Transcript No Slide Title

INSURANCE ASSET MANAG EM ENT
Management of Asset Risk - II
CM - 19
Risk & Capital Management Seminar - 9 July 2002
Types of risk
• Do I have the correct strategy?
– Model Risk
– Strategic Allocation
• Can I implement the strategy?
– Process Risk
– Tactical Allocation
2
Agenda
3
Measures of Risk
• Five axioms of coherence
• Relevance
x  0   ( x)  0
• Monotonicity
x  y   ( y )   ( x)
• Subadditivity
 ( x  y )   ( x)   ( y )
• Positive Hemogeneity
 (  x)     ( x)   0
• Translation
 ( x    r )   ( x)  
4
Measures of Risk
• Variance/Standard Deviation
• Well known

2
 Ex    
2
5
• Symmetric
Measures of Risk
• Probability of Ruin
• Ease of explanation
• Ease of calculation
• Similar to VaR
• Ignores severity
• Single point
P( x)  0
6
Measures of Risk
• Value at Risk
VaR ( X )  infx | P( X  x)   
• Use in Capital Markets
7
• Ignores severity
• Single point
Measures of Risk
• Expected Policyholder Deficit
– EPD
EPD  E x  L | x  L
• Reflects whole distribution
• Difficult to explain
• No parallels
• Almost option price to policyholders
8
Measures of Risk
• Tail Value at Risk
TailVaR ( X )  Ex | x  VaR ( x)
• Reflects whole distribution
9
• Difficult to explain
• No parallels
What is risk?
• Companies have more than one measure of risk
– What is the chance that my surplus will decline?
– What is the chance that I will have to pay more taxes?
– What is the chance that my income will decline two years
in a row?
– What is the chance that my leverage ratio will be greater
than 3?
• Risks can work against each other
• Determine all of the company’s risks in a
qualitative manner
10
Risk #1
14
12
Portfolio B
Return
10
8
11
6
Portfolio A
4
2
0
0
5
10
Standard Deviation
15
20
Risk #2
14
Portfolio B
12
Return
10
8
12
6
Portfolio A
4
2
0
0%
20%
40%
60%
P(5Yr Rtn < 6%)
80%
100%
Customized Risk Measures
• Control volatility of returns
– Risk: Standard Deviation of Total Return
– Reward: Mean Total Return
• Short-Term Hurdle Rate
– Risk: Probability 2 Year return < -10%
– Reward: Total Return
• Long-Term Hurdle Rate
– Risk: Probability 5 year return < 6%
– Reward: Total Return
13
Customized Risk Measures
• Distribution of assets
– Risk: Standard Deviation of Terminal Assets
– Reward: Mean Terminal Assets
• Limit Losses
– Risk: Probability of Unrealized Losses in any year
– Reward: Mean Terminal Assets
14
• Budget cash flows
– Risk:
• (-1)(Paid Dividends)3 if Paid Dividends <= 0
• 0 if Paid Dividends > 0
• Averaged over all scenarios and years
– Reward:
• Sum Paid Dividends over all years
• Averaged over all scenarios
Customized Risk Measures
15
Conditional Asset Allocation
• What do you do if there is a catastrophe?
• Force catastrophe into Model
16
• Re-calculate allocation
• Plan transition