Hedging Strategies for Indexed UL Products Data, Analysis and Implications

Bobby Samuelson

SamuelsonDesign

10/18/11

Abstract

Life insurance carriers are required to record all derivative trades in Schedule DB of the annual statutory Schedule

of Investments section of their annual filings. Analysis of the options trades underlying Indexed UL contracts

reveals almost universal pricing constraints with some notable exceptions that are cause for further investigation

for producers selling Indexed UL. This white paper walks through general observations on Indexed UL return

profiles, options trading practices carriers use to offload equity risk and the mathematical implications of

including real options prices in long-term options profit models.

Outline

1. The Indexed UL Return Profile

2. Hedging Indexed UL Equity Risk

3. Carrier Hedging Data

a. Pacific Life Options Data

b. Aviva Options Data

c. Minnesota Life Options Data

4. The Exceptions – Minnesota Life & Penn Mutual

a. Minnesota Life

b. Penn Mutual

c. Summary

5. Long-Duration Account Options

6. Hindsight & Other Esoteric Options

7. Observations on Options Profit Models

8. Implications for Indexed UL Illustrated Rates

9. Recommendations for Indexed UL Illustrated Rates

10. Technical Appendix

a. Policy Charges – Current Assumption & Indexed UL

b. Policy Charges – Indexed UL vs. Indexed UL

c. Artificial Options Budget Return Leverage

d. Caveats to Assumed Universal General Account Yields

e. Mitigating Factors to Opportunity Cost of Options Purchases

Disclosure

All words herein are solely mine unless specified otherwise.

I did not receive any compensation from any party, directly or indirectly, for authoring and publishing this piece.

This white paper is for open distribution.

The Indexed UL Return Profile

Indexed UL is a general account product offering crediting rate upside based on the performance of an external

equity index and guaranteed downside protection. Upside participation is adjusted via a participation rate and an

interest cap. Most account options available inside IUL products guarantee one of the two limiting factors and

allow the other to float. The most common account option has a floating annual interest cap of between 10% and

15% in current market conditions and a guaranteed 100% participation rate.

The return profile of an Indexed UL product is, by definition, limited when compared to the underlying external

equity index. Floating caps and participation rates change the return profile of Indexed UL in different ways.

Floating participation rates below 100% mimic the general shape of returns for the equity index but with lower

returns and a cluster of returns at the guaranteed floor of 0%. Interest caps simply truncate the upside and

downside tails of the distribution and exactly mirror the external equity index for all points between the

guaranteed floor and the floating cap.

Figure 1 shows hypothetical annual returns for Indexed UL and the S&P 500 excluding dividends since 2000.

Over time, the floating cap strategy will have an exceptionally large number of observations at the floor and cap

because all observations beyond are clumped into a single return pattern. For example, all equity returns above a

12% cap are credited to the policy at 12%, meaning a very large number of observations at the 12% level. Visually,

the distribution of returns for a floating cap strategy looks like a barbell with the vast majority of observations

occurring at the floor and cap. The concentration of returns at the limits of the capped Indexed UL strategy begs

the analogy of flipping a very fat, unevenly weighted coin with one side representing the guaranteed floor and the

other representing the floating interest cap. Since 1950, 73% of years would have been either a 0% credit or a

12% credit (assuming a constant 12% cap historically). Approximately 44% of years would have returned the 12%

cap and 29% would have resulted in the guaranteed floor of 0%. Of the 27% of observations that fell within the 0-

12% bound, the average return skews towards 8%, also indicating the overall skewness of the observations

towards positive returns over negative returns – the uneven weight in the coin. Note that the size of the losses or

gains beyond the cap and floor are irrelevant for long-term returns. 73% of the time the only relevant fact is

whether the return yielded a result within the limits or beyond the limits. The actual return of the index only

matters within the floor and cap, when the product performs identically to the external index.

