Formulas pt 2 Flashcards
1
Q
Forward Pricing Model
A
P(T* + T) = P(T*) * F(T*,T)
- Investment 1: Buy zero coupon bond par value $1 that matures in T* + T yrs. bond will cost $1 * P(T* + T), P(T*+T) is discount factor for payment received at T*+T
- Investment 2: Enter into forward contract valued at F(T*,T) to buy (@T*) a zero coupon bond w/ par value $1 that matures @T. Bond will cost P(T*)F(T*,T) today.
2
Q
Relationship between Spot and Forward Rates
A
xS0 = [(1 + 1S0)(1+1f1)(1+1f2)(1+1f3)…(1+1fx-1)]^(1/x) - 1
3
Q
Yield Curve Factor Model
A
Delta(P)/P ~= -D,L * Change(X,L) - D,S * Change(X,S) - D,C * Change(X,C)
D,L = sensitivity of portfolio valuation to parallel shift in yield curve
D,s = Sensitivity of port val to change in slope
D,C = Sensitivity of port val to change in curvature
4
Q
Value of Callable Bond
A
=Value of straight bond - Value of embedded call option
5
Q
Value of Putable Bond
A
=Value of straight bond + value of embedded put option
6
Q
Effective Duration
A
= [PV(-) - PV(+)] / (2 x PV,0 x Change(Curve))
-Effective Duration of callable and putable bonds cannot exceed the effective duration of otherwise identical option-free bond
7
Q
Effective Convexity
A
= [PV(-) + PV(+) - 2PV,0] / [Change(curve)^2 x PV,0]
- Callable bonds exhibit positive convexity at high rates and negative convexity at low rates. Convexity of a callable bond turns negative when call option is near the money
- Putable bonds exhibit positive convexity throughout all rate environments, as do straight bonds. Convexity of putable bonds becomes greater than that of straight bond when put is near the money
8
Q
Value of Capped Floater
A
=Value of uncapped floater - value of embedded cap
9
Q
Value of Floored Floater
A
=Value of nonfloored floated + value of embedded floor
10
Q
Conversion Value
A
=Market price common stock * Conversion ratio
11
Q
Market Conversion Price
A
= Mrkt price of convertible security / conversion ratio
12
Q
Market conversion premium per share
A
= Market conversion price - current market price
-This resembles the price of a call option
13
Q
Market Conversion Premium Ratio
A
= Market conversion Premium per share / market price common stock
14
Q
Conversion Premium Over Straight Value
A
= (Market price convertible bond / Straight Value) - 1
–Represents the downside risk of a convertible bond. All else equal, a higher conversion premium over straight value, the less attractive the convertible bond . This is flawed in the the straight value is not fixed but changes with changes in rates and spreads
15
Q
Convertible Security Value
A
= Straight Value + Value of call option on stock
16
Q
Bond Value, Credit Exposure
A
[Expected exposure x (1 - default rate)] + (Amt recovered * default rate)
17
Q
Probability of Default (POD), CDS
A
= [Loss given default (LGD) * expected loss] / 100
-This is the most important concept when it comes to CDS pricing
18
Q
POD,t
A
= POS,t-1 * Hazard rate
19
Q
POS,t
A
= POS,t-1 - POD,t
20
Q
Change in Bond Price, Credit Spread
A
= -MD * (New credit rating spread - original credit rating spread)
21
Q
LGD,t
A
=Exposure,t - recovery,t
22
Q
Recovery,t
A
=Exposure,t * recovery rate,t
23
Q
LGD, CDS
A
= 1 - recovery rate
24
Q
Payout Amount, CDS
A
= LGD * Notional Amount
25
CDS Spread
= (1 - recovery rate) \* POD
26
Fair Value, CDS
= Notional Value \* CDS spread
27
Upfront CDS Payment
=PV(Protection Leg) - PV(Premium Leg)
=PV(Expected Loss) - PV(CDS Coupon Payments)
-Computing this is essentially the same as pricing the CDS
28
Upfront CDS Premium %, From CDS Buyer
=(Credit spread - fixed coupon) \* Duration of CDS
29
Present Value CDS (Credit Spread)
=Upfront payment + PV(fixed coupon)
30
Price of CDS per 100 Par
= 100 - upfront premium
31
% Change CDS Price
= Change, bps(Spread) \* duration
32
Profit for Protection Buyer
=Change, bps(Spread) \* duration \* notional
33
Basis, CDS
= CDS market spread - bond market spread
34
Forward Contract Value, Expiration - Long Position
V,T(T) = S,T - F,0(T)
35
Forward Contract Value, Expiration - Short Position
V,T(T) = F,0(T) - S(T)
36
Forward Contract Value, Initiation - Long Position
V,0(T) = S,0 - [F,0(T) / (1+r)^T]
= Current worth of asset - PV(Future obligation)
37
Forward Contract Value, Initiation - Short Position
V,0(T) = [F,0(T) / (1+r)^T]
38
Forward Contract Price, Initiation
F,0(T) = S,0 \* (1+r)^T
39
Forward Contract Value, During Life - Long Position
V,t(T) = S,t - [F,0(T) / (1+r)^(T-t)]
40
Forward Contract Value, During its Life, PV Version
V,t(T) = PV of differences in forwards prices
= PV,t,T [F,t(T) - F,0(T)] = [F,t(T) - F,0(T)] / [(1+r)^(T-t)]
For futures regarding stock indexes =PV,t,T [F,t(T) - F,0(T)] / (e^(r \* T-t))
41
Futures Contract Market Value before Marking to Market - Long Position
V,t(T) = f,t(T) - f,t-(T)
t- represents point in time when last mark to market adjustment was performed
42
Forward price, Carry Arbitrage
F,0(T) = (S,0 - Y,0 + Theta,0)(1+r)^T
This formula also works for bond futures/forward contracts where accrued interest is included in price quote (i.e. Bond dirty price)
43
Unannualized FRA Rate
FRA(0,h,m) = {(1+(L,0(h+m)[(h+m)/360] / ( 1 + (L,0(h) \* (h/360)) } - 1
```
h = # of days until FRA expiration
m = # of days ion underlying hypothetical loan
h+m = # of days from FRA initiation until end of term of hypothetical loan
```
To annualize, multiple above by (360/m)
FRA rate serves as the underlying of interest rate options
44
FRA Payoff, Long Position
= (NP \* [(Market Libor - FRA rate) \* (# of days in loan term / 360) / (1 + [Mrkt Libor \* (# of days in loan term / 360)])
45
Valuing FRA Prior to Expiration
V,g(0,h,m) = NP \*{ [(New Frwrd rate - FRA rate) \* (# of days in loan term / 360)] / [1 + (New forward rate \* ((# of days in loan term + # of days until contract expiration)/360))] }
46
Accrued Interest
= Accrual Period \* Periodic Coupon payment
= (NAD / NTD) \* (c/n)
```
NAD = # of accrued dayts since last coupon payment
