PrefBlog

The Office of the Superintendent of Financial Institutions has released Revised Guidance for Companies that Determine Segregated Fund Guarantee Capital Requirements Using an Approved Model. This is the change we were told to expect in August.

The guts of the change appears to be distribution and correlation requirements for equity indices:

New minimum quantitative calibration criteria are mandated for the scenarios used to model the returns of the following total return equity indexes (henceforth referred to as “listed indexes”):

• TSX
• Canadian small cap equity, mid cap equity and specialty equity
• S&P 500
• US small cap equity, mid cap equity and specialty equity
• MSCI World Equity and MSCI EAFE

The actual investment return scenarios for each of the listed indexes used in the determination of total requirements must meet the criteria specified in the following table.
…
Furthermore, the arithmetic average of the actual investment return scenarios for each listed index over any one-year period (including the one-year period starting on the valuation date) cannot be greater than 10%. All of these criteria must be met for the scenarios of a listed index to be in accordance with the new minimum calibration criteria.

Modeled scenarios of TSX total return indexes must continue to satisfy the CIA calibration criteria at all percentiles over the five- and ten-year time horizons as published in the CIA’s March 2002 report, in addition to the criteria above. Modeled scenarios of S&P 500 total return indexes must satisfy the American Academy of Actuaries’ calibration criteria for equities [footnote] at all percentiles over the five-, ten- and twenty-year time horizons, in addition to the criteria above.

The scenarios used to model returns of an equity index that is not one of the listed indexes need not meet the same calibration criteria, but must still be consistent with the calibrated scenarios used to model the returns of the listed indexes.

Correlation: The scenarios used to model returns for different equity indexes should be positively correlated with one another. Unless it can be justified otherwise, the correlation between the returns generated for any two equity indexes (whether or not they are listed) should be at least 70%. If scenarios are generated using a model that distinguishes between positive and negative trend market phases (e.g. the regime-switching lognormal model with two regimes) then, unless it can be justified otherwise, the scenarios should be such that there is a very high probability that different equity indexes will be in the same market phase at the same time, and a very low probability that different equity indexes will be in different phases at the same time.

Footnote: For example, as published in the June 2005 document entitled “Recommended Approach for Setting Regulatory Risk-Based Capital Requirements for Variable Annuities and Similar Products”.

The table excised from the quotation above is:

These criteria equate, very approximately, to a mean expected return of 8% and a standard deviation of 20.5%. Interested readers can fiddle with the variables and log-normal distributions in the comments.

The American Academy of Actuaries’ Recommended Approach for Setting Regulatory Risk-Based Capital Requirements for Variable Annuities and Similar Products notes:

Short period distributions of historic equity returns typically show negative skewness, positive kurtosis (fat tails) with time varying volatility and increased volatility in bear markets. The measure of kurtosis declines when looking at returns over longer time horizons and successive application of a short-term model with finite higher moments will result in longer horizon returns that converge towards normality. Ideally the distribution of returns for a given model should reflect these characteristics. Of course, due to random sampling, not every scenario would show such attributes.

Unfortunately, at longer time horizons the small sample sizes of the historic data make it much more difficult to make credible inferences about the characteristics of the return distribution, especially in the tails. As such, the calibration criteria are derived from a model (fitted to historic S&P500 monthly returns) and not based solely on empirical observations. However, the calibration points are not strictly taken from one specific model for market returns; instead, they have been adjusted slightly to permit several well known and reasonable models (appropriately parameterized) to pass the criteria. Statistics for the observed data are offered as support for the recommendations.

… and they also provide a table:

where:

The ‘wealth factors’ are defined as gross accumulated values (i.e., before the deduction of fees and charges) with complete reinvestment of income and maturities, starting with a unit investment. These can be less than 1, with “1” meaning a zero return over the holding period.

To interpret the above values, consider the 5-year point of 0.72 at the α = 2.5th percentile. This value implies that there is a 2.5 percent probability of the accumulated value of a unit investment being less than 0.72 in 5-years time, ignoring fees and expenses and without knowing the initial state of the process (i.e., this is an unconditional probability). For left-tail calibration points (i.e., those quantiles less than 50%), lower factors after model calibration are required. For right-tail calibration points (quantiles above 50%), the model must produce higher factors.

To my astonishment, I was able to find a copy of CIA Document 202012 (sounds like an analysis of the Mayan calendar) via the World Bank. I will refer to it as Final Report of the CIA Task Force on Segregated Fund Investment Guarantees. Ths calibration is:

The new standard has a significantly nastier left-tail than the prior standards:

However, in the absence of information regarding the insurers’ models together with detailed data, it is impossible to determine how capital requirements will be affected by the change. This could be a welcome first step towards rationalizing seg fund capital requirements; it could also be window-dressing that OSFI knows will have no effect but makes them look tough. As suggested by Desjardins, we will simply have to wait for commentary in the coming batch of quarterly reports. It will be noted that GWO, SLF and MFC have all warned about the potential for adverse change.

For myself, I am disappointed that while OSFI is addressing intricacies of model calibration, it is not mandating additional disclosures or reviewing their highly politicized cover-up from the Fall of 2008. It became quite apparent during the Panic of 2007 that the currently mandated disclosure of the effect of a 10% decline in equity prices is nowhere near good enough to allow investors to take an informed view on the adequacy of capitalization. Would it really be so difficult and so invasive to mandate a table showing the effects on capital and comprehensive income of the effects of 10%, 20% and 30% declines?