FinQuiz
Formula Sheet
Reading 9: Correlation & Regression 1. Sample Cov X, Y =
r=
! b1 − b1 • Test statistic = t = s b1
0+1 34567 (96 )(97 )
or
5;<()) 5;<(,)
< 0+> 1+
9.
•
Intercept (b0) = b0 = y − b1 x = Slope or regression coefficient = b1 = 345(O,P) 5;<(O)
0+T+1
SSU+SSR SSU
8.
𝑦Z
𝑆𝑆𝑅 𝑘
𝑦Z
𝑆𝑆𝐸 𝑛−𝑘−1
Z\1 >
𝑆𝑆𝑅 𝑆𝑆𝐸
[
= Z\1 >
𝑘
𝑛−𝑘−1
11. Prediction Intervals = Y ± t 3 sm 1
()+))?
0
0+1 9? 6
and
Reading 10: Multiple Regression & Issues in Regression Analysis 1. Yi = b0 + b1X1i + b2X2i + … + bkXki + εi,i = 1, 2, … n 2. Prediction equation = 𝑌Z = 𝑏u + 𝑏1 𝑋1Z + 𝑏> 𝑋>Z +. . . +𝑏w 𝑋wZ + εy , 𝑖
𝑆𝑆𝑇 Total df = n-1
fgg ) h ggi ( ) jkhk/
(
[
=
𝑦Z Z\1 >
3. Adjusted R2 = 𝑅 > = 1 −
−𝑦
[+1 [+w+1
1 − 𝑅>
0+T+1
=
VSS SSU
where, 0 ≤ R2≤ 1
(for single independent variable R2 = r2) 7.
[
=
bce
=
s f = s 2f
F
−𝑦
O+O ?
Coefficient of Determination (R2) = =
MSS
bcd
𝑤ℎ𝑒𝑟𝑒 sm> = s > 1 + +
𝑆𝑆𝐸 Error df = n-k-1
- (P +P)? *./ *
=
SS
−𝑦
O+O P+P
Standard Error of Estimate SEE = SR = SSR
6.
or =
b1 ± t c s b1
𝑆𝑆𝑅 Regression df = k
Linear Regression = Yi = b0 + b1Xi + εi, •
5.
ANOVA
10. F-Statistic or F-Test =
(df numerator = k = 1) (df denominator = n – k – 1 = n – 2)
ANOVA (Analysis of variance) =
t distribution with n −
2 deg. of freedom 4.
Confidence Interval =
•
345(),,)
3. t-test (for normally distributed variables) = t=
H1: b1 ≠ 0 (linear relationship does exist)
•
*./ )* +) ,* +,
2. Correlation Coefficient = r), =
Level II 2017
SST = SSE + SSR(or RSS) Hypothesis Testing: • Null and Alternative hypotheses • H0: b1 = 0 (no linear relationship)
Source of Variability
DoF
Sum of Squares
Mean Sum of Squares
Regression (Explained)
1
RSS
MSR = RSS/1
Error (Unexplained)
n-2
SSE
MSE = SSE/n-2
n-1
SST= RSS + SSE
Total
4. Breusch–Pagan test • H0 = No conditional Heteroskedasticity exists • HA = Conditional Heteroskedasticity exists • Test statistic = n × R2residuals 5. Durbin-Waston Test = 𝐷𝑊 = • ? ~.? }~ +}~k/ • } ? ~./ ~
•
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 t-1 + εt where, b0 ≠ 0 and b1 = 1 By taking first difference yt = xt - x t-1 = b0 + εt
Reading 11: Time Series Analysis 1. Linear Trend Models = yt = b0 + b1t+ εt • Predicted/fitted value of yt in period (T + 1) =
yˆ t +1 = bˆ0 + bˆ1 (T + 1)
2. Log-Linear Trend Models =
yt = e b0 +b1t
3. Autoregressive Time-Series Models: • First order autoregressive AR (1) = xt = b0 + b1 x t-1 + εt • pth-order autoregressive AR (p) = xt = b0 + b1 x t-1 + b2 x t-2 + …..+ bp x t-p +εt 4.
b0 Mean reverting level of xt = 1 − b1
5. Chain Rule of Forecasting: • One-period ahead forecast =
xˆt+1 = bˆ0 + bˆ1 xt •
Two-period ahead forecast=
xˆt+2
= bˆ0 + bˆ1 xt+1
6. Random Walks and Unit Roots: • Random Walk without drift = xt = x t1 + εt where, b0 = 0 and b1 = 1. • Correcting Random Walk = yt = xt - x t-1
7. Using Dickey-Fuller Test = xt - x t-1 = b0 + (b1 -1) x t-1 + εt 8. Smoothing Past Values with n-Period Moving Average =
xt + xt −1 + xt −2 + ..... + xt −( n −1) n 9. Correcting Seasonality in Time Series Models:
Reading 13: Currency Exchange Rates 1. Bid-offer Spread = Offer price – Bid price 2. Fwd rate = Spot Exchange rate +
†4<‡;<ˆ ‰4y0Š9
9‰4Š •O3Ž;0•• <;Š•+(m4<‡;<ˆ ‰4y0Š9/1u,uuu) 9‰4Š •O3Ž;0•• <;Š•
5. Covered interest rate parity:
•
εˆ 2 t = α 0 + α1εˆ 2 t −1 + µ t
where
1 + i∫
ˆ 1’y∫
1 †∫ /‘
F∫ /ˆ = S∫
•
Using day count convention:
ˆ
1’y‘
' ! Actual $* )1+ id # ,= " 360 &%+ (
µt is
' ! Actual $*' 1 * , S f /d )1+ i f # ,) " 360 &%+)( Ff /d ,+ (
σˆ t2+1 = αˆ 0 + α1εˆt2
Reading 12: Excerpt from ‘Probabilistic Approaches , Scenario Analysis, Decision Tree & Simulations’
1 + iˆ = S ∫
•
an error term • Predicting variance of errors in period t+1 =
−1
4. To convert spot rate into forward quote: • Spot exchange rate × (1 + % premium) • Spot exchange rate × (1 - % discount)
• For quarterly data = xt = b0 + b1x t-1 + b2x t-4 + εt • For monthly data = xt = b0 + b1x t-1 + b2x t-12 + εt 10. ARCH model =
1u,uuu
3. Forward premium/discount (in %) =
•
Ff / d
⎛ ⎡ Actual ⎤ ⎞ ⎜ 1 + i f ⎢ ⎟ 360 ⎥⎦ ⎟ ⎣ ⎜ = S f /d ⎜ ⎡ Actual ⎤ ⎟ ⎜ 1 + id ⎢ ⎟ ⎣ 360 ⎥⎦ ⎠ ⎝
6. Uncovered Interest Rate Parity : •
i f − %ΔS e f / d = id
FinQuiz
• • •
Formula Sheet
%ΔS e f / d = i f − id Forward premium or discount: For one year horizon =
Ff /d − S f /d = "i −i % S f /d $ f d ' ≅ S f /d (i f − id ) # 1+ id & •
Using day count convention: ( " Actual % + * $ # 360 '& Ff /d − S f /d = S f /d * (i f − id ) * 1+ i " Actual % * d$ # 360 '& , )
7. Forward discount or premium as % of spot rate:
Ff / d − S f / d S f /d
≅ (i f − id )
If uncovered interest rate parity holds •
=
Ff /d − S f /d = %ΔS ef /d ≅ (i f − id ) S f /d
8. Purchasing Power parity (PPP) • Pf = S f/d × Pd • S f/d = Pf / Pd
qf/d =
⎛ S f / d Pd ⎜ ⎜ P f ⎝
Level II 2017
⎞ ⎛ ⎟ = S f / d ⎜ Pd ⎟ ⎜ P ⎠ ⎝ f
⎛ CPI d q f / d = S f / d ⎜ ⎜ CPI f ⎝
⎞ ⎟ ⎟ ⎠
⎞ ⎟ ⎟ ⎠
or 12. Fisher effect: • id = rd + πεd • if = rf + πεf • if – id = (rf – rd) + (πεf- πεd) • (rf – rd) = (if – id) - (πεf- πεd) 13. When both uncovered interest rate parity and ex-ante PPP hold: • (rf – rd) = %∆ Sεf/d - %∆ Sεf/d = 0 • International Fisher Effect: if – id = πεfπ εd 14. When all the key international parity conditions are held at all times: BOP = Current A/C + Capital A/C + Official Reserve A/C = 0 15. Real exchange rate = 𝑞” = 𝑞” + •
•
𝑟– − 𝑟— − 𝜑– − 𝜑— 16. Interest Rate Differentials, Carry Trades and Exchange Rates
qL/H = qL/H +(iH −i L )−(π Hε − π Lε )−(φH − φL ) 17. Policy Rate under Taylor rule: •
i = rn + π + α (π − π *) + β (y − y*)
•
Neutral real policy rate + Current inf rate + α (Inf gap) + β (Output gap)
18. Exchange rates using the Taylor Rule = q šS›/RšV = q šS›/RšV + r0Rš − r0šS + α
πRš – π ∗Rš − πšS − π ∗šS
+
β yRš − y ∗Rš − yšS − y ∗šS ∅Rš − ∅šS
−
Reading 14: Economic Growth & The Investment Decision 1. Economic growth = Annual % ∆ in real GDP or in real per capita GDP 2. P = GDP
9. Relative version of PPP = %∆S f/d = πf – πd 10. Ex ante version of PPP = %∆Sef/d = πef – π ed 11. Real Exchange Rate
R
¤
£›¤
R
3. Expressing in terms of logarithmic rates:
• (1/T) % ∆P = (1/T) % ∆GDP + (1/T) %∆ (E / GDP) + (1/T) % ∆(P / E)
• % ∆ in stock MV = % ∆ in GDP + % ∆ in share of earnings (profit) in GDP
FinQuiz
+ % ∆ in the price-to-earnings multiple 4. A two-factor aggregate production function: Y = AF (K, L) 5. Cobb-Douglas Production Function = F (K, L) = Kα L1 - α 6. Under the Cobb-Douglas production function: • Marginal product of capital = MPK = α AK α-1 L 1-α = α Y/K • α Y/K = r èα = r (K) / Y = Capital income / Output or GDP
Formula Sheet
• 11. Labor productivity growth accounting equation • Growth rate in potential GDP = LT g rate of labor force + LT g rate in labor productivity
Output per worker or Average labor productivity (Y/L or y): • GDP/Labor input = TFP × capital-tolabor ratio × share of capital in GDP • Or y = Y/L = Akα
8. Contribution of Capital Deepening = Labor productivity growth rate – TFP 9. Contribution of Improvement in technology = Labor productivity growth rate – Capital Deepening 10. Growth Accounting based on Solow Approach = ∆Y /Y = ∆A / A + α ∆K/K + (1 – α) ∆L/ L
Growth rates of output per capita = ∆y /y=
© 1+¨
12. Balanced or Steady State Rate of Growth in Neoclassical Growth Theory: • Growth in physical capital stock = ∆K = sY – δK 13. In the steady state: • Growth rate of capital per worker = ∆k / k = ∆y / y = ∆A / A + α ∆k / k = 1+ ¨
•
è Steady state growth rate of
labor productivity Growth rate of Total output = ∆Y / Y = Growth rate of TFP scaled by labor force share + Growth rate in the labor force =
•
+n
Steady state Output-to-capital ratio = ª «
•
© 1+ ¨
=
1
©
¬
1+ ¨
+ 𝛿 + 𝑛 = 𝛹
Gross investment per worker = © 1+ ¨
+ 𝛿 + 𝑛 𝑘
Slope of straight line = [δ + n + θ / (1 – α)] 14. During the transition to the steady state growth path: •
© 1+ ¨
+ 𝛼𝑠
ª «
− 𝛹
=
+ 𝛼𝑠 (y/k – Ψ)
• Capital-to-labor ratio = ∆k / k = © 1+ ¨
¥¦§
7.
Level II 2017
+ 𝑠
ª «
− 𝛹
=
© 1+¨
+s
(y/k – Ψ) 15. Proportional impact of the saving rate change on the capital-to-labor ratio and per capita income over time: 1
knew • kold
' ! Y $ *α −1 )# & , " K %new , =) )!Y $ , )( #" K &%old ,+
y new ⎡ k new ⎤ = ⎢ ⎥ y old ⎣ k old ⎦ •
α
16. Production function in the endogenous growth model = ye = f (ke) = cke • Growth rate of output per capita = ∆ye/ye = ∆ke/ke = sc – δ – n Reading 15: Economics of Regulation
FinQuiz
Formula Sheet
Level II 2017
Reading 16: Interoperate Investments 1. Summary of Accounting Treatment of Investments Income Statement (I.S)
Held-tomaturity
Held for trading security Designated at fair value
Available -for-sale
§
i income = Market rate at purchase × Initial fair value (FV) of a debt security Ori income = i pmt – Amort i pmt = (Coupon rate × Par value) Amort = i pmt – i income § If debt security is sold: Realized g/l reported on I.S = SP – CV or Amort cost § i income = Market rate × Initial FV § Unrealized g/l = FV at the end of Yr t – Amort Cost at end of Yr t If debt security is sold: § Realized g/l reported on I.S= SP – Recorded FV § i income = Market rate at purchase × Initial FV § Unrealized g/l = FV at the end of Yr t – Amortized Cost at end of Yr t If debt security is sold: § Realized g/l reported on I.S= SP – Recorded FV § i income = Market rate at purchase × Initial Fv If debt security is sold: § Cumulative unrealized g/l is removed from OCI and entire g/l recognized in P&l statement. Where, Realized g/l in I.S = (SP – Recorded FV) + Unrealized g/l
Balance Sheet (B.S)
§ §
Initially, at FV (IFRS) or initial price paid (US GAAP) Subsequently, reported at amort cost at the subsequent reporting date on B.S.
