Memorandum
From: Matti Peltonen, New York State Department of Financial Services
To:
NAIC Investment Risk Based Capital Working Group
Date:
12/02/2013
Re:
Use of Carrying Value in Determining RBC factors – a Concept for Discussion
The purpose of this paper is to provide a few alternatives for the discussion how carrying value should,
or shouldn’t, be used to adjust the bond RBC factors, and whether using a different method for
different bonds is justified.
1. Modeled RMBS and CMBS and Modified Filing Exempt method
Carrying value trigger points (as currently used in modeling and MFE) are used to change designation at
price points where expected loss exceeds the mid-point RBC factor between the NAIC designations.
The advantage of this method is that it reflects the fact that owning a security at a lower (higher)
carrying value entitles the owner to the same cashflows as any other owner, but at a lower (higher)
cost, thereby making the risk of loss lower (higher). The conceptual problem with this method is that a
bond’s NAIC designation and its associated probability of default changes depending on the carrying
value – when in reality, only the magnitude of loss changes, not the probability of default. The reason
the current framework (where designations change at breakpoints) for RMBS, CMBS and other loanbacked and structured securities was created in 2009 was the urgency, at the time, to make carrying
value adjustment fit the then existing general RBC framework.
2. No carrying value adjustment
Used currently for corporate bonds and certain loan-backed and structured securities. This approach is
simple, but its disadvantage is that it does not reflect the different risk profile that is determined by
carrying value, except by subjecting the book-adjusted carrying value to RBC charge.
3. Carrying value adjustment using unchanged NAIC designation
The purpose of RBC is to measure potential loss to surplus. One way to measure it is to apply the
probability and magnitude of default to the carrying value in a way that reflects the changed risk
profile that the carrying value determines - or in a formula:
• Expected loss to surplus = (Carrying value – Recovery) * Probability of default
At par, the RBC charge for each designation set equal to one of the following:
a) RBC factor determined by corporate bond modeling
b) RBC factor determined by RMBS or CMBS modeling, or
c) Method used to determine RBC factor for bonds that are not modeled
The base RBC charge would be adjusted by carrying value for premium or discount.
There should be a minimum RBC charge (e.g. ½ the base charge) for bonds purchased at discount.
The table below (only shown as an example) shows how the approach would work, using 50% recovery
assumption:
Carrying Value
EXAMPLE
Current RBC
Prob of default
Recovery
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
NAIC1
0.40%
0.80%
50.0%
0.20%
0.22%
0.24%
0.26%
0.28%
0.30%
0.32%
0.34%
0.36%
0.38%
0.400%
0.42%
0.44%
0.46%
0.48%
0.50%
0.52%
0.54%
0.56%
0.58%
0.60%
0.62%
0.64%
0.66%
NAIC2
1.30%
2.60%
50.0%
0.65%
0.72%
0.78%
0.85%
0.91%
0.98%
1.04%
1.11%
1.17%
1.24%
1.30%
1.37%
1.43%
1.50%
1.56%
1.63%
1.69%
1.76%
1.82%
1.89%
1.95%
2.02%
2.08%
2.15%
NAIC3
4.60%
9.20%
50.0%
2.30%
2.53%
2.76%
2.99%
3.22%
3.45%
3.68%
3.91%
4.14%
4.37%
4.60%
4.83%
5.06%
5.29%
5.52%
5.75%
5.98%
6.21%
6.44%
6.67%
6.90%
7.13%
7.36%
7.59%
NAIC4
10.00%
20.00%
50.0%
5.00%
5.50%
6.00%
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
11.50%
12.00%
12.50%
13.00%
13.50%
14.00%
14.50%
15.00%
15.50%
16.00%
16.50%
NAIC5
NAIC6
23.00%
30%
46.00%
100%
50.0%
11.50%
12.65%
13.80%
14.95%
16.10%
17.25%
18.40%
19.55%
20.70%
21.85%
23.00% =current RBC
24.15%
25.30%
26.45%
27.60%
28.75%
29.90%
31.05%
32.20%
33.35%
34.50%
35.65%
36.80%
37.95%