CAIA Lvl 2 > Methods and Models > Flashcards

Methods and Models Flashcards

(97 cards)

Study These Flashcards
1
Q

+Normative vs positive models

A

Normative: explain how prices should behave (ex-ante)

Positive: explain how prices actually behave (ex-post)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Theoretical vs Empirical models

A

Theoretical: based on assumptions about behavior/processes

Empirical: based on observed behavior/data (better at dealing with complexity)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Applied vs abstract models

A

Applied: Address real-world problems

Abstract: Address hypothetical situations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Cross-Sectional vs Time-Series models

A

Cross-Sectional models: describe behavior across many assets for a single point in time.

Time-Series models: describe behavior across for a single asset over a long period of time.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Interest Rate Term Structure Modeling (equilibrium and arbitrage-free models)

A

Equilibrium Models: assume short-term interest rate follows random process (e.g. Vasicek, Cox-Ingersoll Ross)
-> these don’t actually explain bond prices!

Arbitrage-Free Models: Currently observed term structure of rates is used to calibrate model (e.g. Ho and Lee, Black Dermot Toy (BDT))

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Vasicek’s interest rate model

A

Mean-reverting process for short-term rate of interest

R(t+1) = Rt + κ (μ-Rt) + σε(t+1)

Issues:
- Not calibrated to yield curve and cannot explain bond prices
- Allows rates to go negative

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Cox, Ingersoll and Ross interest rate model

A

Slight adjustment to Vasicek’s model:

R(t+1) = Rt + κ (μ-Rt) + √Rt*σε(t+1)

As Rt approaches 0, and √Rt approaches 0 (faster), process gets less volatile and mean-reversion term dominates.

Issues:
- Not calibrated to yield curve and cannot explain bond prices

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Ho and Lee interest rate model

A

R(t+1) = Rt + θt + σε(t+1)

θt = time-dependent change in the rate: ensures the model explains empirically observed yield curves

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Black-Derman-Toy (BDT) model

A
  • Binomial model for future path of rates
  • Calibrated to both yield curves and implied volatility of interest rate options
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Adverse selection in the context of credit risk

A

Information asymmetry: borrower knows more than lender about their credit quality

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Moral hazards in the context of credit risk

A

Lender faces consequences of risks taken by borrower

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Expected credit loss

A

Exp. credit loss = P(default) * LGD

LGD = loss given default

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Loss given default (LGD)

A

LGD = EAD * (1-RR)

EAD = exposure at default (principal + interest)
RR = recovery rate

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Recovery rate

A

RR = PV (recovered cash) / EAD

EAD = exposure at default (principle + interest)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Three approaches to credit risk modeling

A

Structural: relates default to capital structure (e.g. Merton, KMV)

Reduced-form: models default as a random event (looks at the data of the results as opposed to what is structurally happening)

Empirical: credit scoring based on historical data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Describing a credit-risky bond under Merton’s structural model

A

Credit risky bond = Rf bond - put (on the company’s assets)

= (So + P - C) - P
= So - C
= covered call

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Four important properties of the Merton Model regarding credit risky bonds:

1) Impact of an increase in maturity?
2) Impact of an increase in vol?
3) Impact of an increase in leverage?
4) Impact of an increase in the risk-free rate?

A

1) Maturity ↑, P(default) ↑, Credit spread ↑ initially and then ↓

2) Asset Vol ↑, P(default) ↑, Credit spread ↑

3) Leverage ↑, P(default) ↑, Credit spread ↑

4) Rf rate ↑, RoA ↑, P(default) ↓, Credit spread ↓

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Advantages and disadvantages for using structural models to price credit risk bonds

A

✔
- Uses liquid market data
- Prices securities with different seniority and/or conversion options

❌
- Equity prices can be irrational
- Not accurate for short term or high quality bonds
- Data on liabilities can be unreliable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Expected time to default

A

1/λ

where λ = ‘default intensity’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Fair credit spread using a recovery rate (RR)

A

λ(1-RR)

where λ = ‘default intensity’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Jarrow-Turnbull reduced-form model

A
  • Assumes the timing of default, recovery is received at maturity
  • Can incorporate rating downgrades
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Duffie-Singleton reduced-form model

A
  • Allows recovery process to occur at any time
  • Recovery = non defaulting bond price at time of default
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Empiric Credit Models

A

Credit scoring using historic data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Five input variables for Altman’s Z-score (Empirical credit model)

When Repaid Everyone Must Smile

A
  1. Working Cap / TA
  2. Retained earnings / TA
  3. EBIT / TA
  4. Mkt Value / Book value of liabilities
  5. Sales / TA

The higher the value the less likely for there to be a default.