§ §
Initially, at FV. Subsequently, at FV at subsequent reporting date on B.S.
§ §
Reported at FV at the end of Yr t Subsequently, at FV at the subsequent reporting date on B.S
§ §
Reported at FV at the end of Yr t Subsequently, at FV at the subsequent reporting date on the B.S.
Statement ofSH’sEq uity N/A
Unrealized g/l (net of tax) = FV at end of Yr t – Amort Cost at end of Yr t • Unrealized g/l (net of tax) is reported as OCI
FinQuiz
Formula Sheet
Level II 2017
2. Goodwill = Cost of acquisition – investor’s share of the FV of the net identifiable assets PP Xxx Less: (% of Ownership Interest × BV of Investee’s Net (xxx) Assets) = Excess Purchase Price Xxx Less: Attributable to Net Assets: -Plant & Equipment (% of Ownership Interest × difference (xxx) b/wBV & FV) -Land (% of Ownership Interest × difference b/wBV & FV) (xxx) = Residual Amount (Treated as Goodwill) Xxx
Add: Unamortized excess PP (Excess PP – Amount attributable to PP&E) = Investment in Investee Transactions with Associates: 4. Upstream Transactions: Investor’s share of Associate’s reported NI (% of Ownership Interest × Reported net income)
xxx xxx
xxx
Less: Amort. of excess purchase price
(xxx)
Less: Unrealized profit (% of Ownership Interest × Profit from upstream sale in Associate’s NI)
(xxx)
3. Amort. of Excess PP: Investment in associate: PP Xxx Add: Investor’s share of Investee’s NI (% of Ownership Xxx Interest × Investee’s NI) Less: Div. received (% of Ownership Interest × Div. paid) (xxx) Less: Amort. of excess PP attributable to plant & equipment (xxx) (Amount attributable to PP&E* ÷ Remaining life of PP&E) = Balance in investment in Investee Xxx Where, *Amount attributable to Plant & Equipment = % of Ownership Interest of investor × (FV of P&E – BV of P&E)
= Equity Income to be reported as a line item on Investor’s I.S*
xxx
Beg net assets Add: NI Less: Div. paid = Ending net assets Investor’s proportionate share of Investee’s recorded net assets (% of Ownership Interest × Ending net assets)
• Composition of Investment account: Investor’s proportionate share of Associate’s net equity = [% of Ownership Interest × (beg BV of net assets) + (Reported NI of associate – Profit from upstream sale in Associate’s NI) – Div. paid by the associate)] Add: Unamortized excess PP (Excess PP – Amort. of excess PP)
Xxx Xxx (xxx) Xxx Xxx
Balance in the investment in Associate to be reported at the end of year: PP xxx Add: Equity income (as calculated above)* xxx Less: Div. received (% of Ownership Interest × Div paid) (xxx) •
= Value of Investment in Associate’s company at the end of year
xxx
xxx
xxx
FinQuiz
5. Downstream Transactions Investor’s share of Associate’s reported NI (% of Ownership Interest × Reported NI) Less: Amort of excess PP Less: Unrealized profit (% of Ownership Interest × Profit from the downstream sale in Associate’s NI) = Equity Income to be reported as a line item on Investor’s I.S
Formula Sheet
xxx
(xxx) (xxx)
xxx
Unrealized profit = % of goods unsold × Profit on the sale to investee Investor’s share of the unrealized profit = Unrealized profit × % of goods unsold Investor’s share of associate’s reported NI (% of Ownership Interest × Reported NI) Less: Amort of excess PP Add: Realized profit (% of goods unsold × Unrealized profit) = Equity Income to be reported as a line item on Investor’s I.S
Level II 2017
Goodwill 9. Full Goodwill = Total FV of the Subsidiary – FV of subsidiary’s identifiable net assets
under acquisition method = BV for A&L of Investor + FV for A&L acquired from Acquiree
10. Partial Goodwill Method: • Goodwill = FV of acquisition – Acquirer’s share of FV of all identifiable tangible and intangible assets, liabilities and contingent liabilities acquired Or • Goodwill = Purchase price – parent’s (acquirer’s) proportionate share of the FV of subsidiary’s identifiable net assets.
xxx
(xxx) xxx
11. Under Acquisition method, the allocation of PP: FV of the stock issued xxx Add: BV of Investee’s net assets xxx = Excess PP xxx
xxx
Business Combinations 6. Merger = Company X + Company Y = Company X 7. Acquisition = Company X + Company Y = (Company X + Company Y) 8. Consolidation = Company X + Company Y = Company Z
FV of the stock issued Less: FV allocated to identifiable net assets = Goodwill
xxx (xxx) xxx
12. Allocation of excess PP: Excess PPP = Sum of diff b/w FV and BV of identifiable assets + Goodwill 13. Combined Assets & Liabilities (A&L) reported on Consolidated B.S under acquisition method: Consolidated B.S
14. Combined Paid-in Capital (PIC) = (FV of the stock issued to effect the transaction – Par value of the stock issued) + Additional PIC of investor 15. Minority Interest = % of subsidiary not owned by the Parent × Subsidiary’s Equity 16. Value of non-controlling interest under full goodwill method = Non-controlling interest’s proportionate interest in subsidiary × FV of subsidiary on acquisition date 17. Value of non-controlling interest under partial goodwill method = Non-controlling interest’s proportionate interest in subsidiary × FVof the subsidiary’s identifiable net assets on acquisition date Goodwill Impairment: 18. Goodwill Impairment Test under IFRS: • Impaired when CA of the Cash-generating Unit > RA of the Cash-generating Unit •
Impairment loss = CA of Cash-generating Unit - RA of Cash-generating Unit where, RA = Higher of Net SP and its VIU Net SP = FV – costs to sell VIU = PV of expected future CF of cash-generating unit
FinQuiz
19. Goodwill Impairment Test under U.S. GAAP (Two Step Approach) • •
•
•
Step 1: Goodwill Impairment Test Impaired when CV of Reporting Unit (including Goodwill) > FV of Reporting Unit (including Goodwill). Step 2: Measurement of Impairment loss = CV of Reporting unit’s Goodwill - Implied FV of Reporting unit’s Goodwill Where Implied FV of Reporting unit’s Goodwill = FV of Reporting Unit – FV of Reporting unit’s net assets
Formula Sheet
5. Net i income = Discount rate × Net Pension asset 6. Net return on plan assets = Actual return on plan assets – (Plan assets × i rate) 7. Actuarial g/l = Actual return – (Plan assets × Expected return)
8. Total Periodic Pension Costs =Sum of components of periodic pension costs •
Reading 17: Employee Compensation: Post Employment & Share-Based • 1. Under DC Plans: Pension exp = Co.’s annual contribution to plans adjusted for ∆ in yr-end accruals 2. Funded Status = PV of DB obligations – FV of plan assets 3. Period pension cost of a Co.’s DB pension plan = ∆ in Net pension liability or asset adjusted for employer’s contributions 4. Net i exp = Discount rate × Net Pension liability where Discount Rate = rate used to calculate PV of future pension benefits
Total periodic pension cost in a given period = ∆in Net pension liability or asset adjusted for employer contributions Total Net periodic pension cost (End Funded Status* – Beg Funded Status*) – Employer Contribution where *Pension liability is treated as a negative
9. Adjusted Total P&L pension exp (income) •
•
= Current service costs + i costs + (-) actuarial losses (actuarial gains) + past service costs (or plan amendments) – (+) Actual return (loss) on plan assets Or = Reported Total P&L pension exp (income) + Expected return on plan assets – Actual return on plan assets
Level II 2017
10. Adjusted Pre-tax Income: • = Reported Pre-tax income + (Actual return on plan assets – Expected return on plan assets) Or • = Reported Pre-tax income + Total reported pension and other postretirement benefits - Current service costs - i exp component of pension cost + Actual return on plan assets 11. Adjusted Net Operating Exp=Reported Net operating exp – Total reported pension and other post-retirement benefits + Current service costs 12. Adjusted i Exp. = Reported i exp. + i exp. component of pension cost 13. Adjusted i and investment Income =Reported i and investment income + Actual return on plan assets 14. Compensation exp. = FV of stock on the Grant Date 16. Compensation exp recognized = š0<•34•0y³•ˆ 040+ 5•9Š•ˆ 34´‰•09;Šy40 •O‰ V•´;y0y0• 5•9Šy0• ‰•
FinQuiz
Formula Sheet
Foreign Subsidiary’s Functional Currency
Reading 18: Multinational Operations 1. Cumulative Translation Adjustment = CTA = Assets – Liabilities – Common Stock – Retained Earnings 2. Balance Sheet Exposure: B.S Exposure When assets translated at current X rate > liabilities translated at current X rate When liabilities translated at current X rate > assets translated at current X rate
Net Asset B.S exposure Net Liability B.S exposure
Level II 2017
Foreign Currency (FC) Strengthens Weakens +ve -ve translation translation adj adj -ve +ve translation translation adj Adj
(X = exchange)
inventories measured at market value under the lower of cost or market rule. ii) Measured at historical costs e.g. PP&E LIABILITIES Monetary liabilities: a/c payable, LT debt, accrued exp., and deferred income taxes. Nonmonetary liabilities: i) measured at current value ii) not measured at current value i.e. deferred revenue
FC
Parent’s Presentation Currency
Current rate
Historical rate
Current rate
Current rate
Current rate
Current rate
Current rate
Historical rate
Historical rates
Historical rates
Beg R.E + translated NI – div. translated at historical rate
Beg R.E + translated NI – div. translated at historical rate
Average rate
Average rate
Average rate
Average rate
Average rate
Historical rate
Average rate
Mixed (a mix of average rate & historical rate)
Net Assets or Net Liabilities
Net monetary assets or Net monetary liabilities
Accumulated as a separate component of equity
Included as g/l in NI
3. Re-measurement Gain = NI − NI before re-measurement gain 4. Re-measurement Loss = NI − NI before Re-measurement loss 5. Rules For Translation Of A Foreign Subsidiary’s FC Financial Statements (F.Ss) Into Parent’s Presentation Currency Under IFRS & U.S. GAAP
EQUITY Other than R.E i.e. Common Stock Retained Earnings (R.E)
Foreign Subsidiary’s Functional Currency FC Translation Method:
Current Rate method
Parent’s Presentation Currency Temporal Method
X rate at which F.Ss are translated from foreign subsidiary’s bookkeeping currency to parent’s presentation currency. ASSETS Monetary assets: Cash, a/c receivables Nonmonetary Assets: i) Measured at current value i.e. marketable securities &
Revenues EXPENSES Most Expenses Expenses related to assets translated at historical X rate e.g. COGS, Dep., & Amort. etc. NI
Current rate
Current rate
Exposure
Current rate
Current rate
Treatment of translation adj. in parent’s consolidated F.Ss
FinQuiz
Formula Sheet
TEMPORAL METHOD:
FC strengthens relative to parent’s presentation currency
FC weakens relative to parent’s presentation currency
Net Monetary Liability Exposure § Rev ↑ § Assets ↑ § Liabilities ↑
Net Monetary Asset Exposure § Rev ↑ § Assets ↑ § Liabilities ↑
CURRENT RATE METHOD § § §
Rev ↑ Assets ↑ Liabilities ↑
NI ↑ SH’ equity ↑ Translation gain
§ §
NI ↑ SH’ equity ↑ +ve Translation adj. Rev ↓ Assets ↓ Liabilities ↓
NI ↓ SH’ equity ↓ Translation loss
§ § §
§ § §
Rev ↓ Assets ↓ Liabilities ↓
§ § §
Rev ↓ Assets ↓ Liabilities ↓
§ § §
§ § §
NI ↑ SH’ equity ↑ Translation gain
§ § §
NI ↓ SH’ equity ↓ Translation loss
§
§ § §
§
§ §
Net Income ↓ SH’ equity ↓ -ve Translation adj.
