QUESTION: When valuing disability benefits, I sometimes incorporate recovery rates. Recovery rates represent the probability that disabled participants regain their health. Upon recovery, the disability benefit stops. The participant may also be assumed to return to work as an active participant. How can I reflect this assumption in valuation liabilities?

ANSWER: There are two methods for incorporating recovery rates in ProVal valuations, depending on whether or not disabled participants return to work upon recovery.

 

Method 1 - Stopping the disability benefit upon recovery

If you are valuing annuities, simply increase the post-disablement mortality by the assumed recovery rates.

Probability of continuing to receive disability benefits	=	Probability of living to next year and not recovering
	=	(1-qx)*(1-recovery ratex)
	=	1-qadjx
Solving for qadjx we get:
Qadjx	=	1 - (1-qx)*(1-recovery ratex)

For example:

age	Qx	recovery ratex	qadjx
55	0.006131	0.35	0.353985
56	0.006618	0.33	0.334434
57	0.007139	0.31	0.314926
58	0.007719	0.29	0.295480
59	0.008384	0.27	0.276120
60	0.009158	0.25	0.256869
61	0.010064	0.23	0.237749
62	0.011133	0.21	0.218795
63	0.012391	0.19	0.200037
64	0.013868	0.17	0.181510
65	0.015592	0.15	0.163253

 

Notes:

• To vary recovery rates and/or post-disablement mortality based on years since disablement, an “age by duration from decrement” mortality table may be used.

• This method will not work if you are valuing post-disablement life insurance benefits.

 

Method 2 – Stopping the disability benefit and returning the participant to active status upon recovery

If it assumed that disabled lives will return to active status upon recovery, then a reasonable proxy is to increase the probability of staying active in the first place.

 

Probability of remaining active	=	Probability of surviving all decrements, unless recovering from disability
	=	1-[qretx + qtrmx + qdthx + qdisx * (1-prob. no recoveryx)]

The “prob. no recoveryx” should be estimated from the recovery rates using your best judgment.

To ensure that the effective rate of disablement remains equal to qdisx, rather than qdisx * (1-prob. no recoveryx), a post-decrement probability equal to 1/(1-prob. no recoveryx) should be applied to the disability benefit.

Notes:

• If using this method, you should not adjust the post-disablement mortality as described in Method 1 above.

• This method only applies to future disablements. If you want to apply this to current disableds, you must value them with an active status.

• This method is not sufficient if recovery rates are select & ultimate – i.e., vary based on years since disablement.