Working capital = Current assets - current liabilities
TA = Total Assets.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Interpretation of altmans Z-Score
Default: Z < 1.81 Grey zone: 1.81 ≤ Z ≤ 2.99 Safe: Z > 2.99
25
Exogenous variable
A value outside a model and taken as a given. An endogenous variable is determined from a model.
26
Default intensity (λ)
A measure the drives the probability of a default in continuous time. The higher the λ, the higher the P(default) over a given time period
27
Default trigger
A value for assets where a debt issuer would be forced into default in the KMV model (not always par)
28
P (measure)
Actual probability of an event occurring
29
Q (measure)
Plays the role of probability of an event occurring in a model but it is not actual probability
30
When do Q-measure valuations = P measure valuations
Under the assumption of no-arbitrage
31
Key point on Q-measures and P measures
P- measure is the ACTUAL probability of an event occuring. This is impossible to predict due to an infinite quantities of specific values. Q-measures assume risk-neutrality (ie no risk premium, only using the rf rate) and so can be calculated and applied
32
Average Compound Returns Problem
Essentially compounded returns used in a binomial tree do not work.
33
Up move in binomial trees (u) This is not a probability. It is the magnitude of an upward move in the stock price for each step of the binomial tree. Stock-based binomial trees
u = e^(σ√t) This is not a probability. It is the magnitude of an upward move in the stock price for each step of the binomial tree.
34
Down move in binomial trees (d) Stock-based binomial trees
d = 1/u u=e^(σ√t)
35
Risk neutral probability of an up move p: Stock-based binomial trees
p = ( (1+Rf) - d ) / (u-d)
36
Value of callable bond
Value (non-callable bond) - Value (call option)
37
Visualization
expressing a model visually to understand its nature, often through excel
38
Utility
level of satisfaction from an outcome Utility ↓, Risk premium expected ↑ e.g. high beta stocks Issue is that different investors have different views on utility
39
A risk premium that is unrelated to factor exposures
an anomaly (a risk factor that is not yet priced/recognised)
40
3 main factor groups when dissecting returns
1) Macroeconomic (e.g. inflation, unemployment etc) 2) Fundamental (e.g. value, size) 3) Statistical / empirically observed (e.g. principal component analysis)
41
'smart beta'
factor-based approach to passive investing. Requires re-balancing
42
Adaptive Market Hypothesis
Competition ↑, Profits ↓ Investors need to adapt -> risk premiums vary over time -> market efficiency is relative over time
43
Time-varying volatility - key points
- Equity market vol tends to be persistent (high autocorrelation) - Equity market vol is higher when returns are negative (stocks rise slower than when they fall, -ve beta)
44
Heston model on vol:
vol is mean-reverting
45
Bates model on vol:
Heston model (vol = mean-reverting) + random jump factor
46
Fama-French model
Market = CAPM 2 factor model: value and size
47
Fama-French-Carhart model
Market = CAPM 3 factor model: value, size and momentum
48
Fama-French 5-factor model
Market = CAPM 5 factor model: value, size, momentum, robust (ROE) and conservative
49
Paradox of market efficiency
Markets can only be efficient when investors believe that they are inefficient (and are actively looking for mispricings)
50
Market divergence
unanticipated stock price movements (strong trends)
51
How to measure the degree of market divergence
signal-to-noise (SNR) ratio: (total price move) / (sum of absolute daily price moves) High for strong trends
52
Market divergence index
average of SNR ratios across markets higher = stronger trends
53
Genetic Algorithm
Trading strategies adapt in line with profits
54
Neural network
Modeled on the human brain
55
EV equation
EV = equity + debt - cash
56
How to calculate fair EV
PV (FCFF)
57
FCFF
FCFF = Net income + non-cash charges (e.g. depreciation) + (interest(1-t)) - investments in fixed assets and working capital
58
Feedback-based managers
Contrarian investment approach
59
Disposition effect
Selling winners early and running losers - due to the impact of loss aversion (pain of losses > pleasure of gains)
60
Representativeness bias
Over emphasizing your past experiences when making forecasts
61
Digital Asset Valuation Methods: Stock-to-flow model
Stock (existing quantity of BTC) / Flow (no. new units created) ↑ ratio, ↓ supply, ↑ value
62
Digital Asset Valuation Methods: Addressable market model
BTC value driven by the potential addressable marketability
63
Digital Asset Valuation Methods: Cost-of-production
PoW: cost of mining process PoS: based on staking yield
64
Digital Asset Valuation Methods: Metcalfe's law
Value driven by number of users: n(n-1) / 2
65
Crisis alpha
Alpha in down markets
66
Prospect theory
irrational decision making through overweighting small probabilities and underweighting large probabilities due to emotional biases
67
Eigenvalues
A number used to describe the proportion of variance that is explained by a factor
