equity items of foreign subsidiary in parent currency terms (&( ? ‰ ))( ) & , , () - 2 - 2 •( •( () = (&) = oe , + ( 1 : && -'% ‰ 122 , = + : • , + ( 1: • , + ( 1: • , , #(*%, : • , N + ‰ = + ,+ ( 1 + ,+ ( 2 + : • , : • , : && -'% ‰ + ( 1 : • : && -'% ‰ = + ( 1# # ) Š( *ℎ (2 1))( ) + ,+ ( 1: • , +( 1 = ≥ 6.0% # # ) Š( *ℎ (2 1))( ) + ,: • # , = + 2(p 2(p - 2 •( 2 • ?( 2(p 1u( *( • ?( 2(p ℎ( •( Learning Module 4 | Analysis of Financial Institutions + 2 • ?( 2 • ?( - 2 •( 2 • ?( 2(p =(* * •( 2 • ?( 2(p si #() (&( ? ? &( ) (&( , = Ex e #() & ( (&( ? ‰ ))( ) & , s #() & ( IFRS d Hyperinflationary Environment , , #(*%, ‰: • , ≥ 8.0% # ) Š( *ℎ (2 1))( ) 14 ≥ 4.5% 2 CFA Level 2 (2024) Formula Sheet – Noesis Exed g '% 2 ‰ : u( *( @ *ℎ ´% , ‰ g '% 2 1))( ) = # , g:# -p•(? (2 ? )ℎ % , |) {%& ( | ℎ) 2 2 ‰) ℎ ? ) ()) ,(u(, u ,%&( = g:# × 30 ? )ℎ % , |) Number of days that bank can withstand a stress level volume of cash outflows for (g:# × 30 days. ,( >% 2 * 1u , ,( $ = , {$># #('% (2 $ {( $ # ,( >% 2 * ,( >% 2 * Property and Casualty Companies ª 2( | (p•( )( : & (2 * = = = g )) (p•( )( + g )) 23%) &( (p•( )( {( • (& %&) ( (2 ª 2( | * (p•( )( {( • (& %&) | ( g )) 2 , )) 23%) &( (p•( )( d 2 , )) 23%) &( (p•( )( Ex e g )) + ª 2( | (p•( )( * (2 \ u 2( 2) • , ?‰ℎ ,2( ) )ℎ (ℎ ,2( ) N oe : & (2 : & = µ¶U·¸ ¹VºV¹·»¹¼ si s \ u 2( 2) • , ?‰ℎ ,2( ) \ u 2( 2) • , ?‰ℎ ,2( ) )ℎ (ℎ ,2( ) = )ℎ (ℎ ,2( ) {( • (& %&) ( (2 + Learning Module 5 | Evaluating Quality of Financial Reports Beneish Model J-)? ( = – 4.84 + 0.920 \$# + 0.528 šJ9 + 0.404 1´9 + 0.892 $š9 + 0.115 \-a9 – 0.172 $š19 + 4.670 1?? % ,) – 0.327 g- 9 where: DSR day sales receivable index = #(?( u ,()j ⁄$ ,()j #(?( u ,()jE ⁄$ ,()jE šJjE šJj e1 − aa-j + :1j /+1j f AQI asset quality index = e1 − aa-jE + :1jE /+1jE f $ ,()j SGI sales growth index = $ ,()jE GMI gross margin index = 15 CFA Level 2 (2024) Formula Sheet – Noesis Exed DEPI depreciation index = \(• (? \(• (? jE j $š1j /$ ,()j $š1jE /$ ,()jE ‰ (&) − : )ℎ & •( ) , ))( ) SGAI sales, general, and administrative expenses index = Accruals = 9 ? &( ( ( (p 2 g(u( *(j LEVI leverage index = g(u( *(jE + Earnings Persistence - - *)jC = ž + Ü - *)j + *)jC = ž + Ü : )ℎ , |j + Ü 1?? % ,)j + N oe si s Ex e d Cash-flow-based accruals = NI – (CFO + CFI) 16 CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 6 | Integration of Financial Statement Analysis Techniques {( h•( * h•( * * h•( = − 1))( ) {h1 1))( ) g , () + , : )ℎ 2 + , + , =R − − S−R S 1))( ) $ℎ - ( & 9 u() &( ) g , () \( = , ?(-)ℎ(( ?? % ,) : )ℎ- , |?? % ,) )(2 )(2 = = {h1j − {h1jE {h1j + {h1jE ⁄2 {9j − :>hj + :>9j {h1j + {h1jE ⁄2 Learning Module 7 | Financial Statement Modeling d Growth Relative to GDP Growth approach Ex e If company’s revenue is forecast to grow at K bps above the nominal GDP growth rate (*%), then company’s revenue growth rate = *% + Ý % If company’s revenue is forecast to grow @% faster than the nominal GDP growth rate si s (*%), then company’s revenue growth rate = *% × R1 + Þ S Market Growth and Market Share approach (? ) (u( %( = J oe > N Return on Invested Capital ROIC = ( )ℎ ( % × 9 2%) ‰ (u( %( {hag1+ 9 u() (2 : • where: {hag1+ = Net operating profit less adjusted taxes 9 u() (2 : • , = h•( * ))( ) − h•( *, 17 , , () CFA Level 2 (2024) Formula Sheet – Noesis Exed CORPORATE ISSUERS Learning Module 1 | Analysis of Dividends and Share Repurchases Dividend Payout Policies Target payout adjustment model (Lintner model) -p•(? (2 + -p•(? (2 g ) = +7 × *) 2 u 2( 2 2 u 2( 2 123%) &( ? = {%& ( ‰( 1 23%) &( ) EPS and BVPS After Share Repurchase ? = - *) ( ( %‰ $ℎ () % ) s %‰ si ( oe -a$ × 123%) &( g ) 8× ? 2 u 2( 2 ( •, ?( :% ( ( *) Ex e Constant dividend payout ratio policy \ u 2( 2 \ u 2( 2 = • ‰ % Video: https://youtu.be/hhcvNiTpZX4 − d where: *( • ‰ % ? −1 ( 2 * ( p? ) %‰ ? % 2) Video: https://youtu.be/Pd0-QQF-VhQ ( %‰ = ? = ,%( ( ( %‰ ? − $ℎ () % ) 2 * N = a$ Analysis of Dividend Safety \ u 2( 2 • ‰ % \ u 2( 2 ? u( >:>- ? u( *( *( = = \ u 2( 2) {( 9 ? &( = {( 9 ? &( \ u 2( 2) >:>\ u 2( 2) + $ℎ ( (•% ?