-40%

-30%

-20%

-10%

0%

10%

20%

30%

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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IUL S&P 500

Figure 2 shows the distribution of S&P 500 and Indexed UL annual returns since 1950 run on each day of the

trading year. Red is the S&P 500 and blue is Indexed UL with a 12% cap and 0% guaranteed floor.

Despite its polarized annual payoff pattern, Indexed UL returns will converge to a relatively stable mean over the

long term, much like one can expect the mean of a series of coin flips to approximately equal 0.50 after sufficient

observations despite perfectly polar individual return observations. The long-term distributions of returns for

Indexed UL is also substantially tighter and converges faster to the mean than the underlying external equity

index because of the absence of negative returns. One way to measure the tangible impact of return volatility in a

distribution over the long-term is to compare its arithmetic mean return to its geometric mean return. The

arithmetic mean return is the sum of all annualized returns divided by the number of observations. The geometric

mean return is the square root of all of the observations multiplied together.

Comparing the arithmetic to the geometric mean for each distribution sheds light on what might be understood

as the “risk premium” for each asset class. The mathematical definition of an expected outcome is to multiply the

probability of occurrence by the magnitude of the outcome. It is impossible to accurately predict the true

probability of occurrence for a particular event in financial markets but historical data provides a proxy.

Arithmetic averages for historical annual returns provides an analogous figure to mathematical expected outcome

because the math is essentially the same, although the probability calculation is not based on an assumed

distribution but rather on the actual occurrence pattern in the data set. A highly volatile asset will most likely have

a high expected return in any given year. However, arithmetic averages systematically underweight large negative

outcomes by treating each annual return observation as an independent outcome. Geometric averages correctly

weight negative outcomes by calculating the average return based on the sequence of returns rather than the

returns as independent outcomes. For instance, the arithmetic average of two annual returns of +50% and -50% is

0%. However, the geometric mean and real dollar outcome is -25%. Geometric means, therefore, shed light into

the volatility of the distribution and adjust average returns for the outsized impact of negative years in each

sequence of returns. By comparing geometric to arithmetic, we capture the difference between the

mathematically expected return (arithmetic mean) and the volatility-adjusted expected return (geometric mean).

The spread between the two averages is a cut-and-dried indicator of the real volatility of returns for the asset

class.

0%

5%

10%

15%

20%

25%-5

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-39

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5%

9%

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17

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37

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Annual Return

Table 1 shows real annual CAUL, S&P 500 and Indexed UL returns since 2000. Indexed UL performance through

2009 is the reported average annual credited rates of an actual in-force IUL block at a major Indexed UL carrier.

CAUL Returns S&P 500 Returns IUL Returns

2000 6.08% -9.10% 5.88%

2001 5.93% -11.89% 0.00%

2002 5.78% -22.10% 0.06%

2003 5.23% 28.69% 6.11%

2004 4.95% 10.88% 9.86%

2005 4.85% 4.91% 6.61%

2006 4.83% 15.79% 8.13%

2007 4.80% 5.49% 9.33%

2008 4.80% -37.00% 0.02%

2009 4.78% 26.46% 2.99%

2010 4.75% 15.06% 12.00% (Assumed) Arithmetic 5.16% 2.47% 5.54% Geometric 5.16% 0.41% 5.47%

Spread 0% 2.06% 0.14%

A spread of 0% implies that Current Assumption UL returns are roughly equivalent to a fixed rate or, in other

words, there should be only a minimal (if any) risk premium in accepting the floating CAUL rate instead of a fixed

rate. This is intuitive. One does not know at onset whether the rates are going to go up or down, but the volatility

is exceptionally low on an annual basis and subject to a floor of 2-4%. Were we to include carrier defaults and

policy charges in the analysis, the numbers may have been more volatile and almost certainly increased the

spread from 0% to some marginally higher number. S&P 500 returns are assumed to be more volatile than CAUL

and the spread between arithmetic and geometric returns corroborates this assumption. The most interesting

outcome, however, is that the spread for Indexed UL is a mere 14 basis points. Based on this data set, one can

make the assumption that the volatility in Indexed UL isn’t worth much in terms of risk premium for long-term

returns. The return profile for Indexed UL appears to be much more like CAUL than the S&P 500.

