Formulas Flashcards
FCFF Firm Value
infinity(Sum)t=1 [FCFF,t / (1+WACC)^t]
-Must add the market value of non-operating assets to value obtained from FCF model when computing company value
Indirect Equity Valuation
Equity Value = Firm value - Market Value debt
Direct Equity Valuation
Equity Value = infinity(Sum)t=1 [FCFE,t / (1 + r)^t]
FCFF, NI
FCFF = NI + NCC + int (1-t) - FCInv - WCInv
FCInv
FCInv = Capex - Proceeds from sale of long term assets
WCInv
WCInv = Change (working cap over the year)
Working Capital
Working Capital = CA (excl. Cash) - CL (excl. ST debt)
FCFF, CFO
FCFF = CFO + int(1-t) - FCInv
FCFF, EBITDA
FCFF = EBITDA(1-t) + Dep(t) - FCInv - WCInv
FCFF, EBIT
FCFF = EBIT(1-t) + Dep - FCInv - WCInv
FCFF to FCFE
FCFE = FCFF - int(1-t) + Net Borrowing
-FCFE approach is preferred when company’s capital structure is relatively stable
FCFE, NI
FCFE = NI + NCC - FCInv - WCInv + Net borrowing
FCFE, CFO
FCFE = CFO - FCInv + Net borrowing
FCFE, EBIT
FCFE = (EBIT - Int)(1-t) + Dep - FCInv - WCInv + Net Borrow
FCFE, EBITDA
FCFE = (EBITDA - Int)(1-t) + Dep(t) - FCInv - WCInv + Net borrow
Uses of FCFF
FCFF = Increase in cash + Net payment to debt providers + net payment to equity providers
Uses of FCFE
FCFE = Increase in cash + Net payments to capital providers
Net payments to debt providers
= Int exp(1-t) + Principal repayment - Net borrowing
Net Payments to Equity (Capital) Providers
Cash dividends + Share repurchase - New equity issues
Single-Stage (Constant Growth) FCFF Valuation
Firm Value = (FCFF,0 * (1+g)) / (WACC - g) = FCFF,1 / (WACC - g)
Single-Stage (constant growth) FCFE Valuation
Firm Equity Value = (FCFE,0 * (1+g)) / (r - g) = FCFE,1 / (r - g)
2-Stage FCFF Valuation
n(Sum)t=1 [FCFF,t / (1 + WACC)^t] + (FCFF,n+1 / (WACC -g)) * (1 / (1 + WACC)^n))
Justified Trailing PE, Terminal Value
TV = Justified Trailing PE * Forecasted Earnings,n
Justified Leading PE, Terminal Value
TV = Justified leading PE * Forecasted earnings, n+1
P/B Ratio
=market value Common SE / Book value common SE
=Market price/shr / book value/shr
Book Value of Common SE
= Total assets - Total liabilities - P.stock
P/S Ratio
=market price/shr / Sales/shr
=P/E * Net Profit Margin = P/E * E/S
P/CF Ratio
(Market price/shr) / (FCF/shr)
EPS
EPS = BVPS * ROE
Justified P/B Ratio
P,0 / B,0 = (ROE - g) / (r - g)
Justified P/S Ratio
P,0 / S,0 = [(E,0 / S,0)* (1-b)* (1+g)] / (r - g)
Justified Dividend Yield
D,0 / P,0 = (r-g) / (1+g)
Justified P/E Ratio, Inflation
P,0 / E,1 = 1 / [P + (1-lamda)I]
P = Real rate of return
Lamda = % of inflation that can pass through to revenue
I = Rate of inflation
Enterprise Value
EV = MV(Equity) + MV(P.stock) + MV(interest-bearing-debt) + Minority Interest (Non Controlling Interest) - Value of cash and short term investments
Unexpected Earnings
UE = EPS,t - E(EPS,t)
Residual Income, Direct
RI = NI - Equity Charge
Equity Charge
= Cost of equity capital * Equity Capital
Residual Income, Alternative
RI = After-tax operating profit - Capital charge
Capital Charge
= Equity charge + debt charge
Debt charge
= Cost of debt*(1-t) * Debt capital
Economic Value Added
EVA = NOPAT - (C% * TC)
NOPAT = Net operating profit after tax = EBIT *(1-t)
C% = Cost of Capital (WACC)
Market Value Added
MVA = MV(Company) - Accounting Book Value(Total Capital)
MV(Company) = MV Equity + MV Debt
Residual Income Model, RI,t
RI,t = E,t - (r * B,t-1)
Residual Income Model, Firm Value
V,0 = B,0 + infinity(Sum)t=1 [RI,t / (1 + r)^t]
-Separately identifiable assets and goodwill should be included in book value of company when performing RI valuation
Alternative Residual Income Model, EPS,t
EPS,t = ROE * (B,t-1)
Alternative Residual Income Model, RI,t
RI,t = (ROE - r)* B,t-1
Constant Growth Residual Income Model
V,0 = B,0 + [(ROE - r) / (r - g)]B,0
= Current Book value + PV(Expected stream of RI)
Tobins q
=MV(Debt + equity) / Replacement Cost (Total Assets)
-Value between 0 and 1 indicates company undervalued. Value above 1 indicates company overvalued
Residual Income Model, Persistence Factor
V,0 = B,0 + T-1(Sum)t=1[E,t - r(B,t-1) / (1+r)^t] + [(E,T - r(B,T-1)) / ((1+r-w)(1+r)^(T-1)]
Implied Growth Rate in Residual Income Model
g = r - [((ROE - r) * B,0) / (V,0 - B,0)]
Capitalized Cash Flow Model (CCM), Firm Value
Firm Value = FCFF,1 / (WACC - g,f)
Capitalized Cash Flow Model (CCM), Equity Value
Equity value = FCFE,1 / (r-g)
CAPM
Required ROE = r,f + (Beta * MRP)
Expanded CAPM
Required ROE = r,f + (Beta * MRP) + Small Stock Premium + Company Specific Premium
Build-up approach
r,f + MRP + Small Stock Premium + Company Specific Premium + Industry Risk Premium
Discount for Lack of Control (DLOC)
=1 - (1 / (1 + control premium))
FCFE, Debt Ratio
FCFE = NI - (1 - Debt ratio)[(FCInv-dep) + WCInv]
Scaled Earnings Surprise
= Earnings surprise / (Std.Dev. of forecasts)
Standardized Unexpected Earnings
= earnings surprise / (Std.Dev. of past unexpected earnings)
-The smallest absolute value for SUE indicates the least difference of forecast to actual results
Future COGS
= (Historical COGS / Rev)* Projected Sales
=(1 - Historical Gross Profit Margin) * Projected Sales
Effective Tax Rate
= Income Tax expense (on income statement) / Pre-tax income
Cash Tax Rate
= Tax actually paid / Pre-Tax income
Return on Invested Capital (ROIC)
= NOPAT / Invested Capital
NOPAT = EBIT*(1-t)
-This measures how much of the comp’s EBITDA is actually making it to net operating profit after tax. Capital providers will be willing to pay more for higher quality EBITDA (as evidenced by a higher ROIC)
Invested Capital
= Operating assets - Operating Liabilities
Return on Common Equity (ROCE)
= Operating Profit / Capital Employed
Capital Employed