68
PCA (principal component analysis) vs Factor analysis
- PCA explains variance as opposed to explicit factors Factor analysis - Requires model assumptions on factors - Conclusions (beta) dependent on several factors PCA - Able to identify factors that are unique to a single security
69
Multicollinearity
Independent variables (Xs) are correlated with one another (in regression with multiple factors) Low t-stats, high R^2 e.g. MSCI World and MSCI ACWI regressed against Equity performance
70
Effects of multicollinearity
Independent variables (Xs) FALSELY look unimportant - Slope coefficient estimates may be wrong - Inflates standard errors of slope coefficients. - R2↑, T-stat ↓
71
Stepwise regression
Carefully selecting independent variables in multi factor regressions
72
What is the conclusion when a fund's beta in up markets is greater than in down markets (βi,diff)
Good stock selection
73
Conditional correlation
Correlation between two variables relative to specific circumstances
74
Positive conditional correlation
Correlation higher in up-markets
75
Negative conditional correlation
Correlation lower in down-markets
76
Factor loadings
Sensitivity of an asset to another component
77
Joint hypothesis
Test result that depends on two hypotheses: 1) Test method is valid 2) Hypothesis is tested
78
Look-back option
An option with a payoff based on the trajectory of the underlying asset, instead of the final price of the asset
79
Bull spread
Long the near-dated contract (short the far-dated contract) Losses are limited to the cost of carry (because you can sell the contract you bought when it gets to the far-dated contract) Clockwise trade - profitable in both contango and backwardated markets when prices go ↻. (Contango: spread narrows, Backwardated: spread widens)
80
Bear spread
Short the near-dated contract (long the far-dated contract)
81
Processing spreads
difference between raw commodity and products derived from them (e.g. crack and crush spreads) used for hedging business risk
82
Crack spread
Long crude oil, short byproduct (e.g. gasoline)
83
Crush spread
Long soybean futures, short byproduct (e.g. soybean oil)
84
Substitution spread
Long coffee, short tea (for example) Substitute t-stat = ln(PriceA/PriceB)
85
Quality spread
Commodities with different 'grades of quality' priced differently (e.g. jet fuel vs heating oil)
86
Carry trade
Borrow low interest rate Deposit high interest rate (e.g. borrow USD at 3%, deposit in EUR at 5%) Risk is the high interest rate depreciates more than the difference
87
Covered interest rate parity
Fair forward exchange rate set by interest rate differential between two currencies i.e. it is the idea that the forward exchange rate is the rate at which the carry trade breaks-even/becomes unprofitable. (1+Rfixed)^t * (Ft/So) = (1+Rvariable)^t
88
When is a random process considered stationary
occurs when key parameters remain consistent (e.g. mean and variance)
89
Depreciation tax shield
Tax savings that result from depreciation = depreciation * tax
90
Depreciation recapture
When you sell a property for more than its book value, the tax that had been saved through depreciation must then be paid for.
91
Impact of faster depreciation
Tax shield ↑, post-tax IRR ↑ depreciation is great from a tax perspective due to the time value of money, despite paying depreciation recapture
92
Transaction-based indices Repeat Sales method for RE indices
Measures changes in the value of properties (with two transactions or more) Uses dummy independent variables (only includes the data held during each given period, so removes a property when its sold) - essentially reflects the average return in each period. Advantages - Uses two transactions in the same property avoids need to adjust for differences in properties - Well-specified regression Disadvantages - Small sample of transactions - Assumes property undergoes no changes - Current transactions updates can impact historical results
93
Transaction-based indices Hedonic Pricing Method
- Regresses transaction prices with attributes of property - Model then used to value properties that did not transact Provides the ln(priceX) - so remember to convert back to simple price (e^X) Advantages - Uses all transaction data - Accounts for property attributes - No backward adjustment necessary Disadvantages - Large data input required for variables - Small sample bias - Model may be misspecified (omitted variables)
94
Appraisal-based indices
Sales comparison approach (use similar property as proxy) Cost approach (book/land value) Income approach (PV(NOI)) Advantages - No small sample bias issues - Frequent appraisals Disadvantages - Very subjective and backward looking - Smoothing - Poor quality comparable data
95
Estimation errors in Real Estate
1/√N N = number of transactions used in the appraisal
96
Reservation price
Lowest price a seller would be willing to receive for a property
CAIA Lvl 2
flashcards
Decks in class (11)
# Cards
Brainscape helps you reach your goals faster, through stronger study habits.
© 2026 Bold Learning Solutions. Terms and Conditions