Table 2 shows arithmetic and geometric averages for 10 Year Treasuries, S&P 500 and hypothetical Indexed UL

returns since 1950.

10 Year Treasuries S&P 500 Returns Indexed UL Returns

Arithmetic Average 6.29% 12.51% 7.25%

Geometric Average 6.26% 11.05% 7.11%

Spread 0.03% 1.50% 0.14%

Like Current Assumption UL, the miniscule 3bps spread for 10 year Treasuries implies a relatively riskless asset.

The spread for Indexed UL since 1950 is identical to the spread from 2000-2010 despite the fact that the risk

premium (and average return) for the S&P 500 increased. This result is highly intuitive. The return profile of an

Indexed UL product remains that of a fat, unevenly weighted coin toss regardless of the level of returns for the

S&P 500. The level of Indexed UL returns floats somewhat in accordance with the S&P 500 but in a

counterintuitive way. Indexed UL returns could stay flat even if the S&P 500 increased dramatically if the S&P 500

grew in a highly volatile fashion, with infrequent, extremely large gains. What matters to Indexed UL returns is not

the size of S&P 500 returns but instead the frequency of occurrence. Indexed UL looks best compared to the raw

index when the S&P 500 grows at a consistent, conservative rate. Ironically, that is precisely the scenario where

Indexed UL would be the least valuable as a hedge against downside risk.

Note also that Indexed UL returns are going to be systematically skewed to the positive in an analysis that does

not capture the effect of policy charges. Years when the policy credits 0% to the cash value will actually show a

decline in return because of policy charges. Comparing the arithmetic and geometric means for real cash-on-cash

yield in Indexed UL products would yield different risk adjusted returns across Indexed UL products with identical

caps and floors due to differing charge structures. As discussed in other publications, policy charges should be of

paramount concern for producers selling Indexed UL because they represent the real downside risk of each

product. Policy charges, in effect, inject substantially more risk into the product than we can see by just looking at

hypothetical historical crediting rates. This effect is well documented in Variable UL actual policy performance.

Hedging Indexed UL Equity Risk

The return profile of Indexed UL is fundamentally mismatched to the returns of the fixed income assets

comprising the vast majority of a carrier’s general account. Generally, returns on fixed income assets only change

if the asset is sold prior to maturity or if the issuer defaults. Indexed UL returns are polarized at the guaranteed

interest rate and floating cap, virtually never matching exactly with the fixed income asset yields of the carrier’s

general account.

The issuing carrier is, in effect, placing an equity based liability on its fixed asset balance sheet when it writes an

Indexed UL product. The carrier has a few options to deal with the liability. The simplest is to retain the risk by

simply writing the liability and gambling that fixed income assets will cover the equity liability over the long term.

This strategy has several negative implications. First, it exposes the carriers to swings in product profitability

based on swings in the equity markets. A long stretch of consistent growth in the S&P 500 would cause a major

mismatch between the crediting rate on the Indexed UL product and the earned rate on the fixed income assets

in the general account. Second, it builds perverse incentives for the carrier to lower the cap rate at the moment

when it believes that equities are going to rise. Finally, it lends itself to periods of historically overstated and

understated performance depending on the pricing assumptions used for illustrative purposes.

The vast majority of carriers choose to offload the equity risk in Indexed UL products to a third-party financial

services entity, most commonly investment banks. The mechanics of the transaction are deceptively simple. The

carrier uses the earned rate on its fixed income assets as the budget to purchase protection against the Indexed

UL equity risk liability. The carrier effectively transforms the equity risk of an Indexed UL product into fixed

income risk. Equity returns are irrelevant to long-term carrier profitability because any payoff from the equity

hedge will be immediately transferred, dollar for dollar, to policy cash values. The only risk the carrier takes is that

it can’t earn enough to cover the budget of the purchased equity hedges. Options profits go to the policyholder.