ℎ )() 18 ,%( )ℎ ( %‰ ( %‰ ? ? CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 3 | Cost of Capital: Advanced Topics Weighted average cost of capital Š1:: = |… 1− … + |q q + |X X where: |… = Weight of debt in capital structure |q = Weight of preferred equity in capital structure |X = Weight of common equity in capital structure … = Pre-tax cost of debt q = Cost of preferred equity X = Cost of common equity Cost of equity, = X = ‘ + : (2 )• ( 2 ‘ + -#a + 9#a d … Ex e Cost of debt, =( ?ℎ& (% 9#a = Idiosyncratic risk premium where: -#a = Equity risk premium = 2(p a ()( ,%( a ()( ,%( + #() 2% , ,%( g( )( a ‰&( ) g()) oe si s Leases = − #) ( (( > ,%( g()) + 9 g( )(2 1))( Equity Risk Premium *( ( ?ℎ& 2(p ( % Gordon Growth model -#a = N Historical Approach (Ex-Post) 1u( -#a = \ − +*− 19 1u( ‘ *( ) (( ( ) \ (? ,: ) ) á CFA Level 2 (2024) Formula Sheet – Noesis Exed Grinold-Kroner Model -#a = e\ + Δ a⁄- + + * + Δ$f − where: \ = Dividend yield of market index Δ a⁄- = Expected growth rate in P/E = Expected inflation = Câãäåæçèéêæë ìíîï Câãäåðñò ‘ −1 * = Expected growth rate in real earnings per share Δ$ = Expected change in shares outstanding Cost of Equity Two-Stage DDM a = ! " = \ +* a d X Ex e Gordon Growth Model \j 1+ X j + a! 1+ X ! si s Bond Yield Plus Risk Premium Approach (BYPRP) X = … + # ) • (& %& oe Capital Asset Pricing Model (CAPM) X = ‘ + Ü × -#a N Fama-French model Three-factor model Five-factor model X = X ‘ = ‘ + Ü -#a + Ü $J= + Üó @Jg + Ü -#a + Ü $J= + Üó @Jg + Üô #JŠ + Üõ :J1 where: $J= = Size premium @Jg = Value premium #JŠ = Profitability premium :J1 = Investment premium 20 CFA Level 2 (2024) Formula Sheet – Noesis Exed Expanded CAPM X = + ÜqXX‚ -#a + $a + 9a + $:#a ‘ where: $a = Size premium (for smaller, privately held companies) 9a = Industry risk premium $:#a = Company-specific risk premium Build-Up Approach X = ‘ -#a 2(u(, •(2 & + -#a + $a + $:#a Country Spread Model -#a = ( +ö×: % ‰ ) • (& %& Ex e d where: ö = Level of exposure of the company in the local country : % ‰ ) • (& %& = $ u( ( * ‰ (,2 )• ( 2 (,2 (&( * * & ( 2) 2( & (2 ℎ( ?% ( ?‰ − ℎ( 2(u(, •(2 & ( Aswath Damodaran’s CRP ) • (& %& = $ u( ( * ‰ (,2 )• ( 2 × si ‰ oe : % (,2 2(u(, •(2 & ( * u( &( 2) s $ u( ( * ‰ (,2 = )• ( 2 N where: v÷Dø jù = Volatility of the local country’s equity market vO•!… = Volatility of the local country’s bond market International CAPM - X = ‘ + Üú û-. üB 0 − ‘ý + ÜŽ û- where: -. üB 0 − ‘ = Risk premium of a global index Ž = Wealth-weighted foreign currency index return 21 Ž − ‘ý v÷Dø jù vO•!… CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 4 | Corporate Restructuring Evaluating Materiality Based on Size ,%( - ( • )( u ,%( ) ? ?'% For Acquisition/Divestiture: : ) ) u *) $ ,() For Cost Restructuring: + ( u( • (& %&, a#J = \a − $a $a ‰ d Premium Paid Analysis * ? &• N oe si s Ex e where: \a = Deal price per share of the target company $a = Unaffected stock price of the target company (i.e., pre-announcement) 22 CFA Level 2 (2024) Formula Sheet – Noesis Exed EQUITY VALUATION Learning Module 1 | Equity Valuation Applications and Processes VE – P = (V – P) + (VE – V) where: ÷ = Estimated intrinsic value a = Market price = Intrinsic value Conglomerate discount = Sum-of-the-parts value – Market value Learning Module 2 | Discounted Dividend Valuation \ 1+ + j \ 1+ + ⋯+ \! 1+ + ! a! 1+ ! oe si Gordon Growth Model \ \ 1+* = = −* −* Ex e = j" :>j 1+ s = ! d Discounted Dividend Valuation N Fixed-rate perpetual preferred stock \ = Value of stock = Value of a company + Present value of growth with zero-growth opportunities (PVGO) = + a šh - = a 1 a šh = + - If dividend and earnings growth rate is constant, \ = +* a 23 CFA Level 2 (2024) Formula Sheet – Noesis Exed Two-Stage Dividend Discount Model = ! j" \ 1 + *‡ 1+ j j + \ 1 + *‡ ! 