=Debt Capital + Equity Capital
Gordon Growth Model
V,0 = D,1 / (r-g)
- This model implies a constant payout ratio, meaning g reflects growth in both divs and earnings, and expected growth in comp’s stock price
- As divs and stock price are growing at same rate, div yield will remain unchanged overtime
Present Value of Growth Opportunities (PVGO), V,0
V,0 = (E,1 / r) + PVGO
PVGO
PVGO = Mrkt Price - No Growth Value per share
No Growth Value Per Share
= E,1 / r
Justified Trailing P/E Ratio
= (D,1 /E,0) / (r - g) = [(1-b)(1+g)] / (r-g)
Justified Leading P/E Ratio
= (D,1 / E,1) / (r-g) = (1-b) / (r-g)
Noncallable Fixed Rate Perpetual Preferred Stock, V,0
= D / r
General 2-Stage DDM
V,0 = n(Sum)t=1[(D,0(1+g,s)^t) / (1+r)^t] + [(D,n*(1+g,L) / ((1 + r)^n * (r - g,L))
V,0 = (D1 + P1) / (1+r)
H-Model
V,0 = [(D,0 \* (1 + g,L)) / (r - g,L)] + [(D,0 \* H \* (g,s - g,L)) / (r - g,L)] H = half-life = 0.5 x the length of the high growth period (period where growth is declining lineraly) D0 = First dividend of the linearly declining growth period
USE THIS FOR TERMINAL VALUE WHEN THERE ARE OTHER PERIODS OF GROWTH
H-Model Required Return
r = (D,0 / P,0) * [(1 + g,L) + H(g,s - g,L)] + g,L
Sustainable Growth Rate
g = b * ROE = Retention Rate * ROE
b = 1 - Dividend Payout Ratio
Leading P/E Ratio, PVGO
Leading P/E Ratio = (1/r) + (PVGO / E,1)
1/r = Value of PE for no growth company
PVGO / E,1 = Component of P/E ratio relating to growth opportunities
Perceived Mispricing
= True Mispricing + Error in estimate of intrinsic value
=V,E - P = (V - P) + (V,E - V)
V,E: Estimate of intrinsic value
P: Market price
V= True (unobservable) intrinsic value
Dividend Yield
=D,H / P,0
Price Appreciation Return
=(P,H - P,0) / P,0
Holding Period Return (HPR)
=Dividend Yield + Price Appreciation Return
= (PH - P,0 + D,H) / P,0
Expected (Realized) Alpha
=Expected Return (Actual HPR) - Required Return
Expected Return
=Required Return + Convergence Return
Intrinsic Value, Stable Dividend
V,0 = D1 / (k,e - g)
k,e: Required return
k,e (IRR), Stable Dividend Growth
k,e = (D1 / P0) + g
Gordon Growth Model, ERP Estimate
ERP = (D1 / P0) + g - r,LTGD
Farma French Model (FFM)
r,i = R,f + [B,i,mrkt * RMRF] + [B,i,size * SMB] + [B,i,value * HML]
RMRF: Return Market less Return risk free, = ERP
SMB: Small Cap return premium, = R,small - R,big
HML: Value Return premium, = R,HBM - R,LBM
Pastor-Stambaugh Model (PSM)
r,i = R,f + [B,i,mrkt * RMRF] + [B,i,size * SMB] + [B,i,value * HML] + [B,i,liq * LIQ]
RMRF: Return Market less Return risk free, = ERP
SMB: Small Cap return premium, = R,small - R,big
HML: Value Return premium, = R,HBM - R,LBM
Baseline value for liquidity beta is 0, which represents average liquidity
Adjusted Beta
= 2/3 * (Unadjusted Beta) + [1/3 * (1)]
-Beta is difficult to estimate consistently
Asset Beta
B,asset = B,equity * [1/ (1+ (1-t)(D/E)]
Equity Beta
B,equity = B,asset * [1+ (1-t)(D/E)]
Ibbotson and Chen’s Model (ICM)
ERP = {[(1 + EINFL)(1 + EGREPS)(1 + EGPE) - 1] +EINC} -Exp. R,f
EINFL: Expected INflation
EGREPS: Expected growth rate in real earnings per share
EGPE: Expected growth rate in P/E ratio
Expected Inflation (EINFL), ICM Model
can be estimated as the difference between LT T bonds and TIPS of similar security
EINFL = [(1 + YTM of 20-yr T bonds) / (1 + YTM of 20yr TIPS)] - 1
Expected Growth Rate in Real Earnings Per Share (EGREPS)
Can be estimated as the sum of labor productivity growth and labor supply growth
Unlevered Net Income
=Net income + net interest after tax
Net Interest After Tax
=(Int expense - Int income)*(1-t)
Net Operating Profit Less Amortized Taxes (NOPLAT)
NOPLAT = unlevered net income + Change(deferred taxes)
FCFF, NOPLAT
FCFF = NOPLAT + NCC - Change(net working capital) - Capex
FCFF Terminal Value,T, Constant Growth
=FCFF,T * [(1+g) / (WACC - g)]
Takeover Premium (TP)
TP = (DP - SP) / SP
DP: Deal price per share
SP: Share price
Target Shareholders Gain
=Takeover Premium = P,T - V,T
P,T: Price paid for target
V,T: Pre-merger value of target
Acquirer’s Gain
=Synergies - Premium = S - (P,T - V,T)
Initial Outlay for New Investment (IO)
IO = FCInv + NWCInv
Net Working Capital Investment (NWCInv)
=Change(Noncash CA) - Change (Nondebt CL)
Annual After-Tax Operating Cash Flow (ATOCF)
(S-C)(1-t) + tD
S: Sales
C: Cash operating expenses
D:Depreciation
t: tax rate
Profitability Index (PI)
PI = 1 + (NPV/IO)
Terminal Year After-Tax Non-Operating Cash Flow (TNOCF)
TNOCF = Sal,T + NWCInv - t(Sal,T - BV,T)
Initial Outlay for Replacement Project (IO)
IO = FCInv + NWCInv - Sal,0 + t(Sal,0 - BV,0)
Annual After-Tax Operating Cash Flow (ATOCF), Replacement Project
=Change(Cash flows)
=Change(S) - Change(C) + t*Change(D)
S: Sales
C: Cash operating expenses
D:Depreciation
Terminal Year After-Tax Non-Operating Cash Flow (TNOCF), Replacement Project
TNOCF = Change(Sal,T) + NWCInv - t* Change(Sal,T - B,T)
Post-Merger Value of Combined Company
VA* = V,A + V,T + S - C
V,A: Pre-merger value, acquirer
V,T: Pre-merger value, target
S: Synergies created
C: Cash paid to target shareholders
Expected Decrease in Share Price Ex-Div
P,W - P,X = [(1-T,D)/(1-T,CG)] * D
P,W = Share price with right to receive Div
P,X = Share price without right
Effective Tax Rate on Dividends, Double Tax System
-Under this system, earnings are first taxed at corporate level and then again at shareholder level if they are distributed to taxable investors as dividends
ETR = CTR + [(1-CTR) * MTR,D]
Effective Tax Rate on Divs, Split Rate System
- Under this system, earnings that are distribute as divs by company are taxed at lower rate than earnings that are retained by company. Divs are then taxed again at shareholder level as ordinary income.