Level II 2017
7. Restatement Factor =
·¸<<•0Š P<¹ 9 ‰
8. Restated Capital Stock = Capital stock original value × ·¸<<•0Š P<¹ 9 ‰
9. Restated Revenue = Revenue original value ×
·¸<<•0Š P<¹ 9 ‰
10. Loss from holding beg balance in cash = -Beg balance in cash × ·¸<<•0Š P<¹ 9 ‰
11. Loss from increase in cash during the yr = -Increase in cash × ·¸<<•0Š P<¹ 9 ‰
12. Gain from holding note payable = Notes payable × ·¸<<•0Š P<¹ 9 ‰
6. Impact of Changing Exchange Rates on Exposure Foreign Currency Strengthens Weakens CURRENT RATE METHOD: Net Assets Net Liabilities TEMPORAL METHOD: Net Monetary Assets Net Monetary Liabilities
Hyperinflationary Economy
Gain Loss
Loss Gain
Gain Loss
Loss Gain
13. Avg. effective tax rate =
U;O RO‰ ¤<•Š;O ½334¸0Šy0• ¤<4myŠ9
14. Organic sales growth = Net sales growth + Foreign X impact + Acquisition/Divestiture impact.
FinQuiz
Reading 19: Evaluating Quality of Financial Reports 1. DSR (days sales receivable index) = (Receivablest/Salest) / (Receivablest– 1/Salest–1) 2. GMI (gross margin index) = Gross margint–1 / Gross margint 3. AQI (asset quality index) = [1 – (PP&Et+ CAt)/TAt ] / [1 – (PP&Et–1+ CAt-1)/TAt-1] 4.
SGI (sales growth index) = Salest/Salest–1
5. DEPI (depreciation index) = Dep ratet– 1/Dep ratet where, Dep rate = Dep/(Dep + PP&E) 6. SGAI (sales, general, and admin exp index) = (SGAt/Salest) / (SGAt–1/Salest–1) 7. Accruals = (Income before extraordinary items – Cash from operations)/TA 8. LEVI (leverage index) = Leveraget / Leveraget–1 where, Leverage = Debt / Assets 9. Earnings t+1 = α + (β1 × Earnings t) + ε 10. Account receivable turnover = (365/DSO)
Formula Sheet
11. Z-score = 1.2 × 3.3 × 1.0 ×
RÃÄU U½ S;»•9
¿•Š À·
+ 1.4 ×
U½
+ 0.6 ×
Level II 2017
V.R U½
Ç.È 4m RɸyŠP Ã.È 4m »y;¼y»yŠy•9
+
+ •
U.½
(Cash t + ST invstmnt. t)} – {Total liab t – (Total LT debt t + Debt in current liab.)}] B. S based Accruals Ratio = ¿ß½~ +¿ß½~k/ ¿ß½~ ’¿ß½~k/
Reading 20: Integration of Financial Statement Analysis 1. DuPont Analysis: • ROE = Tax Burden × Interest Burden × EBIT margin × TATO × Financial Leverage • ROE = NI/EBT × EBT/EBIT × EBIT/Sales × Sales/Assets × Assets/Equity • ROE = Net profit margin × asset turnover × leverage • Adjusted Asset base = Adjusted Total Assets = Total Assets of the company – Investments in Associates • Adjusted NI = NI of Co – NI from Associates • Adjusted Tax Burden =
>
3. CF based aggregate accruals: • Aggregate Accruals = NI t – (CFO t + CFI t) • CF based Accruals Ratio = ¿ÄÚ +(·†ßÚ ’·†ÄÚ ) (¿ß½Ú ’¿ß½Úk/ ) >
• •
Op. CF before interest and taxes = Op. CF + cash i paid + cash taxes paid Op income adjusted for accounting ∆ = Profit before i& taxes + amort. of goodwill
4. Cash Return on Assets =
߉.·† ½5• U.½
5. Cash Flow to Reinvestment = ߉.·† 3;‰yŠ;» •O‰•0ˆyŠ¸<•9
¿Ä+RɸyŠP y034´• RÃU
•
6. Cash Flow to Total Debt =
Adjusted TATO = ÏÐÑ ÒÐÓ ÔÕkÒÐÓ Ö×.Ø-ÑÙÚÛ-Ú.ÜÖ-‘ ÔÕkÖ-‘ Ö×.Ø-ÑÙÚÛ-Ú
߉.·† ¼•m4<• y0Š•<•9Š & áâãä¬ U.›
>
7. Capacity to pay debt (in years) Accruals and Earnings Quality 2. B.S based aggregate accruals • Aggregate Accrualst = NOAt – NOAt-1 where, NOAt = Net operating Assets t = Op Assets t – Op Liab t = [{TA t –
=
U.› ߉.·†+·;‰yŠ;» RO‰•0ˆyŠ¸<•9
8. CF Interest Coverage =
߉.·† ¼•m4<• Z& áâãä¬ Z ¤;yˆ
FinQuiz
Formula Sheet
Decomposition and Analysis of the Co’s Valuation: 9. Parent Co. pro-rata share of subsidiary/affiliates = (Subsidiary’s share price in FC× Shares held by Parent Co. × X- rate)/Parent Co. total market capitalization 10. Implied Value of Parent Co. (excl. subsidiary/affiliates) = Parent Co.’s Mkt Cap - Value of subsidiary/affiliate holdings 11. P/E ratio of Parent Co =
¤;<•0Š ·4.’9 ´TŠ ·;‰ ¿Ä 4m ¤;<•0Š ·4.
12. Implied P/E ratio of Parent Co. = Implied Value of Parent Co. (excluding subsidiary/affiliates) NI of Parent Co. −Equity Income from subsidiary/affiliates 13. Discount to Benchmark = ê Ö
Reading 21: Capital Budgeting 1. Depreciable Basis = Purchase price + any Shipping or handling or installation costs
Off-Balance Sheet Leverage from Operating Leases 14. Adj. Fin Lev =
U.½ ’ ¤È 4m »•;9• ‰;P´•0Š9
15. Adj. D-to-E ratio =
U.R U.›’¤È 4m »•;9• ‰;P´•0Š9
16. Adj. i-coverage Ratio = RÃÄU+›•‰ •O‰’V•0Š RO‰ Z •O‰’½99¸´•ˆ Z •O‰ 40 »•;9•9
U.R
9. Profitability index = PI = 1 + (NPV/Initial investment) when PI > 1, invest and when PI < 1, do not invest.
Expansion Project 2. Initial Outlay = FCInv + NWCInv NWCInv = ∆non-cash current assets – ∆non-debt current liabilities= ∆NWC
10. CAPM = ri = R F + βi [E (R M) – R F]
3. Annual after-tax operating cash flow = CF = (S – C – D) (1 – T) + D or CF = (S – C) (1 – T) + TD
12. Economic Income = AT CF from investment + ∆ in MV = AT CF from investment + (End MV – Beg MV) OR = AT CF from invstmnt. – (Beg MV – End MV)= AT CF from invstmnt. – Eco. Dep
4. Terminal year after-tax non-operating cash flow = TNOCF = Sal T + NWCInv – T (Sal T – B T) Replacement Project 5. Initial Outlay = FCInv + NWCInv – Sal 0 + T (Sal 0 – B0)
Õ03Ž´;
Level II 2017
6. Annual after-tax operating cash flow (incremental) • CF = (∆S – ∆C – ∆D) (1 – T) + ∆D or • CF = (∆S – ∆C) (1 – T) + T∆D 7. Terminal year after-tax non-operating cash flow = TNOCF = ∆Sal T + NWCInv – T (∆Sal T – ∆B T) 8.
(1 + Nominal rate) = (1 + Real rate) (1 + Inf rate)
Economic and Accounting Income 11. Accounting income = Rev – Exp
13. Economic Profit (EP) = NOPAT– $WACC where, NOPAT = net operating profit after tax i.e. EBIT (1 – Tax rate) EBIT = earnings before interest and taxes $WACC= dollar cost of capital = WACC × capital Capital (after Year 1) = investment = Initial Investment – depreciation 14. MVA or NPV =
R¤Ú ì Š\1 (1’À½··)Ú
15. Total value of Co. = original investment + NPV 16. Residual income (RI) = NI – Equity Charge • RI t = NI t – (re × B t-1)
FinQuiz
Formula Sheet
where,
•
VÄÚ ì Š\1 1’< Ú Ð
V=D+E= Ä0Š•<•9Š ‰;P´•0Š9 40 ˆ•¼Š
•
MVA =
•
Total value of Co. = NPV (PV of RI) + Original Equity investment + Original Debt investment
•
Reading 23: Dividends & Share Repurchases Analysis
+
·49Š 4m ˆ•¼Š (RÃÄU – y0Š•<•9Š ‰;P´•0Š9 40 ˆ•¼Š) ·49Š 4m •É¸yŠP
8. Systematic Risk = βa =
Claims Valuation 17. Total value of Co. = value of liabilities + value of equity
Level II 2017
› È
βd +
R È
βe
βe = βa + (βa – βd) (D/E)
9. AT cost of debt = BT cost of debt × (1 – Marginal tax rate)
Reading 22: Capital Structure 1. WACC = rÀ½·· = R È
› È
10. MM Proposition I with Taxes: Co.’s value is maximized at 100% Debt • V L = V U + (t ×D) • Value of Unlevered all equity Co. =
×rˆ × 1 − t +
×r•
VU =
2. Total value of Co. = V = D + E • 3. WACC › È
without
×rˆ +
R È
taxes
=
rÀ½·· =
Ä0Š•<•9Š ‰;P´•0Š9 40 ˆ•¼Š
·49Š 4m ˆ•¼Š (RÃÄU – y0Š•<•9Š ‰;P´•0Š9 40 ˆ•¼Š)
› R
+
11. MM Proposition II with Taxes: WACC is minimized at 100% Debt
› R
• +
re = r0 + (r0 –rd)(1 – t)
› R
(r0 –rd)(1-t) = Slope coefficient * *(r0- r d)(1 – t) < (r 0 - r d)
6. According to MM proposition I: V L = V and E = V – D 7. According to MM proposition II: • Cost of Equity = r• = ru + (ru − rˆ )
·49Š 4m ˆ•¼Š (RÃÄU – y0Š•<•9Š ‰;P´•0Š9 40 ˆ•¼Š)(1 – Š) ·49Š 4m •É¸yŠP
4. Cost of Equity = r• = ru + (ru − rˆ )
·49Š 4m •É¸yŠP
<ðÕññ Ä0Š•<•9Š ‰;P´•0Š9 40 ˆ•¼Š
V=D+E=
×r•
5. V = D + E =
RÃÄU 1 – Š
•
Share is sold (after share goes ex-div.) 2. CF from Sale = Sale price – cap gains tax (owed on sale) + AT amount of div. = Px– (Px– Pb) (TCG) + D (1 – TD) 3. When Px = Pw then Pw – (Pw – Pb) (TCG) = Px– (Px– Pb) (TCG) + D (1 – TD) P‡ − PO = D
1+Uò 1+Uñó
or ∆P = D
1+Uò 1+Uñó
where, ∆P = ∆ in price when the stock goes from with div to ex-div 4. Double Taxation Method: ETR= Corp. tax rate + {(1 – Corp. tax rate) (Indiv. tax rate)}
›
WACC with taxes: rWACC = ×rd× (1 – R
U
Share is sold just before it goes ex-dividend: 1. Cash flow from Sale = Sale price – capital gains tax owned on the sale = Pw – (Pw – Pb)(TCG) where, Pw = price with the right to receive dividend Pb = purchase price where b is for buy TCG = marginal tax rate on capital gains
È
t)+ ×re È
12. Static trade-off theory of capital structure VL = V U + tD – PV(Costs of financial distress)
5. Dividend imputation tax system: ETR = SH’s Marginal Tax Rate 6. Split tax system: ETR = Corp. tax rate on div + {(1 – Corp. tax rate on div.) (personal tax rate)}
FinQuiz
Formula Sheet
Payout Policies: 7. Stable Div. Policy • Expected ↑ in Div. = ↑ in Earnings × Target payout ratio × Adj. factor • Adj. factor = 1/no. of yrs. over which adj. in div. will take place • Expected Div = Last div. + (Expected ↑ in earnings × Target payout ratio × Adj. factor)
Reading 26: Mergers & Acquisitions 1. Statutory Merger = Co. X + Co. Y= Co. X 2. Subsidiary Merger = Co. X +Co. Y=(Co. X + Co. Y)
Equity % in capital structure) or •
Div. = Zero, whichever is greater.
9. Div. Payout Ratio =
›y5.
• •
Unlevered NI = EBIT × (1- tax rate) NOPLAT = Unlevered NI + ∆ in deferred taxes
11. FCF = NOPLAT + NCC – ∆ in Net WC – Capex
3. Consolidation = Co. X + Co. Y = Co. Z 4. New shares issued by Acquirer = ÇTŠ 3;‰ 4m U;<••Š
8. Residual Div. Policy • Div. = Earnings – (Capital budget ×
Level II 2017
9Š43T ‰
5. Post-merger no. of shares outstanding = Acquirer’s pre-merger total shares outstanding + new shares issued by Acquirer
12. FCF = NI + net interest after-tax + ∆ in deferred taxes + net noncash charges – ∆ in NWC – Capex Terminal Value: 13. Using constant growth formula Terminal ValueU =
¿Ä
10. Div. Coverage Ratio =
¿Ä ›y5.