NTD = # of total days during coupon payment period
n = # of coupon payments per year
```
47
Forward Price of Stock Index
F,0(T) = S,0e^[r,c - y,c + theta,c)\*T]
-Can also equal S,o \* (1 + r)^T - accumulated value of divs received over life of futures contract per contract
48
Quoted Futures Price, Clean Price Bond
QF,0(T) = (1 / CF(T)) \* {[B,0(T+Y) + AI,0 - PVCI,0,T] \* (1+r)^T - AI,T}
```
B,0(T+Y) = Price of bond today
T = Expiration of forward contract
Y = Period from expiration of forward contract to maturity of bond
PVCI,0,T = PV of coupon income received on bond during term of forward contract
```
49
Continuously Compounded Forward Exchange Rate
F,0,PC/BC = S,0,PC/BC \* e^[(r,PC - r,BC)\*T]
50
Forward Currency Contract Value, Prior to Expiration
V,t(T) = (F,t,PC/BC - F,0,PC/BC) / [(1+r,PC)^(T-t)]
51
FRA Naming Convention
" X x Y"
X = # of months until FRA expiration
Y = # of months until hypothetical loan expires
52
Swaps, Net Fixed Rate Payment,t
=[Swap Fixed Rate - (Libor,t-1 + spread)] \* (# of days / 360) \* NP
53
Swap Fixed Rate
= { (1-B,0(N)) / (B,0(1) + B,0(2) +...+B,0(N) } \* 100
B,0(N) = the current PV factor as of today (swap initiation, t=0) for a payment that will be received on day N of swap
54
Swap Value, Plain Vanilla Interest Rate Swap
V = NA \* (PSFR,0 - PSFR,t) \* Sum of PV factors of remaining payments as of t=t
55
Currency Swap Value
V = NA,PC \* (PSFR,PC \* (Sum of PV factors of remaining coupon payments,t) + PV factor for return of NA,t) -S,t,PC/BC \* NA,BC \* (PSFR,BC \* Sum of PV factors of remaining coupon payments,t + PV factor of return of NA,t)
56
Call, Intrinsic Value
c,T = Max[0, S,T - X]
c,T Euro-Style = MAX[0, S,T - (X/(1+r)^T)]
-As volatility approaches 0, option values approach these lower bounds
57
Put, Intrinsic Value
pT = Max[0, X - S,T]
p,T Euro Style = Max[0, (X/(1+r)^T) - S,T]
-As volatility approaches 0, option values approach these lower bounds
58
Put-Call Parity
c,0 + [x / (1+r,f)^T] = p,0 + S,0
59
Call Option Value
c = [pi(c+) + (1-pi)(c-)] / (1+r)
60
Hedged Portfolio, Risk Neutral Probabilities (Equities)
pi = (1+r-d) / (u-d)
also represents the r,f probability
-Risk neutral probs with valuing interest rate options or options on bonds are assumed to be 50%
61
Call-Hedge Ratio
h = [(c+) - (c-)] / [(S+) - (S-)]
= [(c+) - (c-)] / [(u-d)S]
62
No Arbitrage Call Valuation Replication
c = hS,0 + PV(-h(S-) + (c-)) = hS,0 + PV(-h(S+) + C+)
63
Expectations Approach, Call Valuation
c= PV,r[E(c,1)]
=PV[pi(c+) + (1-pi)(c-)]
64
Expectations Approach, Call Valuation in 2-period setting
c = PV[pi^2(c++) + 2pi(1-pi)(c+-) + (1-pi)^2(c--)
65
Put Option Delta
= Call option delta - 1
66
of units of hedging instrument
N,H = - (portfolio delta / Delta,H)
67
Estimate of Changes in Option Prices, Gamma Delta and Vega
c + change(c) = c + change(c) \* change(S) + (1/2 \* r,c \* change(s)^2) + vega \* change (Std.dev of S)
r=gamma
If underlying increases by a large amount, delta plus gamma valuation will overstate call price. If underlying decreases by large amount, it will understate call price
68
Appraisal Index Return
= (NOI - Capex + (End MV - Beg MV)) / Beg. MV
69
Real Estate Return
= Cap Rate + Capital Return
70
Cap Rate (Income Return)
= NOI / Beg. MV
71
Capital Return, Real Estate
= (End MV - Beg MV - Capex) / Beg. MV
72
Net Operating Income, Real Estate
NOI = EGI - Operating Expenses
73
Effective Gross Income (EGI)
= PGI - Vacancy & Collection Losses
74
Potential Gross Income (PGI)
= Rental Income @ Full Occupancy + Other Income
75
Cap Rate When Value & Income are Growing @ Same Rate
Cap Rate = Discount Rate (Required return) - Growth Rate
76
All Risks Yield (ARY)
= Rent,1 / Sale of Comp
77
Gross Income Multiplier
= Selling Price / Gross Income
78
Value of Subject Property, Gross Income Multiplier
= Gross Income Multiplier \* Gross Income of Subject Property
79
Real Estate Value, Direct Capitalization Method
Value = NOI,1 / Going-in Cap Rate
80
LTV Ratio, Real Estate
LTV = Loan Amt / Appraised Value
81
Debt Service Coverage Ratio, RE (DSCR)
= NOI / Debt Service
82
Equity Dividend Rate, Real Estate
= 1st Year Cash flow / Equity Investment
83
Funds From Operations (FFO)
= Accounting Net earnings + D&A Charges on RE + Deferred Tax Charges +(-) Losses (Gains) from Sales of Property and Debt Restructuring
84
Adjusted Funds From Operations (AFFO)
= FFO - Non-Cash Rent - Maintenance Type Capex and Leasing Costs
85
Post VC Invest Value
POST = PRE + I
86
Proportionate Share of VC Investor
= I / POST
87
Distributed to Paid-In (PPI), AKA Cash on Cash Return
= Cumulative Distributions / Paid In Capital (PIC)
88
Residual Value to Paid In (RVPI)
= NAV After Distributions / PIC
89
Total Value to Paid-In (TVPI)
= DPI + RVPI
90
Futures Price, Convenience Yield
Futures Price = Spot Price + Storage Cost - Convenience Yield
-Convenience yield is the benefit of holding the physical product, rather than a contract/derivative product. This means that C.yield will go down if supply of the product increases, and vice versa
91
NAVPS, REITs
1) Est. Next 12 months NOI
2) Est. Gross Asset Value
3) Calculate NAV
4) NAV / Shares outstanding = NAVPS
92
Estimating Next 12 months NOI, RE
Step 1 in Calculating NAVPS
Est. Next 12 Months NOI = Last 12 months NOI - Noncash Rent + Full Year rent of acquired Property + Next 12 months NOI Growth
93
Estimating Gross Asset Value, RE
Step 2 in calculating NAVPS
Gross Asset Value = [(Next 12 months Est. NOI) / Cap rate] + tangible assets
94
Calculating NAV, RE
Step 3 in calculating NAVPS
NAV = Gross Asset Value - Total Debt & other liabilities
95
Post-Money Value, VC
= Exit value / [(1 + Required rate of return)^(# of Yrs to exit)
96
Carhart Model
E(R,p) = R,f + B,p,1(RMRF) + B,p,2(SMB) + B,p,3(HML) + B,p,4(WML)
97
Macroeconomic Factor Model
```
R,i = a,i + b,i,1(F,INFL) + b,1,2(F,GDP) + e,i
a,i = Expected return on stock i
F = Surprise in factor
