Applications

Question 1

Describe the three broad solutions used by insurers to match their VA balance sheet exposures

Answer 1

Asset Transfer Programs
- reallocate client discretionary funds based on ITM and policy duration
- higher fixed income allocation when ITM (AV < BB)
- lower fixed income allocation when OTM (AV > BB)
Volatility-Managed/Risk-Controlled Funds
- fund features dynamically rebalance allocation to equities depending on a target for realized volatility
- equity/fixed income allocation positions are adjusted in response to market signals of risk
- Capped Volatility - cap expected volatility if fund returns at some level
- Target Volatility - target and maintain a constant volatility level of fund returns
- Capital Preservation - fund risk position declines if prior performance is poor, or if positions are used to hedge company guarantees
Market-Linked Rider Fees
- fee feature that adjusts the level of rider fees ties to a prevailing market index
- VIX fees - higher VIX means higher fees
- US Treasury Indexed - lower IRS means higher fees

Question 2

Describe the three challenges of “first generation” solutions

Answer 2

Performance Benchmarking
- improper benchmarks used (such as S&P for risk control)
- clients oversold on benefits of volatility management had false expectation, creating dissatisfaction in bull markets
- lack of transparency caused investors to blame underperformance on risk-control features
Loss of Upside Potential
- risk management reduces risk but also expected returns
- loss of upside means less beneficial to policyholders
Clarity of Investment Thesis
- difficult for policyholders to understand risk management solutions
- growing skepticism due to “black box” features
- policyholders unable to distinguish if policies are beneficial to them

Question 3

Describe three objectives of risk management for insurers

Answer 3

Write profitable business - Guarantee Cost
Stabilize ALM and hedging performance - hedge ratios, hedgeability, basis risk
Optimize capital requirements - reserve impact, volatility

Question 4

Describe three objectives of risk management for policyholders

Answer 4

Maintain upside investment potential - return and volatility, long term equity allocation, cumulative fees
Minimize impact to guarantee value - guaranteed income levels

Question 5

Describe parameter considerations for the “next generation” approach

Answer 5

Capped Volatility
- trigger level for the volatility cap
- goal to minimize tail risk
VIX-Indexed Fees
- fee floor and ceiling
- VIX target
- slope - sensitivity to VIX movement
- cap on periodic changes
- goal to minimize body risk

Question 6

State key formulas for Asset Transfer Programs

Answer 6

Guarantee Ratio: 1 - AV/BB
Threshold: min(50%, 10% + Policy Duration * 2%)
Fixed Income Allocation: (Guarantee Ratio - Threshold) / Band
- band is another arbitrary parameter (10% in reading)

Question 7

State formulas for Capped Volatility

Answer 7

21 day realized volatility: sqrt((252*sum of 21-days worth of returns^2)/(21))
Equity Ratio: min(100%, Volatility Cap Trigger / Realized Equity Volatility)

Question 8

State formulas for target volatility

Answer 8

Equity Ratio: min(110%, Volatility Target / Realized Equity Volatility)

Question 9

State formulas for VIX Indexed Fees

Answer 9

Fee = Base Fee + VIX Sensitivity Slope*(VIX - VIX target)

- usually subject to caps and floor, maximum movement per period (quarter)

Question 10

Define model risk in the context of hedging

Answer 10

Deviation between the financial market model that reflects the true state of the economy and the company hedging model

Question 11

Describe the payoff structure of a VA with a GMDB and a GMAB

Answer 11

GMDB: max(A_t, G_t)
GMAB: max(A_T, G_T)
Payoff = max(A_t, G_t) = max(G_t - A_t, 0) + A_t

Question 12

Describe how model risk impact hedge effectiveness

Answer 12

Less model risk, grater hedging effectiveness
Changes in the slope and curvature have a roughly equal impact on GMDB/GMAB and GMWB
Not hedging stochastic volatility has a greater impact than not hedging all the movements of the term structure

Question 13

Describe how hedge P&L changes when adding a rho hedge for a VA rider

Answer 13

Little model risk, rho hedge significantly improves the hedging loss
More model risk, still significant reduction in RMSE of the hedged loss, but less impact on CTE
Interest rate risk important for both GMAB/GMDB and GMWB

Question 14

Explain whether companies should hedge rho in a low interest rate environment

Answer 14

Rho hedge hurts profitability when IRs rise, but insurers can still benefit when rates remain low
Rho hedge still leads to a risk reduction across all scenarios

Question 15

Describe the hedge impact on P&L using a delta - rho hedge

Answer 15

Hedged loss will tend to increase with stock market volatility
- makes sense because the hedge does not protect against vega from stochastic volatility in a real world financial market model

