Valuation and Capital: Segregated Fund Guarantees Workshop on Options in Financial Products Fields Institute – December 8, 2000 Allan Brender, OSFI

Actuarial Valuation of Liabilities The object of valuation of actuarial liabilities is not to determine a market price. Provision sufficient to meet policy liabilities Cash flows contingent upon uncertain future events over a long term Assumptions about the future include margins for adverse deviations

Actuarial Valuation of Liabilities Actuarial liabilities represent an apportionment of the company’s assets required to satisfy obligations to policyholders. Assets are segmented to back specific portfolios of business. Insurers’ investment policy is long term, buy and hold, and built around ALM.

Actuarial Valuation of Liabilities Policy cash flows are discounted at the yield earned on the supporting asset portfolio, or The actuarial liability is equal to the statement value of the supporting asset portfolio.

Actuarial Valuation of Liabilities Why not use market interest rates? With market interest rates, separate provision would be required for asset/liability mismatch. When insurance portfolios do trade, the trade usually involves transfer of the supporting asset portfolio.

Actuarial Valuation of Liabilities Based upon projection of all relevant cash flows Use a variety of economic scenarios Policy cash flows may be sensitive to the economic scenario Requires dynamic investment policy

Actuarial Valuation of Liabilities Assume economic scenarios are generated stochastically. We obtain a distribution of the cost of meeting obligations to policyholders. We use this distribution to determine both the valuation of the liability and required capital.

Actuarial Valuation of Liabilities How do we allow for economic uncertainty in the liability valuation ? Use the risk-neutral (Q) measure and set the liability value equal to the mean, or Use the ‘realistic’ (P) measure and set the liability value at some point in excess of the mean. Actuaries choose this approach

Segregated Fund Guarantees Individual seg fund product is similar to a mutual fund. A seg fund is required when the return to the policyholder is directly related to a specific block of assets (ICA). Guarantees of return of at least 75% of premiums upon death or maturity are required by provincial securities laws.

Segregated Fund Guarantees OSFI requires (1971) Guarantees not to exceed 100% of gross premiums (investments) Maturity period of at least 10 years Liabilities for seg fund guarantees to be established in an insurer’s general fund

Segregated Fund Guarantees Initially, all seg funds carried 75% guarantees and maturities at a high (retirement) age. In the mid-1980’s, one large insurer moved to 100% guarantees. In the mid-1990’s, the market heated up, offering 10 year maturity periods and resets.

Segregated Fund Guarantees In the mid and late 1990’s, we had low policy liabilities no capital requirement for these guarantees in spite of results of the U.K. Maturity Guarantees Working Party unfolding experience in Japan

Segregated Fund Guarantees OSFI and the Canadian Institute of Actuaries (CIA) both expressed concern over the situation. In 2000, the CIA’s Task Force on Segregated Fund Guarantees developed an approach to liability valuation and required capital.

Segregated Fund Guarantees The Task Force’s approach is through projection of cash flows under stochastically generated scenarios, to generate the distribution of costs of these guarantees. The resulting distribution is strange – ‘all tail’ with a large probability mass at 0.

Segregated Fund Guarantees The Task Force considered a variety of economic models. Not wishing to choose among them, the Task Force developed calibration criteria for the various models to ensure reasonably thick tails.

Calibration – Maximum Returns Accumulation Period 2.5 percentile 5.0 percentile 10.0 percentile 1-year 0.76 0.82 0.90 5-year 0.75 0.85 1.05 10-year 1.35

Segregated Fund Guarantees An interesting new model is the Regime Switching Lognormal Model developed by Prof. Mary Hardy of the University of Waterloo Six parameters Makes maximal use of calibration points

Segregated Fund Guarantees Two levels are specified in the distribution The first for the liability value The second for the total of liabilities and required capital Levels are specified in terms of the Conditional Tail Expectation at the xth percentile, CTE(x)

Capital Requirements OSFI has selected CTE(95) for the total of liabilities and required capital. Required capital is subject to the usual MCCSR multiplier. There is a phase-in over 2000-2001. For 2000, required capital is to be determined through a factor-based formula.

Use of Internal Models If internal models are used to determine capital requirements, these will be subject to a regime similar to that applied to banks’ models for determining capital for trading risk. Audit of models by OSFI Required risk management program with oversight by OSFI

Use of Internal Models Credit for dynamic hedging requires modelling of the hedging activity. The economic scenario generator will have an underlying P-measure. It must incorporate a Q-measure generator to price hedges at future time points within any scenario.

Use of Internal Models Credit for dynamic hedging requires modelling of the hedging activity. Hedges will increase costs in all scenarios. Hedge pay-offs in unfavourable scenarios will reduce costs.

Valuation and Capital: Segregated Fund Guarantees Allan Brender abrende@osfi-bsif.gc.ca