- Note that earnings that are distributed as divs are still taxed twice, but lower tax rate on earnings that are distributed mitigates the penalty
ETR = CTR,D + [(1-CTR,D) * MTR,D]
Expected Increase in Dividend, Stable Divided Policy
- For PER SHARE CALCULATIONS: [(Expected earnings * Target Payout ratio) - Prev. Div.] * Adjustment factor
- FOR TOTAL CALCULATIONS =Expected increase in earnings * TPR * Adjustment Factor
-Unbder s table dividend policy, divs would remain the same amount regardless of earnings volatility
Dividend, Residual Dividend Policy
D= Residual earnings = Earnings - (Cap budgeting * % Equity in cap structure), OR 0 (whichever is greater)
Earnings Yield
=EPS / P,0
Dividend Payout Ratio
=Divs/Net Income
Dividend Coverage Ratio
= Net Income / Dividends
FCFE Coverage Ratio
= FCFE / (Divs + Share Repurchases)
Leveraged Company Value
V,L = V,U + tD
=(Int / r,D) + [(EBIT - Int)(1-t) /r,E]
= EBIT (1-t) / (WACC)
Required Return on Equity, Leveraged Company (w/ Taxes)
r,E = r,0 + (r,0 - r,D)(1-t)(D/E)
Periodic Pension Cost
=End Net Pension Liabilities - Beg. Net Pension Liabilities + Employer Contribution
Net Pension Liabilities = Plan Assets - Benefit Obligation
Employer Contributions
=End FV(Plan Assets) - Beg. FV(Plan Assets) - Act. Return on plan assets + Benefits Paid
Full Goodwill, Goodwill
=Fair value 100% entity - Fair value 100% net identifiable assets
-This is the only goodwill method allowed by US GAAP
Pension Expense (IFRS) included in P&L
=Service Cost + Net Interest Income/expense
Pension Expense (US GAAP)
=Current service costs + Int expense - Expected return on plan assets
Remeasurement (IFRS)
=Actuarial gain + [Actual return - (r * FV(Plan assets))
-This is recognized in OCI. Actuarial gains and losses are not amortized into P&L under IFRS
Net Interest Expense/Income, Pension Accounting
=(Opening Pension Obligation * r) - (FV Plan Assets * r)
Full Goodwill, NonControlling Interest (NCI)
NCI = % of NCI * Subsidiary’s fair value
Goodwill, Partial Goodwill
=Purchase price - Fair Value of Proportionate share of acquired net assets
Partial Goodwill, NonControlling Interest (NCI)
=% of NCI * Fair value of subsidiary’s identifiable net assets
Additional Paid In Capital, Acquisition Method
=Parent APIC + Current Market Value of Shares Issued - Par Value shares issued
Goodwill impairment IFRS
Impairment Loss = Carrying Value of unit - Recoverable Amount of unit
Goodwill Impairment, US GAAP
Implied Goodwill = FV(Unit) - FV (Net identifiable assets)
Impairment Loss = Recognized goodwill - implied goodwill
Adjusted Operating Profit (US GAAP)
=Reported Operating Profit + Pension Expense - Current Service Costs
Adjusted Income Before Taxes
=Reported Income Pre-Tax + (Act return on plan assets - Expected Return on plan assets)
Combined Ratio
=Loss & loss adjustment ratio + Underwriting expense ratio
-This is a measure of the efficiency of an underwriting operation. Combined ratio of less than 100% is considered efficient, greater than 100% considered inefficient (underwriting loss)
Loss & Loss Adjustment Expense Ratio
=(Loss expense + Loss Adjustment expense) / net premium earned
Underwriting Expense Ratio
= underwriting expense / Net premiums written
-Indicator of efficiency of money spent on new premium
Dividends to Policyholders Ratio
dividends to policyholders / net premiums earned
Combined Ratio After Dividends
combined ratio + dividends to policyholders ratio
Covered Interest Rate Parity
(1 + i, BC) = [(1 + i,PC)(S,PC/BC) / F,PC/BC]
- If this holds, the return to a foreign investor with a fully hedged domestic currency exposure would be the same as the one-year PC LIBOR rate
- As this is based on arbitrage, it is the only interest rate parity relationship expected to hold over the short run
Forward Rate Calculation, Covered*
F,PC/BC = S,PC/BC * [(1 + (i,PC * act/360)) / (1 + (i,BC * act/360))]
*Replace F,PC/BC with Se,PC/BC for uncovered
Forward Premium/Discount, Covered*
=F,PC/BC - S,PC/BC
=S,PC/BC * [((i,PC - i,BC) * (act/360)) / (1 + (i,BC * act/360))]
*Replace F,PC/BC with Se,PC/BC for uncovered
Estimated Forward Premium/Discount
~=F,PC/BC - S,PC/BC
~= i,PC - i,BC
Law of 1 Price
P,x,PC = P,x,BC * S,PC/BC
Absolute PPP
GPL,PC = GPL,BC * S,PC/BC
-This tends not to hold in the long run bc product mixes and consumption baskets differ across countries and there are transaction costs and trade impediments
Relative PPP
E(S,T,PC/BC) = S,0,PC/BC * [(1 + pi(PC)) / (1 + pi(BC))] ^ T
-This works better in the long run than in the short run
Estimated Change in Spot Rate, Relative PPP
%Change(S,PC/BC) ~= Pi(PC) - Pi(BC)
Estimated Change in Future Spot Rate, Ex-Ante PPP
%Change(S,e,PC/BC) ~=Pi,e(PC) - Pi,e(BC)
Fischer Effect
i = r + pi,e
i = nominal rate
International Fischer Effect
(i,PC - i,BC) = (pi,e,PC - pi,e,BC)
Real Interest Rate Parity
(r,PC - r,BC) = (i,PC - i,BC) - (pi,e,PC - pi,e,BC)
-This is the assertion that real rates will converge to the same level across countries. It requires that both uncovered interest rate parity and ex-ante PPP hold
GDP and PE
P = GDP * (E/GDP) * (P/E)
P = Aggregate Price/value of earnings
Neoclassical (Solow’s) Model, Growth Rate in Output
Y = theta / (1 - a) + n
theta = TFP growth rate
a = elasticity of output with respect to capital
(1-a) = Labor cost in Total Factor Cost
n = labor supply growth rate