Question 16

Describe how rebalancing frequency impacts hedge effectiveness

Answer 16

Little or no model risk, frequent rebalancing effective

Higher model risk reduced benefit due to larger accumulation of hedging errors

Question 17

Describe the impact of using stochastic interest rates on hedging effectiveness

Answer 17

Using stochastic rates results in a greater reduction of hedging error for the GMDB/GMAB than the GMWB
GMWB more sensitive to the shape of the term structure (annuity type payoff)
- under realistic market environment, GMWB requires a more sophisticated interest rate model
Including a rho hedge is more important than including stochastic interest rates

Question 18

State the benefit of using a historical measure of volatility

Answer 18

Method yields a stable estimate of volatility over time

Method is simple and easy to understand

Question 19

State the drawbacks of using a forward looking measure of volatility

Answer 19

VAs have long maturities, and most implied volatility surfaces in the market only have 2-3 years term
Two different models calibrated to the implied volatility surface may lead to very different price and hedge ratios
Simulations shows using forward volatility can lead to worse hedging

Question 20

State the five steps involved in the Volatility Target Mechanism

Answer 20

Choose time frequency
- h - length of time in years
- H - risky asset historical volatility estimate period
Set the volatility target
- typically calibrated as the historical volatility of the risky asset over the most recent time period of length H
Estimate V_t
- historical annualized volatility over H
Assign weights
Rebalance

Question 21

State the three drawbacks of the volatility target mechanism

Answer 21

Works best in specific market environments
- failing and high volatility, rising and low volatility
Rule based nature of the strategy can cause significant losses in a nonstandard environment
May not be sufficient to solely define portfolio management decisions and should be combined with other asset allocation strategies

Question 22

Describe sources of revenue from variable annuities

Answer 22

Rider charge - compensation for the cost of providing an investment guarantee
M&E fee - compensation for providing the base VA contract, administering, and servicing the product
Surrender charge - offset the cost of early lapse

Question 23

Describes expenses for variable annuities

Answer 23

Acquisition costs - costs to bring the policy inforce (agent commissions, marketing, underwriting)
Hedging costs - cost to mitigate market risks from investment guarantees

Question 24

Describe three ways the guarantee base of a VA can grow

Answer 24

Rollup - guarantee base accrues at a guaranteed rate
Step up/ratchet - guarantee base increases with account value at the end of each period
- Lifetime High Step Up: G_t+1 = max{G_t, F_t+1}
- Annual High Step Up: G_t+1 = G_t / F_t * max{F_t, F_t+1}
Rollup + Ratchet - takes the higher of the guarantees

Question 25

Describe differences between equity-indexed annuities and variable annuities

Answer 25

Cash flows - no separate account for EIA, benefits through GA
Risk and reward - EIAs only offer a certain percentage of returns and may be capped
Fees - no fees for EIAs, cost controlled through participation rate and cap
Regulation - EIAs don’t need to be registered with the SEC

Question 26

Describe the difference between book profit and distributable earnings

Answer 26

Book Profit = (Revenues - Expenses - Benefits)*(1-Tax Rate)
Distributable Earnings = Book Profit + Surplus on Interest - Increase in Target Surplus

Difference due to taxation and withholding of additional capital

Question 27

Describe three different profit measures of distributable earnings

Answer 27

Net Present Value (NPV) - discount earnings at the yield required by shareholders
Internal Rate of Return (IRR) - discounting rate that makes NPV of all distributable earnings equal 0
Profit Margin (PM) - NPV of distributable earnings as a percentage of premiums

Question 28

Explain why no arbitrage pricing is not commonly used to determine fees for VA products

Answer 28

No arbitrage does not allow explicitly for expenses and profits
Premiums are generally transferred to third party fund managers, who do not disclose the exact mix of assets, so it is difficult to build a replicating portfolio

Question 29

Explain whether to hedge the gross liability or the net liability

Answer 29

Net liability

• equity risk lingers on the fee income side if hedging only gross liability
• with low equity returns, fee incomes may not be sufficient to cover the cost of the gross liability
• better hedge effectiveness by hedging the net liability

Question 30

Describe account value growth in a structured product variable annuity

Answer 30

Instead of daily AV changes, payouts are based on the price of an underlying reference asset
Payoff are credited to the AV at fixed points in time

Question 31

Describe three different crediting strategies for SPVAs

Answer 31

Step PPN - pays a fixed amount if the return on the underlying asset is positive
Capped PPN - pays for positive returns at maturity up to a specified cap
Buffered + Capped PPN - buffer on losses but unlimited growth or loss
- exposes investor beyond the buffer level
- investor chooses buffer percentage, then issuer selects the appropriate cap
- cap levels not disclosed until the segment start date
- most common spVA crediting strategy

Question 32

Describe the impact of segment length and volatility on spVAs

Answer 32

Segment length - longer segment lengths decrease value because net position of the payoff is short theta
Volatility - higher volatility decreases value due to increased probability of a large negative return