1 + *þ 1 + ! − *þ Video: https://youtu.be/7vXWsTKiSPE The H-Model = \ 1 + *þ + \ @ * − *þ − *þ d where: @ = half-life in years of the high-growth period * = Short-term growth-rate *þ = Long-term growth rate PRAT model Sustainable growth rate, * = × #h- Ex e Video: https://youtu.be/IAMFZXSPKOY si {9 − \ u 2( 2) {9 $ ,() +1 × × × {9 $ ,() +1 +- oe *= s Video: https://youtu.be/MnfRRRhuGpA Learning Module 3 | Free Cash Flow Valuation N Free Cash Flow to the Firm (FCFF) Valuation Approach > & ,%( = j" >:>>j 1 + Š1:: If non-operating assets = 0 j Equity Value = Firm Value – Market Value of Debt FCFE Valuation Approach -'% ‰ ,%( = j" >:>-j 1+ j 24 CFA Level 2 (2024) Formula Sheet – Noesis Exed Single-Stage (Constant Growth) FCFF and FCFE Model FCFF Valuation Approach > & ,%( = FCFE Valuation Approach -'% ‰ >:>> >:>> 1 + * = Š1:: − * Š1:: − * ,%( = >:>>:>- 1 + * = −* −* Free cash flow to the Firm, FCFF Ex e d FCFF = NI + NCC + Int(1 – Tax Rate) – FCInv – WCInv = CFO + Int(1 – Tax Rate) – FCInv = EBIT(1 – Tax Rate) + Dep – FCInv – WCInv = EBITDA(1 – Tax Rate) + Dep(Tax Rate) – FCInv – WCInv oe si s where: NI = Net income available to common shareholders NCC = Net noncash charges (e.g. depreciation) Int = Interest expense FCInv = Fixed capital investments = Maintenance Capex + Growth Capex = Δš )) aa- = Δ{( aa- + \(• (? WCInv = Investment in working capital Free cash flow to the Equity, FCFE N FCFE = FCFF – Int(1 – Tax Rate) + Net borrowing = CFO – FCInv + Net borrowing where: Net borrowing = Debt issued – Debt repaid Video: https://youtu.be/rtIvIy6Fl0A If (FCInv – Dep) and WCInv funded using Debt (based on debt ratio): FCFE = NI + Dep – FCInv – WCInv + Net borrowing where: Net borrowing = DR(FCInv – Dep) + DR(WCInv) \( \# = \( = 1))( ) 25 CFA Level 2 (2024) Formula Sheet – Noesis Exed If company issues preferred shares: FCFF = CFO + Int(1 – Tax Rate) + Preferred dividends – FCInv Two-Stage Free Cash Flow Models > & u ,%( = ! j" >:>>j 1 + Š1:: -'% ‰ u ,%( = ! j" j + >:>>!C 1 ] ^ Š1:: − * 1 + Š1:: ! >:>-j >:>-!C 1 + ] j 1+ −* 1+ ! ^ Value of Firm = Value of operating assets + Value of nonoperating assets (PV of FCFF) d Learning Module 4 | Market-Based Valuation Price and Enterprise Value Multiples Ex e Enterprise value, EV = Market value of common stock + Market value of preferred equity + Market value of debt + Minority interest – Cash and Short-term investments Actual N P/B P/S 1− s J ( • ?( •( )ℎ ( (? ) (2 -a$ u( (p 12 & oe > si Trailing P/E Leading P/E J ( • ?( •( )ℎ ( -a$ u( • (u %) 12 & ℎ) Justified J = J ( • ?( •( )ℎ ( u ,%( •( )ℎ ( ( • ?( •( )ℎ $ ,() •( )ℎ ( 26 ( ℎ) 1+* −* 1− −* #h- − * −* Video: https://youtu.be/c0vmCUtDpZs $ = 1− 1+* × $ −* or $ = 1− × $ −* CFA Level 2 (2024) Formula Sheet – Noesis Exed Trailing D/P Leading D/P > Actual 4×J ) J Justified −* 1+* (?( '% ( ,‰ 2 u 2( 2 ( • ?( •( )ℎ ( (? ) 2 u 2( 2) u( ℎ( (p ‰( J ( • ?( •( )ℎ ( -a$ a ?( •( )ℎ Earnings yield −* ( Underlying Earnings = EPS – non recurring gains + non recurring loss −* 1− 1+* Normalized Earnings Method 2: Average ROE Approach ! " " -a$ #h- × :% ( = u ,%( •( )ℎ a/* % s Normalized EPS = 1 ! Ex e Normalized EPS = 1 d Method 1: Average EPS Approach Price-to-Earnings Growth (PEG) Ratio = oe si a-š Momentum Indicators N Earnings surprise = Reported EPS – Expected EPS µ ·¹ ·µ¸»V» ¼ ¼ ¸o¸V¼· = #(• (2 -a$ − -p•(? (2 -a$ v 1 ,‰) (? ) -a$ Standardized unexpected earnings (SUE) = Portfolio P/E Š( *ℎ (2 ℎ & ÷G‚! !ü‡ ø‚q‚ ‡X ÷G‚! !ü‡ ø‚q‚ ‡X ? &( where: | = Weight of stock i in portfolio = P/E of stock i 27 = 1 ∑!" | ( CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 5 | Residual Income Valuation Economic Value Added (EVA) - 1j = -=9+j 1 − + − Š1:: × 9 u() (2 : • Market Value Added (MVA) J 1j = J ( u ,%( #9j = -j − Residual Income Model Residual Income, RI == +] #9 1+ ,jE > &j − 9 u() (2 : • × =jE + = #h- − #9 1+ + ,j × =jE #9ó 1+ ó +⋯^ d Video: https://youtu.be/O0KTBkEtP9M Ex e Single-stage residual income valuation model #h- − × = #9 == + == + −* −* Video: https://youtu.be/82GJu5umrB0 )´ = J ( u ,%( 2( + J #(•, ?