Mundell-Flemming Model, High Capital Mobility
Expansive FP, Expansive MP: Ambiguous
Expansive FP, Restrictive MP: DC Appreciates
Restrictive FP, Expansive MP: DC Depreciates
Restrictive FP, Restrictive MP: Ambiguous
Mundell-Flemming Model, Low Capital Mobility
Expansive FP, Expansive MP: DC depreciates
Expansive FP, Restrictive MP: Ambiguous
Restrictive FP, Expansive MP: Ambiguous
Restrictive FP, Restrictive MP: DC appreciates
Effect of Capital Deepening on Growth
=Growth rate of productivity - Growth rate of TFP
Difference between Acquisition Method and and Equity Method
Under equity method, revenues recognized will be only those of the parent. Under acquisition method
fail-to-reject-the-null region
In a hypothesis test, this region is centered on the hypothesized value of the population parameter
In a confidence interval, this region is centered on the estimated parameter value from sample data
Which Corrections for violations of regression assumptions have an impact on regression coefficients
Serial correlation, conditional heteroskedasticity, and multicollinearity do not directly have an impact on regression coefficient esitmates, they have an impact on their standard errors. HOWEVER
Mutlicollienarity is corrected for by performing step-wise regression, which eliminated one indep variable at a time. elimination of indep var (esp when it is highly correlated with other indep vars) has an impact on regression coefficient esitmates.
Positive Serial Correlation
- This is a serial correlation in which positive regression errors for one observation increases the possibility of observing a positive (negative) regression error for another observation.
- It causes the standard errors for regression coefficients to be underestimated, leading to inflated t-stats and incorrect rejection of null hypothesis (Type I errors)
- While the DW Stat and regression coefficients remain unchanged after correcting for this, the standard errors change. DW stat can range from 0 (where serial correlation equals +1) to 4 (where serial correlation =-1). DW stat above 2 = negative serial correlation. DW stat =0 indicates no serial correlation
Chi-Squared Test
- Used to test whether a hypothesized value of variance is equal to the true population variance
- Calculated as the product of the number of observations in the sample and the coefficient of determination in a 2nd regression (where squared residuals from original regression are regressed against the indep vars in the regression)
Growth Accounting Equation
Growth rate of output = Rate of tech change + Growth rate of capital + Growth rate of labor
-Both capital and labor are assumed to have negigable growth rate in long run, leaving tech as drive of LR growth
Change(Y)/Y = Change(A)/A + [a*(Change(K)/K)] + {(1-a)*(Change(L)/L)]
a = Capital contribution to output
1 - a = Labor contribution to output
Convergence Hypothesis
-Predicts that growth rates will be higher in developing countries relative to developed. Postulates that the gap between developed and developing will narrow over time. Empirically the data are mixed
Taylor Rule
-Used to estimate the target interest rates for domestic and foreign countries
I = r,n + pi + a(pi - pi*) + B(y + y*)
r,n = neutral policy rate
pi = current inflation rate
a = inflation mandate weight
pi* = target inflation rate
B = output mandate weight
y + y* = current output gap
For forex questions, calc difference between Target rate calcd above and current policy rate in both countries and see which interest rate is expected to fall more. The one whos rate is expected to fall more will experience depreciation
Data Preparation (Cleansing)
The process of examining, identifying, and minimizing errors in raw data
Data Wrangling (Pre Processing)
Involves making data ready for ML model training
Trimming/Truncation
Part of Data Wrangling
Extreme values/outliers are removed from dataset
Winsorization
Part of data wrangling
Extreme values/outliers are replaced with the max and min values from data that are not considered outliers
Multicollinearity
- Occurs when 2/more indep vars (or combos of indep vars) in a regression model are highly (but not perfectly) correlated with each other.
- While it does not effect the consistency of OLS estiamtes and regression coeffs, it makes them inaccurate and unreliable. Standard errors for regression coefficients are inflated, leading to t-stats becoming too small and less powerful
- Can be detected by a high R^2 and significant F-stat, coupled with insignificant T-stats
-Also can be detected if there is high pairwise correlations
Heteroskedasticity
The result of error terms differing across observations.
Use Bruesch-Pagan test to determine if regreesion error terms are this
Should only be concerned with conditional heteroskedasticity, which occurs when error variances are condition on the values of the indep vars.
Conditional heteroskedasticity results in overtatement of regression’s overall significance and sig of indv regression coefficients
Can correct for with robust standard errors or generalized least squares regression
T-Stat Calculation
t = (sample data - hypothesized value) / Standard error of sample
Interest Parity Relations
CDS Physical Settlement
Protection buyer delivers underlying debt instrument to protection seller, with par value of bonds delivered equaling the notional amount of CDS.
