Unwinding of discounts

Hi Graham,

My understanding of "Unwinding of Discounts" is that it's basically a fancy way of saying "Methods used to find the discount rate" but I'm not sure if that's true. Is my understanding correct or am I missing something here?

Thank you

Comments

  • That isn't quite what unwinding is. Here's an example:

    • Suppose you bought a phone on Jan 1, 2021 for $500 but you don't have to pay until 1 year later on Jan 1, 2022.
    • Let's say you earn 3% interest in your bank account so that the present value of the cost of the phone is $500/1.03 = $485.44. That's the amount you have to set aside to be able to pay the $500 on Jan 1, 2021. The effect of the discounting is $14.56.
    • The unwinding of this 3% discount is then done Jan 1, 2022 by adding $14.56 in earned interest to the original PV of $485.44 to get to the $500 you owe for the phone.
    • In other words, unwinding simply means adding back the effect of discounting.
  • edited February 2023

    thanks for the explanation of unwinding in simple words. Given that the effect of discounting is calculated at locked-in rates, and unwinding allows the use of distinct discount rates (for the last 2 methods), does this mean that unwinding will not necessarily cancel out the effect of discounting added back? Is this related to the deviation of actual rates vs locked in rates?

  • All 3 methods are using the same opening discount curve and since it is locked in, you are not changing the yield curve. The 3 methods represents different theories for the future discount rate based on the current yield curve. So from year to year, you may see different unwinding amounts, but the total unwind over the life of the liability when the LIC is extinguished should be the same for all 3 methods. This is not related to the deviation of actual rates (new yield curve) vs locked in yield curve

  • so when expectation hypothesis refers to term structure determined by market expectations of future interest rate changes, what does it mean by rate changes if the rate has to be locked?

  • well you lock the rates to calculate your unwind -> But rates can and will change through the life of the policy. The diff between the locked in rates and current rates goes into AOCI or P&L. If you don't lock in a rate, your unwind of discount will be wonky throughout the life of the policy and it will be hard to discern the actual impact of discounting and the effect from changes in interest rates

  • Is it correct to think of unwinding as "earning" the discount amount, similar to how we would earn premium over the life of a contract? If so, is the dollar amount "earned" in every period predetermined at inception using locked in rates?

  • in a way, yes - However, discounting increases revenue as it reduces the liability. So its more like an unearning of the discount as it is an IFE

  • Gotcha, thanks!

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