(&( ? ) Continuing Residual Income j" #9j 1+ N == + ãE = Persistence factor ( u ,%( ('% ‰ , ))( ) s á si + oe Tobin’s Q j + 1+ − #9ã 1+ ãE 0≤ ≤1 If RI declines to Long-run level in mature industry, with premium over book value == + ã j" #9j 1+ j + aã − =ã 1+ ã Video: https://youtu.be/vhRW3q70E0w Clean surplus relationship: =j = =jE + -j − \ uj 28 CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 6 | Private Company Valuation Capitalized Cash Flow Method (CCM) > & u ,%( = -'% ‰ u ,%( = >:>> 1 + * Š1:: − * -'% ‰ > & J = − u ,%( u ,%( → >:>- 1 + * −* ( u ,%( \( Excess Earnings Method (EEM) *) ('% (2 • u 2( ℎ( ('% (2 ( (% ¸ V» µoVUµ, 2 ¶V ·¹ µ¼¼·U¼ ℎ( * ,( ))( ) = -p?()) −* Ex e ,%( *) d ·¼¼ { & , •(2 = − ·µ¸»V» ¼ ( *) Value of the firm = Working capital + Fixed assets + Intangible Assets s Video: https://youtu.be/137ga1xgAbA Control Premium oe si -'% ‰ u ,%( -'% ‰ u ,%( = × 1+: | ℎ? , • (& %& | ℎ % ? , • (& %& , • (& %& = : N 123%) (2 ? , • (& %& × 71 + Discount for Lack of Control and Marketability Discount for Lack of Control (DLOC) \gh: = 1 − 1+: Total discount = 1 – (1 – DLOC)(1 – DLOM) \ghJ = ,%( 1+J • $ℎ ( • ?( 29 1 , • (& %& , • (& %& \( 8 1))( ) CFA Level 2 (2024) Formula Sheet – Noesis Exed FIXED INCOME Learning Module 1 | The Term Structure and Interest Rate Dynamics \>O = \>• × >•,OE• Forward Pricing Model 1 1 + •O >•,OE• = .1 + O 1 •,OE• 0 OE• Forward Rate Model 1 + •O O = 1 + •• • .1 + OE• •,OE• 0 d \>O = Ex e where: where: •O = Spot rate for period = •,OE• = = − 1 forward rate that starts in period 1 Calculating spot rate from one-period forward rates 0.1 + s •ã = û 1 + • .1 + si , , 0 … .1 + ãE , 0ý ⁄ã −1 oe Boostrapping Spot Rates From Par Rates N Video: https://youtu.be/-FnweFO172Q Fixed swap rate )ã = 1 − \>ã 1 − \ )? % = ∑ãj" \>j $%& > ? \ )? % g ) a ‰&( > ? ) Swap spread = YTM of swap rate – YTM of government bond (same maturity) TED spread = LIBOR – YTM of T-bill (same maturity) LIBOR-OIS spread = LIBOR – OIS Fixed rate For Parallel shifts in yield curve: %∆a = −J 2\% × ∆ +J %∆a = −- ∆a = −J 2\% × ∆ +J × a \% × ∆:% u( ∆a = −30 \% × ∆:% u( × a CFA Level 2 (2024) Formula Sheet – Noesis Exed Non-parallel shifts (i.e. change in slope or curvature): %∆a = −œ(‰# (\% × ∆œ(‰ # ( Learning Module 2 | The Arbitrage-Free Valuation Framework : 1+• Arbitrage-free Value of Bond = + : 1+• + ⋯+ > +: 1 + •! ! where: •! = Spot rate for period n Þ + 0.5 × 1+ þ +: d Backward Induction Valuation Methodology 0.5 × = 2 u ,%( ‰ 2( = Ex e where: Þ = bond’s value if the higher forward rate is realized one year hence þ = bond’s value if the lower forward rate is realized one year hence : = coupon payment that is not dependent on interest rates si s Video (Backward Induction Valuation): https://youtu.be/DhAVQ3hIXlQ oe Video (Backward Induction with Financial Calculator): https://youtu.be/FycX2UwJxCM Video (Pathwise Valuation): https://youtu.be/3oM-220oi7o ,Þ = ,ÞÞ = ó,ÞÞÞ ,þ ( = ,þþ ( N Binomial Interest Rate Tree ô ó,þþþ ( ,Þþ = ó,ÞÞþ ,þþ ( = ó,þþþ ( ô ó,þþÞ 31 = ó,þþþ ( CFA Level 2 (2024) Formula Sheet – Noesis Exed Equilibrium Term Structure Models Cox-Ingersoll-Ross (CIR) Model 2 = ¨− 2 = Vasicek Model 2 + v Y j 2• j ¨− j 2 + v2• where: = Speed of reversion (> 0) ¨ = Long-run interest rate v = Interest rate volatility j = ¨j 2 + v2•j Ex e 2 Ho-Lee Model d Arbitrage Free Models si where: ¨j = Time-dependent drift term s Kalotay-Williams-Fabozzi (KWF) Model 2 ln j = ¨j 2 + v2•j oe Learning Module 3 | Valuation and Analysis - Bonds with Embedded Options Callable and Putable Bonds N Value of callable bond = Value of straight bond – Value of issuer call option Value of putable bond = Value of straight bond + Value of investor put option Video (Valuing a callable bond): https://youtu.be/lWLSodiqZaM Video (Valuing a putable bond): https://youtu.be/qmUnAtpXIAg - (? u( 2% - (? u( ? = aE − a C 2 × Δ:% u( × a u(p ‰ = a + a C −2×a a × Δ:% u( E 32 CFA Level 2 (2024) Formula Sheet – Noesis Exed Capped and Floored Floaters Value of capped floater = Value of straight floater – Value of cap Value of floored floater = Value of straight floater + Value of floor Video (Valuing a capped floater): https://youtu.be/d4LNMdXV9vU Video (Valuing a floored floater): https://youtu.be/YJZU0THHBNE Convertible Bonds ºµ ,( ( ? u( ) • ?