e,i = Stock=specific (unsystematic risk)
```
-Factor sensitivities are estimated last in macroeconomic factor models
98
Fundamental Factor Model
```
R,i = a,i + b,i,1(F,DY) + b,i,2(F,PE) + e,i
a,i = intercept term
F = return associated with relevant factor
Factor sensitivities (b,i,1 and b,i,2) are usually standardized
```
-Factor sensitivities are generally specified first in fundamental factor models
99
Active Return
= Returns from factor tilts + return from asset selection
=Security selection value added + Active allocation value added
100
Active Risk Squared
=s^2(R,p - R,b)
=Active factor risk + active specific risk
101
Information Ratio
=(R\_,p - R\_,b) / (s\*(R,p - R,b)
=(R\_,p - R\_,b) / Tracking error
- This measures the consistency of Active return , also is a measure of relative expected/realized reward to risk
- This is unaffected by the aggressiveness of active weights (deviations from benchmark weights) bc both active return and active risk increase proportionally
102
Fixed Income 1st and 2nd Order Yield Effects on Bond Price
Change(B) / B = -D\* [Change(y) / (1+y)] + 1/2 \* c \* [change(y)^2 / (1+y)^2]
103
Delta
=change(c) / Change(S)
- CALLS: Call option delta in range of 0 - 1. As expiration approaches, delta approaches 1 for deeply in the money calls and 0 for deeply out of the money calls
- PUTS: Put option delta in range of 0 - (-1). As expiration approaches, delta approaches -1 for deeply in the money puts and 0 for deeply out of the money puts
104
Gamma (r)
= Change(Delta) / Change(S)
-Increases as option approaches in-the-money
105
Vega
=Change(c) / Change (Std.dev, s)
-The vega of a call option is the same as the vega of an otherwise identical put option
106
VaR
z = (R - h) / (std.dev)
z = critical z stat given from corresponding confidence interval (i.e. Confidence interval of 16% -→ z-stat of -1)
R = value at risk
h = expected annual return
107
Value Added (Active Returns) Equation
```
R,A = N(SUM)i=1 [Change(w,i)\*R,Ai]
R,Ai = R,p - R,b
Change(w,i) = Active weight = Portfolio weight - benchmark weight
```
108
Active Returns, more than 2 assets
```
R,A = M(SUM)j=1[W,p,j\*R,A,j] + M(SUM)j=1[Change(w,j)R,B,j
M = # of assets
```
109
Sharpe Ratio
SR,P = (R,p - r,f) / STD(R,p)
- Sharpe ratio is unaffected by the addition of cash/leverage in a portfolio and would thus not be app to evaluate a port in which leverage or an allocation to cash was a key part of investment decision process
- Use sharpe ratio to evaluate performance when asked on a risk-adjusted basis
- Measures the absolute risk-return trade-off for a portfolio
110
2-Asset Portfolio Volatility
sigma^2,p = sigma^2,1(w^2,1) + sigma^2,2(w^2,2) + 2Cov1,2\*(w,1\*w,2)
111
Information Ratio, Active Return
IR = Active return / Active risk
= R,A / sigma(R,A)
= (R,P - R,B) / sigma(R,A - R,B)
112
Sharpe Ratio, Information Ratio
SR^2,p = SR^2,B + IR^2
113
Optimal Amount of Active Risk, Unconstrained Portfolio
Sigma\*(R,A) = [IR / SR,B] \* Sigma(R,B)
114
Optimal Active Weights
```
Change(w\*,i) = [u,i / sigma^2,i] \* [sigma,A / (IC \* RAD(BR))]
u,i = forecasted active return on security i
sigma^2,i = Forecasted volatility of active return on security i
sigma,A = Active portfolio risk
```
115
Forecasted Active Return on Security i
```
u,i = IC\*sigma(i)\*S,i
S,i = set of standardized forecasts of expected returns across securities, AKA scores
```
116
Basic Fundamental Law
E(R,A)\* = IC\*RAD(BR)\*sigma(A)
=IR \* sigma(A)
117
Information Ratio of Unconstrained Portfolio
IR\* = IC \* RAD(BR)
118
Active Risk of Managed Portfolio
sigma(A) = RAD{N(SUM)i=1 [Change(w\*^2,i)\*sigma^2(i)]}
119
Full Fundamental Law
E(R,A) = TC(IC)RAD(BR)sigma(A)
120
Information Ratio of Constrained Portfolio
IR = TC(IC)RAD(BR)
121
Max Value of Constrained Portfolio's Sharpe Ratio if Optimal Amount of Aggressiveness is built into Portfolio
SR^2,p = SR^2,B + (TC^2)(IR\*^2)
122
Value Added Without Constraint Induced Noise, Realized IC
E(R,A | IC,R) = TC(IC,R)RAD(BR)Sigma(A)
123
Value Added With Noise
R,A = E(R,A | IC,R) + Noise
124
Contribution of Forecasting Success to Active Return Variance
= TC^2
125
Contribution of Constraint Induced Noise to Active Return Variance
= 1 - TC^2
126
Fundamental Law of Active Management Parameters
- A managers forecast must correspond at least somewhat to the realized returns if the manager is to generate a positive relative return (IC)
- Manager must overweight securities for which he has forecasted the best relative returns in order to generate positive relative returns (TC)
127
Information Coefficient (IC)
IC = correct calls - incorrect calls
-The more ambitious the forecasts, the greater the value of the IC in the fundamental law
128
Breadth of Active Management Given Correlations between Active Security Returns
BR = N / [1 + (N-1)p]
129
Estimate of Active Return, Accounting for Uncertainty in IR
E(R,A) = [IC / Sigma(IC)] \* Sigma(A)
130
Effective Spread Transaction Cost Estimate
Trade size \* {[Trade price - ((bid + ask) / 2) for buy orders] / [((bid + ask)/2) - Trade price for sell orders]}
131
Precision
AKA the True Positive Rate, most useful when cost of a false positive is high
P = TP / (TP + FP)
132
Modigliani and Miller Proposition I & 2, Div Irrelevance Theory
1. Assuming no taxes, the value of firm is independent of its capital structure
2. Assuming no taxes, the cost of equity rises linearly as the debt-to-equity ratio rises. So, WACC is constant across all debt-to-equity ratios bc the rising cost of equity exactly offsets the benefit of adding lower cost debt
Div Irrelevance theory states that the div decision is not relevant to the net wealth of company's shareholders
133
Current Rate Method (All-Current Method)
Used to translate financial statements presents in the functional currency (FC) into amounts expressed in parent's presentation currency (PC). If local currency is deemed to be functional currency (LC = FC ≠ PC), use this.
