Spring 2014 Q22
Is risk margin impacted by the change in investment yields? If yes, what is the relationship between those two?
My understanding is that with low investment yields, FV of loss reserve would be close to statutory undiscounted reserves. So when we add a risk margin on top of the discounted reserve, FV reserve would be higher than statutory reserve.
Comments
In the U.S., risk margins are generally done implicitly by using conservative judgment. For example, selecting higher LDFs or higher frequency & severity trends would be conservative because it makes the reserve estimate higher. (Canada by contrast, uses explicit risk margins. Reserves are increased by a specific percentage to account for the risk of misestimation.)
But there is no direct connection between the implicit risk margin in the U.S. and changes in investment yields. An actuary might choose to adjust the implicit risk margin if investment yields change but it isn't necessary. (If you're talking about investment risk then there is a direct correlation between risk and return but I think that's different from what you're asking about.)
About your second point: I think you mean PV(loss reserves) rather than FV. In that case, you're correct. With low investment yields, the discounted and undiscounted reserves would be closer together, with discounted reserves being the smaller of the two. (You wouldn't get much benefit from the time value of money if yields are low.) If you add an implicit risk margin to the discounted reserves, it may or may not push it higher than the statutory reserves - it depends on the the magnitude of the risk margin. (Although note that I don't think you'd be permitted to add a risk margin to the discounted reserves and not to the undiscounted reserves. You have to start with the same nominal estimate.)
Let me know if this doesn't answer your question.
Thanks. Your explanation added insights to my understanding of the topic, but I still have trouble to understand the solution (my issue).
Can you explain further why FV of reserve can be higher than the statutory reserve when the investment yield is low? Thank you.
Sorry, I didn't quite understand your question. Let's look at 2 examples:
Example 1
If you add a margin to FV(reserves) greater than $1, this will make FV higher than SAP. (Remember that FV is the price at which two willing parties will exchange the reserves. The seller is the party that pays so the buyer may require a risk margin to boost the price to an acceptable level. It's reasonably likely that the buyer would require a margin higher than $1.)
Example 2
You would have to add a margin of at least $10 to FV to make it higher than SAP. It seems unlikely the margin would be this high, so in this environment of high yields, FV of reserves (after adding a risk margin) would probably not be higher than SAP reserves.
Again, please let me know if you want to discuss further.
thanks a lot. Your explanation makes sense to me now. I was calculating the FV with discounting using 100/1.1 and 100/1.01 instead, and that's why the solution did not make sense to me at the beginning.
Great!