In return, portection seller pays buyer the par value of the debt (which is equal to CDS notional amount)
CDS Cash Settlement
Protections seller pays protection buyer an amount of cash equal to the difference between notional amount and current value of the cheapest to deliver bonds. Protection buyer can then sell unerlying bonds –>
total payoff = Payment from protection seller + sale proceeds from bonds
Payment from protection seller = NA * (1 - post-default MV % of par on CTD)
Confidence Interval Creation
Confidence Interval = Relevant Coefficient from regression +/- [Critical t-stat (from t-table) * Standard error of regression coefficient]
Critical Values for 2 Tailed z-Stat tests
1% Sig Level = 2.58
5% Sig Level = 1.96
10% Sig Level = 1.65
Critical Values for 1 Tailed Z-stat Test
1% Sig Level = 2.33
5% Sig Level = 1.65
10% Sig Level = 1.28
2-Way Dupont Decomposition
ROE = ROA * Financial Leverage
Return on Assets (ROA)
= Net income / Avg. Total Assets
Financial Leverage Ratio (AKA Equity Multiplier)
= Avg. Total Assets / Avg. Total Common SE
3-Way Dupont Decomposition
ROE = Net Profit Margin * Asset Turnover * Financial Leverage
Net Profit Margin
= Net income / Revenue
5-Way Dupont Decomposition
ROE = tax burden * interest burden * EBIT Margin * Asset Turnover * financial Leverage
Tax Burden
= Net income / EBT
= 1 - avg. tax rate
Interest Burden
= EBT / EBIT
Return on Equity (ROE)
= Net income / Avg. Total Equity
Residual Income Calculation Table
EPS/BV Calculation Table
Year 15 16 17
Beginning Book Value (B,t-1)
+ EPS (= ROE,t * B,t-1)
-Divs
=Ending Book Value (B,t)
RI Calculation Table
EPS
-Equity Charge (=cost of equity * B,t-1)
=Residual Income
ALL CAPITAL CHARGES ARE BASED ON THE BOOK VALUE
Autoregressive Conditional Heteroskedasticity (ARCH)
- The situation where the variance of the error terms in a model are dependent on the variance of the error term in previous periods
- Can be identified by regressing squared residuals with lagged values of themselves as squared residual represents the variance of the error term
- Should ARCH exist in a model, by definition, it can be used to predict the variance of the error term in the model
Regulatory Capture
Occurs when regulation arises to protect the interests of the regulated. Most likely to occur when the regulated entities have the most influence over the policy of the regulator
Dornbusch Model
Predicts that a decrease in domestic money supply will most likely lead to appreciation in the SR followed by depreciation over time to a level that is still higher than the initial exchange rate
In SR, since prices are not flexible, a decrease in domestic money supply results in decrease in real money supply. Real rates rise, resulting in capital inflows and substantial domestic currency appreciation. It appreciates to a level higher than predicted by PPP.
In LR, prices are flexible so the currency settles at the value implied by PPP. As the currency overshoots in SR, it depreciates over LR to a level predicted by PPP, which is still higher than initial exchange rate
Carry Trade Distribution and Return Calculation
The carry trade is profitable during times of stability, though it can suffer severe losses should volatility/crises erupt. As such the distribution of returns tends to be negatively skewed with fat tails (i.e. drawn toward negative outliers and experiences more frequent extreme outcomes than normal distribution would imply)
Carry trade predicated on uncovered interest rate parity not holding. Carry trade works bc higher domestic rates attract foreign capital flows, increasing demand for domestic currency and causing it to appreciate
Total Return on Carry Trade = (1 + yield on investment currency)*(S,t,PC/BC / S,0,PC/BC) - (1+ yield on funding currency)
In above equation, investing currency is PC and funding currency is BC
Uncovered Interest Rate Parity
-Says that the change in the domestic exchange rate will approximately equal the real interest rate differential between foreign and domestic economies. If this held true, domestic currency would appreciate when foreign rate is above domestic.
Cary trade predicated on uncovered interest rate parity not holding
-This works better in the long run than in the short run
Logistic Regression Coefficients
Are used to find the probability of positive sentiment. A mathematical function is then used to convert the regression coefficient to a probability
Consumption-Hedging
During bad economic times, equities have poor consumption hedging properties and performance relative to IG corp bonds
-For an asset to serve as a hedge against bad consumption outcomes, covariance between investor’s expected ITRS (inter temporal rate of substitution) and the future price of the asset must be positive. This results in a higher price for the asset and a lower risk premium
Dividend Imputation Tax System
- Under this system, earnings that are distributed as dividends are effectively taxed only once, at shareholders marginal tax rate. Therefore, effective tax rate on divs = Investors marginal tax rate
- Under such system, company’s earnings are fixed taxed at corporate level. If investors marginal tax rate < corporate tax rate, will receive tax credit (AKA Franking credit) for taxes paid by comp on distributed earnings. If investors marginal tax rate > corporate tax rate, must pay additional taxes so total taxes paid are in line with marginal tax rate.
Factors that tend to lead to companies using more debt in capital structure:
-Weaker legal systems, high levels of info asymmetry, and higher personal tax rates on divs
Coefficient of Determination (R^2) Concepts
-When introducing a new explanatory variable:
- If new variable has explanatory power, RSS will increase relative to SST and new R^2 will be greater than original R^2
- If new variable has 0 explanatory power, RSS will remain the same and new R^2 would equal original R^2
- Not possible for new R^2 to be less than original R^2 as R^2 of second regression would at least account for variation in dep var thats explained by the 2 indep vars
-If k is greater than 1, R^2 will always be greater than adjusted R^2
-Adjusted R^2 of original regression can be greater than, less than, or equal to adjusted R^2 of new regression
-R^2 represents the proportion of the variation in the dependent variable explained by the model . I.e. An R^2 of 0.36 means the model explains 36% of the variation in the dependent variable
Equilibrium vs Arbitrage Free Term Structure Models
- EQ structure models typically require estiamtion of fewer parameters than AF structure models, but this comes at cost of less precision in modeling the observed yield curve
- EQ structure models typically make assumption regarding term premium, while AF models do not
MM Capital Structure Irrelevance Assumptions
- Investors have homogenous expectations regarding the cash flows from an investment in bonds/stocks
- Capital markets are perfect. No taxes, no transaction costs, no bankruptcy costs, no asymmetric info
- Investors can borrow and lend at risk free rate
- There are no agency costs - mgmt always acts in best interests of shareholders
- The financing and investment decisions are independent of eachother
Regression Analysis Tests
- Dickey Fuller test is used to investigate the presence of a unit root in a time series
- Durbin Watson test is used to test for serial correlation in a model, except for autoregressive models where serial correlation must be investigated through direct autocorrelation analysis
- BP test is used to test for heteroskedasticity. The BP test is a 1-tailed test as C. Het is only a problem if it is large
Extendible Bond
This is equivalent to a putable bond with the option to put the bond at the end of the bonds original maturity for bond par value
Mutually Exclusive Projects with Unequal Lives
Method 1: Least Common Multiple of Lives Approach
-Both projects are repeated until their “chains” extend over the same time horizon, being the least common multiple
Method 2: Equivalent Annual Annuity Approach (EAA)
-First calculate projects NPV. Use this NPV as the PV in financial calculations, with FV=0 and i = cost of capital and N = project life→ calculate payment. Project with highest pmt (EAA) should be selected
Dickey Fuller (Engle-Granger) Test
- Used to test for a unit root in an AR(1) model, thereby testing for covariance stationarity
- Null hypothesis for the test is that the time series has a unit root, while alternative hypothesis is that the error term in regression is covariance stationary.