( · = 2 = : J ( ? u( ) J = • (& %& •( )ℎ ( J ( ? u( ) • (& %& : u( ) u ,%( u( ,( : u( ) 2 • ?( ( ? u( ) • ?( J ,%( $ , % 2( ,‰ * ^ *ℎ 2 − ª 2( ,‰ * )ℎ • ?( ( ? u( ) • (& %& •( )ℎ ª 2( ,‰ * )ℎ ( • ?( u( $ ( ( ,( 2 • ?( −1 *ℎ u ,%( N oe : a (& %& u( = $ *ℎ u ,%( = µ ] u( ) d ª 2( ,‰ * : × )ℎ ( • ?( Ex e V»V ? u( = s J u( ) u ,%( si : Convertible Bond (With No Additional Options) ,%( ? ,, ,%( ,%( = + • *ℎ 2 ? u( ,( 2 ) ))%( á ) ) ? Callable Convertible Bond ? ,%( u( ,( 2 = ) ,%( *ℎ Putable Convertible Bond ? ,%( u( ,( 2 = ) ,%( *ℎ ,%( ,%( ? ,, + − ))%( ? ,, • 2 • ))%( á ) ) ? ,%( ? ,, + + • 2 á ))%( ) ) ? 33 ,%( u() •% • CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 4 | Credit Analysis Models š-)• ( 2 = +J : • ( 2 − +J š u( g )) * u( -p•(? (2 #(? u( ‰ = × R1 − S (p• )% ( 2( %, ( &( 2 g )) #(? u( ‰ =1− )(u( ‰ ( Expected Loss = Probability of Default × Loss Given Default u ,%( ) ‰ = > u ,%( ))%& * 2( 23%) &( , : 1= 2 : (2 ,% − 123%) &( %, ! -gj 1+ j j" j = ah\ × gš\ =1 Ex e : (2 u ,% 2 1+ d > ? (2 2 ( jE ×@ • oe ah\j = 1 − @ • si s where: -gj = Expected loss of bond at time t ah\j = Probability of default of bond at time t gš\j = Loss given default at time t = -p•(? (2 -p• )% (j − #(? u( ‰j j = Risk-free rate at time t = Bond’s remaining tenor -gj a (p•(? (2 , )) •( 2 = 1+ j j 2 ( N Approximation of credit spread ≈ Annual hazard rate × (1 – Recovery rate) Video (Probability of Default): https://youtu.be/e7K4x48Eg4U Video (Valuing a Credit Risky Bond – Zero Interest Rate Volatility): https://youtu.be/2I9bgu-o7aI Video (YTM of Corporate Bonds – Default and Non-Default): https://youtu.be/K253Y7c2Yto Expected percentage price change of a corporate bond a , ‰ ? (2 & * where: %∆a = −J 2\% × ∆? (2 )• ( 2 34 × %∆a CFA Level 2 (2024) Formula Sheet – Noesis Exed Structural Model 1j = \ , + + $j In terms of… Equity Debt Call options - + = J pe1 + − œ, 0f Put options \ + = 1 + − J pe1 + − œ, 0f - + = 1 + − œ + J peœ − 1 + , 0f \ + = œ − J peœ − 1 + , 0f Learning Module 5 | Credit Default Swaps d where: $j = -'% ‰ u ,%( &( 1ã = 1))( u ,%( &( + œ = > ?( u ,%( 2( Ex e CDS payout amount = Payout ratio × Notional = (1 – Recovery rate of CTD bond) × Notional Upfront payment = PV of protection leg – PV of premium leg s a a ª• = − • (& %& : (2 $• ( 2 > p(2 : %• a ?( oe si : (2 > p(2 ≈7 − 8 × :\$ \% $• ( 2 : %• :\$ •( 100 , = 100 − ª• N :ℎ *( % :ℎ *( = × \% :\$ • ?( )• ( 2 •) 35 • (& %& CFA Level 2 (2024) Formula Sheet – Noesis Exed DERIVATIVES Learning Module 1 | Pricing and Valuation of Forward Commitments Forward Contracts Forward Pricing: > =$ 1+ ã > = $ + :: − := > = $ (‚ ã ã ‚ CŽŽEŽO ã si s Ex e where: $ = Current spot price > = Forward price (set today) = Annually compounded risk-free rate = Continuously compounded risk-free rate :: = PV of Carry cost := = PV of carry benefits :: = Continuously compounded cost of carry := = Continuously compounded carry benefit d > =$ ( 1+ ã = >j − > > = $j − ãEj 1+ 1+ = $ã − > N j oe Forward Valuation (Long Position): =0 ãEj 36 CFA Level 2 (2024) Formula Sheet – Noesis Exed Forward Rate Agreement (FRA) » >#1 • ‰ >#1 = 7 1 + gã 1 + gw · oV¸µUV » ã w − 18 7 1 B >#1 = ,egB − >#1 f 1 + \B B { 8 Valuation at time = * (prior to FRA expiration): { ,%( g * >#1 * = B ,.>#1ü − >#1 0 1 + \ãEü ãEü Ex e d where: \B = Discount rate for m periods at t = h ℎ = FRA tenor & = Tenor of the underlying rate + = ℎ + & = Maturity of underlying instrument B Video (Pricing an FRA): https://youtu.be/uBmAt_z9f3Y Video (Valuing an FRA): https://youtu.be/AYKRVdaYvxY oe si Pricing: ´% (2 % % () : u( ) > = × ? • ?( = > = + 19 − 19ã − > :9 s Fixed Income Forwards and Futures N Valuation for fixed income forward contracts: u ,%( 2 ( ( ?( | 2 • ?() j = a ()( = a e>j − > f Valuation for fixed income futures contracts: j = Price change since previous day’s settlement where: = = Quoted bond price {%& ( ?? %(2 2 ‰) ) ?( , ) ? %• 19 = + , 2 ‰) 2% * ℎ( ? %• • ‰&( 37 • ‰&( •( 2 × 1 % , ? %• : %• ('%( ?