11. FCFE Coverage Ratio = †·†R [›y5.’SŽ;<• V•‰¸<3Ž;9•9]
FCFE = CFO – FCInv + Net Borrowings Reading 24: Corporate Performance, Governance & Business Ethics
6. Post-Merger EPS =
7. Post merger P/E (if market is efficient) =
¤<• ´•<••< 9Š43T ‰
8. No. of acquirer shares received by each shareholder (in target Co.) = No. of target shares he/she owns × X ratio
1. Share Overhang = ¿4.4m 9Ž;<•9 <•‰<•9•0Š•ˆ ¼P ŠŽ• ߉Šy409 U4Š;» 04.4m 9Ž;<•9 4¸Š9Š;0ˆy0•
100
Terminal ValueU = FCFU ×
¤ †·†
15. EV =MV of debt + MV of equity – cash & cash equivalents
¤49Š ´•<••< R¤S
9. HHI = Reading 25: Corporate Governance
14. Using Market Multiple
½3ɸy<•<¹ 9 ‰<• ´•<••< R;<0y0•9’U;<••Š¹ 9 ‰<• ´•<••< R;<0y0•9 ¤49Š ´•<••< 0¸´¼•< 4m 9Ž;<•9 4¸Š9Š;0ˆy0•
†·†Ô (1’•) (À½··ü‘ýþÙÚБ +•)
câöä¬ ÷ø ÷ùáúùá ÷— ¦Zøû Z [ Z ¥÷áâö câöä¬ ÷ø ÷ùáúùá ÷— ûâøwäá ×
2
10. Unlevered NI = NI + Net Interest after-tax • Net interest after-tax = (i exp – i income) × (1 – Tax rate) Or
16. Takeover Premium = takeover (deal price) per share (of target Co.) – current stock price of target Co. =
›¤ + S¤ c§
17. Estimated takeover price of Target = Estimated stock price of Target based on Comparables + Estimated takeover premium •
When takeover premium is given in %, Estimated takeover price of Target
FinQuiz
= (Estimated stock price of Target based on Comparables) × (1 + Takeover premium in %) 18. Target Shareholders’ gain = Premium = P T –VT where, P T = price paid for target company V T = pre-merger value of target company
Formula Sheet
• •
V–P: True Mispricing VE–V: Valuation Error where,VE = estimated value P = market price V = intrinsic value
2. Residual Income Model = NI – (cost of equity × Beg value Equity)
7. IRR: • Intrinsic value= D1 / (k-g) • If asset (fairly priced), market price = intrinsic value: k = (D1 / P0) + g
9. GGM Intrinsic value = D1/ (k-g)
20. Post-merger value of the combined company = V A* = V A + V T + S – C where, V A = pre-merger value of the acquirer C = cash paid to target SH i.e. cash paid = cash price paid per share of target co. × no. of shares outstanding of target co.
2. Price appreciation R = (PH-P0)/P0
1. Mispricing = VE – P = (V- P) + (VE – V) • VE–P: Mispricing
{(V0 – P0)/P0} = estimate of return from convergence over period
Reading 28: Return Concepts 1. Dividend yield or investment income = (DH/P0)
Reading 27: Equity Valuation: Applications & Processes
•
8. Req ROE = Rf + ERP
19. Acquirer’s gain = Synergies – Premium = S – (P T – V T)
21. In Stock offer = P T = (N × P AT) where, P T = price paid for target co. N = No. of new shares target receives P AT = price per share of combined firm after merger announcement
Level II 2017
3. HPR = r = {(DH + PH) / P0} – 1 OR r = {(P1 – P0+CF1) / P0 4. Expected Alpha = Exp. R – Req. R 5. Realized Alpha (Ex-post alpha) = (Actual HPR) – (Contemporaneous Req. R) 6. Expected HPR: • When an asset’s intrinsic value ≠ market price, the investor expects to earn = RR + return from the convergence of price to value • When an asset’s intrinsic value = price, the investor expects to earn RR only. • E (RT) ≈ rT + {(V0 – P0) / P0} where,rT = periodic required RoR,
Macroeconomic Model Estimates (Supply side models): 10. ERP = [{(1+EINFL) (1+EGREPS) (1+EGPE)-1} +EINC]-Expected Rf R • where EINFL= expected inf.( forecasted as) {(1+YTM of 20-yr Tbonds) / (1+YTM of 20-yr TIPS)} – 1. • EGREPS = expected growth rate in real EPS. • Real GDP growth rate = labor productivity growth + labor supply growth rate Labor supply growth rate = population growth rate + increase in labor force participation rate • EGPE = expected growth rate in P/E ratio. (For efficient markets 1+EGPE = 1+0 = 1.
FinQuiz
•
EINC = expected income component (includes dividend yield & reinvestment R)
11. CAPM: Required Return on share i = Current expected Rf R + Bi (ERP) • where ERP = Expected R on mkt portfolio – RF R • Beta = Cov of returns with mkt R /mkt portfolio var. 12. Adjusted Beta = (2/3) (Unadjusted beta) + (1/3) (1.0) 13. Beta Estimation for Thinly Traded Stocks and Nonpublic Companies • Bu ≈ [1/ {1+ (D/E)}] ×Be • Be’ ≈ [1+ (D’/E’)] ×Bu 14. Multifactor Models = r = Rf+ (RP)1 + (RP)2 + … + (RP)k • RPi = (Factor sensitivity)i × (Factor RP)i. 15. The Fama-French Model (FFM): ri =Rf + Bimarket × RMRF + Bisize× SMB + Bivalue × HML • •
RMRF = RM –Rf SMB(small minus big) = Avg. R on 3 small-cap portfolios – avg. R on 3 large-cap portfolios.
Formula Sheet
•
HML (high minus low) = Avg. R on 2 high Book-to-market portfolios – avg. R on 2 low book-to-market portfolios.
16. Pastor-Stambaugh Model (PSM): ri = Rf + Bimarket×RMRF + Bisize× SMB + Bivalue × HML+ BiLiq× LIQ 17. 5-factor BIRR Model: ri = T-bill rate + (sensitivity to confidence risk × confidence RP)–(sensitivity to time horizon × time horizon RP) – (sensitivity to inf. risk × inf. RP) + (sensitivity to business cycle risk × business cycle RP) + (sensitivity to mkt. timing risk × mkt. timing RP)
Level II 2017
Reading 29: Industry & Company Analysis 1. % of sales (specific geographic region) = Sales of a particular region / Total sales of a co. 2. Co.’s projected Rev. growth = Projected mkt. share × Projected sales of a given product mkt. 3. Forecasted variable costs = % of rev. Or = Unit volume × Unit variable costs 4. COGS =Raw materials + Direct labor + Overhead (in producing the goods)
18. Build-Up Approaches for Private Business Valuation: ri = rf + ERP + Size premi +Specific Co. premi
5. Finance costs = (Fixed i rate on debt × Gross debt at beg. of period) – (i income rate × cash position at beg of period)
19. Bond yield Plus RP (BYPRP) cost of equity = YTM on the co.’s LT debt + RP
6. Gross debt = LT financial debt + ST financial debt + Accrued interest
Country Spread Model 20. ERP estimate = ERP for a developed mkt + Country prem. • Country Prem. = yield on emerging mkt bonds (denominated in currency of developed market) – yield on developed mkt. govt. bonds
7. Net debt = Gross debt – Cash and cash equivalents 8. Effective i rate = i exp / Avg gross debt
21. Cost of Capital = WACC = {D/(D+E)}rd (1-Tax rate) + {E / (D+E)}rE
9. i rate on avg cash position =i income / Avg cash position 10. i rate on avg. net debt = Net i exp / Avg. net debt
FinQuiz
Formula Sheet
11. Deferred tax asset/liability = Profit and loss (reported) tax amount – Cash tax amount
18. Post cannibalization revenue =Precannibalization revenue – Estimated impact on rev. from cannibalization
12. Projected A/C receivable = Forecasted annual sales (assuming all credit sales) × (Assumed DSO/ 365)
19. Overall organic rev. growth = [(1 + volume growth) (1 + % of price/mix contribution to rev. growth)] -1
13. Projected inventory = Assumed COGS / Assumed Inventory TO ratio
20. Construction of Pro Forma I.S: Sales Less: COGS = Gross profit Less: Admin. exp. Less: Distrib. Exp. Add: Other income from operation = EBIT Add (Less): Other operating income (exp.) Less: Finance costs & other financial exp. = Profit before tax Less: Income Tax Add: Income from associates = Profit from continuing operations Add (Less): Profit (loss) from discontinued operations = Net profit for the year Less: Non-controlling interests = Owners of the co.
14. ROIC= NOPLAT / Invested Capital = EBI / (Operating assets – Operating liab.) 15. ROCE = Op. profit / Capital employed (i.e. debt and equity capital) 16. Rev. loss for co. due to cannibalization of demand = Projected no. of units of product cannibalized by the new substitute product × Estimated ASP Where, • Average selling price (ASP) = ·4´‰;0P¹ 9 •9Šy´;Š•ˆ ;5•. <•5. ·4´‰;0P¹ 9 •9Šy´;Š•ˆ 9Žy‰´•0Š9 4m ‰<4ˆ¸3Š
•
No of units of a product cannibalized by the new substitute product = Expected no. of product shipments × % representation of each category (e.g. consumer & non-consumer) × Cannibalization factor for the category
17. Post cannibalization shipments =Precannibalization shipments – Expected cannibalization
21. EBITDA = EBIT + Dep. & amort. exp.
Level II 2017
22. Forecasted CF Statement CF from operating activities: NI (profit after taxes) Adj. to determine CF: Add: dep. ↓ in a/c receivable ↓ in inventory ↑ in a/c payable Total adjustments Net CF from operating activities CF from investing activities: 𝐴𝑑𝑑: ↓ in plant and equipment Net CF from investing activities CF from financing activities: ↑ in notes payable ↑ in LTD Less: Dividends paid Net CF from financing activities Forecasted ↑ in cash 23. Forecasted B.S PP&E Add: Investment in associates Add: Other financial assets Add: Deferred tax assets = Total non-current assets Inventories Add: Trade and other receivables Add: Cash & cash equivalents Add: Other current assets =Total current assets Total assets = Total non-current + Total current assets Share capital
FinQuiz
Add: Share premium Less: Treasury shares Add: Consolidated reserves+Net profit to co. owners Plus: Translation reserve +/-: Profit or loss recorded in equity = Equity attributable to shareholders Plus: Non-controlling interest = Equity LT financial debt Add: Provision for employee benefits Add: LT provisions for liabilities and charges Add: Deferred tax liabilities = Total non-current liabilities ST financial debt and accrued interest Add: Trade and other payables Add: Income tax payable Add: ST provisions for liabilities and charges Add: derivative financial instruments Add: Liabilities held for sale = Current liabilities 24. FCFF: Normalized operating profit Less: Taxes = Normalized operating profit after tax Add: Dep. & amort. ∆ in WC Less: Capital expenditures = FCFF
Formula Sheet
Level II 2017
Reading 30: Discounted Dividend Valuation
6. GGM for Preferred stock (fixed rate perpetual preferred stock) = Vu =
1. Asset’s value is PV of its expected future ·†Ú 0 Š\1 1’< Ú
CFs i.e. Vu =
2. RI = NI – (cost of equity × Beg. BV of common equity) 3. In RI Model: Value of stock = BVPS at t = 0 + PV of expected future residual earnings • where, BVPS = common SHs’ equity / no. of common shares outstanding • RI model (assumes Clean Surplus Accounting holds) i.e. BV t = BVt-1 + NIt – Divt 4. DDM • With Single HP = Value of Stock = PV of expected Div. + PV of expected Selling Price at the end of year one = Vu = •
›/ (1’<)/
+
¤/ (1’<)/
›/
+
›? (1’<)?
+
¤?
8. Actual value of a company’s share = Vu = R/ <
•
• •
+ PVGO where, PVGO =Sum of PV of expected profitable opportunities of reinvesting the earnings. E1/r = no-growth value per share When P0 = V0 then. PVGO = Pu −
›Ú
1 <
+
0 Š\1 1’< Ú
For n-HPs = Vu =
•
When HP is extended into indefinite future: Vu =
+
R/
R/
¤
<
or = R
¤È£ß R/
¤
¤#
R
R/
=
›/
R/ <+•
1’< -
›Ú ì Š\1 (1’<)Ú
or
¤#
R/
where, 1/r = value of P/E for nogrowth company. PVGO/E1 = component of P/E value that represents growth opportunities.
¤-
•
È#
Can be restated as
9. Leading ratio =
(1’<)?