- If Null hypothesis is rejected, the error term in regression is covariance stationary. Therefore, the 2 time series are cointegrated. This means the parameters and SEs from linear regression will be consistent and will allow testing of the hypothesis about the long-term relationship between the 2 series
- The dependent variable is the first difference, while the indep var is the first lag
Economic Profit
=NOPAT -
Coefficient of Determination (R^2) Calculation
R^2 = Explained variation / Total Variation
= Regression sum of squares (RSS) / [RSS + Sum of squared Errors (SSE)]
Sum of Squared Errors (SSE) = Residual Sum of Squares
=(Sum of squared differences - Sum of squared residuals) / (Sum of squared differences)
-Correlation coefficient = RAD(R^2)
Factors Affecting Pension Obligation
- Discount Rate - Inverse relationship. The higher the discount rate, the lower the PO (PV of promised future pmts)
- Current Service Costs - Direct relationship. This is the increase in PO as a result of an employees service in current period
- Interest Expense - Direct relationship. This is the increase in value of obligation due to the passage of time
- Past Service Costs - Direct Relationship. This is the increase in PO from retroactive benefits given to employees for yrs of service provided before date of adoption
- Changes in actuarial assumptions (e.g. discount rate, rate of future compensation increases, life expectancy)
- Actuarial Loss - Changes in actuarial assumptions that increases the pension obligation
- Actuarial Gain - Changes in actuarial assumptions that decreases the pension obligation
- Year to attain Health Care Trend Rate (-) - If the year at which the ultimate health care trend rate is reached is moved earlier, pension expense and pension obligation will decrease
Ex-Ante Alpha
- Ex-Ante means before the fact
- Ex-ante alpha = Expected return - required return
Adjusted R^2 Calculation
= 1 - [(n-1) / (n - k - 1)] * (1 - R^2)
-if adjusted R^2 after adding additional variable is less than adjusted R^2 of regression before addition of new variable, new variable should not be added to analysis
PV of Expected Loss
=PV of Cash Flow - PV of Risk-free cash flow
- PV of Cash flow = PV of cash flow, using a rate including credit spreads
- PV of risk free cash flow = PV of cash flow using the risk free rate
Interest Rate Swaptions
- A receiver swaption is one that receives-fixed, pays-floating. Payoff = Max(0, x-c)*SUM(PV factors)
- A payer swaption is one that receives-floating, pays-fixed. Payoff = Max(0,c-x)*SUM(PV factors)
x = periodic exercise rate
c = periodic SFR calculated using current term structure
Steps to Calculate VaR
- Perform necessary adjustments (unannualize or annualize). If you are given annual expected return and volatility, but are asked to calculate daily VaR→ Daily return = (ann. return / 250 trading days). Daily Std. Dev = (ann. volatility / RAD(250))
- Multiply daily std. dev by T,crit given by confidence level one a 1-tailed test. i.e. if tased with determining 5% one-day VaR, multiply daily std. dev by 1.65
- Now subtract the answer in step 2 from period-specific expected return. As VaR is expressed as an absolute number, take the positive value of this
- Multiple answer in 3 to portfolio value
Mean-Reverting Level
-At the mean-reverting level, X,t+1 = X,t
Rearranging the AR(1) Model gives the mean reverting level as
Mean reverting level = b,0 / (1 - b,1)
b,0 = intercept
Poison Put
-A pre-offer defense mechanism that allow the target firm’s bondholders to sell (put) their bonds back to the company. Result is that an acquiring firm must be prepard to refinance the target which increases the need for cash and raises cost of acqusition
Flip-in Poison Pill
-Pre-Offer Defense Mechanism that makes the target company less attractive by creating rights which allow for the issuance of shares of the target company’s stock at a substantial discount to market value
Flip-Over Poison Pill
-Pre-Offer defense mechanism where the target company’s shareholders receive the right to purchase shares of acquiring company at a significant discunt from market value
Differences between Equity Method and Proportionate Consolidation (IFRS)
- Under equity method, profit-and-loss will have a single line-item showing acquirer’s proportionate share of targets net profit
- Under proportionate consolidation, Acquirer’s revenues and net profit would reflect the proprtionate share of target’s revenue and net profit
- While both methods show the same net profit, proportionate consolidation shows higher revenues
Data Input and Their Effect on Private Company Valuation
- Restricted Stock Grants (Unregistered Shares) - a DLOM based on values of these would underestimate the true discount bc these shares will enjoy ready marketability (no such guarantee for private company shares). Therefore, value estimate of company will be inflated
- IPOs: Post-IPO prices tend to be higher than pre-IPO prices due to other factors besides greater marketability. So, DLOM based on differences between pre- and post-IPO prices would overestimate the true discount and understate value est. of company.
