Topic 3: Models Flashcards
What is the difference between EXOgenous and ENDOgenous variable?
EXO: determined outside a model and thus taken as a given
ENDO: determined inside a model, takes on the value the model prescribes
Normative vs Positive
Normative:
- aims to describe how participants and prices SHOULD behave
- thus if any deviation, potential mispricing. assumes actual prices converge towards normative model
- factors of rational financial decisions
e.g. arb-free models like put call parity
Positive:
- how it ACTUALLY behaves like technical trading
Theoretical vs Empirical
Theoretical: SIMPLE and not practical for complex securities
Empirical: COMPLEX securities. Observations of historical data but require variables to be constant to change in predictable ways.
Applied vs Abstract
Applied: Real World
Abstract: Theoretical
Cross Sectional vs Time Series
Cross: relationship across variables at a SINGLE POINT in time
Time Series: behaviour across time
Vasciek Model means
Mean-reverting; Short term to trend towards long term
i.e. Next = Current + Factor(Long Term - Current) + Vol of Change of Interest Rate
*Unbiased Expectations Theory for term structure = all credit-risk free bonds expected to earn same rate of return.
Cox Ingersoll and Ross Model is a variant of the Vasciek model. In what way>
Variance of short term rate is proportional to short term rate. When rates approach 0, vol approaches 0.
Arbitrage-Free Model, e.g. Ho and Lee
Assumes short term rates follow normally distributed process.
Uses binomial pricing in current zero coupon bond prices
Describe BDT Binomial
Models 1yr Spot Rates
- at each rate, next year has 2 possible rates with 0.5 probability
- Tree Calibrated to:
1) LEVELS: Returns of 2yr zero
2) SPREADS: between up and down = implied rate vol
BDT Short Term Rate
r upper = r lower x e ^ 2vol
What is Adverse Selection and Akerlof? How to reduce effects of adverse selection?
Adverse Selection: Asymmetric Info before financial transaction is complete, i.e. borrowers expose lenders to credit risk
Akerlof: Markets for LEMONS
- In the presence of asymmetric information between buyer and seller, quality of goods decline
Define Moral Hazard and how to reduce effects of moral hazard?
Assumes more risk to the detriment of other party. E.g. after taking insurance, person takes more risks, or after taking loan, borrower invests in riskier projects
- Restrict loan proceeds
- Limit size of loan to risky borrowers
- Monitor behaviour etc.
Describe the 3 types of credit risk modelling approaches
- Structural: S+P = B+C
- Reduced-form
- Empirical
Merton Model: Strengths and Weaknesses
STRENGTHS
- intuitive and basis for more complex models
WEAKNESSES
- parameters not readily observable, e.g. market value of firm, vol
- Model predicts very low credit spread for short term debt, contradict empirical data
Merton’s EQUITY VALUE
Max (A - K,0)
Merton’s Risky DEBT Value
K - Max (K-A,0)
Altman Model: X1 to X5
Working Capital / Total Assets
Retained Earning / Total Assets
EBITDA / Total Assets
Equity Value / BV of Liability
Sales / Total Assets
The credit spread generated by the Merton model DECLINES when which of the following variables INCREASES?
- debit maturity
- asset volatility
- leverage
- risk-free interest rate
Risk-Free Rate
Increases in all of the other inputs of the Merton model (i.e., debt’s maturity, assets’ volatility, and firm’s leverage) result in an increase in the credit spread (and in the probability of default).
Assumptions of Merton Structural Credit Risk Model
- Only equity and bonds
What is the default trigger in Merton vs KMV Model?
Merton: assets < face value of zero coupon bond
KMV: assets < all of short term debt + part of long term debt (weighted). This is based on assuming that short-term debt has to be serviced sooner than long-term debt and thus is more time-sensitive.
Company has Altman Z score of 1.6. Which of the following best describes the financial health of the company?
Altman Z-score default-based categories
Z < 1.81: Default group
1.81 ≤ Z ≤ 2.99: Gray zone
Z > 2.99: Non-default group
Which of the following credit risk models take a firm’s default as exogenous?
1. Reduced
2. Structural
3. Empirical
Reduced form
Merton’s: Which of the following most accurately represents the value of the firm’s risky debt at the debt’s maturity date?
K - max(AT – K, 0)
max(AT, K)
K – max(K – AT, 0)
max(AT – K, 0)
K – max(K – AT, 0)
Which of the following most accurately represents the value of the firm’s equity at the debt’s maturity date?
K – min(AT – K, 0)
max(AT – K, 0)
min(AT, K)
K – max(K – AT, 0)
max(AT – K, 0)
Define “factor” in a model
Unique source of return/premium not highly correlated with other factors.
1. sound economic foundation
2. supporting research
3. shows that premium persist
What are the 3 differences between the original Fama French model vs CAPM?
- MARKET RETURN: Spread between market portfolio and risk free portfolio
- VALUE:
- spread between returns on high Book to Market stocks vs Low
- stock price fluctuate to BtM ratios - SIZE :
- spread between returns small and large cap
stock price fluctuate in proportion to size
What is the difference between original FF model and FF-Carhart model
Momentum.
Thus FF-Carhart has 4 factors: Return, Size, Value, Momentum
What is the difference between original FF model and the Five Factor model?
- Robust - Weak: e.g. operating profitability
- Conservative - Aggressive: less risk taking
What is factor investing?
Asset allocation based on exposure to risk factors
Discount factor vs Discount rate
1 / Discount Factor - 1
= Discount rate
What are the three categories of factors that drive assets returns?
- Macroeconomic: growth, inflation etc.