<
7. GGM ERP = 1-yr. forecasted div. yield on market index + consensus LT earnings growth rate – LT govt. bond yield
Value of stock for 2 years HP = Vu = (1’<)/
›
10. Trailing P/E ratio =
¤# R#
=
=
1+¼ <+•
›# (1’•) (<+•)
R#
=
(1+¼)(1’•) (<+•)
5. Gordon Growth Model (GGM) = Vu = ›# × 1’• <+•
or =
›/ <+•
11. GGM can be used to derive required RoR =r=
›# (1’•) ¤#
+g=
›/ ¤#
+g
FinQuiz
Formula Sheet
SŽ;<•Ž4»ˆ•<9¹ •É¸yŠP U4Š;» ½99•Š9
12. Two-Stage Div Discount Model = Vu = ›Ú 0 Š\1 (1’<)Ú
+
È-
SŽ;<•Ž4»ˆ•<¹ 9 •É¸yŠP ¿Ä
(1’<)-
=
where, •
V0 =
•
Vu =
¿Ä
15. ROE =
›# × 1’•& - 1’•'
¿Ä
=
U4Š;» ½99•Š9
S;»•9
S;»•9 U4Š;» ½99•Š9 U4Š;» ½99•Š9
×
×
=
SŽ;<•Ž4»ˆ•<9¹ •É¸yŠP
<+•'
›# (1’•& )Ú 0 Š\1 (1’<)Ú
×
Level II 2017
= Net profit margin × Asset Turnover × Leverage
+
›# ×(1’•& )- ×(1’•' ) 1’< - (<+•' )
Reading 31: Free Cash Flow Valuation
13. H-Model •
Vu =
•
Vu =
1. PV of FCFF = Firm Value =
›# × 1’•' › ×º× •& +•' + # or <+•' <+•' ›# × 1’•' ’ ›# ׺×(•& +•' )
14. Estimating Sustainable Growth Rate = g = b × ROE •
g=
¿Ä+›y5yˆ•0ˆ9
¿Ä U4Š;» ½99•Š9
×
¿Ä S;»•9
×
S;»•9 U4Š;» ½99•Š9
×
SŽ;<•Ž4»ˆ•<9¹ RɸyŠP
• •
7. CF from operating activities = CFO = NI + NCC – WCInv.
†·††Ú ì Š\1 (1’À½··)Ú
(<+•' )
where, gL= normal LT div. growth rate after year 2H gS= initial ST div. growth rate H = half-life in years of the highgrowth period i.e. high growth period = 2H years
g = PRAT i.e.. g = profit margin (P) × retention rate (R) × asset turnover (A) × financial leverage (T)
2. WACC = Tax rate
ÇÈ 4m › ÇÈ 4m ›’ÇÈ 4m R ÇÈ4m R
+
× rˆ × 1 −
ÇÈ4m ›’ÇÈ4m R
× r•
3. PV of FCFE = Equity value =
ì †·†RÚ Š\1 (1’<)Ú
4. Constant-Growth FCFF valuation Model = Firm Value = Vu =
†·††/ À½··+•
=
†·††# ×(1’•) À½··+•
5. Constant-Growth FCFE valuation Model = Equity Value = Vu =
†·†R/ <+•
FCInv = End gross PPE – Beg. gross PPE b) When LT assets are sold during the yr: FCInv = Capital expenditures – proceeds from sale of LT assets or FCInv = (End. gross PPE – Beg. gross PPE) - Proceeds from sale of LT assets WCInv = ∆ in Current assets excl. cash & cash equivalents – ∆ in Current liab. excl. ST debt
=
†·†R# ×(1’•) <+•
6. Computing FCFF from NI = FCFF = NI + NCC + Int × (1 – Tax rate) + Preferred stock div. – FCInv – WCInv a) When no LT assets are sold during the yr:
8. Computing FCFE from FCFF • FCFE = FCFF – Int ×(1 – Tax rate) – preferred stock dividends + Net Borrowing + issuance of preferred stocks – redemption of preferred stock • FCFE = NI + NCC – FCInv – WCInv + Net Borrowing + issuance of preferred stocks – redemption of preferred stock • FCFE = CFO – FCInv + Net Borrowing + issuance of preferred stocks – redemption of preferred stock • Total value of Equity (common) = Total Firm value – Market value of Debt – Preferred stock 9. Finding FCFF and FCFE from EBIT or EBITDA • FCFF = EBIT (1 – Tax rate) + Dep – FCInv – WCInv
FinQuiz
FCFF = EBITDA (1 – Tax rate) + Dep (Tax rate) – FCInv – WCInv • FCFE = FCFF – Int (1 – Tax rate) + Net borrowing + issuance of preferred stocks – redemption of preferred stock 10. Forecasted FCFF = Forecasted [EBIT ×(1 – Tax rate) – FCInv – WCInv]
Formula Sheet
Required rate of return (real) [in %]
•
11. Incremental fixed capital expenditures as a proportion of sales increases = ·;‰yŠ;» •O‰+›•‰ •O‰ Ä03<•;9• y0 9;»•9
12. Incremental working capital expenditures as a proportion of sales increases = Ä03<•;9• y0 À· Ä03<•;9• y0 9;»•9
13. FCFE = NI – (FCInv – Dep) – WCInv + Net borrowing where, Net borrowing = DR×(FCInv – Dep) + DR×(WCInv) Or FCFE = NI – (FCInv – Dep) – WCInv + (DR) ×(FCInv – Dep) + (DR) ×(WCInv) Or FCFE = NI - (1-DR) ×(FCInv – Dep) – (1 – DR) ×(WCInv)
Level II 2017
15. Single-Stage FCFF and FCFE Model for International Valuation: FCFFu ×(1 + g <•;» ) Value of firm = Vu = WACC<•;» − g <•;» FCFF1 = WACC<•;» − g <•;»
Reading 32: Market based Valuation: Price & Enterprise Value Multiples 1. Trailing P/E or Current P/E = ·¸<<•0Š ÇTŠ ¤
2. Forward P/E or Leading P/E or Prospective P/E =
Value of Stock = Vu FCFEu ×(1 + g <•;» ) = r<•;» − g <•;» FCFE1 = r<•;» − g <•;» 16. Two-stage FCFF valuation model equation is: •
Firm Value = †·††-Ü/ (À½··+•)
•
×
†·††Ú 0 Š\1 (1’À½··)Ú 1
†·†R-Ü/ (<+•)
×
U4Š;» R;<0y0•9 À•ŽŠˆ ½5• 04.4m 9Ž;<•9 ;3Š¸;»»P 4/9 ˆ¸
4. Diluted EPS =
U4Š;» R;<0y0•9 ¿4.4m 9Ž;<•9 4/9 ‡Ž•0 Ž4»ˆ•<9 4m •O3•<3y9•ˆ ŠŽ•y< 4‰Šy409 Š4 4¼Š;y0 34´´40 9Š43T
5. Justified Forward P/E = P0/E1 =
(1’À½··)-
+
3. Basic EPS =
+
Two-stage FCFE valuation model equation = Equity Value = 0 †·†RÚ Š\1 (1’<)Ú
·¸<<•0Š Ç;
1 (1’<)-
17. Excess Cash = Total Cash Available −
6. Justified Trailing P/E = P0/E0 = =
1+¼ ×(1’•) <+•
ò/ Ö/
<+•
=
1+¼ <+•
›# (1’•)/R# <+•
where
P = price; E = earnings; D = dividends; r = required rate of return; and g = dividend growth rate
Total Assets of Firm× 14. Modified Build-Up method to estimate real discount rate: Country return (Real) [in %] +/ - Industry Adjustment [in %] +/ - Size Adjustment [in %] +/ - Leverage Adjustment [in %]
Ç•ˆy;0 »•5•» 4 m Ä0ˆ¸9Š
7. PEG ratio =
SŠ43T¹ 9 ¤/R RO‰•3Š•ˆ R;<0y0•9 £<4‡ŠŽ V;Š• y0 %
8. Yardeni Model CEY = CBY – (b × LTEG) + Residual where,
FinQuiz
Formula Sheet
CEY = current earnings yield on the mkt. index i.e. E/P. CBY = current Moody’s Investors Service A-rated corporate bond yield. LTEG = consensus 5-year earnings growth rate forecast for the mkt index. b = coefficient (measures weight, the mkt gives to 5-year earnings projections). •
By taking inverse:
¤ R
=
1 ·Ã,+¼ × +UR£
9. Own Historical P/E: Justified price = Benchmark value of own historical P/Es × Most recent EPS 10. Terminal Value (T.V) based on Fundamentals: • T.V in yr n = (justified trailing P/E) × (forecasted earnings in year n) • T.V in year n = (justified leading P/E) × (forecasted earnings in year n+1) 11. Terminal Value based on Comparables: • T.V in yr n = (Benchmark trailing P/E) × (forecasted earnings in year n) • T.V in yr n = (Benchmark leading P/E) × (forecasted earnings in year n+1) 12. P/B = •
¤
where
04.4m 34´´40 9Š43T 9Ž;<•9 4/9
* It includes preferred stock and div. in arrears on preferred stock. BVPS for whole company = Š4Š;» ;99•Š9 – Š4Š;» »y;¼y»yŠy•9
=
Sº¹ 9¹ •É¸yŠP – Š4Š;» •É¸yŠP 5;»¸• 3»;y´9 ŠŽ;Š ;<• 9•0y4< Š4 34´´40 9Š43T∗ # 4m ·.S 9Ž;<•9 4/9
19. Dividend Yield = •
13. Justified P/B = P0/B0 =
•
VßR+•
=
›y5 ‰•< 9Ž;<• ¤
Trailing Div Yield = Leading Div Yield = †4<•3;9Š•ˆ ›y5 ‰•< 9Ž;<• 45•< ŠŽ• 0•OŠ P<
<+•
·¸<<•0Š ´TŠ. ¤
¤È 4m •O‰•3Š•ˆ m¸Š¸<• <•9yˆ¸;» •;<0y0•9
20. Div Yield (by using GGM) = Justified Div Yield =
Ãu
15. P/S =
¤
·¸<<•0Š ´TŠ ¤
14. Justified P/B based on RI model = P0/B0 = 1+
›
›y5yˆ•0ˆ V;Š•
0¸´¼•< 4m 9Ž;<•9 4¸Š9Š;0ˆy0•
›u ¤u
=
<+• 1’•
¤
where Net Sales = Total Sales – returns– customer discounts 16. P/S ( in terms of Gordon Growth Model = Justified P/S =
¤# S#
Ö# &#
=
1+¼ (1’•) (<+•)
where, E0/S0 = Business’s profit margin 17. g = Retention rate (b) × ROE g = b × PM0 × U4Š;» ½99•Š9
S;»•9 U4Š;» ½99•Š9
×
SŽ;<•Ž4»ˆ•<9¹ RɸyŠP
where, PM0 = Profit Margin at t = 0 18. Price To Cash Flow
BVPS for equity shareholders = U½ – U+ – ¤.S
•
Level II 2017
•
=
•
=
•
=
•
=
¤
Or
Or
21. EV = MV of Common equity + MV of preferred stock* + MV of debt – Cash & Short-term Investments • MV of Common equity = No. of shares o/s × Price per share • Cash & Investments = cash, cash equivalents, short term investments etc. *If minority interest exists and it is not included elsewhere, then it should be added back. 22. ROIC =
߉•<;Šy0• ‰<4myŠ ;mŠ•< Š;O U4Š;» y05•9Š•ˆ ·;‰yŠ;»
23. Total Invested Capital = TIC = MV of Common equity + MV of preferred stock + MV of debt
Or 24. Earnings surprise UEt = EPS t – E (EPS t) where, UEt= unexpected earnings for quarter t
FinQuiz
•
Formula Sheet
EPSt= reported/actual EPS for quarter t E(EPSt) = expected EPS for the quarter Percent Earning Surprise =
•
R;<0y0•9 S¸<‰
•
RO‰•3Š•ˆ R¤S
•
Scaled Earnings Surprise = R;<0y0•9 S¸<‰
•
Level II 2017
=NOPAT – Total Capital Charge = NOPAT – Debt Charge – Equity Charge = NOPAT – (AT cost of debt × Debt Capital) – (cost of equity × Equity Capital) RI (with preferred stock) = NI – Equity Charge – Preferred Stock Div RI = (ROIC – Effective Capital Charge) × Beg. Capital
•
=
R¤SÚ +R (R¤SÚ ) . [R¤SÚ +R (R¤SÚ )]
where, EPSt= reported/actual EPS for time t E (EPSt) = expected EPS for the time t σ [EPSŠ − E (EPSŠ )] = S.D of [EPSŠ − E (EPSŠ )] over some historical time period. 26. Relative strength indicator =
SŠ43T¹ 9 ‰•
27. Harmonic Mean = XH=
0 - (/) *./ 6 *
Reading 33: Residual Income Valuation 1. End. BV of equity = Beg. BV of equity + Earnings – Div. B t = B t-1 + E t – Dt & D t = E t - (B t - B t-1) = E t + B t-1 - B t
3. EVA = NOPAT – (C% × TC) Or = [EBIT (1 – t)] – (WACC × invested capital) where, C% = cost of capital TC = Total capital WACC × invested capital = dollar cost of capital Invested capital = net WC + net fixed assets = BV of LT debt + BV of equity 4. MVA = MV of Co. – Accounting BV of total capital = MV of Co – (BV of Debt + BV of Equity)
ì Š\1 (1’<)Ú
•
Vu = Bu +
VÄ/ (1’<)/
+
VÄ? (1’<)?
+
VÄ/ (1’<)/
+
⋯ 6. RI Model (general) = Vu = Bu + ì VßRÚ +< ×ÃÚk/ Š\1 1’< Ú ¤
¤#
Ã
Ã#
7. Justified =
=
VßR+• <+•
= 1 +
VßR+< <+•
where, Justified Price is the stock’s Intrinsic value i.e. P0 = V0 BV of equity = B0 = Total assets – total liab. 8.