‰ CFA Level 2 (2024) Formula Sheet – Noesis Exed Interest Rate Swaps (IRS) 1−a ! ∑!" a >$ = a = 1 + $• ( R 1 \ ‰) J % 360 ‰ Pay-fixed, receive-floating IRS ,%( $| • = { ! , × >$j − I " Receive-fixed, pay-floating IRS ,× I − >$j " a d $| • = { ! a Ex e ,%( S Video (Pricing an Interest Rate Swap) : https://youtu.be/0QvtKZutr5E Video (Valuing an Interest Rate Swap): https://youtu.be/_A2a909etvg oe si s Currency Swap Pricing for fixed leg of currency swap in currency 1 − a !,G >$G = ! ∑ " a ,G G L = >$G = >$L ! " ! " N Value of a fixed-for-fixed currency swap ,G × Ž = { a a ,G ,L +a +a !,G !,L ×a ×a G L = = ,%( G − $j × { ?% ( ?‰ ,%( ?% ( ?‰ $j = Spot exchange rate at time (quoted as ⁄ ) ,L × ,(* L (?( u( ,(* • ‰ Video (Pricing a currency swap): https://youtu.be/XZlxcVByc00 Video (Valuing a currency swap): https://youtu.be/3h4mElS48aA 38 CFA Level 2 (2024) Formula Sheet – Noesis Exed Equity Swap Value of equity swap (receive fixed-rate, pay equity return) $j : − ×{ ,−a j a ÷ ,j = $jE ,%( Cash flow for equity leg = { -'% ‰ g(* = , × a( $j ×{ $jE −{ , , 2 ? ('% ‰ ( % Hedge Ratio ℎ Gƒƒ Ex e Learning Module 2 | Valuation of Contingent Claims d where: : = Value at time of a fixed-rate bond initiated with coupon : at Time 0 $j = Current equity index level $jE = Equity index level at last reset date = •C − •E ≤0 $C − $E ?=ℎ oe No-arbitrage Approach: si s ℎqøj = ?C − ?E ≥0 $C − $E Gƒƒ $ +a −ℎ Gƒƒ $ C + ?C = ℎ Gƒƒ $ +a −ℎ Gƒƒ $ E + ?E N • = ℎqøj $ + a .−ℎqøj $ C + •C 0 = ℎqøj $ + a .−ℎqøj $ E + •E 0 Expectations Approach: ™= where: % = Up factor 2 = Down factor = Risk-free rate 1+ −2 %−2 39 CFA Level 2 (2024) Formula Sheet – Noesis Exed One-period Binomial Model ?= ™? C + 1 − ™ ? E 1+ ™•C + 1 − ™ •E •= 1+ where: ™ = Risk-neutral probability of an up-move Note: For interest rate options, ™ = 0.5 and discount expected option payoff using the 1-period forward rates. Video (Valuing interest rate options): https://youtu.be/X4R8j_cf8SA d Two-period Binomial Model: ™ •CC + 2™ 1 − ™ •CE + 1 − ™ •EE 1+ s •= Ex e ™ ? CC + 2™ 1 − ™ ? CE + 1 − ™ ? EE ?= 1+ si For 2-period American-styled call option with dividend in t = 1: oe $C = % × $ − a N $E = 2 × $ − a 2 u 2( 2) 2 u 2( 2) Video: https://youtu.be/U_XkIZjJIAU 40 ) ) (( (( ( ( CFA Level 2 (2024) Formula Sheet – Noesis Exed Black-Scholes Option Pricing Model ? = ${ 2 − ( E‚ã { 2 • = ( E‚ã { −2 − ${ −2 $ 1 ln R S + R + v S + 2 2 = v √+ 2 = 2 − v √+ • + $ = ? + ( E‚ã Put-call parity: d Hedge ratio for calls = { 2 Probability that the call option expires in the money = { 2 = a Hedge ratio for puts = { 2 − 1 = −{ −2 Probability that the put option expires in the money = 1 − { 2 a $ã < = { −2 Ex e • • • • BSM model with carry benefits ? = $( E ã { 2 − ( E‚ã { 2 − $( E ã { −2 s • = ( E‚ã { −2 si $ 1 ln R S + R − ! + 2 v S + v √+ N oe 2 = Put-call parity: 2 = 2 − v √+ • + $( E ã 41 = ? + ( E‚ã $ã > CFA Level 2 (2024) Formula Sheet – Noesis Exed Black Option Valuation Model European Options on Futures ? = ( E‚ã e> + { 2 • = ( E‚ã { −2 2 = − { 2 f − $( E ã { −2 > + 1 ln ] ^+ 2v + v √+ 2 = 2 − v √+ d ? = ( E‚ã e> + − f + • Put-call parity: Interest Rate Options , KE • = 1a ( E‚.jM"l Cj#0 û# ( E‚ã { −2 , oe N B 0{ B0 s KE − # ( E‚ã { 2 ý − >#1.0, 1 6 + R2 v S $% B 0{ −2 ý KE 2 = 2 − v Y KE Payer Swaption a1 , KE v Y KE si 2 = >#1.0, ln 4 2 Ex e ? = 1a ( E‚.jM"lCj# 0 û>#1.0, = 1a × e# { 2 −# { 2 f× ! K" Receiver Swaption #-: $% = 1a × e# { −2 2 = ln R −# { −2 f × # 1 + v + # S R2 S v √+ 2 = 2 − v √+ 42 a ! K" K 1 a K 1 CFA Level 2 (2024) Formula Sheet – Noesis Exed Video (Interest Rate Options & Swaptions Equivalences: https://youtu.be/uZQO50sEzso Optimal Number of Hedging Units (for Delta Hedging) {Þ = − a , \(, 2(, Þ Video: https://youtu.be/v8RcvkQKFpw Option Greeks \(, Gƒƒ qøj = ( E&ã { 2 = −( E&ã { −2 • = • + \(, qøj $v √+ { 2 1 × '$ + š && 2 × '$ s Gƒƒ ( E&ã Gƒƒ si ? = ? + \(, qøj = 1 × '$ + š && 2 qøj oe Gƒƒ = š && × '$ N š && Ex e where: © = Continuously compounded dividend yield d \(, 43 CFA Level 2 (2024) Formula Sheet – Noesis Exed ALTERNATIVE INVESTMENTS Learning Module 1 | Introduction to Commodities and Commodity Derivatives $• • ?