Over time, the product risk profile of a fully hedged Indexed UL product looks very much like CAUL to the carrier.

If crediting rates on CAUL are unsustainable based on fixed income yields, the carrier lowers crediting rates. If

hedging costs for Indexed UL are unsustainable at the current participation limits based on fixed income yields,

the carrier lowers participation limits and thereby reduces the cost of protection against equity risk. Regulators

have confirmed the similarity between fully hedged IUL and CAUL by giving them effectively the same reserving

treatment, tacitly equating the risk profiles (more reserve would imply more risk, vice versa). Actuarial Guideline

36 sets out 3 methods for reserving for Indexed UL contracts. One method applies only for fully hedged IUL

polices, the other two methods apply to partially or dynamically hedged IUL policies. The key parameter for

determining reserves for fully hedged IUL policies is the statutory equality of historical hedging (options) costs to a

guaranteed crediting rate for future returns in accordance with the Cash Value Reserve Methodology reserving

regime used for CAUL. Note that projections of future strategy returns are irrelevant for reserving. Only the cost

of hedging the policy is important.

Carrier Hedging Data

Every carrier must file a statutory annual report containing, amongst a variety of other things, a schedule of

investments that contains details on every asset held, terminated or acquired during the year. Schedule DB

contains details for all derivative transactions. Hedges on Indexed UL policies are derivative instruments and are

listed in Section 1 of Schedule DB under the caps and floors section. Analyzing the hedging trades underlying the

Indexed UL contracts provides insight into how carriers actually participate in the market and what it may mean

for policyholders in the long run.

Reading the Schedule DB to look for Indexed UL trades can be exceptionally difficult for two reasons. First, a

carrier writing Equity Indexed Annuities and Indexed UL will most likely execute multiple options trades a day that

have nothing to do with Indexed UL policies. The process of sifting through thousands of trades to look for the

ones specifically linked to Indexed UL can be arduous. Second, some carriers provide sparse information in

Schedule DB as to the exact parameters for each trade. For instance, they will only list one strike of a packaged

two-strike cap trade. If both factors are present, the data is virtually worthless for analysis because one will not be

able to reliably differentiate between Indexed UL and Indexed Annuity trades.

The ideal carrier for analyzing Indexed UL trades only has Indexed UL contracts and provides complete detail for

each trade. Pacific Life qualifies. Aviva writes Indexed Annuities but executes its IUL trades near or on the 10th and

25th of each month and provides a high level of detail, making their books relatively easy to read as well. Pacific

Life and Aviva also serve as excellent proxies for other reasons. They are ranked number 1 and number 2 in

Indexed UL sales, respectively. Pacific Life has held its cap constant at 12% since the inception of the product in

2005 through 2010. Aviva has several in-force products on the books with different pricing methodologies and

different caps. Both carriers serve as de facto benchmarks for pricing for the rest of the industry.

Pacific Life Options Trades

Most of the analysis will focus on Pacific Life primarily because the product pricing hasn’t changed since inception

and many carriers still have approximately a 12% cap, making the historical performance of the product

particularly applicable to current market conditions. Options prices are quoted as a percentage of the notional

covered. For instance, a 5% option means that it costs $50,000 to cover the equity index liability on $1,000,000 of

Indexed UL cash value.