Tobin’s q =
ÇÈ 4m ›•¼Š ;0ˆ RɸyŠP V•‰»;3•´•0Š 349Š 4m U4Š;» ½99•Š9
9. Single-Stage RI Valuation = Vu = Bu + VßR+< <+•
•
×Bu
Implied Growth rate in RI = g = r − Ã# VßR+< È# +Ã#
5. RI model • RIt = E t – (r × B t-1) = (ROE – r) × B t-1 • Two components of intrinsic value of stock/equity i. Current BV of Equity that is B0. ii. PV of expected future RI
2. Residual Income (RI) • = NI – Equity Charge = NI – (Equity Capital × Cost of Equity Capital)
= Bu +
RÚ +<ÃÚk/
25. Standardized Unexpected Earnings = SUE t
VÄÚ ì Š\1 1’< Ú
Vu = Bu +
VÄ? (1’<)?
+
VÄ/ (1’<)/
+⋯
VÄ/ (1’<)/
10. Multi-Stage RI Valuation = V0 = B0 + (PV of interim high-growth RI) + (PV of continuing RI) • PV of continuing RI in year T–1 =
+ •
VÄÔ where, 1’<+2 1’< Ôk/
ω=
persistence factor, 0 ≤ ω ≤ 1 Assumptions about Continuing RI:
FinQuiz
Formula Sheet
o RI is at +ve level currently and will persist at this level in the future indefinitely: PV of continuing RI in year T-1 =
VÄÔ
=
1’<+2
VÄÔ 1’<+1
=
VÄÔ <
o RI will become 0 from the terminal yr forward. PV of continuing RI in year T-1 =
VÄÔ 1’<+2 1’< Ôk/ VÄÔ
1’<+u 1’< Ôk/
=
To value Equity directly = V =
†·††/ <+•
2. Excess Earnings or RI = Normalized earnings – [(RR on WC × value of WC) + (RR on fixed assets × value of fixed assets)]
1’< Ôk/
VÄÔ 1’<+2 1’< Ôk/
o RI declines to long-run mean level of mature industry. Where premium over book value is assumed at the end of time horizon T (PT – Bt), current value (V0) =
(ROEt − r )Bt −1 + PT − BT B0 + ∑ (1 + r )T (1 + r )T t =1 T
1 1’·40Š<4» ¤<•´y¸´
†·††/ À½··+•3
Value of Equity = Vf – MV of Debt
•∗ •
1 + 𝑟 𝑇∗ + 𝑇 1 + 𝑟 𝑇∗
5. Lack of Marketability Discount = DLOM =
1 + 𝑟 𝑇∗ + 𝑇
5. Yield Curve Movement and the Forward Curve
• F (T*, T) = § §¥∗ ¥∗’¥
È;»¸• 4m ";Š–ŠŽ•–´40•P" ‰¸Š 4‰Šy40
• P* (T) = § §á ’á ¥ • F*(t, T*, T) = §∗ §∗ ¥∗ ¥∗ ’+¥+á á
5;»¸• 4m 9Š43T ¼•m4<• ;0P ›+ßÇ
6. Total Discount = [1 – (1 – DLOC in %) × (1 – DLOM in %)]
• F*(t, T*, T) =
6 (~Ü•∗ Ü•k~) 6 (~) 6 (~Ü•∗ k~) 6 (~)
=
§∗ (¥∗ ’¥) § (¥∗)
=
F (T*, T) Reading 35: The Term Structure & Interest Rate Dynamics 1. Discount Factor = P (T) =
1 1’¬ú÷áøâáä •
Active Bond Portfolio Management 6. 1-yr. HPR = =
1’ø (¥) •
Reading 34: Private Company Valuation 1. Capitalized CF to the firm = Vm =
DLOC = 1 −
1
Where PT =BT × (forecasted P/B ratio)
Forward rate model can be expressed as:
= 1 + 𝑓 𝑇 ∗, 𝑇
4. Calculation of Lack of Control Discount =
VÄÔ
r (T) = {[ 1 + r (1)] [1 + f (1,1)] [1 + f (2,1)] [1 + f (3,1)] … [1 + f (T – 1,1)]} (1/T) -1
3. MVIC = MV of Debt + MV of Equity
=
o RI declines to 0 as ROE approaches r over time (& RI will become 0 eventually). i.e. 0 ≤ ω ≤1 PV of continuing RI in year T-1=
•
•
Level II 2017
2. Forward pricing model: P (T* + T) = P (T*) × F (T*,T) 3. Forward rate model = [1 + r (T* + T)] (T* + T) = [1 + r (T*)] T* × [1 + f (T*, T)] T 4. Spot rate for a security, having maturity of T > 1
1’ø ¥’1 •Ü/ 1’— 1,¥ •
= 1 + 𝑟(1)
(when the spot curve one year from today is today’s forward curve) 7. Return of the 2-year zero-coupon bond over 1-yr HP = ¤
+P< ³•<4+34¸‰40 ¼40ˆ 1 P< m<4´ Š4ˆ;P ¤¸<3Ž;9• ‰
1
−
FinQuiz
•
Formula Sheet
15. Interest rate volatility for a security with
Price of a 2-yr zero-coupon bond 1 yr from today = §âø7âöùä÷—8÷[–
maturity T at time t = σ (t, T) =
(1’¦9–øâáä—÷ø1:ø8÷[–1:ø—ø÷ûá÷–â:)
•
Price of a 3-yr zero-coupon bond 1 yr from today = §âø7âöùä÷—8÷[– (1’¦9–øâáä—÷øá9÷:ø8÷[–1:äâø—ø÷ûá÷–â:) §âø7âöùä÷—8÷[–
=
C
∆D (~.•) D (~,•)
Ƈ
Reading 36: The Arbitrage Free Valuation Framework
1’— 1,>
8. Swap Spread = Fixed-rate of an interest rate swap – Interest rate on “on-the-run” Govt. security ¬ (¥) ¥ á\1 1’ø á Ú
•
Level II 2017
+
1 1’ø ¥ •
↓ 𝑓𝑖𝑥𝑒𝑑𝑟𝑎𝑡𝑒𝑙𝑒𝑔
=1 ↓ 𝑓𝑙𝑜𝑎𝑡𝑖𝑛𝑔𝑟𝑎𝑡𝑒𝑙𝑒𝑔
9. TED spread = LIBOR - T-bill rate of matching maturity 10. Libor–OIS spread = Libor - Overnight indexed swap (OIS) rate 11. Local expectations theory =
1 § (á,¥)
=
1 + 𝑟 1 1 + 𝑓 1,1 1 + 𝑓 2,1 𝑓 3,1 … [1 + 𝑓 𝑇 − 1,1 ]
1+
12. Cox–Ingersoll–Ross (CIR) Model = dr = a (b – r) dt + σ 𝑟𝑑𝑧 13. Vasicek Model = dr = a(b – r)dt + σdz 14. Ho-Lee model = drt = θtdt + σdzt
Reading 37: Valuation & Analysis: Bonds with Embedded Options 1. Value of callable bond = Value of straight bond – Value of issuer call option 2. Value of issuer call option = Value of straight bond – Value of callable bond 3. Value of putable bond = Value of straight bond + Value of investor put option 4. Value of investor put option = Value of putable bond – Value of straight bond 5. The rate in the up state = Ru = Rd × e2σ 𝑡 where, Rd = Rate in the down state σ = Interest rate volatility t = Time in years between “time slices” 6. Duration =
Èk +ÈÜ
8. Effective
∆Gùø7ä ? × §F#
10. Value of capped floater = Value of straight bond – Value of embedded cap 11. Value of floored floater = Value of straight bond + Value of embedded floor Analysis of a Convertible Bond 12. Conversion Ratio (CR) = No. of shares of C.stock from exercising call option 13. Conversion Price (or stated conversion price) = Par value of convertible bond ÷ CR 14. Conversion Value (or Parity) = Market price of C.stock × CR 15. Straight Value or Investment Value = Market value of a security without conversion option 16. Min. Value of a Convertible Security is (greater of conversion value or straight value) 17. Market Conversion Price or Conversion Parity Price = ·V
ÈÜ ’Èk + >×È#
>× È# × ∆, ? ¤Èk + ¤ÈÜ Duration = >× ∆·¸<5• × ¤ÈE
§Fk ’ §FÜ + >× §F#
Ç;
>×È# × ∆,
7. Convexity =
9. Effective Convexity =
18. Market Conversion Premium per share = Market Conversion Price – Current Market Price
FinQuiz
Formula Sheet
19. Premium Payback Period = Ç;
20. Favorable Income Differential per share = ·4¸‰40 y0Š•<•9Š+ ·V ×·.9Š43T ›y5.‰•< 9Ž;<• ·V
21. Premium over straight value = Ç;
–1
2. Credit spread = Yield to maturity of a risky bond – Yield to maturity of a Govt. bond 3. Put option’s price = Value of risky debt – Value of riskless debt 4. Black-Scholes Option pricing Formula =
St = At N(d1 ) − ke−r(T −1) N(d2 ) Where,
⎛ A ⎞ 1 ln⎜⎜ t ⎟⎟ + r (T − t ) + σ 2 (T − t ) K 2 d1 = ⎝ ⎠ σ T −1
22. Non-callable/Non-putable Convertible security value = Straight value + Value of Call option on stock 23. Callable Convertible bond value = Straight value + Value of call option on stock – Value of call option on bond 24. Callable & Putable Convertible bond value = Straight value + Value of call option on stock – Value of call option on bond + Value of Put option on bond 25. Value of Call Option – Value of Put Option = PV (Forward price of bond on exercise date – Exercise price) Reading 38: Credit Analysis Models 1. Expected loss = Full amount owed – Expected recovery or = Loss given default × Probability of default
d2 = d1 – σ T − 1 5. Value of debt = D (t, T) = PV of payoff on co.’s debt if default occurs + PV of payoff on co.’s debt if default does not occur =
At N (−d1 ) + Ke − r (T −1) N (d 2 ) •
where, N (d2) = Risk neutral probability of the co.’s debt not defaulting
6. Credit Risk Measures • Probability of the debt defaulting = Prob. (AT< K) = 1 – Prob. (AT ≥ K) = 1 – N(e2) Where,
Level II 2017
•
⎛ A ⎞ 1 ln⎜⎜ t ⎟⎟ + u (T − t ) + σ 2 (T − t ) K 2 e1 = ⎝ ⎠ σ T −t
• e2 = e1 - σ T − 1 7. Co.’s asset R in CAPM (a static one-period model): Co.’s asset R = Rf + β of co.’s asset (Expected R per year on Mkt. portfolio – R f) = Rf+ (β of co.’s asset × Mkt.’s ERP) 8. Price of debt𝐷 𝑡, 𝑇 = 𝐸
« 1’ø/ ∆ 1’ø/Ü∆ … 1’ø•Ü∆
9. Credit risk measures in reduced form model: • Default probability over [0,T] = Prob 𝑡 ≤𝑇 =1− 𝐸 •
á IJ « 1’K I# ∆ ’ 1’K I∆ … 1’K I•k∆ ∆
Expected loss = ¥+∆ 𝐸á\u
•
á IJ « 1’K I# ∆ ’ 1’K I∆ … 𝜆 1’K IJ ∆
𝑋Z ∆
Present value of the expected loss = K P (t,T) – D (t,T)
10. Historical Estimation • Probability of default over [t, t+∆] =
1
Prob (t) =
N
1+ e
−α − ∑ bi X i t i =1
FinQuiz
•
Formula Sheet
Parameters estimation:
Reading 39: Credit Default Swaps
Level II 2017
•
N
⎛ dt ⎞ i ln⎜ ⎟ = α + ∑ bi X t Where ⎝ 1 − dt ⎠ i =1 •
dt = {1 if default, 0 if no default} To estimate the loss given default: N
t(Xt) =
c 0 + ∑ ci X i t i =1
Where {ci for i = 1, …, N} are constants.
1. Upfront premium = Credit spread – Standard rate • 2. Expected Credit Loss (%) = Payout ratio = 1 – Recovery rate (%) 3. Expected Credit Loss Amount or Payout amount = Payout ratio × Notional amount
• • •
11. Price of the coupon bond (assuming no arbitrage and frictionless markets) T −1
BG (t) =
∑ CP(t , i) + (C + F ) P(t, T ) i =1
12. Credit spread (t) = Avg. yields on risky zero-coupon bond – Avg. yields on riskless zero-coupon bond Or = [Average yields on the risky zero-coupon bond – Average yields on riskless zerocoupon bond] + Liquidity premium or = Expected % loss per year on the risky zero-coupon bond + Liquidity Premium 13. PV of expected loss = PV of CF of riskless debt – PV of CF of risky debt = [P (t,T) – D (t,T)] XT Where, XT = Promised CF at T of a risky Co.