( >% % () $ *( : = + − • ?( •ℎ‰) ? , ? && 2 ‰ ? )) g *( ( & {( ( & : ,( 2 % % () ? ? ? = − % % () ? )• ( 2 ?, ) * • ?( ?, ) * • ?( a ?( ( % :% ( • ?( − a (u %) • ?( a (u %) • ?( g *( ( & {( ( & ? − % % () ? ? ¬ % % () ? a( ?( *( ℎ( • ) ?, ) * • ?( ?, ) * • ?( ℎ( % % () ? ? = × {( ( & ( * ,,(2 % % () ? ? ?, ) * • ?( , + (% #( s + , a ?( # ,, : ,, ( = + + (% (% (% (% Ex e d # ,, ( % = u( ( ?( ‰ (,2 , ? * 2(p ,‰ si Learning Module 2 | Overview of Types of Real Estate Investment oe Net and Gross Leases Retail Rent #( •( )'% ( ( N {( = =š J &%& ( •( )'% ( )) ( + $ℎ − h•( (% × * (p•( )() #(u( %( •( { % , ( • − )'% ( •( )'% ( Appraisal-based index #( % = {h9 − : • , =(* * - 2 * +R − S -p•( 2 % () ( u ,%( & ( u ,%( & =(* *& ( u ,%( 44 CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 3 | Investments in Real Estate Through Publicly Traded Securities Net Asset Value Approach {1 •( )ℎ (= •( ,%( ,%( + , 2( + − * () ( 2, , () ℎ( ))( ) {%& ( )ℎ () % ) 2 * If valuation of operating real estate is not provided: ,%( •( * () (= {h9 : • ( Video: https://youtu.be/WncC3BZmfs8 š )) ( , -) & (2 u ? ?‰ − (u( %( ? ,,(? ) , )) − h•( * (p•( )() Funds from Operations: ? &( + Ex e Relative Value Approach >>h = {( 2 d {h9 = \(• (? 2 & • − si s Adjusted Funds from Operations: { ? )ℎ #(?% 1>>h = >>h − − ( š ) ) ,( g )) ) ,( + • •( ‰ • •( ‰ * ? • , (p•( 2 % ( 2 ,( ) * ? ) ) #-9+ )ℎ N ,%( oe Two-Stage Dividend Discount Model (=a 2 u 2( 2) + a 45 ( & , u ,%( CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 4 | Hedge Fund Strategies Equity Market Neutral Pairs Trading 1& % $ℎ a ) hu( u ,%(2 $ ? =− =( % 2( u ,%(2 ) ? × 1& % =( u( u ,%(2 ) ? 9 u() (2 Merger Arbitrage Strategy For a stock-for-stock deal: &( *( ) )%??()) %, = {• × a• − {ã × aã Ex e where: {• = Number of acquirer’s shares to short sell a• = Share price of acquirer post announcement {ã = Number of target’s shares to buy aã = Share price of target post announcement d a ‰ Conditional Factor Risk Model si s # ,j = ž + Ü , > ? 1 j+Ü, > ? 2 j + ⋯ + Ü ,Ý > ? œ j+ +\j Ü , > ? 1 j + \j Ü , > ? 2 j + ⋯ + \j Ü ,Ý > ? œ j + ( N oe where: # ,j = Return of hedge fund in period Ü ,Ý > ? œ j = Exposure to risk factor œ for hedge fund in period during normal times \j Ü ,Ý > ? œ j = Incremental exposure to risk factor œ for hedge fund in period during financial crisis periods \j = Dummy variable that equals 1 during financial crisis periods (0 otherwise) ž = Intercept for hedge fund ( ,j = Random error with zero mean and standard deviation v 46 ,j CFA Level 2 (2024) Formula Sheet – Noesis Exed PORTFOLIO MANAGEMENT VOLUME 5 Learning Module 1 | Exchange-Traded Funds: Mechanics and Applications End-of-day ETF premium or discount (%) -+> • ?( − {1 •( )ℎ {1 •( )ℎ ( ( Intraday ETF premium or discount (%) • % =# % 2 • 2( ? ) 2( ? ) % = h ( | ‰ ? && )) % +J d # % 2 2? ) ( *(&( (( % % × 2 + = 2 ) )• ( 2 % Ex e @ ,2 * •( -+> • ?( − 9 2 ? (2 {1 •( )ℎ 9 2 ? (2 {1 •( )ℎ ( Learning Module 2: Using Multifactor Models Arbitrage Pricing Theory (APT) si s - #q = # + ö Üq, + ⋯ + öÝ Üq,Ý N oe where: - #q = the expected return to portfolio p # = the risk-free rate Üq,K = the sensitivity of the portfolio to factor j öK = the expected reward for bearing the risk of factor j œ = the number of factors Carhart Four-Factor Model -.#q 0 = # + Üq, #J#> + Üq, $J= + Üq,ó @Jg + Üq,ô ŠJg where: #J#> = Return on a value-weighted equity index minus one-month T-bill rate SMB = small minus big; average return on three small-cap portfolios minus the average return on three large-cap portfolios HML = high minus low; average return on two high book-to-market portfolios minus average return on two low book-to-market portfolios WML = winners minus losers, a momentum factor; return on a portfolio of past year’s winners minus return on a portfolio of past year’s losers. 47 CFA Level 2 (2024) Formula Sheet – Noesis Exed Macroeconomic Factor Model # = + > + > +⋯+ Ý >Ý + where: > = the surprise in the factor k = the sensitivity of the return on asset i to a surprise in factor k, k = 1, 2, …, = Expected return on the portfolio Fundamental Factor Model Value of attribute for asset − Average value of attribute = v Values of attribute Return Attribution & *( , " , , =( ?