- Fundamental, style, investment, dynamic: value, size, quality etc.
- Statistical: based on empirical data, e.g. certain return correlations are explained by 3-5 components (observation)
Difference between tradable and non-tradable variables in a factor model
Non-tradable: inflation, economic productivity
Tradable: stock return, spreads between 2 index returns (easily established and liquidated)
An analyst is planning to use a time-varying volatility model as a stochastic process for part of her research. If she wants to includes jumps in the model to reflect the recent volatile environment, which of the following would be the best model to use?
- Bates
- Merton
- Brownian
- Heston
- Bates
- Heston model assumes that volatility MEAN-REVERTS over the long run
- Brownian motion is a STOCHASTIC process used by the Heston model to describe how volatility CHANGES OVER TIME.
- Bates: Incorporates a JUMP.
- Merton model used to price risky debt
Which of the following is an important implication of time-varying volatility?
A.
An asset’s return distribution generally follows a Markov process.
B.
An asset’s return distribution is generally NORMALLY distributed over a finite time period.
C.
An asset’s return distribution is generally NOT normally distributed over a finite time period.C.
C.
An asset with time-varying volatility has a return distribution that is generally not normally distributed over a time period. Therefore, factors such as skewness have risk premiums.
Describe what the original Fama-French model formulate value and size portfolios?
LONG high book to market, SHORT low book to market
LONG small cap, SHORT big cap
How to set up empirical return model?
- Calculate EXCESS RETURN as dependent variable
- Potential factors as independent variable
- Use statistical analysis to identify factors significantly correlated with returns
What is a generally successful risk-premium-based strategy?
- __ small cap; ___ big cap
- ___ commods in backwardation; ___ commods in contago
- ___ bonds in currencies with high ir; ___ bonds in ccy with low ir
- ___ illiquid assets, ___ similar but otherwise liquid assets
BUY ; SELL
- BUY small cap
- BUY backwardation
- BUY bonds in high I/r
- BUY illiquid
Which of the following accurately describes the implied volatility premium strategy?
___ implied vol
___ realised vol
SHORT implied volatility and LONG realized volatility
It is based on implied volatility generally being higher than realized volatility, and thus the benefit of shorting implied volatility.
Which of the following apply to risk-averse investors?
i) They have a negative degree of risk aversion.
ii) They have concave utility functions.
iii) Their utility functions increase at an increasing rate.
Risk-averse investors have CONCAVE utility functions (which means that their utility functions increase at a DECREASING rate). A log utility function is an example of a concave function.
POSITIVE degrees of risk aversion.
Which of the following represents the shape of an efficient frontier of a portfolio comprised of a risky asset and a riskless asset?
Concave; Convex; Linear
Linear
What is the Lambda of a risk neutral investor?
-1; 1; 0
0
Risk-neutral investors have degrees of risk aversion of zero. Their expected utilities are based only on an investment’s expected return.
What are the common constraints for the MVO Model?
LIMIT:
1. Weights to be NON-NEGATIVE (i.e., no short sales).
2. LIMIT MAX ALLOCATION to one or more assets.
3. Limit ESTIMATED CORRELATIONS.
4. Limit divergences of portfolio weights from BENCHMARK / MARKET weights
What is the Risk Parity Approach when it comes to constructing portfolios
Equally weigh the risk contribution of each asset class = each asset class contributes the same amount of risk
Risk parity vs volatility weighted approach
Risk-parity approach and the volatility-weighted investment approach generate the same portfolio weights when the return CORRELATION of all the assets in each portfolio are the same.
What is naive asset allocation
Evenly distributed
What are the advantages of core-satellite approach?
- Diversification without foregoing potential from high returns from actively-managed strategies
- Flexibility to tailor portfolio to specific objectives
- Ability to control exposure to specific risks
- Ability to put more effort in satellite portfolio
What is volatility anomaly?
L
ow-volatility stocks offer higher expected risk-adjusted returns than high-volatility stocks.
What does betting against beta mean
Buy low-beta stock
In which of the following cases are portfolio weights of a volatility-weighted portfolio the same as those of a risk-parity portfolio?
A. Correlations between asset returns are equal.
B. Variances of asset returns are equal.
C. Expected returns of assets are equal.
The volatility-weighted and risk-parity approaches generate the same portfolio weights when the portfolios have only two assets or when correlations between asset returns are the same.
Which of the following statements LEAST applies to the risk parity approach to portfolio construction?
A. It is based on minimizing total portfolio risk.
B. It equally weights the risk of each asset class.
C It is based on risk diversification.
D. It is not a trading strategy that can be implemented by active managers.
It is the mean-variance approach that minimizes total portfolio risk, not the risk parity (RP) approach.
describes a factor of an asset pricing model
unique source of return
NOT highly correlated
with other factors
i.e. INDEPDENT VARIABLES
in MVO, describe the shrinkage technique
reduces CONFIDENCE INTERVALof statistical parameters.
What is the term used in derivative models to denote the statistical probability that represents an unbiased likelihood of an outcome?
P measure
How does P measure differ from Q?
Q is risk neutral
Briefly describe EQUILIBRIUM and ARBITRAGE term structure of interest rates models, and give an example of each.
EQ: assumes short term interest rate to determine expected path of future interest rates (Vasicek, CIR)
ARB-FREE: model future interest rates so consistent with observed term structure (Ho and Lee)
Briefly describe what it means to calibrate a model such as the Black-Derman-Toy model.
- Adjust the model’s potential outcomes
- No arbitrage opportunities occur
- Given observed market prices or rates