4. Loss Given Default: • Expected loss = Full amount owed – Expected recovery • Expected loss = Loss given default × Probability of default • Prob. of default (at some point during T years) = 1 – Prob. of no default during T years 5. Value of protection leg = Expected payoff of bond/loan with credit risk - Expected payoff of bond/loan with no credit risks 6. Value of premium leg = PV of pmts. made by the protection buyer to the protection seller 7. Upfront pmt = PV of protection leg – PV of premium leg 8. Credit spread ≈ Prob. of default × Loss given default (%) 9. Credit spread Pricing Conventions
Upfront premium = PV of credit spread – PV of fixed coupon Or = (Credit spread – Fixed coupon) × D of the CDS PV of credit spread = Upfront prem. + PV of fixed coupon Credit spread ≈ (Upfront prem./D) + Fixed coupon Upfront premium in % = 100 – Price of CDS in currency per 100 par Price of CDS in currency per 100 par = 100 – Upfront premium %
10. Profit for the buyer of protection ≈ ∆ in spread in bps × D × NP 11. % change in CDS price = ∆ in spread in bps × D 12. Basis = CDS spread (prem.) – Bond’s credit spread* *Bond’s Credit spread = Yield on bond Investor’s cost of funding Bond yield = Rf rate + Funding spread + Credit spread where, Rf + Funding spread = LIBOR 13. Synthetic CDO = Portfolio of default-free securities + CDS holdings
FinQuiz
Reading 40: Pricing & Valuation of Forward Commitments Pricing & Valuing of Forwards & Futures 1. Forward contract value (Long) VT(T) = ST – F0(T). 2. Forward contract value (short)VT(T) = F0(T) – ST. rcT
3. FV(S0) = S0e . (compounded continuously) 4. FV(S0) = S0(1 + r)T (compounded annually) 5. Vt(T) = PVt,T[Ft(T) – F0(T)] 6. Forward Price (carry arbitrage): F0(T) = Soe(rc−γ)T 7. F0(T) = FV0,T(S0) 8. Future Value (adj. for carry cash flows) = F0(T) =FV0,T(S0+θ0−γ0) 9. PVt,T[Ft(T)−F0(T)] 10. F0(T) = FV0,T(S0 + θ0 – γ0) 11. F0(T)=𝑆u 𝑒 (<3’©-‐‑N)U (carry arbitrage: continuous compounding)
Formula Sheet
13. Interest Paid = TA – NA = NA[L0(m)tm] FRAs 14. Settlement amount at h for receivefloating: NA{[Lh(m)−FRA(0,h,m)]tm}/[1+Dh(m)t m] 15. Settlement amount at h for receive-fixed: NA{[FRA(0,h,m)−Lh(m)]tm}/[1+Dh(m)t m] 16. FRA(0,h,m)={[1+L0(h+m)th+m]/[1+L0(h) th]−1}/tm
QF0(T) = [1/CF(T)]{FV0,T[B0(T+Y)+AI0]−AIT−FVCI0,T} Currency Forward & Fututre Contracts: 22. F0(£/€,T) =FV£,T(1)/[FV€,T(1)S0(€/£)]= S0(£/€)FV£,T(1)/FV€,T(1) 23. Vt (T)=PV£,t,T[Ft(£/€,T)−F0(£/€,T)] Pricing & Valuing Swap Contracts: Interest Rate Swap Contracts: Floating Leg Cash Flow: 24. Si=CFFLT,i=APFLT,irFLT,i=(
17. FRA Value at time g = FRA(0,h,m)={[1+L0(h+m)th+m]/[1+L0(h) th]−1}/tm
25. FS=CFFIX,i=APFIX,irFIX,i=(
Fixed Income Forward & Future Contracts:
26. FB=C
18. Accrued interest = Accrual period × Periodic coupon amount Or AI = (NAD/NTD) × (C/n)
27. Swap Pricing =
Fixed Income Forward/Future Price including conversion factor: 19. F0(T)=QF0(T)CF(T) 20. FV0,T[S0−PVCI0,T]=B0(T+Y)+AI0−PVCI0,T]
Interest Rate Forward & Future Contract: 12. Terminal Amount = TA = NA[1 + L0(m)tm]
Level II 2017
21. Conversion factor adj. FV adj. for carry =
OPQRS•,J ¿U›RS•,J
OPQRTU,J ¿U›RTU,J
)rFLT,i
)rFIX
Value of Floating Rate Bond: [ Z\1 𝑃𝑉u,áZ (1)+PV0,tn(1) 1+¤Èu,Š0(1) j §F #,~J (1)’ J./
28. Value of fixed rate swap at time t = V=NA(FS0−FSt) [Z\1 PVt, ti 29. Value of fixed rate bond in currency k: FBk=Ck [Z\1 𝑃𝑉u,áZ,w (1) + 𝑃𝑉u,Š0,T (Park)
FinQuiz
Formula Sheet
30. Equilibrium Fixed Swap rate = rFIX,b=
Level II 2017
23. E(c2) = π2c++ + 2π(1 – π)c+– + (1 – π)2c
where probability of an up move π = [FV(1) – d]/(u – d)
1+§Fu,á[,8(1) §F#,~J,X (1)
24. E(p2) = π2p++ + 2π(1 – π)p+– + (1 – π)2p– –
31. Va=NAa,0(rFIX,a,0 [Z\1 𝑃𝑉á,áZ,â + 𝑃𝑉á,á[¹,â )−StNAb,0(rFIX,b,0 [Z\1 𝑃𝑉á,áZ,8 + 𝑏 )
Expected terminal option payoffs 11. E(c1) = πc+ + (1 – π)c
BSM Model 25. c = SN(d1) – e–rTXN(d2)
12. E(p1) = πp+ + (1 – π)p–
32. Vt = FBt(C0) – (St/St–)NAE – PV(Par – NAE)
26. p = e–rTXN(–d2) – SN(–d1) 13. Put Call Parity = S + p = PV(X) + c where
Reading 41: Valuation of Contingent Claims 1. Call Value = cT = Max(0,ST – X) 2. Put Value pT = Max(0,X – ST)
•
d1 =
For calls: 14. c++ = Max(0,S++ – X) = Max(0,u2S – X)
•
d2=d1− 𝜎 𝑇
15. c+– = Max(0,S+– – X) = Max(0,udS – X)
One Period Binomial Model: 3. Up factor = u=
c’
16. c
¬
4. Down factor = d=
c+ ¬
5. Call Hedge ratio h= 6. Put Hedge ratio =
Y Ü +Y k c Ü +c k
úÜ +úk c Ü +c k
≥0
≥0
––
= Max(0,S
––
–
7. single-period call = c = hS + PV(–hS + c ) 8. single-period put= p = hS + PV(–hS– + p–) 9. c = PV[πc+ + (1 – π)c–] 10. p = PV[πp+ + (1 – π)p–]
C ¥
27. Replicating strategy cost = nSS + nBB 28. nS = N(d1) > 0 for calls
2
– X) = Max(0,d S – X)
29. nS = –N(–d1) < 0 for puts
For puts: 17. p++ = Max(0,X – S++) = Max(0,X – u2S)
30. nB = –N(d2) < 0 for calls
18. p+– = Max(0,X – S+–) = Max(0,X – udS)
31. nB = N(–d2) > 0 for puts
19. p– – = Max(0,X – S– –) = Max(0,X – d2S)
Carry Benefit-Adjusted BSM Model 32. c = Se–γTN(d1) – e–rTXN(d2)
20. Two period Binomial Hedge Ratio h+= –
ö[(c/I)’(ø’C>/>)¥
Two Period Binomial Model:
Y ÜÜ +Y Ük
33. p = e–rTXN(–d2) – Se–γTN(–d1)
c ÜÜ +c Ük
21. c = PV[π2c++ + 2π(1 – π)c+– + (1 – π)2c– –]
carry benefit-adjusted put–call parity: 34. p + Se–γT = c + e–rTX
22. p = PV[π2p++ + 2π(1 – π)p+– + (1 – π)2p– –]
35. E(cT) = Se(r–γ)TN(d1) – XN(d2)
Expected terminal option payoffs:
36. E(pT) = XN(–d2) – Se(r–γ)TN(–d1).
FinQuiz
European Options on Futures 37. c = e–rT[F0(T)N(d1) – XN(d2)]
Formula Sheet
44. RECSWN = (AP)PVA[RXN(–d2) – RFIXN(– d1)]
Price of Interest Rate call & Put options: 40. C= 𝐴𝑃 𝑒 +ø á\+1’áû [FRA(0,tj−1,tm)N(d1)−RXN(d2)] 41. p= (𝐴𝑃)𝑒 -‐‑ø(á\-‐‑1’áû) [RXN(−d2)−FRA(0,tj−1,tm)N(−d1)] where, • •
d1=
ö[[¦dP(u,á\-‐‑1,áû)/dI]’(C>/>)á\-‐‑1 C á\-‐‑1
d2=d1−σ
𝑡𝑗-‐‑1
Receiver swaption Model Value: 46. RECSWN = PV[E(RECSWN,T)],
55. 𝑝−p ≈ Deltap ( 𝑆 − 𝑆 ) +
where • E(PAYSWN,T) = erTPAYSWN • E(RECSWN,T) = erTRECSWN.
Reading 42: Derivative Strategies
Option Greeks & Implied Volatility
Reading 43: Private Real Estate Investments
47. Call Deltac = e–δTN(d1)
1. Rent of Net Lease = Gross rent – Op. exp.
48. Put Deltap = –e–δTN(–d1) 49. Optimal # of Hedging Units = NH =−
§÷øá—÷öZ÷–äöáâ Qäöáâ^
Change in option Price based on Delta Approximation: 50. 𝑐−c ≅ Deltac(𝑆−S)
for calls
Payer Swaption: 43. PAYSWN = (AP)PVA[RFIXN(d1) – RXN(d2)] Receiver swaption:
bâûûâc
54. 𝑐−c ≈ Deltac ( 𝑆 − 𝑆 ) +
Swaptions PV of annuity matching Forward Swap payment: 42. PVA= [\\1 𝑃𝑉u,á\ (1)
Delta-plus- Gemma Approximation:
Payer Swaption Model Value: 45. PAYSWN = PV[E(PAYSWN,T)]
38. p = e–rT[XN(–d2) – F0(T)N(–d1)] 39. Futures option put–call parity: c = e– rT [F0(T) – X] + p
Level II 2017
51. 𝑝−p ≅ Deltap(𝑆−S)
for puts 52. 𝑐=c+Deltac(𝑆−S)
Gamma: 53. Gammac = Gammap =
ä kaÔ SC ¥
n(d1)
>
( 𝑆-‐‑𝑆 )>
for calls bâûûâd >
( 𝑆-‐‑𝑆 )>
for puts
2. Lease Rent = Min. rent + % of sales rev above a certain level • In case of natural break-point, Lease Rent = % of sales rev. above a certain level × Tenant’s sales 3. Implied land value = Value after construction – Cost to construct a building 4. Appraised value of a property =
¿ßÄ ·;‰yŠ;»y³;Šy40 <;Š•
where, • NOI = Net operating income for the subject property • Gross potential income = Rental income at full occupancy + Other income
FinQuiz
•
• •
Formula Sheet
Effective gross income =Gross potential income – Vacancy and collection loss NOI = Effective gross income – Op. exp. OR NOI = Gross potential income – Estimated vacancy losses – Estimated collection losses – Insurance – Property Taxes – Utilities - Repairs and maintenance exp.
