Discount Rates in General Insurance
Pricing
Peter Mulquiney, Brett Riley,
Hugh Miller and Tim Jeffrey
© Peter Mulquiney, Brett Riley, Hugh Miller and Tim Jeffrey
This presentation has been prepared for the Actuaries Institute 2014 General Insurance Seminar.
The Institute Council wishes it to be understood that opinions put forward herein are not necessarily those of the Institute and the Council is not
responsible for those opinions.
Why this paper?
•
•
•
•
Discount rates often overlooked
Challenge – yield curve projection
Response to research request
Discount rates important
– Low interest rate environment
Key findings
•
•
•
•
•
Two models & their rates
Risk free rate & ERP: negative correlation
Understand relationship b/w ROE & TSR
Be careful using ground up ROE estimate
M-C is contentious: can allow for frictions
Key findings
• Yield projection
– Across cycles, spot & forward rates close
– Spot better for normal yield curve
– Alternative formula: further improvement
• Using single rates vs spot – may distort ROE
• Shifting investments to replicating portfolio
Background
•
•
•
•
No recent major advances in discount rates
Academic literature
Regulated vs unregulated classes
Discount rates affect idea of “fair price” in
regulated classes
Pricing Models – IRR
Investment
income
Claims +
expenses
Tax
T=0
-∆Assets
T=1
Net
shareholder
cash flow
Premium
T=2
• Net shareholder cash flows discounted
with single discount rate (ROE)
• The single discount rate ROE reflects
time value of money and riskiness of
cash flows
• Premium chosen to set NPV to zero
• Model well understood:
– Expected values for cash flows
– Franchise value & intangibles?
– How to choose ROE?
Pricing Models – Myers-Cohn
Investment
income
Claims +
expenses
Tax
T=0
-∆Assets
T=1
Net
Shareholder
Cash flow
Premium
T=2
• Considers same cash flows as IRR
• Premium chosen to set NPV of
shareholder cash flows to zero
• Key difference: each cash flow
discounted using separate rate
reflecting riskiness of cash flow
– Claims + expenses: RL(return on
liabilities)
– Investment returns: RA (asset return)
– Taxes: RL and RF (risk free rate)
Pricing Models – Comparison
• In practice IRR is preferred for a number of reasons
IRR
MC
Underlying assumptions
Practicality
Interpretation
Ability to account for individual risks
• Following slides on discount rate assumption setting
will focus on IRR
Assumption Setting – Risk Free Rates
• Role in IRR is indirect
– discount rate for claims liabilities which
impacts capital projections
• Most accept CGBs as best proxy for risk free
– Required by APRA for general insurance
liability valuations.
– Some argue for a loading for illiquidity risk
– Allowed for some life insurance annuities
12 month change in credit spread
on 3year BBB bonds
Assumption Setting – Return on Equity
6.0%
4.0%
• Unregulated classes: ROE
only limited by market
realities. Tends to be stable
y = -1.0904x
R² = 0.559
2.0%
0.0%
-5.0% -4.0% -3.0% -2.0% -1.0% 0.0%
1.0%
2.0%
-2.0%
-4.0%
-6.0%
12 month change in 3 year yield on Commonwealth
Government Bonds
3.0%
• Regulated classes: ROE
should be set based on an
appropriate asset pricing
model. CAPM – one
common model
Assumption Setting – Return on Equity
• ROE vs TSR
• Ground-up estimates of ROE possible
– Approach similar to Myers-Cohn
– Produces premiums consistent with free competition
– Needs adjustment to allow for market imperfections
(frictions).
Example – Single Discount Rate
CTP sensitivity
Using spot rates
Class of Business
CTP
Motor
Result
Context
ROE (IRR)
Cohort
9.4%
30.1%
Profit Margin
Cohort
12.6%
7.3%
Net loss ratio
Cohort
(inflated & discounted)
75%
69%
Gross expense ratio
Cohort
12%
19%
Capital Base to GWP
Steady state
portfolio
134%
29%
Net Accounting Loss
Ratio
Steady state
portfolio
92%
ROE
(NPAT / Net Assets)
Steady state
portfolio
9.4%
30.1%
Insurance Margin
Steady state
(Insurance Profit / NEP) portfolio
12.7%
9.8%
73%
Base single rate
Upward
curve
Inverted
curve
Result
Context
ROE (IRR)
Cohort
9.4%
9.9%
8.5%
Profit Margin
Cohort
12.6%
12.6%
12.6%
Net loss ratio
(inflated & discounted)
Cohort
75%
75%
75%
Gross expense ratio
Cohort
12%
12%
12%
Capital Base to GWP
Steady state
portfolio
134%
132%
135%
Net Accounting Loss
Ratio
Steady state
portfolio
92%
92%
93%
ROE
(NPAT / Net Assets)
Steady state
portfolio
9.4%
10.1%
8.4%
Insurance Margin
Steady state
(Insurance Profit / NEP) portfolio
12.7%
13.5%
11.3%
Example – IRR Sensitivity
Assumption
Variation
Net claim cost per
$100 gross premium
(inflated & disc.)