- Put Options: Put prices primarily reflect the cost of downside protection (not the price of attaining marketability). Using put prices to estimate DLOM would overestimate the true discount and understate the value of the company
FX Gains and Losses
`-Can be recognized as either operating or non-operating items
Equity Method of Accounting
- Investment is intially recognized on investor’s balance sheet at cost under noncurrent assets
- Investors proportionate share of investee earnings increase carrying amt of investment, while its prop share of losses and divs decreases carrying value
- Investors prop share of investee earnings is reported withing a single line item on its income statement
- While Dividends reduce the carrying value of the investment in the addiliate on parents balance sheet, they do not impact amount reported on income statement. I.e. investment income from equity method investment = %prop. share of investment * investee income
Pooling of Interests Method
- 2 firms are combined using their historical book values, and their operating results are restated as if they had always operated as a single entity
- Fair values not used in accounting for a business combo in this method
- As value of depreciable assets is lower under this method (since they are measured at historical cost) , depreciation expense is lower and reported income and asset turnover is higher
Purchase (Acquisition) Method
- Combination is accounted for as a purchase of net assets, where net assets are recorded at fair values
- All assets, liabilities, revs, and expenses of acquiree are combined with those of parent
- Only acquirer’s retained earnings are carried over to combined entity
Diminishing Marginal Returns to Capital
- If share of capital in GDP (a) is close to 1, diminishing marginal returns to capital are not significant
- Marginal Product of capital can be expressed as a(Y/K). The higher the output-capital ratio, the higher the marginal product of capital
Convertible Straight Bond Value
- Use par value (FV) and issued coupon rate to determine PMT
- use YTM of comparable option-free bond as i
- Calc PV
Consumption Substition and Hedging
- The real risk-free rate and the inter-temporal rate of substitution (ITRS) are inversely related. Therefore, the higher the real risk free rate, the lower the willingness to substitute current consumption with future consumption. This means that current consumption becomes more important relative to future consumption
- For an asset to serve as a hedge against bad consumption outcomes, the covariance between the investor’s expected ITRS and the future price of the asset must be positive. This results in a higher price for the asset and a lower risk premium
Reclassification of Securities
-You are able to reclassify securities designated at fair value and available for sale securities to held-for-trading status, as well as equity method investments if you do not have control/significant influence over the investment
Proportionate Consolidation
- This is an alternative to the equity method
- It includes the proportional amount of each asset, liability, revenue, and expense account of the subsidiary in the corresponding acct of the parent
Appropriate Interpretation of Cash Flow From Economic Perspective, Employer Contribution and total periodic pension cost
-If total periodic pension cost is over the Employer contribution to the pension plan, the difference can be considered a source of financing (borrowing), which is a financing inflow
Results of an omitted variable being correlated with variables already in the model
-Result in biased and inconsistent parameter estimates and inconsistent SEs
Sample Variance of dependent variable Calculation From Regression
=Sum of squares total / (N - 1)
F-stat Concepts
- F-stat tests whether all the slope coefficients in a linear regression are equal to 0
- To determine if the F-stat is significant at a certain confidence level, look to the F-stats corresponding p-value: If p-value < Confidence level → reject null hypothesis of a slope equal to 0. If P-value> Confidence level→ accept null hypothesis of a slope equal to 0
Futures Contracts Sources of Returns
Roll Return: The yield on rolling over one maturing contract to a far-term contract. This depends on the difference between spot and futures prices
Price Return: The % change in futures contract prices over time
Collateral Return: The yield on the margin acct required to open and maintain a position in any futures contract. The return is a function of interest rates
Held-For-Trading Classification
Equity Income = Change in MV + Divs received =(MV1 - MV0 + Div)
Carrying Value (FI) = MV at end of year
Designated at Fair Value Classification
Equity income = change in MV + Divs received
Available-for-Sale Classification
_Equity income is just the divs received = Divs
- Carry value (FI) is the MV at the end of the year
- Gains and losses on these bypass the income statement under IFRS and GAAP. Gains/Losses reported directly to equity. Consistent recordings of losses on these should be adjusted for in net income used for finding residual income
Held-to-Maturity Classification
Carrying Value (FI) = original cost
Underlying on an Interest Rate Call Option on 3-month LIBOR that Expires in 6 Months
- Underlying is an FRA on 3-month Libor that expires in 6 months.
- The underlying of the FRA is a 3-month Libor deposit that is made after 6 months and matures 9 months from option initiation
Option Valuation Relations
- Dividend yield (-): Increase in div yield leads to lower est. fair value of options
- Assumed volatility (+): increase in assumed volatility results in higher est. fair value of stock options
- Risk free rate (+): increase in risk free rate results in higher est. fair value of stock options
- Increase in option value is a conservative choice as it results in higher compensation expense and lower net income
Text Cleansing
- Numerical values removed as they have no use for sentiment prediction
- % and $ symbols substituted with word annotation
- semi-colons, commas and special characters such as “+” and “©” are removed
Probability Firm defaults on at least one coupon payment or its face value at maturity
-First, calc prob that the firm survives each payment
=(1 - Cond. POD)^(# of payment periods)
1 - prob firm survives each payment = prob firm defaults on at least one payment
Inside Bid-Ask Spread (AKA Market bid-ask Spread)
The difference between the highest bid price and the lowest ask price
OAS and Volatility
Callable Bonds: OAS = z-spread - Call option cost
-This makes the OAS and volatility Inversley related (i.e. an increase in volatility assumption leads to an increase in call option cost and therefore reduces the OAS)
Putable Bonds: OAS = z-spread + Put option cost
- Makes OAS and volatility directly related (i.e. an increase in volatility assumption leads to an increase in put option cost and therefore increases the OAS)
- For bonds that have otherwise similar characteristics, the bond with the higher OAS is underpriced while that with the lower OAS is overpriced
Health Care Plan Facts
- Cost of future benefits under defined benefit health care plan results from current employee service. While these costs will be paid out in future period, they are expenses of the current period and therefore may expected to be funded. But, employers arent normally required by regulation to pre-fund plans involving other post-employment benefits, so they usually do not
- Since health care plans are an optional employee benefit provided by employer, plan could be eliminated in future if costs became burdensome and/or comp preferrs to use those assets in current operations/other alternative ways
Disclosures about Pensions and post-employment benefits, including actuarial assumptions
- These are normally disclosed in the notes to the financial statements
- While Pension Plan documents would define the terms and benefits, it would not define the assumptions used to value the assets and liabilities
Total Cash Outflow related to Post-employment costs
-This is the sum of the employer contributions for the year to all post-employment plants
=Sum(Employer Contributions)
Influence of the Current Account on Exchange Rates
All of the below are long run impacts
- The flow supply/demand Channel: A country than exports more than it imports will see an increased demand for its currency, resulting in currency appreciation
- The Portfolio Balance Channel: A country operating at a trade surplus will have more of a deficit country’s currency than it wants, resulting in downwards pressure on deficit country’s currency
- Debt Sustainability Channel: If country runs persistent deficits, it will be indebted to foreigners and its currency will be depreciated so current account deficit narrows
Vertical Mergers
- Mergers in which both companies are in the same production chain
- Vertical Merger with Backward Integration: A merger in which a company expands its role to fulfill tasks formerly completed by businesses up the supply chain. When a company buys another company that supplies the products/services needed for production. I.e. a retailer purchases a manufacturer. A company tries to increase ownership over companies that were once its suppliers
- Vertical Merger with Forward Integration: A company tries to increase ownership over companies that were once its customers. i.e. a clothing label purchases its own retailers
Bootstrapping Effect of Earnings
-An acquiring firm’s EPS will increase when pre-acquisition P/E of acquirer is higher than pre-acquisition P/E of target firm
Post-Offer Defense Mechanisms
- White Knight Defense: A friendly acquirer enters the bidding war
- Pac-Man Defense: The target company attempts to acquire the acquirer
- Greenmail is when acquirer purchases enough shares in a company so that target company will need to repurchase its shares at a premium
Weighted Harmonic Mean, PE
= 1 / (SUM(Weight, i / PE,i)
-Harmonic mean tends to mitigate the impact of large outliers. It may aggravate the impact of small outliers, but such outliers are bounded by 0 on the downside
Effective Duration, Bond Types, and Interest Rate Regimes
-Callable Bonds: When rates rise and are high compared to bonds coupon rate, call option is out of the money and price would be the same as a straight bond. So, the effect of rate change on price of callable and straight would be similar, meaning the effective duration of callable and straight would be similar. Effective duration would rise to about the same level as straight bond
Meaning effective duration of callable bonds and interest rates have a positive relationship. When rates rise, effective duration of callable bonds rise
-Putable Bonds: When rates rise and are high compared to bonds coupon rate, put option is in the money and price of putable will not fall as much as straight bond bc investor can put the bond. Thus, effective duration of putable bond is lower than effective duration of straight bond in this scenario.
