3.1 Modeling Overview and IR Models Flashcards
What are the two key variables involved in a financial model (e and e)? What is the difference, what are they similar to (dep/indep) and example of endowment?
Two key variables are exogenous variable, and endogenous variable.
Exogenous comes from outside the model and is assumed to be valid. It is effectively the independent variable.
Endogenous comes from the model - it is the dependent variable.
Example for an endowment - cash donations would be the exogenous variable, while the percentage allocation to a new alternative asset class is an endogenous variable.
What is the difference between normative and positive models (how people/prices ____ behave).
Fundamental vs technical analysis.
Both models are used to - e.g. what prices will do…
Normative model attempts to explain how people and asset prices SHOULD behave, while positive model seeks to understand how people are ACTUALLY behaving.
Normative is like fundamental analysis, by exploring the drivers of rational decision-making under idealized scenarios, while positive is like technical analysis looking at observed historical price patterns.
Both models are used to predict future behavior.
Trading strategies based on normative model anticipate that future prices will converge on normal values - e.g. by using an arbitrage-free model like put-call parity.
Those based on a positive model attempt to infer future actions based on price patterns, e.g. using moving averages and price patterns.
Theoretical vs empirical models:
1. complexity
2. theoretical are similar to NM
3. which is more used by managers (illiquidity, changing risks etc).
- theoretical works well under simplified situations, empirical better for more complex (more data points, changing relationship between variables)
- theoretical similar to normative models as draw conclusions about behavior from existing observations of underlying behavior
- empirical models are often the better choice for alternative investors
Applied vs abstract models
1. key difference
2. abstract aka
3. example of applied model (M)
4. most asset pricing models are ___ and managers mostly use _____
- applied is designed to solve actual real-world challenges in the present day, while abstract is for hypothetical real-world challenges set in the future
- abstract aka ‘basic model’
- Markowitz model (used to identify efficient diversification opportunities for current application)
- most asset pricing models are applied models, and applied models are mostly used by managers
What are the three different ways that analysts can consider data as it relates to time (models)? (CS, TS and PDS/LDS)
REIT example.
- cross-sectional (analyze relationships at a specific point in time)
- time series (analyze relationships over a period time)
- panel datasets / aka longitudinal datasets (multiple variables with observation over a period)
Perhaps an analyst wants to study a basket of REITs relative to an index that is simply an arithmetic average of each constituent REIT. The analyst could begin by considering the impact of changes in equity prices, Treasury yields, and mortgage rates on the index over time. This is a time-series model. Next, the analyst considers the differences in the long-term average returns of each REIT in the index as of today. This is a cross-sectional model. Then, the analyst regresses the returns of individual REITs against factors like geographic location, leverage, and property type. This would be panel data.
Equilibrium models of the term structure (a.k.a. FGM combine assumptions about fixed-income markets with economic logic to infer BP and the TS of IR. Two such models were devised by V and the team of C, I, and R.
Equilibrium models of the term structure (a.k.a. first-generation models) combine assumptions about fixed-income markets with economic logic to infer bond prices and the term structure of interest rates. Two such models were devised by Vasicek and the team of Cox, Ingersoll, and Ross.
What is the formula for the Vasicek model? It is a SFM which assumes constant V and MR.
E(rt+1) = rt + k(µ – rt) + σE(εt+1)
µ is the long-term average of the short-term rate. formula is mean reverting, which means that if the current value is below (above) the long-term average, then it is expected to increase (decrease) in value.
k is the speed of the mean-reverting adjustment. (0 to 1, higher means faster movement toward the mean).
σ - volatility of change in interest rates
Volatility is further adjusted for noise
εt+1, which is assumed to be normally distributed with a mean of zero and a standard deviation of 1.
Example of Vasicek model.
If the long-term average rate is 4.25%, the current rate is 3.75%, the volatility of interest rates changes is 1%, and the speed of adjustment is assumed to be 0.65, then the estimated rate for next period is? This example assumes zero noise.
E(rt+1) = 0.0375 + 0.65(0.0425 – 0.0375) + 0.01(0) = 4.075%
In the Vasicek model, general slope of the yield curve is driven by the relationship between _____. (upward vs downward? humped?)
the current rate and the long-term mean
The upward- (downward-) sloping line reflects an upward (downward) movement toward the mean. A humped line shows risk aversion.
Two criticisms of the Vasicek model?
1. vol
2. neg
- It assumes that the volatility of interest rate changes is constant
- It allows negative short-term rates (this is resolved by the CIR model)
What does the CIR model fix about Vasicek’s model?
It adjusts Vasicek’s original model to make the variance of the short-term rate proportional to the rate itself - so prevents negative short-term rates. This methodology disallows negative rates because as rates approach zero, their volatility also approaches zero.
Formula for CIR model (how does it differ from Vasicek?)
rt+1 = rt + k ( μ - rt ) + √rtσεt+1
i.e. the last term has been altered from volatility to variance. This makes sense because the volatility of rates tends to be high if short-term rates are also high. disallows negative rates because as rates approach zero, their volatility also approaches zero.
Arbitrage-free models of the term structure (a.k.a. SGM) use parameters that are based on the ______. This method is used in support of the risk-neutral idea that ________.
Arbitrage-free models of the term structure (a.k.a. second-generation models) use parameters that are based on the current yield curve. This method is used in support of the risk-neutral idea that arbitrage opportunities should not exist.
What is the notable distinguishing factor for arb-free models of term structure? What is the result?
The current yield curve is used to infer parameters for the model. Result is that the theoretical output of these models is consistent with current observations.
Ho-Lee model is a SFM that assumes a normal distribution for short-term rates and incorporates a DP that directly connects the model with the current yield curve. Formula is:
Ho-Lee model is a single-factor model that assumes a normal distribution for short-term rates and incorporates a drift parameter that directly connects the model with the current yield curve. Formula is:
rt+1 = rt + θt + σεt+1