+ / - 10%
Gross expense rate
+ / - 2%
Inflation
+ / - 1%
Discount rate
Motor ROE sensitivity 1
Red
Amber
Green
>4%
2-4%
<2%
●
●
●
●
+ / - 0.5%
Outstanding claims
risk margin (APRA)
+ / - 4%
Premium liability risk
margin (APRA)
+ / - 4%
1
CTP ROE sensitivity 1
Red
Amber
Green
>2%
1-2%
<1%
Measures absolute value of change in ROE
●
●
●
●
●
●
●
●
Example – Myers-Cohn
Liability Beta
0
0.1
-0.5
-0.4
-0.3
-0.2
-0.1
Equity Risk Premium
3%
4%
5%
6%
11%
13%
14%
16%
10%
11%
13%
14%
9%
10%
11%
12%
8%
9%
10%
10%
7%
8%
8%
8%
6%
6%
6%
6%
Risk Free Rate
2.1%
3.1%
4.1%
5.1%
13%
13%
13%
12%
12%
11%
11%
11%
10%
10%
10%
10%
9%
9%
9%
9%
8%
8%
8%
8%
6%
6%
6%
6%
0.2
0.3
0.4
0.5
5%
5%
5%
4%
4%
4%
3%
2%
3%
2%
2%
1%
2%
1%
0%
-1%
2%
0%
-2%
-3%
5%
5%
5%
5%
4%
4%
4%
4%
2%
2%
3%
3%
1%
1%
1%
1%
0%
0%
0%
0%
Yield projection – the issue
• Time gap between pricing and
premium creates interest rate risk
• Can “lock in” yield curve by
hedging, but not common
• A “full powered” projection is
difficult and unjustified
• Two simpler approaches are
‘expectations’ (shifted forward
curve) and ‘static’ (assume curve
remains fixed. Neither necessarily
optimal
30%
Return on equity
25%
20%
15%
10%
5%
0%
Target
Actual
Performance of simple predictors
Average bias (basis points)
Yield curve
Inverted
Flat
Normal
Normal - steep
Expect.
Forward
Static
Spot
Diff.
26
0.21
0.16
0.04
-0.25% to 0.25%
25
-0.00
0.00
-0.00
> 0.25%
77
-0.15
-0.02
-0.13
> 1%
37
-0.33
-0.13
-0.20
128
-0.05
0.02
-0.07
Slope
No. months
< -0.25%
Total
Root MSE (basis points)
Yield curve
Inverted
Flat
Normal
Normal - steep
Total
Expect.
Forward
Static
Spot
Diff.
26
0.43
0.40
0.02
-0.25% to 0.25%
25
0.53
0.54
-0.00
> 0.25%
77
0.64
0.61
0.03
> 1%
37
0.72
0.66
0.06
128
0.58
0.56
0.02
Slope
No. months
< -0.25%
Overall performance is
very similar, but static
approach has slight
advantage when yield
curve has unusual shape
Our alternative approach
Estimated 𝛽𝛽 (percentage)
Colour key – width of 90% confidence interval:
15% 30% 45% 60% 75% 90% 105% 120% 135% 145%
𝒇𝒇𝒕𝒕 (𝒔𝒔 + 𝜹𝜹) ≈ 𝜷𝜷𝒇𝒇𝒕𝒕+𝜹𝜹 𝒔𝒔 + 𝟏𝟏 − 𝜷𝜷 𝒇𝒇�𝒕𝒕
With
𝒇𝒇𝒕𝒕 (𝒔𝒔) =Forward rate at time 𝑠𝑠,
term 𝒕𝒕
𝜹𝜹 = Projection period
A combination of expectations
and mean reversion. Estimated
by linear regression on data,
1996 - 2014
• Our formula leads to 20-30%
reduction in error, and a 65%
“win rate” vs expectations
method.
• Dampens extreme
movements
• Our ‘mean’ curve has slowly
lowered over time
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Jul-92
Jul-93
Jul-94
Jul-95
Jul-96
Jul-97
Jul-98
Jul-99
Jul-00
Jul-01
Jul-02
Jul-03
Jul-04
Jul-05
Jul-06
Jul-07
Jul-08
Jul-09
Jul-10
Jul-11
Jul-12
Average squared error in estimation, terms 0
through 2
Improved prediction
Formula
Expectations hyp
Static
Implications
Changes to premiums of
around 1-2%, depending on
method
Currently the extra mean
reversion leads to higher
projected yields (lower
premiums)
Key findings
•
•
•
•
•
Two models & their rates
Risk free rate & ERP: negative correlation
Understand relationship b/w ROE & TSR
Be careful using ground up ROE estimate
M-C is contentious: can allow for frictions
Key findings
• Yield projection
– Across cycles, expectations & static rates
close
– Expectations can show some bias
– Alternative formula: further improvement
• Using single rates vs spot – may distort ROE
• Shifting investments to replicating portfolio