Reading 3.1 Flashcards
Variables used in models may be classified:
And give examples of each
- An exogenous variable is a value that is determined outside a model and thus taken as given.
- An endogenous variable is determined inside a model and thus takes on the value the model prescribes.
For instance, in an endowment fund’s cash management model, an exogenous variable may be the amount of cash received from donations and income from investments, and endogenous variables may be decision variables such as the amount of money invested in new deals.
Four common distinctions of models
1) normative vs. positive,
2) theoretical vs. empirical,
3) applied vs. abstract,
4) cross-sectional vs. time-series.
NORMATIVE VS. POSITIVE STRATEGIES - describe the 2 models and give examples
1) Normative models - aim to describe how market participants and asset prices should behave.
- These models are used to identify driving factors of rational financial decisions based on idealized assumptions and conditions.
- They may also be used to identify potential mispricings by identifying how assets should be priced. Normative reasoning assumes that actual prices converge toward prices predicted by a normative model.
EX: For instance, arbitrage-free models describe relationships that should hold given that arbitrageurs’ actions will eliminate arbitrage opportunities. For example, a normative strategy is a strategy based on put-call parity.
2) Positive models - explain/predict how market participants and asset prices
actually behave.
These models are often used to identify potential mispricings by identifying patterns in actual price movements.
EX: For instance, technical trading is based on positive models. For example, a positive strategy is a strategy based on point-and-figure charts
THEORETICAL VS. EMPIRICAL MODELS - describe the 2 models and give applications (examples of use)
1) Theoretical models - describe behavior based on assumptions that reflect well-established underlying behavior.
► They provide a reasonable explanation of simple behavior, but are not practical for securities with complex attributes and relationships. A single theoretical model does not exist that can explain all relationships in different markets.
EX: An application of theoretical models includes theoretically determining the price of an option based on assumptions such as perfect markets, stock prices that follow a particular process, and absence of arbitrage.
2) Empirical models - describe behavior based on observations of historical data. They require underlying variables to be relatively constant or to change in a predictable way. They also require large data sets to produce reasonable results.
►Empirical models are often used to explain complex behavior. As such, they are most effective for alternative investments due to the investments’ illiquidity, time-varying risks, and use of dynamic strategies.
EX: Applications of empirical models include analyzing complex securities with option features and approximating the relationship between observed prices of options and their underlying variables.
APPLIED VS. ABSTRACT MODELS - describe the 2 models and give applications
1) Applied models - used for solving real-world problems. For instance, the Markowitz model of portfolio management is an applied model that provides a useful approach to achieve diversification efficiently.
EX: Most asset pricing models used in traditional and alternative investing are applied.
2) Abstract models (or basic models) - typically theoretical and explain hypothetical behavior in unrealistic situations. They do not address real-world problems.
EX: For instance, an abstract model might describe how two people trade securities in a world with only two people and two risk factors.
CROSS-SECTIONAL VS. TIME-SERIES MODELS - describe the 2 models
1) Cross-sectional models - analyze relationships across variables observed at a single point in time (e.g., using investment returns to explain differences in risk premiums).
2) Time-series models - analyze the behavior of an asset or a set of assets across time.
Which Type of Model is referred to as a panel study
What is Panel data sets and what are the other names for it?
When a model is both: Models cross-sectional and time-series, using data composed of multiple assets over multiple time periods.
Panel Data Sets: data composed of multiple assets over multiple time periods
Other names: cross-sectional time-series data sets, or longitudinal data
A _____ model may be constructed that explains the REIT index returns over time by ____ the index returns against mortgage rates and stock returns. A ____ model is then used to explain why various REITs have different returns by _____ individual REIT returns against variables such as region and property type.
time-series
regressing
cross-sectional
regressing
Some asset pricing models may be classified in more than one way. For instance:
1) ______ models tend to be normative and theoretical
2) ____ models tend to be empirical and positive.
In some studies, complementary modeling approaches may be combined. For instance:
1) a ____ model can be designed and then tested in an empirical framework.
2) ____, ____ and ____model - An analyst identifies a profitable trading opportunity by specifying an asset’s equilibrium price and recommending trades when the asset’s actual price deviates from its equilibrium price.
3) ____, ____ and ____ model - An analyst identifies a statistical trading pattern and uses the pattern to generate trading signals.
abstract
applied
theoretical
Theoretical, normative and applied
Empirical, positive, and applied
What is term structure of interest rates? With what does it help?
It shows how interest rates vary across different maturities, typically ranging from short-term to long-term.
The term structure helps investors and policymakers understand market expectations regarding future interest rates, inflation, and economic conditions.
There are two broad approaches to modeling the term structure of interest rates:
equilibrium models
and
arbitrage-free models
Describe Equilibrium models of the term structure (also referred to as ____)
First-generation models
make assumptions about the structure of fixed-income markets and then model bond prices and the term structure of interest rates based on economic reasoning.
The equilibrium models, model the yield on long-term bonds by taking the short-term interest rate as given and assuming that the unbiased expectation hypothesis holds for bond prices (which implies that credit risk-free bonds of all maturities have the same expected return over the short term).
The unbiased expectations hypothesis (UEH) is
a theory in finance that suggests that the forward rate, which is the expected future spot rate of interest, is an unbiased predictor of the future spot rate.
two equilibrium models
Vasicek (1977)
and
Cox, Ingersoll, and Ross (1985)
Vasicek’s model is a
single-factor model of the term structure that assumes constant volatility
and that the short-term interest rate drifts toward a specific long-term mean.
Vasicek’s model describes the mean-reverting process for the short-term interest rate as
The Vasicek model may be expressed in terms of the next period’s expected short-term rate as:
The CIR model is a _____-factor model that describes the short-term interest rate process as:
single
The Ho and Lee model describes the short-term rate as (formula)
CALIBRATING THE LEVEL OF RATES BASED ON AVERAGE RETURNS:
Averaged short-rate total return formula
CALIBRATING THE SPREAD OF RATES BASED ON VOLATILITIES
An analyst, calibrating a Black-Derman-Toy two-period binomial tree model, observes that the second-period short rate in the down state is 3.8% and the implied continuous volatility of the short rate in the second period is 14%. What is the value for the second-period short rate in the up state?