- Income statement accts translated at historical rate (or average rate for practical purposes)
- Balance sheet accounts (except common equity) translated at current rate
- Capital stock translated at rate that applied on date of capital contribution
- Divs transalted at rate that applied when they were declared
- Cumulative Translation gain/loss for period is balancing amount which is included as a line-item on the equity section of balance sheet
134
Temporal Method (AKA Remeasurement)
Used to translate financial statements presented in a local currency (LC) into amounts expressed in functional currency (FC). If presentation currency is deemed to be functional currency (LC ≠ FC = PC), use this
- Monetary assets and monetary liabilities are translated at current rate. Monetary assets = cash and receivables, most liabilites are monetary liabilities
- Nonmonetary assets and liabilities measured at \*historical cost\* are translated at historical rates, as well as shareholders equity. Nonmonetary assets include PP&E and intangible assets
- Revs and expenses (other than expenses related to nonmonetary assets) translated at average rate
- If foreign currency is weakening, under this method a net monetary liability exposure will result in a translation gain
135
Cox-Ingersoll-Ross (CIR) Model
- Model uses just the short-term interest rate to determine the entire term structure of interest rates
- The interest rate is modeled as mean-reverting
- The stochastic term makes volatility directly proportional to short-term
- Model allows interest rate volatility to vary with the level of interest rates
136
Arbitrage Pricing Theory (APT)
Similar to CAPM, this is used to estimate a stock's required return on equity, with both including betas. APT differs from CAPM in that APT is a multifactor model while CAPM only includes one equity risk premium
137
Substantive Law
Focuses on the rights and responsibilities of entities and relationships amongst them
138
Procedural Law
Focuses on the protection and enforcement of substantive laws
139
When is a Series Covariance Stationary
A series is covariance stationary when it has:
- A constant mean
- Constant variance
- Constant covariance with laggered values of itself overtime
140
Probability of Default (POD), Bonds
POD = Expected Loss / LGD
141
Statutory Merger
These occur when target company ceases to exist and becomes wholly owned by acquiring firm
142
Cost Approach, Real Estate Value
Property Value = Land Value + Building Replacement Cost - Total Depreciation - Any Obsolescence
143
Credit Migration Risk
This is downgrade risk tin the credit rating for a company or bond issuer. Credit spread migration typically reduces expected return for 2 reasons
1. The probabilities for change are skewed toward a downgrade rather than upgrade
2. The increase in credit spreads is much larger for a downgrade than decrease in spread for upgrades
144
Structural Models
* Require “inside” information, known to company mgmt
* Use option-valuation models
* Based on the premise that a firm defaults on its debt if value of assets falls below its liabilities
* probability of default has characteristics of an option
145
Reduced-Form Credit Model
* Reduced-form models use publicly available data about company
* use regression analysis
* assume that default can occur at any time
146
Neoclassical Model
* in the short-term, country's capital-labor ratio and output per worker would both increase in response to increase in savings rate, decrease in labor force growth rate, or decrease in depreciation rate
* an increase in growth rate of tech results in short term decline in capital-labor ratio and output per worker, but long term increase in their respective growth rates
* marginal product of capital is constant
* Predicts that convergence will occur
* Developing countries have less capital per worker. As a result, marginal product of capital is higher. Thus, the rate of return on investments should be higher in countries with low capital to labor ratios and lower in countries with high capital to labor ratios
147
Classical Growth Theory
Technological progress has no impact on long-term growth in per capita output
148
Endogenous Growth Theory
Marginal product of capital is constant
- Externality of human capital is part of this theory, and the theory does not support convergence
- If the externalities associated with knowledge and human capital are large, the higher income country can maintain its lead through high rates of investment in these capital inputs
149
Receive Floating, Pay Fixed FRA
If exercise rate equals current FRA rate, then a long position on interest rate call option cmbined with short position on interest rate put option is equivalent to this
Taking a long position on interest rate cap and short position on interest rate floor with same exercise rate
150
Black-Scholes-Merton (BSM) Model
c = SN(d,1) - e^(-rT)XN(d,2)
P = e^(-rT)XN(-d2) - SN(-d1)
N(d,2) = Probability that call option expires in the money.
1 - N(d,2) = N(-d,2) = Probability that put option expires in the money
Equations represent no arbitrage approach to replicate call or put option, respectively. I.e. To replicate a call option you would buy N(d,1) units of stock, financed by selling N(d,2) zero coupon bonds
- Futures prices follow geometric Brownian Motion (GBM) for the Black Option Valuation model
- Assumes that the continuously compounded return (or logarithmic return), ***NOT*** annualized return, is normally distributed
151
Receive-Fixed, Pay-Floating FRA
* If exercise rate = current FRA rate, long position on interest rate put option combined with short position on interest rate call option would replicate this
* Taking a long position on interest rate floor and short position on interest rate cap with same exercise rate is also equal to this
152
Sources of ETF Premiums/Discounts
* Timing Difference - Arises due to differences in exchange closting times between the underlying and exchange where ETF trades. Makes NAV a poor fair value indicator for ETFs which hold foreign securities
* Stale Price - Refers to ETFs that trade infrequently. If ETF has not traded in hours leading to market close, NAV may have significantly risen/fallen during that time owing to market movement
*
153
Investment Value recognized by Investing Company, Equity Method
=Purchase Price
+ Proportionate share in net income
- proportionate share of Divs paid
- Amortization of excess purchase price attributable to PPE
- Proportionate share of unrealized profit on downstream sale
- Proportionate share of unrealized profit on upstream sale
154
Inventory Turnover
=COGS / Avg. Inventory
155
Days of Inventory on Hand (DOH)
of days in period / Inventory Turnover
156
Receivables Turnover
=Revenue / Avg. Receivables
157
Days of Sales Outstanding (DSO)
of days in period / Receivables turnover
158
Payables Turnover
Purchases / Avg. Trade Payables
159
of Days Payable
of days in period / Payables Turnover
160
Cash Conversion Cycle
DSO + DOH - # of days payable
-Lower of this the better
161
Working Cap Turnover
Revenue / Avg. Working Cap
-Higher of this indicates higher operating efficiency
162
Pooling of Interests Method
Combines companies at historical cost.
Main benefitfor immediate future periods is lower fixed asset base, which generates lower depreciation expense and resulting in a higher net income.
Total equity is generally lower under pooling vs methods based on fair value bc of the use of historical cost.
Revenue is not affected
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Z-Spread
The constant basis point spread that when added to spot rates forces the PV of cash flows to be equal to bond's market value.
The process of determining the Z-spread ensures credit risk and liquidity risk are considered bc both risks are reflected in the market price of the bond
Does not consider bond embedded options
164
TED Spread
=LIBOR - YTM Treasury of same duration
165
Negative Risk Reversal Quote
This indicates that put options on the base currency are more expensive than the call options. This means the market is attaching a higher probability to a large depreciation of the base currency
166
Net Return on Plan Assets
= Actual Return - (Plan assets \* Discount Rate)
167
Sources of Financing, Pension Accounting
The difference between a company's periodic contribution and its periodic pension cost
- If periodic contribution \> periodic pension cost, the excess can be viewed as a reduction in the pension obligation, similar to a principal payment on a loan. Therefore, amount is classified as a financing cash outflow
- If periodic contribution \< periodic pension sots, difference can be viewed as an increase in the pension obligation, similar to taking a loan. Therefore, amount is classified as a financing cash inflow
168
Inputs Selected to Estimate the Equity Risk Premium from Historical data should include:
1. A broad equity index (preferably market-value weighted)
2. A time period that is long enough to be reliable but not so long as to violate stationarity
3. Either a geometric or arithmetic mean
4. A risk-free rate surrogate
169
Total Discount, Lack of Marketability + Lack of Control
Total Discount = 1 - (1 - DLOM)(1 - DLOC)
170
ICT Spending
This is spending on info, computers, and telecommunications. It allows people to communicate through interenet and work more productively - a type of network externality that can boost growth rate of potential GDP
Non ICT spending results in capital deepening and lower marginal returns, and will have less of an impact on potential GDP growth
171
Futures Price Basis
Futures Basis = Spot Price - Futures price
- If this is negative (futures price \> spot price), market is in contango
- If this is positive (spot price \> futures price), market is in backwardation
172
Managerialism
A motive for mergers when managers hope to retain their jobs while increasing the size of the firm.