meaning effective duration of putable bonds and interest rates have a negative relationship. When rates rise, effective duration of putable bonds fall
Key-Rate Duration vs One-Sided Duration
- Key rate duration captures a bonds sensitivity to changes in the shape of the yield curve due to changes in steepness and curvature (i.e. steepening or flattening)
- One-sided duration is better than effective or 2-sided duration at capturing rate sensitvity of callable/putable bond, but only for a parallel shift in yield curve, not for changes in yield curve
- The higher the coupon rate, the lower the chance of the bond having some negative key rate durations
Effective Spreads
Compare trade execution prices with the midquote price at the time the order is entered
Effective Spread for Buy Order: (Trade Price - ((Bid + Ask)/2)) x 2
Effective Spread Transaction Cost estimate for Buys = Trade Size * (Trade Price - ((Bid + Ask)/2))
Effective Spread for Sell Order: (((Bid + Ask)/2) - Trade Price) * 2
Effective Spread Transaction Cost estimate for Sells = Trade size * (((Bid + Ask)/2) - Trade Price)
-Sensible esimate of transaction costs when orders are filled in single trades, poor est of transaction costs when traders split large orders into many parts
VWAP Transaction Cost Esimtates
Compare trade prices to the prices obtained by other traders trading at the same time
VWAP Transaction cost esitmate for buys = Trade size * (Trade VWAP - VWAP benchmark)
VWAP Transaction cost estimate for sells = Trade size * (VWAP Benchmark - Trade VWAP)
Implementation Shortfall Method
Includes consideration of all explicit and implicit costs, as well as impact costs, delay costs, and opportunity costs
Inflation-Linked Bond Factoids
- The break-even inflation rate incorporates the yield difference between inflation linked and non-inflation linked govt bonds of the same maturity
- The difference in yields between nominal and inflation-linked bonds reflects the uncertainty about the quantity of goods and services investors will be able to consume in the future
- Increases in uncertainty about future inflation would be associated with high break-even inflation rates
Explicit Trading Costs
-Direct costs of trading, such as broker commissions, transaction taxes, stamp duties, and exchange fees. They are costs for which a trader could receive a receipt
Implicit Trading Costs
-Indirect costs caused by the market impact of trading. Small orders have limited market impact while alrger orders have greater impact. Implicit costs result from the following issues
Bid-Ask Spread
_Market (Price) Impact-_The effect of the trade on transaction prices
Delay Costs (Slippage)-Arise from the inability to complete the desired trade immediately
Opportunity Costs (Unrealized profit/loss)-Arise from failure to execute a trade promptly
Inside Spread
The spread between the best (highest) bid price and the best (lowest) ask price
Private Equity Fund Return Calculation
-Prior Operating Results
(-) Called-down capital
=Gross Cash flow (return to fund)
(-) Mgmt fees and carried interest
=Net cash flow (return to LPs)
Growth Relative to GDP Growth Approach
_Analyst considers how a company’s growth rate will compare with growth in nominal GDP
Insurance Life Cycles
-Hard Market: Hard markets (specifically for P&C insurers) feature higher premium prices, increased profitability, and an increased ability for insurers to maintain adequate capital. Good times attract new competitors, which lowers premium prices, profitability, and capital typically depletes as markets soften, making capital adequacy difficult to achieve
Types of Share Repurchases
- Fixed Price Tender Offer: These normally require a premium over current market price
- Negotiated Purchase Agreement: Equally as likely to take place at prices lower than market as they are to take place at prices above market, particularly when shareholders are trying to meet liquidity needs
- Open Market Purchases - market based, can be timed to avoid price impact
Liquidity Preference Theory
- Investors require a liquidity premium to lend over longer maturities.
- Forward rates are an upwardly biased estimate of expected future spot rates, and yield curve will typically be upwards sloping
- A downward sloping yield curve is possible only if expected future spot rates decline by enough to offset the liquidity premium
Segmented Markets Theory
- Shape of yield curve is determined by supply/demand for funds at each maturity
- Depending on the nature of supply and demand mismatch, a downward/upward sloping yield curve is possible
- theory does NOT state that institutions will deviate from their preferred maturities if they are adequately compensated. This is ONLY true under the preferred habitat theory
Unbiased Expectations Theory
- Frward rates are an unbiased predictor of expected future spot rates
- THeory can explain upward/downward sloping yield curve
- Assumes risk neutrality and only applies to risk-free assets, not risky assets
Modern Theories of Term Structure
- CIR, Vasicek, and Ho-Lee have the same structure in that they have a drift term and a stochastic term. Composition of drift term for CIR and Vasicek models is the same, while its different for Ho-Lee model. Stochastic term are different for all 3
- Interest rate volatility is constant for Vasicek and Ho-Lee models, but for CIR volatility increases with the level of rates
- Both CIR and Vasicek models are mean reverting in that they assume ST rates converge to LT rates over time. Ho-Lee model does NOT make this assumption
- HoLee model is most likely to be arbitrage free in ST
Credit Valuation Adjustment (CVA)
CVA,t = LGD,t x POD,t x DF,t
- Fair Value of bond and CVA are inversely related, meaning when CVA increases, bond fair value decreases
- An increase in CVA and resulting decrease in bond fair value results in an increase in YTM and credit spread
- A higher interest rate volatility assumption results in a lower CVA, meaning a higher fair vlaue of bond