5. Capitalization rate =
†y<9Š+P•;< ¿ßÄ ¤<4‰•<ŠP 5;»¸•
6. Discount rate = Cap rate + Growth rate 7. Value of property = NOI / (discount rate – Growth rate)
•
•
• •
(Discount raVVVVVVVate – growth rate) Loss in income due to renovation = Post-renovation NOI of a property NOI of a property during renovation time-period PV of the lost income è Loss in value = Loss in income due to renovation / (1 + discount rate) Value of a property = Post-renovation Value - Loss in value OR Value of a property = {NOI of a property during renovation timeperiod + [Post-renovation NOI of a property (1 + growth rate)] / (Discount rate – growth rate)]} / (1 + discount rate)
13. Avg. no. of months vacant until the lease is renewed = Lease Non-renewal probability × No. of months vacant if not renewed
8. Capitalization rate = ¿ßÄ S;»• ‰
9. Reciprocal of the cap rate =
¤
10. All Risks Yield = ARY = V•0Š V•3•0Š 9;»•9 ‰
11. Mkt. value =
V•0Š ½V,
14. Vacancy rate = Avg. no. of months vacant until the lease is renewed / (Lease term + Avg. no. of months vacant until the lease is renewed) 15. Gross income multiplier = GIM = S;»•9 ¤
12. Stabilized NOI i.e. (NOI of a nonrenovated property or post-renovated NOI of a property) • Post-renovation Value = Postrenovation NOI of a property /
16. Total capital value = PV of income until the rent review + PV of what the property could be sold for at rent review (PV of estimated rental value or ERV)
Level II 2017
17. Under Layer Method Value of a property = PV of current contract rent in perpetuity + PV of expected incremental rent after the rent review 18. When effective age of property < its economic life, Physical deterioration = % worn out = Effective age / Economic life 19. Incurable depreciation deduction = (Replacement cost + Developer’s profit – curable depreciation costs) × Physical deterioration 20. Amount of functional obsolescence = Income loss due to the functional obsolescence / cap rate 21. Amount of locational obsolescence associated with building only = Total Loss in the value - Loss in land value 22. Cost Approach Calculations • Total depreciation = Physical deterioration + functional obsolescence + Locational obsolescence + Economic obsolescence • Depreciated building value = (Replacement cost + Developer’s profit) – Total depreciation • Final Appraisal value èEstimated value of the property = Depreciated building value + Land value
FinQuiz
Formula Sheet
• 23. Valuation in an international context when land and building are valued separately: • Income to the building = NOI – assumed land lease payment • PV for building = Income to the building / Cap rate or discount rate • Total value = PV for Building + Value of the land (from sales comparison approach) 24. The NCREIF Property Index (NPI): • Total Return of individual Property = ¿ßÄ+·;‰•O’(R0ˆy0• ÇÈ+Õ•.ÇÈ) Õ•.ÇÈ
• • •
Income return = Cap rate = NOI / beginning value Amount of cash flows available each quarter = NOI – Capex Capital return =
R0ˆy0• ´ ;
Total Index Return = Value-Weighted average return for individual properties 25. Private market real estate debt • Loan-to-value = Loan / value of the property • Max. loan amount based on LTV ratio = LTV ratio (in %) × Appraisal value of property (in $) • Debt serve coverage ratio = NOI/Debt service • Debt service=Interest + Principal payments on the mortgage. •
• •
Principal payments=Part of the loan payment that amortizes the loan over the loan term. Max.debt service based on DSCR = NOI/DSCR When the loan is interest-only, Max.loan amount based on DSCR= Max. debt service based on DSCR / Debt interest rate
26. Equity dividend rate or Equity yield rate = Cash flow / Equity where, Cash flow = NOI – Debt Service Equity = Price – Mortgage 27. Calculating Leveraged IRR: CF received by the equity investor from the sale = Sale price – Mortgage balance PV = – Initial investment PMT = Cash flow n = Holding period FV = Cash flow received from sale CPTà I/Y è Leveraged IRR. 28. Calculating Unleveraged IRR: Cash flow received by the equity investor from the sale = Sale price + NOI in the 1st year PV = – Initial investment PMT = NOI in the 1st year n = Holding period FV = Sale price CPT à I/Y èUnleveraged IRR.
Level II 2017
Reading 44: Publicly Traded Real Estate Securities 1. Rent paid by Tenants = Net rent + Proportionate share of the common area costs of the mall (based on space leased) 2. NAVPS = (MV of R.E Co.’s assets – MV of R.E Co.’s liab.) / # of shares outstanding 3. Appraised value = NOI / Cap rate 4. Estimating NAVPS: • Pro forma cash NOI = NOI – Non cash rents* + Adj. for full impact of acquisitions • *Non-cash rent = Avg. contractual rent over the leases’ terms – Cash rent actually paid. • Estimated future expected cash NOI = Pro forma cash NOI + Expected growth in NOI • Estimated value of operating real estate =Estimated future expected cash NOI / Cap rate • Estimated gross asset value = Estimated value of operating real estate + BV of Cash & equivalents + BV of Land held for future development + BV of a/c receivables + BV of Prepaid/other assets • Net asset value = Estimated gross asset value – Total debt – Other liab. (but not deferred taxes)
FinQuiz
•
NAVPS = Net asset value / # of shares outstanding
Formula Sheet
• •
5. P/FFO = Current stock prices / Yr-ahead estimated FFO • FFO = Net earnings + Dep. Exp. on R.E + Deferred tax charges – g/l from sales of property and debt restructuring + Losses on sales of property and debt restructuring OR • FFO = EBITDA – Interest Expense 6. P/AFFO = Current stock prices / Yr-ahead estimated AFFO • AFFO = FFO – Non cash rent* – Recurring Maintenance type Capital expenditures – Leasing costs (i.e. leasing agent’s commissions – Tenants’ improvement allowances) • *Non-cash rent = Straight-line rent Cash rent paid during the period 7. Estimated Value of a REIT Co. in yr N = (P/FFO of overall REIT group for yr N) × REIT co.’s expected FFO in yr N or = (P/AFFO of overall REIT group for yr N) × REIT co.’s expected AFFO in yr N Reading 45: Private Equity Valuation 1. PIC:
PIC = Cumulative capital (CC) called down PIC Multiple = PIC / CC
2. DPI = Sum of distb. / CC called down (or PIC) 3. RVPI = NAV after distb. / CC called down (or PIC) 4. TVPI = DPI + RVPI 5. Mgmt. fees = % fee × PIC 6. Carried interest= % × (NAV before distb. –CC) in year when NAV before distb. Is first > CC Thereafter, Carried interest = % × ΔNAV before distb. 7. NAV before distb.t = NAV after distbt-1 + called down capitalt– mgmt feest+ operating resultst 8. NAV after distbt = NAV before distb.t– carried interestt – distb.t 9. CF for Gross IRRt= – Capital called down at the beg of periodt+1 + Op. resultt-1 10. CF for Net IRRt = – Capital called down at the beg of periodt+1 + Op. resultt-1– mgmt.. feest– carried interestt Venture Capital Method:
Level II 2017
11. General Case: NPV Method Step 1: POST = V / (1 + r) t Step 2: PRE = POST – I Step 3: F = I / POST Step 4: y = x [F / (1 – F)] Step 5: p1 = I / y 12. Alternative Method using IRR: Step 1: W = I (1 + r) t Step 2: F = W / V Step 3: y = x [F / (1 – F)] Step 4: p1 = I / y Step 5: POST = I / F or p1 × (x + y) Step 6: PRE = POST – I or PRE = p1 ×x 13. NPV Method with multiple (two) rounds of financing: Step 1: Compound interest between dates: • T1 and T2 = (1 + R1) • T2 and T3= = (1 + R2). Step 2: POST2 = V / (1 + R2) Step 3: PRE2 = POST2–I2 Step 4: POST1 = PRE2 / (1 + R1) Step 5: PRE1 = POST1 –I1 Step 6: F2 = I2 / POST 2 Step 7: F1 = I1 / POST 1 Step 8: y1 = x1[F1/ (1 – F1)] Step 9: p1 = I1/ y1 Step 10: x2 = x1 + y1 Step 11: y2 = x2[F2/ (1 – F2)] Step 12: p2 = I2/ y2 14. Accounting for Risk in Venture Capital
FinQuiz
•
By adjusting Discount Rate = r = 1’ø 1+e
– 1
15. By adjusting terminal value using Scenario analysis = Adj. TV = (% prob. scenario 1 × expected E × expected P/E multiple) + (% prob. scenario 2 × expected E × expected P/E multiple) + … + (% prob. scenario n × expected E × expected P/E multiple) Reading 46: Commodities & Commodity Derivatives: An Introduction 1. Theory of Storage states: Future Prices = Spot Price of the physical commodity + Direct Storage costs – Convenience Yiled 2. Price Return = (Current Price – Previous Price)/Previous Price 3. Total Return = Price Return + Roll Return + Collateral Return Reading 47: The Portfolio Management Process & the Investment Policy Statement
Reading 48: An Introduction to Multifactor Models 1. Multifactor Model = Ri = ai + b i1I1 + bi2I2+ …..+ biK IK+ εi 2. Arbitrage Pricing Theory = E (R p) = RF + λ1β p,1 + λ2β p,2 + …..+ λk βp,k
Formula Sheet
3. Carhart Four Factor Model = E (Rp) = RF+ βp1RMRF + + βp2SMB + + βp3HML ++ βp4WML…..+ ℰ P RMRF = Portfolio’s sensitivity to Mkt. Index SMB = small minus big HML = high minus low WML = winners minus losers 4. Macroeconomic Factor Model = Ri =ai + b i1 F1 + bi2 F2+ …..+ biKFK+ εi 5. biK =
Fâöùä ÷— w —÷ø ⬬äá Z +P7äøägä 7âöùä ÷— w C (—÷ø 7âöùä¬ ÷— w )
6. Actual Inf. = Predicted Inf. + Surprise Inf.
Level II 2017
Reading 49: Measuring & Managing Market Risk 1. Std. Normal Dist. (z-dist.)= 2. To obtain a 5% VaR =
d+n C
𝐸 d§ −
1.65𝜎§ (−1) Portfolio Value 3. Equity Exposure Measure = E(Ri) = RF + βi[E(RM) – RF] 4. Fixed Income Exposure Measure using ∆h h
= −𝐷
∆: 1’:
5. Fixed Income Exposure Measure using
8. Active R (decomposition)= 1 w 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑠𝑒𝑛𝑠𝑡𝑖𝑣𝑖𝑡𝑦 − 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑠𝑒𝑛𝑠𝑡𝑖𝑣𝑖𝑡𝑦 w × 𝐹𝑎𝑐𝑡𝑜𝑟 𝑅 w + 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑦 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛 9. Tracking Error TE = s(RP-RB) 10. Information Ratio = =
𝑤Zâ > 𝜎}>J
Where 𝑤Zâ = ith asset’s active weight 𝜎}>J is ith asset’s residual risk
Duration = 7. Active R = 𝑅ú − 𝑅h
[ Z\1
13. Active specific risk =
Duration & Convexity = 1 >
𝐶
∆h h
= −𝐷
∆: 1’:
+
∆: ? 1’: ?
6. Delta =
∆ Z[ ÷úáZ÷[ 7âöùä ∆ Z[ 7âöùä ÷— ù[–äøö:Z[g ∆ Z[ Qäöáâ
7. Gemma = 8. Vega =
∆ Z[ 7âöùä ÷— ù[–äøö:Z[g ∆ Z[ ÷úáZ÷[ 7âöùä
∆ Z[ 7÷öâáZöZá: ÷— ù[–äøö:Z[g
Vm +VÒ 9 Vm +VÒ
11. Active risk squared = s2(RP-RB) 12. Active risk squared = Active factor risk + Active specific risk
Reading 50: Economics & Investment Markets 1. Present Value Model = ¿ 9\1
RÚ ·†qÚÜÙ 1’»Ú,Ù ’rÚ,Ù ’s*Ú,Ù
Ù
FinQuiz
Formula Sheet
2. Price of default-free bond certain to pay off one unit of real consumption at time s = PŠ,9 = EŠ 1mŠ,9 = EŠ mŠ,9 3. One period Rf interest rate lŠ,1 =
1 RÚ ´Ú,/
1+¤Ú,/ ¤Ú,/
=
−1
4. Sharpe Ratio SR =
= 𝑃á,¬ =
e~ §~Ü/,tk/ 1’ö~,/
+ 𝑐𝑜𝑣á 𝑃á’1,¬+1 , 𝑚á,1
6. Expected Holding period return = 𝑟á,¬ = e~ §~Ü/,tk/ +§~,t §~,t
7. Pricing for real default free i rate =𝑃áZ =
14. Fundamental Law: E(RA) =
d6 +du c.Q d6
(TC)(IC) 𝐵𝑅𝜎P =
dv c.Q d6
6. 𝑆𝑅§> = 𝑆𝑅h> + 𝐼𝑅 >
Risk premium on risky assets:
5. Alternate way to view the pricing relation
d6 +dR c.Q d6
5. Information Ratio IR =
7. S.D(RA) =
4. Relation b/w expected value and Cov. = 𝐸á 𝑥𝑦 = 𝐸á 𝑥 𝐸á 𝑦 + 𝐶𝑜𝑣 𝑥, 𝑦
Level II 2017
xd cdu
•
×𝑆. 𝐷 𝑅h
Single factor statistical model =𝑅PZ = 𝑅Z − 𝑅h Multi factor statistical model = 𝑅PZ = 𝑅Z − w\\1 𝛽\,Z , 𝑅\
9. Mean-var optimal security wghts for uncorrelated active R subject to limit on active portfolio risk = 𝜇Z 𝜎P ∆𝑤Z∗ = > ? 𝜎Z O nJ Z\1 C ?
J G¦~Üt O t ¬\1 1’ö~,t
J
10. Grinold Rule = 𝜇Z = 𝐼𝐶𝜎Z 𝑆Z Reading 51: Analysis of Active Portfolio Management 1. Benchmark Portfolio = 𝑅h = 2. Portfolio Return = 𝑅§ =
O Z\1 𝑤h,Z 𝑅Z
O Z\1 𝑤§,Z 𝑅Z
3. Value added return = RP-RB
11. ∆𝑤Z∗ =
nJ
xd ∗ cdu
𝜎h
16. 𝑆𝑅§> = 𝑆𝑅h> + 𝑇𝐶
8. Active Security R as residual R in •
15. 𝜎P = 𝑇𝐶
Cv
CJ? xG hd
12. Anticipated value added for Active portfolio = E(RA) = IC 𝐵𝑅𝜎P 13. Transfer Coefficient TC= Cor(𝜇Z 𝜎Z , ∆𝑤Z 𝜎Z )
>
𝐼𝑅 ∗
>
Ex Ante Measurement of Skill 17. 𝜎P = 𝜎xG 𝑁𝜎db 18. 𝐸(𝑅P ) =
xG 𝜎 CT} P
19. Breadth BR =
O 1’(O+1)~
Reading 52: Algorithmic Trading & High Frequency Trading