When 2 subpar firms merge, likely that mgmt are hoping to maintain/increase their salaries at the expense of shareholders
173
Bond Yield Plus Risk Premium Approach
Cost of equity = YTM on outstanding bonds + risk Premium
174
Optimal Level of Residual Risk, Given Aversion to Residual Risk
w\* = IR / [2(Lamda,R)]
w\* = optimal residual Ris
Lambda,R = Aversion to Residual Risk
175
Lognormal Assumption Interest Rate Volatility, Binomial Interest Rate Tree
Time Period 1 Rates:
Higher time period 1 rate = Lower time period 1 rate x e^(2xVolatility assumption)
Lognormal assumption means interest rates on every path will be positive, and when rates are higher, higher volatility is built in
176
Business Combinations
Merger = Company A + Company B = Company A
Acquisition = Company A + Company B = Company A + B
Consolidation = Company A + Company B = Company C
177
Total Asset Turnover
= Revenue / Avg. Total Assets
178
Operating Cash Flow Equation
OCF = (S - C - D)(1-t) + D
179
Partitioning Cleansed and Preprocessed Data
Training sets, cross-validation sets, and test sets are partitioned using a common ratio of 60:20:20, respectively
180
Minimum Value of Convertible Bond
Equal to the greater of 1) the conversion value or 2) the value of an option-free (not convertible) bond that is otherwise identical to convertible bond
181
Justified P/CF Ratio
= Fundamental Value per share / Trailing cash flow per share
fundamental value per share = [FCFE,0 \* (1+g)] / (r - g)
182
Change in Pension Plan Assets
= Actual Return on plan assets + employer contributions - benefits paid
183
Change in Benefit Obligation
= Service costs + interest costs + actuarial loss - benefits paid
184
Root Moon Squared Error
A lower of this for out of sample forecasting signals better model accuracy
185
M-Score
Intercept term is -4.84, and the quality of financial results fall as M-score moves toward 0 / positive. Beneish recommended a -1.78 threshold for earnings manipulation
186
Long/Short CDS Trade
Party takes a long position in one CDS and short position in another, where two swaps are based on ***different*** underlying bonds.
- Represents a bet that credit quality of one entity will improve relative to that of another
- Investor would sell protection on entity whose credit quality is expected to improve (go long on CDS), and purchase protection on entity whose credit quality it expected to deteriorate (go short on CDS)
187
CDS Curve Trading
--With upward sloping credit curve, a steepening (flattening) of the curve means that long-term credit risk has increased (decreased) relative to short-term credit risk
- Investor whos believes long term credit risk will increase relative to short-term credit risk (Credit curve steepning) will purchase protection (go short) on long-term CDS and sell protection (go long) on short-term CDS
- Investor who believe long term credit risk will decrease relative to short-term credit risk (credit curve flattening) will sell protection (go long) on long term CDS and buy protection (go short) on short term CDS
188
Static Trade-Off Theory
As the proportion of debt in capital structure increases, when there are taxes and costs of financial distress, the after-tax cost of debt rises as well as the cost of equity.
- As the WACC initially falls then rises, there is an initial increase in value of leveraged firm followed by an eventual decline
- Under the static tradeoff theory, the target capital structure is the optimal capital structure, which is the capital structure where the comp's WACC is minimized
189
US GAAP to IFRS DB Pension Plan Adjustments
- Analyst must adjust US GAAP complia financial statements to
- Reflect past service costs in P&L
- Exclude past service cost amortization
- Use the discount rate instead of an expected rate of return
190
Dividend Irrelevance Theory
- MM proposed that under perfect capital markets (no taxes, transaction costs, and symmetric info), a company's div policy has no impact on its cost of capital / company value
- Based on the assumption that comp's div policy is indep of its investment and fiancing decisions, and can be explained through concept of homemade dividends
- Due to market imperfections, theory does not hold up in real worls. Companies incur floatation costs while shareholders incur transaction costs, while volatile stock prices make it problematic to create homemade divs
191
Dividend Bird in the Hand Argument
- Argues that divs matter, as even under perfect capital markets, shareholders prefer current divs over equivalent amount of potential capital gains from reinvesting earnings bc there is uncertainty associated with capital gain.
- All else equal, comp that pays for divs (as opposed to one that reinvests earnings) will have lower cost of equity as divs are less risky
- MM Counterargument is that paying/increasing current divs has no impact on risk of future cash flows. As cash divs only lower ex-div price of share, overall shareholder wealth remains the same
192
The Clientele Effect
- Refers to the existence of groups of investors that prefer different div policies and lean towards investing in comps that match their desired div policies.
- Change in div policy does not affect shareholder wealth (Clientele effect does not contradict div irrelevance), it woudl result in a switch in clientele
193
Forward Contract Trading Strategies
if F,0(T) \> FV(S,0) → Carry Arbitrage: Buy underlying and sell forward contract. Unederlyings price will increase and forward price will fall until F,0(T) = FV(S,0)
if F,0(T) \< FV(S,0) → Reverse Carry Arbitrage: Buy forward and sell underlying. Forward price will increase and underlying's price will fall until F,0(T) = FV(S,0)
194
Pension Plan Funded Status
-This is the PV of the company's defined benefit obligation - fair value of pension plan assets
Funded Status = Pension Obligation - Fair value of Plan Assets
-Assets that can be recorded is the lower of the funded status or the PV of future economic benefits
195
Company has subsidiary in country thats experiencing a weakening currency environment. Company has low D/E and the subsidiary's monetary liabilities are greater than its monetary assets. Explain effects on DE ratio under different translation methods:
- Current Method: Company has positive net assets (as D/E ratio is low) in a weakening currency environment-→causes forex loss in cumulative translation adjustment account→ results in lower equity (Higher DE ratio)
- Temporal Method: Company has negative net monetary assets in a weakening currency environment→ will cause forex gain in income statement→ results in higher equity (lower DE ratio)
196
Testing for Serial Correlation
- If the model is not an AR model, able to use DW test.
- If model is an AR model, not able to use DW test→ must examine the autocorrelations of the error term
To do this, take the coefficients from the autocorrelations of Residuals and calculate t-stat for each:
t-stat = coefficient / standard error
Standard error = 1 / RAD(number of observations)
If any of the t-stats are greater than then critical t-value (given by confidence level), able to determine that the autocorrelations of those lags are significantly different from 0→ can conclude model is misspecified due to serial correlation between the residuals
197
Recommended Procedures for Compliance with Standard III(B): Fair Dealing
- Communicate recommendation changes within the firm and to customers simultaneously
- Limit the number of people involved in the recommendation dissemination process
- Shorten the time frame between decision and dissemination
198
When Can you Use Multiple Linear Regression
- Multiple Linear Regression requires the error term in regression to be covariance stationary
- If at least one time series (dep var or indep var) has a unit root while at least one time series (dep var or indep var) does not, error term in regression cannot be covariance stationary→ Multiple linear regression cannot be used
199
The CAMELS Approach
-Widely used approach to analyze a bank which assigned a number 1-5 to each component, with 1 being the best rating
C: Capital Adequacy - adequate capital so that potential losses can be absorbed
A: Asset Quality - The amount of existing and potential credit risk assopciated with banks financial assets
M:Management Capabilities
E: Earnings - all earnings should be of high quality and upward trading, ideally derived from recurring sources
L: Liquidity POsition
S: Sensitivity to Market Risk (and interest rate risk)
200
Bias Error
- This is error from erroneous assumptions in the learning algo.