ℎ& > ? 8 −7 8 6 ×R )( ) u ‰ u ‰ (% d a 47 )( ) +- = ) #P − #O 9# = #P − #O ) #P − #O Ex e 9 ? = Ý s + = #P − #O si 1? u( ( % N oe Active risk squared = Active factor risk + Active specific risk 48 S + $(?% )(,(? ‰ CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 3 | Measuring and Managing Market Risk Parametric VaR (Using Normal Distribution) ,%( #) , # = −û-.#q 0 − • × vq ý × a , ,%( where: -.#q 0 = Portfolio expected return vq = Portfolio standard deviation Two-asset portfolio: -.#q 0 = | - # +| - # Ex e d vq = | v + | v + 2| | s , v v Scaling from daily returns to annual returns (Assuming 1 year = 250 trading days): #…G ƒù × 250 2 * 2 ‰) Scaling from daily standard deviation to annual standard deviaton: # 9 # = # ( ?ℎ *( − s , si 9 ? (&( v…G ƒù × √250 oe Percentage change in bond price: ΔB ≈ −\% = Δ‰ 1 + : 1+‰ 2 # ( N New put price: • + Δ• ≈ • + Deltaq Δ$ + Gammaq Δ$ No formula. 49 *( Δy u(p ‰ 7 8 1+‰ New call price: ? + Δ? ≈ ? + Delta Δ$ + Gamma Δ$ Learning Module 4 | Backtesting and Simulation ( ?ℎ + (* + (* Δv q Δv CFA Level 2 (2024) Formula Sheet – Noesis Exed VOLUME 6 Learning Module 1 | Economics and Investment Markets One-period real-risk free rate: ,j, = 1 ) j, ý -j û& where: ) j, ý = Inter-temporal rate of substitution -j û& a ?( where: ÷ûP*+,l,é"l ý Cƒ+,l -ûa*jC ,‡E ý + ? uj ûa*jC 1 + ,j, = risk neutral present value ,‡E ) j, ý ,& ) j, ý = covariance between investor’s inter-temporal rate of substitution ,& and the random future price the investment at t + 1, based on the information available to investor today. ) = time to maturity of investment d ,‡E Ex e ? uj ûa*jC ) ‰ ))( = −1 Default-free nominal coupon-paying bond :>jC‡ s ‡" 1 + ,j,‡ + ¨j,‡ + ™j,‡ ‡ oe si aj = % N where: ,j,‡ = Real-risk free rate ¨j,‡ = Expected inflation rate ™j,‡ = Uncertainty in future inflation rate ¨j,‡ + ™j,‡ = Breakeven rate of inflaton Short-dated nominal zero-coupon government bonds (e.g., T-bills) aj = :>jC‡ 1 + ,j,‡ + ¨j,‡ 50 ‡ CFA Level 2 (2024) Formula Sheet – Noesis Exed • Taylor Rule = 9j + ™j + 0.5 ™j − ™j∗ + 0.5 j j − ∗ j where: • j = policy rate at time t 9j = level of real short-term interest rates that balance long-term savings and borrowing in the economy ™j = rate of inflation ™j∗ = target rate of inflation j = logarithmic level of actual GDP ∗ j = logarithmic level of potential real GDP ∗ j − j = output gap Corporate bond 1 + ,j,‡ + ¨j,‡ + ™j,‡ + !j,‡ where: !j,‡ = Credit premium Equity s - jC‡ ý -j û:> 1 + ,j,‡ + ¨j,‡ + ™j,‡ + !j,‡ + .j,‡ si aj = ‡ d ‡" - jC‡ ý -j û:> Ex e aj = % ‡" N oe aj = ‡" - jC‡ ý -j û:> 1 + ,j,‡ + ¨j,‡ + ™j,‡ + öj,‡ ‡ ‡ where: .j,‡ = Equity premium relative to risky bonds öj,‡ = !j,‡ + .j,‡ = Equity risk premium Commercial Real Estate aj = % ‡" where: /j,‡ = liquidity risk premium - jC‡ ý -j û:> 1 + ,j,‡ + ¨j,‡ + ™j,‡ + !j,‡ + .j,‡ + /j,‡ 51 ‡ CFA Level 2 (2024) Formula Sheet – Noesis Exed Learning Module 2 | Analysis of Active Portfolio Management Active return, #• = #P − #O 1,•ℎ , žq = #q − Üq #O ,%( 22(2, #• = $#P = $#O + 9# ä K" ∆|K #O,K + ä K" |P,K #•,K For optimal Sharpe ratio, & 9: ≈ 2 a : ( , ‰ +: = : ?( , 9: = : ˆ 7 , ∆| v 8 v Ex e 9 ?( , #• ˆ , 8 7 v v s ) ( : ( 9# v #O $#O *ℎ ? ,, − 1 si + v #• = d v #P = v #O + v #• oe Forecasted active return, ˆ = 9: × v × $ N where: $ is set of standardized forecasts of expected returns across securities Mean-variance optimal weights Full Fundamental Law ∆| ∗ = ˆ v• v 9: √=# - #• = +: × 9: √=#v• 9# = +: × 9: √=# v #• = +: × 9# ∗ v #O $#O $#P = $#O + +: 52 9#∗ CFA Level 2 (2024) Formula Sheet – Noesis Exed Performance Measurement #• = - #• |9:1 + { )( +: = Proportion of variation in realized performance attributed to realized information coefficient where: 9:1 = realized information coefficient - #• = Independence of Investment Decision { 1+ {−1 s N oe si s Ex e =# = 9: v vŽ • d Ex-ante measurement of skill 53