Theoretically, a carrier could hedge its capped index liability by purchasing a call option at a strike of 0% gain and

writing a call option with a strike of a 12% gain. From 0% to 12%, the carrier receives a return in lock-step with the

index. From 12% and beyond, the carrier receives money from the purchased call and owes exactly the same

amount on the call option written at 12%, producing a net-zero payoff above 12%. The net cost of the option is

the paid premium of the 0% option less the received premium of the 0% option. Carriers usually simplify the

process by simply purchasing a packaged call spread from an investment bank. The option provides coverage from

exactly 0% to 12%, mimicking the payoff of a call spread, for a single price and with a single counterparty. The

advantage to the carrier is that it involves less trading and less complications with individual options. The cost of a

call spread package is simply the premium divided by the notional covered.

Table 3 shows Pacific Life’s 1 year Point-to-Point capped account options trading activity in each month from 2006

through 2010. The stated cap in all years was 12%. Average cost across all years was 5.45%.

2006 2007 2008 2009 2010

January 5.50% 5.62% 5.68% 5.52% 4.84%

February 5.38% 5.50% 5.53% 5.46% 4.94%

March 5.35% 5.63% 5.55% 5.25% 4.82%

April 5.46% 5.59% 5.41% 5.14% 4.74%

May 5.44% 5.65% 5.36% 4.98% 5.37%

June 5.91% 5.72% 5.57% 5.28% 5.45%

July 5.95% 5.78% 5.50% 5.22% 5.47%

August 5.82% 5.93% 5.35% 5.17% 5.40%

September 5.71% 6.07% 5.61% 5.10% 5.31%

October 5.58% 5.94% 5.55% 5.03% 5.24%

November 5.50% 5.96% 5.70% 5.04% 5.04%

December 5.57% 5.86% 5.53% 5.07%

Average 5.60% 5.77% 5.53% 5.19% 5.15%

This data points to several observations. First, that PacLife determined a 12% cap to be sustainable on the same

policy charge structure even as the options cost fluctuated from between 6.07% and 4.75% and their general

account rate stayed relatively constant at approximately 5.15% (including in-force). Second, that options costs

haven’t fluctuated to the degree that one might expect based on the exceptional market turmoil over the data

period. Third, that options cost are not correlated to the normal market bellwethers of the CBOE market implied

volatility index (VIX) and short term rates in accordance with Black-Scholes options pricing theory.

Figures 3 & 4 show options prices in relationship with external benchmarks.

The external benchmark most closely related to costs of Pacific Life’s packaged call spreads appeared to be the

AAA composite yield as recorded by the Federal Reserve. While somewhat counterintuitive, the fact that

packaged call spread options are closely correlated to the AAA composite signals support for the idea that

Indexed UL returns are relatively stable compared to equities with very little premium for riskiness. It follows that

options pricing should be largely based on opportunity cost of capital for which the AAA composite serves as a

proxy. We could construct detailed narratives for why options prices move with AAA bonds but, ultimately, those

would fall short. The most pertinent metric is that the average differential between the AAA composite and 0-12%

options since 2006 is 1 basis point. Despite short term volatility, the two appear to be highly related at least over

the short time period in question.

Figure 5 shows the AAA composite and Pacific Life’s call spread option costs

Aviva Options Data

Aviva’s options trades bear a striking resemblance to Pacific Life’s. The primary trading difference between Aviva

and PacLife is that PacLife purchases options once in the middle of the month and Aviva trades near the 10th and

25th of every month. Some of the difference in options prices can be attributed to timing.

Table 4 compares options purchases for 12% caps on Aviva and PacLife products throughout 2009.

2009 Data Aviva PacLife Differential

Cap Rate 12% 12%

January 5.46% 5.52% -0.05%

February 5.41% 5.46% -0.06%

March 5.25% 5.25% -0.01%

April 5.15% 5.14% 0.01%

May 5.12% 4.98% 0.14%

June 5.22% 5.28% -0.06%

July 5.08% 5.22% -0.14%

August 5.11% 5.17% -0.06%

September 5.06% 5.10% -0.04%

October 5.02% 5.03% -0.01%

November 5.03% 5.04% -0.01%

December 5.01% 5.07% -0.06%

Average 5.16% 5.19% -0.03%

Aviva’s notional for its 12% capped block of business was just over $200 million and Pacific Life’s was

approximately $266 million. However, Aviva also has older Indexed UL lines with caps at 11% and 10% with

notional totaling more than $1.1 billion. Aviva’s primary counterparties were Bank of NY Mellon, SunTrust, BNP

Paribas, Societe Generale and Barclays. Pacific Life traded mostly with Credit Suisse, BNP Paribas and Barclays as a

distant third. Since 2006, BNP Paribas has traded with Pacific Life by far more than any other financial institution.