- High Bias can cause algo to miss relevant relationships between features and target outputs (underfitting)
201
Variance Error
- This is error from sensitivity to small fluctuations in the training set
- High variance can cause overfitting: modeling the random noise in the training data, rather than the intended outputs
202
Operational Efficiencies and Mergers
- Operational Efficiences can be achieved through both horizontal and vertical mergers
- Much less likely to occur when 2 unrelated firms merge to form a conglomerate. Some conglomerate mergers experience almost 0 synergies
203
IFRS Classification and CFO Calculation
- Interest Received can be classified as CFO or CFI. Only if it is classified as CFI should it be added to CFO to compute FCFF
- Interest paid can be classified as CFO or CFF. Only if its classified as CFO should after-tax interest paid be added back to CFO to compute FCFF
- If divs paid are classified as CFO, must be added back to compute cash available to all providers of capital
204
REITs, REOCs, and Private Direct Property Ownership
--A disadvantage of publicly traded RE vehicles like REITs and REOCs vs Private direct ownership is that publicly traded equity securities cannot pass on tax losses to investors like private investment vehicles can
-REITs can often avoid double taxation at both the corporate and investment income levels, which is not usually the case for private RE investment vehicles
205
Seasonality in Time Series Models
- Seasonality will lead to the error term of model having a positive autocorrelation with the lagged error term for the time where the seasonality is occuring.
- This will lead to high autocorrelation coefficients for the residuals of the time series of the model
206
Jensen's Free Cash Flow Hypothesis
- Asserts that higher debt levels force mgmt to use comp funds as efficiently as possible so that comp can satisfy debt servicing obligations in a timely manner
- Basically states that higher debt levels limit opportunities for mgmt to misuse cash
207
Pecking Order Theory
- Assets that mgmt prefer modes of financing that offer the least info content to company outsiders
- So, in this order: Internal financing, debt, equity
208
Frequency Analysis
-Filters unnecessary tokens (features); meaning those which are too frequent to provide meaning/too frequent to indicate belonging
209
Lemmatization
Converts inflected forms of a word into its root
210
Information Ratio, Given Alpha T-Stat and Years
IR = (Alpha t-stat) / RAD(Y)
211
FRA Positions
- Long position is the fixed payer, floating receiver (think of long position as the party that has committed to take a hypothetical loan @ FRA rate)
- Short position is the floating payer, fixed receiver (think of short position as the party that has committed to give a hypothetical loan @ FRA rate)
212
FRA and Interest Rate options Settlement
FRAs are typically advanced set, advanced settle where as interest rate options are typically settled in arrears (settlement payment made at end of settlement period)
213
FRA Eurodollar Replication
- Long position on FRA can be replicated by going long a longer-term eurodollar time deposit and at the same time shorting (or owing) on a shorter-term eurodollar time deposit
- Short position on FRA is replicated by going short a longer-term eurodollar time deposit and at the same time going long a shorter-term eurodollar time deposit
214
Temporal Method Translation Process
- Balance Sheet is translated using both current and historical rates.
- The resulting retained earnings balance is used to calculate the translation gain or loss
- Translation gain/loss is included in the income statement to ensure that retained earnings for the period match the retained earnings balance
215
Interest Rate Volatility Assumptions and Binomial Pricing Trees
- If binomial interest rate trees are properly calibrated, they should come to the same value for an option-free bond regardless of the volatility assumption. Calibrating an interest rate tree can be accomplished using spreadsheet software and is thus relatively easy to do without the knowledge of special programming and without great expense
- This is not the case when dealing with bonds that have embedded options
- A decrease in assumed interest rate volatility will cause the spread of the forward rates in the tree to narrow
216
Standard Error of Estimate Caluclation
SEE = RAD (Sum of squared residuals / (n - 2))
-SEE is the standard deviation of the regression residuals
Sum of Squared Residuals = SSE
217
Held-for-Trading Classification Treatment
- Company A owns 15% ownership in company B classified as Held for Trading
- A would include a 15% share of B's Dividends in its profit before taxes, and any change in the market value of the investment
218
Effects of Exchange Rate Movements, Temporal Method, Foreign Currency Strengthening
**_Net Monetary Liability Exposure_**
- Revs UP
- Assets UP
- Liabilities UP
- Net Income DOWN
- Shareholders' Equity DOWN
- Translation Loss (in Income Statement)
**_Net Monetary Asset Exposure_**
- Revenues UP
- Assets UP
- Liabilities UP
- Net Income UP
- Shareholders' Equity UP
- Translation Gain (in income statement)
219
Effects of Exchange Rate Movements, Foreign Currency Weakening relative to PC, Temporal Method
**_Net Monetary Liability Exposure_**
- Revs DOWN
- Assets DOWN
- Liabilities DOWN
- Net Income UP
- Shareholders Equity UP
- Translation gain (on income statement)
**_Net Monetary Asset Exposure_**
- Revs DOWN
- Assets DOWN
- Liabilties DOWN
- Net Income DOWN
- Shareholders Equity DOWN
- Translation loss (on income statement)
220
Effects of Exchange Rate Movements, Current Rate Method
**Foreign Currency Strengthens relative to parent's PC:**
- Revs UP
- Assets UP
- Liabilities UP
- Net Income UP
- Shareholders Equity UP
- Positive Cumulative Translation Adjustment (on Balance sheet)
**Foreign Currency Weakens Relative to Parents PC:**
- Revs DOWN
- Assets DOWN
- Liabilities DOWN
- Net Income DOWN
- Shareholders Equity DOWN
- Negative Cumulative Translation adjustment (on balance sheet)
221
Goodwill Calculation, Equity Method
Goodwill =
Purchase Price
-Prop share in book value of target's net assets
=Excess Purchase Price
- Attributable to PPE =(% of Interest \* (FV PPE - BV PPE)
- Attributable to Land =(% of interest \* (FV Land - BV Land)
=Goodwill
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Equity Income Calculation, Equity Method
=Prop share in Targets earnings
- Amortization of excess purchase price attributable to PPE=[% of interrest \* (FV PPE - BV PPE)] / Years of depreciation
- Prop share of unrealized profit on downstream sale= [% of interest \* total unrealized profit]
- Prop share of unrealized profit on upstream sale =[% of interest \* total unrealized profit]
=Equity Income
223
Equity Method Investment Value Calculation
Purchase Price (or YE BV of investment)
+ Equity Income
-Prop share of Divs paid by target
= New YE Investment value
224
When to Use Temporal vs Current Rate Method
- Can assume temporal method is used when subsidiary has a net liability balance sheet exposure as under the current rate method, unless a comp has negative SE, it will have a net asset balance sheet exposure
- Temporal method should be applied when activities of parent and sub are well-integrated
- Current rate method should be applied when sub's operating, financing, and investing decisions are made independently from parent
225
Non Cash Charges (NCC)
=Depreciation expense + restructuring charges + Impairment on intangible assets - Amortization of bond premiums + amortization of bond discounts
226
Up/Down Duration and Bond Types
- Callable Bond: up-duration \> down-duration
- Puttable and Straight Bond: Down duration \> up duration
227
Appreciation/Depreciation %
- This is measured in terms of the ***base currency***
- % change in BC = (S,t,PC/BC - S,0PC/BC) / S,0PC/BC
% Change in PC = [(1 / StPC/BC) - (1/S0PC/BC)) / (1/S0PC/BC)
228
Forward Bond Position Value
=[(PV of differences in forward prices) / par value of underlying bond] x Contract value x Number of contracts
PV of Differences in forward prices = PV,t,T[QF,t(T) - QF,0(T)]
229
Valuing Equity Swaps
-First determine the annual coupon payment given the SFR.
