Objective 2 Flashcards
What are 2 approaches to model extreme events?
(FERM12)
- Generalized Extreme Value Distribution
- Generalized Pareto Distribution
Describe the general principle behind the Generalized Extreme Value Distribution
(FERM12)
- It considers the maximum observation (Xm) from each sample (of iid RVs), and pools them together to form an extreme loss data population
- As the size of a sample increases, the distribution of the maximum observation converges to the generaized extreme value (GEV) distribution
What is the cummulative distribution function of the GEV?
(FERM12)

What are 2 methods to take extreme values?
(FERM12)
- Return level approach
- Take the highest obervation in each block of data
- Return period approach
- Set a level above which an observation could be regarded as extreme
- Take the observations higher than the level in each block of data
What is a major drawback of the GEV distribution?
(FERM12)
By using only the largest value(s) in each block of data, it ignores a lot of potentially useful information
Describe the idea behind the Generalized Pareto Distribution
(FERM12)
- G(x) is the distribution of a RV X in excess of a fixed hurdle u given that X is greater than u
- Assume the observations are iid
- As the threhold increases, the distribution of the conditional loss distribution converges to a GPD
What is the cummulative distribution of GPD?
(FERM12)

What is a key consideration when using GPD?
(FERM12)
Choosing the right omega threshold
What are 3 characteristics of financial time series?
(FERM14)
- Serial correlation does not exist to the extent that it is possible to make money from it
- There is strong serial correlation in a series of absolute or squared returns
- The distribution of market returns appears to be leptokurtic (i.e., extreme values tend to occur closely together)
What are 3 characteristics of multivariate return series?
(FERM14)
- Correlations do exist between stocks, and between asset classes and economic variables
- There is little evidence of cross-relation (i.e., change in stock price t has little effect on stock price t+1)
- The time series of extreme returns are individually leptokurtic and they have jointly fat tails
What are the 3 most common ways to measure spread?
(FERM14)
- Nominal Spread
- Static Spread
- Option-Adjusted Spread
What is nominal spread and how is it calculated?
(FERM14)
- The difference between the gross redemption yields of the credit security and the reference bond (e.g., a treasury bond)
- Quick and easy to measure/calculate
NS = rGY - rREF
What is static spread and how is it measured?
(FERM14)
- The addition to the risk-free rate required to value cash flows at the market price of a bond
- It considers the full risk-free term structure and the constant (spread) SC added to the yield at each duration
Bond Price = Sum over t [CashFlowt / (1 + rf,t + SC)]
What is the option adjusted spread and how is it applied to calculate Bond Price?
(FERM14)
- Allows for a large number of stochastically generated interest rates (rf,t,sim) such that the expected yield curve is consistent with that seen in the market
- It considers any options that are present in the credit security (OAS)

How are government bonds’ expected returns estimated?
Both domestic and overseas government bonds are risk-free
Returns are estimated from the gross redemption yield, an annual compound interest rate
What is the difference between corporate bonds and government bonds?
What is credit spread?
(FERM14)
- Corporate bonds are not risk-free and have a chance of default, so their expected returns should consider a risk premium
- Credit spread represents the additional return offered to investors with repect to the credit risk being taken
What are 5 reasons why the credit spreads are higher than historical studies’ findings?
(FERM14)
- Credit risk premium - reward for volatility relative to risk free securities
- Liquidity risk premium - reward for lower liquidity compared to government bonds
- Risk aversion premium - reward for possibility of extreme events and skeyness of bond payoff structure
- Tax premium - less favorable treatment compared to government
- Correlation premium - correlation between credit spreads and interest rates is typically negative
What CAPM and what is the formula behind it?
(FERM14)
Capital Asset Pricing Model
rx = r* + ßx (ru - r*) where
rx = rate of return on individual investment X
r* = risk-free rate of return
ru = market return
ßx = σxpx,u / σu
What are the 6 properties of a good benchmark?
(A good benchmark is important when considering market risk!)
(FERM14)
- Unambiguous (components and constituents should be well-defined)
- Investable (can buy components of a benchmark and track it)
- Measurable (can quantify the vaue of a benchmark with reasonable frequency)
- Appropriate (consistent with investor’s style and objectives)
- Reflective of current investment opinion (contains components about which investor has opinions)
- Specified in advance (known by all participants before the period of assesment)
What is are 8 specific criteria against which a benchmark can be measured in its appropriateness?
(A good benchmark is important when considering market risk!)
(FERM14)
- Proportion (should contain a high proportion of the securities held in the portfolio)
- Turnover (benchmark’s constituents’ turnover should be low)
- Allocations (shoud be investable position sized)
- Position (investor’s active position should be given relative to the benchmark)
- Variability (benchmark variability to the portfolio should be lower than market variability to portfolio)
- Positive correlation between rX - rU and rB -rU
- Zero correlation between rX - r<span>B</span> and rB -rU
- Style exposure (must be similar between portfolio an benchmark)
What is the Black-Scholes Model used for?
What are the formulas?
(FERM14)
Used to model European call and put options
Call = C0 = X0 N(d1) - Ke-r*T N(d2)
Put = P0 = Ke-r*t N(-d2) - X0 N(-d1)
where
d1 = [ln(X0/K) + (r* + σ2X/2)T] / [σX sqrt(T)]
d2 = d1 - σX sqrt(T)
What are two types of interest rates?
(FERM14)
- Spot rates
- (1 + rt)-1 = e-st
- Forward rates
- e-st = e -(f1 + f2 + … + fT)
What is the bootstrapping approach?
(FERM14)
Constructing a spot rate curve from the gross redemption yields on a series of bonds with a range of terms
What are 6 single-factor interest rate models?
(FERM14)
