4.50%

5.00%

5.50%

6.00%

6.50%

1/13/2006 1/13/2007 1/13/2008 1/13/2009 1/13/2010

Options Cost AAA

The similarity in trading costs for Aviva and Pacific Life signals that options pricing places carriers at the mercy of

the market. Aviva trades substantially more options than Pacific Life yet does not appear to receive any financial

benefit for doing so. Furthermore, BNP Paribas and Credit Suisse accounted for virtually all of Pacific Life’s options

trades in 2009 but the costs were in line with Aviva’s pricing after bidding out a larger group of competitors. This

may corroborate the conclusion that options prices are the best guess at actual Indexed UL yields.

Minnesota Life Options Data

To hedge its Eclipse Indexed UL product, Minnesota Life purchases at-the-money call options with unlimited

upside and writes a call option at the cap, currently set at 15%. The data allows for a comparison between the

pricing for Minnesota Life’s unlimited upside options and Pacific Life’s cap options written on the same days and

at the same strikes.

Table 5 shows Minnesota Life’s unlimited cap options prices in comparison to Pacific Life’s 12% cap call packages.

Purchased Premium Minn Life Pacific Life Additional Date Notional Strike Paid Call Cost 12% Call Cost Cost

10/15/2009 6,000,000 1,097 514,200 8.57% 5.03% 3.54%

11/19/2009 10,000,000 1,095 897,596 8.98% 5.04% 3.94%

12/17/2009 10,000,000 1,096 863,000 8.63% 5.07% 3.56%

1/14/2010 10,000,000 1,148 711,000 7.11% 4.84% 2.27%

2/18/2010 10,000,000 1,107 755,000 7.55% 4.94% 2.61%

3/18/2010 5,500,000 1,166 378,400 6.88% 4.82% 2.06%

4/15/2010 7,000,000 1,212 486,500 6.95% 4.74% 2.21%

5/20/2010 5,000,000 1,072 571,000 11.42% 5.37% 6.05%

6/17/2010 8,000,000 1,116 721,600 9.02% 5.45% 3.57%

7/15/2010 10,000,000 1,096 977,000 9.77% 5.47% 4.30%

8/19/2010 10,000,000 1,076 996,000 9.96% 5.40% 4.56%

9/16/2010 9,000,000 1,125 787,950 8.76% 5.31% 3.45%

10/16/2010 12,000,000 1,174 1,049,400 8.75% 5.24% 3.51%

11/18/2010 25,000,000 1,197 1,980,000 7.92% 5.04% 2.88%

12/16/2010 15,000,000 1,243 1,063,560 7.09% 5.00% 2.09%

Totals 152,500,000 12,752,206 8.49% 5.12% 3.37%

Figure 6 shows Minnesota Life’s unlimited cap options costs against PacLife’s options cost and the S&P 500

950

1,000

1,050

1,100

1,150

1,200

1,250

1,300

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

11.00%

12.00%

10/1/2009 1/1/2010 4/1/2010 7/1/2010 10/1/2010

ML Unlimited Cap PL 12% Cap S&P 500

Minnesota Life’s data brings forth three interesting observations. First, that the expected return for purchasing

unlimited cap options is 8.49% on average. Since 1950, the average one year return for every day the S&P 500

traded is 8.51%. This appears to corroborate the notion that options prices are accurate reflections of expected

returns over the option duration and fundamentally profit-neutral to purchasers in the aggregate. Second, that

unlimited cap options appear to be highly inversely correlated to the S&P 500 and, consequently, much more

volatile than Pacific Life’s 12% cap options.