Ann. Coupon = SFR \* NA
- Next, value the fixed leg using the SUM(ann. coupon pmt,i \* discount factor (given current term structure of rates),i)
- Then, Value the equity leg as [1 + % change in equity] \* NA
- Value of swap to receive-fixed, pay-equity would = Fixed leg value - Equity leg value
230
Portion of Compensation Expense Related to Stock Option Component
= {(Options granted x Option Price on grant date) / # of Service years} \* Proportion of Yr options were granted
231
Loss Reported in OCI Pension Plan IFRS
=Actuarial Gain - Actuarial loss + Net return on Plan assets
Net return on Plan assets = (Actual return - Expected return) \* Beg. FV(PA)
232
P-Value
- This is the smallest level of significance at which the null hypothesis can be rejected.
- If p-value\> Sig Level → unable to reject null hypothesis, result not statistically significant
- If P-value \< Sig level → able to reject the null in favor of the alternative hypothesis, the result is statistically significant
233
The Coase Theorem
-This states that if an externality can be traded and there are no transaction costs, then the allocation of property rights will be efficient and the resource allocation will not depend on the initial assignment of property rights
234
Valuing Intangibles using the Excess Earnings Method (CCM)
- First, must calculate the return on intangibles
- Return on Intabgibles = Normalized income - Return on working cap - Return on fixed assets
- Return on working cap = (Working cap \* Require return on working cap)
- Then, use CCM:
Value of intangibles = Return on intangibles / (Required return on intangibles - Est. Growth rate)
235
Price-to-Earnings Growth Multiple
=PE / Earnings growth (in whole number) i.e. 16.6% = 16.6
236
Residual Income Model Use and Factoids
- RI model is used when company's FCF are expected to remain negative for the foreseeable future
- RI models should, depending on assumptions and adjustments (i.e. provided a clean surplus relationship and minimal adjustments for accruals and deferred expenses), provide the same calculation of value as DDM and FCF models
- RI models are absolute valuation models
\_RI models have an appealing focus on economic profitability
237
P/E and E/P (earnings Yield)
- PE ratio becomes meaningless when earnings are less than 0. When earnings are near 0, PE ratio can become very large and outliers can skew analysis results
- So, use earnings yield when earnings are negative or close to 0
238
Basis Trade
- This tries to exploit a price difference between the bond market and CDS market
- For example, if bond yield reflects 200bps spread while corresponding CDS is priced at a 175bps spread, basis trade would buy (go long) the bond and buy (go short) the CDS. Effectively, yield on bond is too high and spread on CDS is too low. When they correct, bond yield will fall and/or CDS spread will widen
239
Revaluation in Hyperinflationary Environments
- In hyperinflationary conditions, the historical cost of nonmonetary assets should be increased to account for the rise in the price index
- Financial assets should be valued at fair market prices (no inflation change)
240
Calculating Retained Earnings with Current Rate Method
- 1st translate Net income to PC at the average rate
- 2nd translate dividends at the historical rate of when Divs were declared
- Translated Net income - translated Divs = translated SE
241
Interest Rate Options Payoff
-Cash flow that occurs at t=2 is the payoff of the interest rate option at t=1
Floorlet Payoff = MAX(0, (X - r)/m) \* Notional
Caplet Payoff = MAX (0, (r - X)/m) \* Notional
X = exercise rate
r = rate at the previous time period
242
Forward Currency Contract Price
F(0,T) = S,0PC/BC \* [(1+r,pc)^T/(1+r,bc)^T]
243
CDS Pricing and Valuation Concepts
Cost of insuring a bond = PV(Expected Loss) = PV(Credit Spreads)
244
Types of Real Options
- Timing options: Give comp option to delay making an investment
- Sizing Options: Include abandonment and growth options
- Flexibility Options: Give mgmt choices regarding certain operation aspects of project. Include price-setting and production-flexibility options
- Fundamental Options: Essentially options embedded in the project itself. E.g. for a company that owns an oil well, decision to drill is governed by the price of oil
245
Hybrid Approach to Valuation
- Combines elements of both top-down and bottom-up analysis and can be useful for uncovering implicit assumptions/errors that may arise from using a single approach
- Top/Down may not consider company specific limitiations/complications
- Bottom-Up may not consider industry/demographic changes
246
Company-Specific Factors in Valuation
-Stage in life cycle, size, overlap of shareholders and mgmt, quality and depth of mgmt, quality of financial and other info, short-term pressure from investors, tax concerns
247
Stock-Specific Factors in Valuation
-Liquidity of equity interest in comp, concentration of control, agreements restricting liquidity
248
Adjusting Discount Rate for Private Company Valuation
- Private companies may have less access to debt financing than similar public company, meaning they may need to rely more heavily on equity financing which would increase WACC
- In evaluating an acquisition, finance theory indicates the cost of capital used should be based on target company's capital structure and riskiness of target comp's cash flows - buyer's cost of capital is irrelevant
- Mgmt of private company (whom analysts rely for forecasts) may have less experience forecasting future financial performance
249
Application of DLOC and Valuation Method
- Guideline Transaction Method (GTM) includes a control premium as the basis of valuation is that of control, therefore DLOC should be applied.
- Guideline Public Company Method (GPCM) basis of valuation is typically that of a minority, therefore a DLOC should not be applied.
- CCM/FCF basis of valuation depends on the cash flows
250
-Types of Futures Traders
- Speculator: These trade commodities without ever taking physical possession and speculate on future price paths of the commodities
- Arbitrageur: Have the ability to inventory physical commodities and can capitalize on mispricing between the commodity and futures price by physcially taking a position in commodity in spot market and holding it in storage until future date
- Informed Investors: Primarily keep commodity markets efficient by capitalizing on mispricining attributable to lack of info in marketplace. AS with speculators, they do not take physical possession of commodity
251
Survivorship Bias
- A common problem in backtesting. This can be considered a form of look-ahead bias
- This reflects only conclusions in a model about companies that have survived to the point of prediction
- Recommended to use point-in-time data which includes both survivors and casualities to accurately reflect viability of forecasting model
252
Data Snooping
- A common problem to backtesting
- A form of look-ahead bias which occurs when analyst backtests several strategies and selects the one with best results. Violates the assumption of a logical economic rationale for the model
- Methods to overcome this are higher significance levels and cross-validation
253
Look-Ahead Bias
-A common problem to backtesting which involves using info unavailable during the historical periods over which the backtest is conducted. Involves index changes, reporting lags, and revisions
254
Historical Simulation
-A form of backtesting that incorporates randomness by drawing returns randomly rather than chronologically from historical data.
