V5M1 page 89
Exhibit 27: Investment Strategies and Effects on Bank/Insurer Asset and Liability Volatility
Surrender penalties → Decreases σ ΔL/L
For typical life insurance, annuities,
and bank deposits, such penalties
cushion losses to financial institutions
for having to pay back liabilities
“at par” when rising interest rates
would otherwise have reduced the
discounted present value of the
Prepayment penalties on debt investments → Increases ρ
When interest rates are declining,
borrowers must incur a penalty to
repay loans at par to refinance.
Also, prepayment penalties help
institutions offset rising values of
their fixed-rate liabilities in falling
I struggle to understand why both being a penalty, surrender penalties decrease volatility of banks/insurers’ liability but prepayment penalties increase the correlation of volatility between asset and liability
ρ (A,L) = cov (A,L) / σA.σL, the decrease of volatility of liability and the increase of correlation are not contradictory.
We need to think on different sides of the balance sheets.
Surrender penanlities effect annuities written by the instiution. These are on the liability side of the balance sheet. Surrenders would happen if rates rise but the penalityis there ir prevent this or give compensation if it does. It reducesthe volaitility in the chnage in laibilites - ie. the potentail chnage in laibilities is less. You not suddently going to see all the annuities surrended and the laibilities of the instution go to zero.
Prepayment penalties effect assets the instution own. They prevent borrowers from the institution paying back early. if rates fall the PV Liabilties will increase which would be offset by PV of assets increasing but if borrows can redeem early that assets woudl vanish. If the penanlties prevent early redeemtion it means the assets will remain in place the correlation will remain high.
Liabities with no surrnder are like putable instruments when rates rise they are are dedeemed. But if rates fall the liabilitiy gets bigger.
Assets with to penalities are like callable instruments when rates fall redeemtion happens.
What I miss is why under prepayment penalities it does nto also say it reduces the voliatitity of the percentage chnage in assets.
same argument can be applied to surrender penalties no?
yes i totally agree