Brehm Ch3

Question 1

Projection Risk

Answer 1

Arises from projecting past trends into future
Focus for projecting parameter risk

Question 2

Parameter Risk

Answer 2

Estimation Risk (From sample vs population)
Projection Risk (Past trends into future)
Model Risk (Wrong models to begin with)

Question 3

Copula

Answer 3

A function that forces correlation between two distributions

Takes in 2 percentiles, so defined on unit square
Drawn with each variable on each axis
Returns prob of being in rectangle from origin to point

Question 4

Common Copulas in order of right tail weight

Answer 4

Frank
Normal
Gumbel
HRT

Question 5

Comparing copulas

Answer 5

Can’t be done unless they have same correlation (tau)

Question 6

Frank Copula

Answer 6

-weak corr in tails
-C1 can be inverted (easy to simulate)

Question 7

Normal Copula

Answer 7

-easily simulated
-generalizes to multi-dimensions

Question 8

Gumbel Copula

Answer 8

-more tail concentration
-asymmetric (more weight in right tail)
-not invertible

Question 9

HRT Copula

Answer 9

-Heavy right tail
-Less weight in left
-Invertible

Opposite is called Clayton

Question 10

Tail Concentration function

Answer 10

Quantifies tail strength to help choose copula

-One function per tail
-Look at right and left tail concentration functions on either side of .5 (LR Graph)
-Use same percentile for both dists, just called z

Question 11

Joint Probability Plots

Answer 11

Visual comparison of copulas

Darker rings in top right = heavier right tail (More prob density)

Question 12

Projection Risk - Small vs Large Firms

Answer 12

Coeff of Variation of total loss higher for small firms
Impact of projection risk not as pronounced since already volatile

Large firms impacted more