When number of simulations needed is larger than size of historical dataset, analyst must draw randomly with replacement, known as *bootstrapping*
255
Dividend Discount Model Factoids
- For all DDMs, use cost of equity as discount rate
- DDMs are less subject to short term fluctuations and better predictor of LT company value
256
Busted Convertible
- When underlying share price is well below initial conversion price, bond exhibits mostly bond risk-return characteristics
- Call option is OTM, so share price movements do not significantly affect price of call option and thus the price of convertible bond
- Price movement of convertible bond closely follows that of straight bond, such factors as rate movements and spreads significantly affect convertible bond price
- As share price approaches 0, value of bond will fall to approach the PV of the recovery rate in bankruptcy
- Exhibits even stronger bond risk-return characteristics when call option is OTM and conversion period is approaching expiration bc time value of option decreases towards 0, making it highly likely conversion option will expire worthless
257
ITM Convertible
- When underlying share price is above initial conversion price, convertible bond exhibits mostly stock risk-return characteristics
- Call option is ITM, so price of call option and thus the price of convertible bond, is significantly affected by share price movements. It is mostly unaffected by factors driving value of otherwise identical option free bond
- Such convertible bonds trade at prices that closely follow the conversion value of bond, and their price exhibits similar movements to that of underlying stock
258
Cost of Capital and its effect on NPV and IRR
- Cost of capital and NPV are inversley related, so an increase in cost of capital would decrease a projects NPV
- IRR is strictly determined by cash flows of project, so IRR is unaffected by changes in cost of capital
259
Basel III Regulatory Framework for Banks
- The minimum liquidity requirement specifies that a bank must hold an adequate amount of high-quality liquid assets to cover its liquidity needs in a 30 day liquidity stress scenario
- Stable funding requirement specifies that a bank must have a minimum amount of stable funding relative to banks liquidity needs over a 1-yr horizon, where stability of funding is based on the tenor of deposit and type of depositor. Longer term deposits considered more stable than shorter term deposits and consumer deposits are considered more stable than funding from interbank market
260
Premium for Control, Given Control Premium
Premium for Control = Control Premium (CP) \* Weight of equity
-Use 1+Premium for control to adjust valuation multiples
261
Principal-Principal Problem
- Arises when companies have concentrated ownership and concentrated voting power, such as what occurs under a dual class share structure.
- Controlling shareholders may be able to allocate resources to their own benefit at expense of minority shareholders
262
Principal-Agent Problem
- Arises when voting power and ownership are both dispersed, leading to weak shareholders and strong managers
- In this situation, mgmt may seek to use company resources to pursue their own interests
263
Primary application of ETFs Use
--Portfolio Efficiency- The uses of ETFs to better manage a portfolio for efficiency or operational purposes
- Asset Class Exposure Mgmt - The use of ETFs to achieve/maintain core exposure to key asset classes, market segments, or investment themese on a strategic, tactical, or dynamic basis
- Active and Factor Investing-The use of ETFs to target specific active/factor exposures on basis of an investment view/risk mgmt need
264
Efficient Portfolio Mgmt ETF Use
- Portfolio liquidity mgmt - Cash flow mgmt
- Portfolio Rebalancing
- Portfolio Completion Strategies - used to fill a temp gap in exposure
- Transition Mgmt
265
Asset Class Exposure Mgmt ETF Use
- Core exposure to asset class or sub asset class
- Tactical strategies - implement mrkt views and adjust port risk on more short-term practical basis
266
Active and Factor Investing ETF Use
- Factor (smart beta) ETFs
- Risk mgmt
- Alternatively weighted ETFs
- Discretionary Active ETFs
- Dynamic asset allocation and multi-asset strategies
267
Different Values
- Fair Market Value: A price agreed to by a willing buyer and seller, both of whom are acting with free will and all available info
- Investment Value: Applies when an investment is worth more than fair market value to a particular buyer
268
Implied Volatility and Cost of Options
- If implied volatility is decreasing as strike price of options is increasing, then the using out-of-the-money options to hedge is more expensive than establishing a long position with OTM options
- Options to hedge are put options. Put option are OTM when strike price is low. Therefore, using OTM put options implies low strike price, which results in higher implied volatility (higher cost).
Options to establish long positions are call options. Call options are OTM when strike price is higher. Therefore, using OTM call options implies high strike price, which results in lower implied volatility (lower cost).
269
Volatility Smile (Normal Skew)
--In a volatility smile, implied volatility goes down and then up as the strike price goes down and then up
-In this, using OTM options to establish either long or short positions is more expensive than using at the money options
270
Statistical Factor Model
- Use factor analysis to produce factors that are portfolios of securities that best explain historical return covariances.
- Alternatively, they use principal component analysis to derive factors that are portfolios of securities that best explain historical return variances
271
Active Factor Risk Exposure Calculation
=Active Factor Risk Squared / Active Risk squared
272
Data Analysis Steps
- Feature Selection: The process of identifying and removing unneeded, irrelevant, or redundant features in a dataset
- Feature Engineering: The process of combining, consolidating, or creating new features that do not exist in the current dataset
273
One-Hot Encoding
The process of decomposing a single categorical feature with multiple values into indv features by type, and recording teh resulting in binary form
274
Name Entity Recognition
\_A process when using an existing library/package that can be applied in many programming languages to analyze the indv tokens and their surronding semantics to tag an object class to the token, such as org, location, and date
275
Differences Between Normalization and Standardization
- Standardization is the process of both centering and scaling the variables. This requires the data is normally distributed, and resulting standardized variable will have an arithmetic mean of 0 and a std dev of 1
- → Standardization: (Num - Avg) / Std dev
- Normalization is the process of rescaling numerical values in the range of [0,1]. This can be used when distribution of data is not known but treatment of outliers is necessary
→ Normalization: (Num - Min) / Max
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Net Income under Mgmt's Direct Control
-INCLUDES Net Income attributable to non-controlling interests, but EXCLUDES income from investments in associates
277
Principal of No Arbitrage
-Applies to risk free securities and portfolios, not to risky ones. Two conditions must hold:
***Lack of Dominance*** The price of any 2 risk free securities with the same timing and amount of payoffs must be the same
***Value Additivity*** The price of any portfolio of securities must equal the sum of the prices of the indv securities in the portfolio
Principal does not state anything about a relationship between risk and expected return of risky securities
278
Monte Carlo Forward Rate Simulation
- Randomly generates a large number of interest rate paths that will correctly value benchmark bonds only by change. A fixed amount, known as a drift term, is added to every forward rate on every simulated path to calibrate the simulation so that values estimated for benchmark bonds equal their market prices
- Requires simulation of a limited (though large) number of interest rate paths out of all possible paths. In binomial tree valuation, all paths on interest rate tree are considered
- Monte Carlo simulation is commonly applied to securities with path-dependent cash flows while interest rate trees cannot be used to value these securities
279
Types of Leases
-***Net Lease*** - Requires the tenant to pay operating expenses in addition to the based fixed rent
***Triple-Net Lease (NNN Lease)***-Require the tenant to pay its share of 3 types of expenses: common area maintenance (CAM) and repair expenses, property taxes and building insurance costs, in addition to based fixed rent
***-Gross Lease*** - Requires the owner to pay the operating and other expenses
280
F-Stat Calculation
F-Stat = MSR / MSE
= Regression Sum of Squares (RSS) / [Residual Sum of Squares (SSE) / (n - k - 1)]
281
Expected Loss,t
Expected Loss,t = POD,t \* (1 - recovery rate)