The logic behind the inverse correlation between options prices and the S&P 500 will be the subject of a separate

piece. In short, the options appear to be adjusting prices to match long-term pricing expectations (or average

annual return expectations) with temporary movements in the stock market. This idea flies in the face of the

Black-Scholes options pricing theory, which posits that stock prices have implicit return expectations based on a

replicating portfolio of borrowed capital at the risk-free money market rate and purchased stocks and that

volatility in options prices, ceteris paribus, comes from changes in expectations of volatility in the underlying

stock. A Black-Scholes theorist would claim that expected volatility increased as stocks fell and options prices

increased to reflect new volatility expectations. We generally downplay the notion that volatility is itself volatile

and posit that options prices are constantly attempting to match market expected returns with current price

movements under mostly static volatility assumptions. Again, this is a topic for another paper. For a more

technical dismantling of Black-Scholes, see Taleb and Haug, 2009.

The question that arises from comparing Pacific Life’s 12% packaged call spread options to Minnesota Life’s

unlimited cap options is one of accurate return expectations. We can safely say that Minnesota Life’s options do

not behave like the fat, unevenly weighted coin of packaged call spreads and that an average 8.49% cost appears

to accurately reflect the historical annual returns of the S&P 500. What is less clear, however, is the applicability

of packaged cap options prices to the actual returns for those options. Packaged cap options benefit from the

“volatility smile” phenomenon that appeared after the stock market crash on Black Monday in 1987 and has

persisted since. Simply put, the volatility smile means that, holding all else constant, at-the-money options are

cheaper than out-of-the-money options on a risk-neutral pricing basis. Practically, it means that packaged call

spread options benefit from buying a “cheap” at-the-money option and writing an “expensive” out-of-the-money

option at the cap. This may allow some, uncertain degree of additional profitability to accrue to a consistent

purchaser of call spread options. Conversely, insurance carriers purchase packaged call spread options from

investment banks and there is some anecdotal evidence that investment banks price a profit margin into the cost

of the options over and above the real expected payoff, potentially negating the impact of the volatility smile on

long-term profitability. Also, the volatility smile isn’t necessarily symmetrical around the strike and may evolve

into a “smirk” that could wipe out the long-term profitability of call spread options under a smile assumption.

The Exceptions – Minnesota Life and PennMutual

We have reason to believe that the vast majority of carriers with Indexed UL products employ replicative hedging

akin to Aviva and Pacific Life at least for their most popular account options, typically a capped 1 year Point-to-

Point as referenced above. Some carriers may not fully hedge using external options for less popular, more

esoteric account options that would more expensive to hedge than to hold on the books due to the illiquidity of

the market or quirkiness of the risk profile. We also have evidence that at least two carriers, Minnesota Life and

PennMutual, are employing different pricing and/or hedging strategies that allow them to provide account

options with participation limits in excess of the market norms.

Minnesota Life Hedging

Minnesota Life’s Eclipse Indexed UL product has had elevated caps since its inception, falling from 17% to 15% in

recent years. The market benchmark for an annual point-to-point cap is between 11% and 13%. The annual floor

for Eclipse IUL is the standard of 0%. Two factors partially account for Eclipse’s ability to have a higher cap have

nothing to do with hedging. First, Eclipse IUL is designed to be profitable through the charge structure rather than

retained earnings on the yields of invested assets. As such, its charge structure is higher than many of its peers,

especially in the years at and beyond LE. The effect is that Minnesota Life theoretically has a higher budget to

spend on options.

Second, and more importantly, Eclipse IUL credits indexed interest to the account based on the account value at

the end of the segment rather than the mid-point account value. The effect is that indexed interest is credited to a

smaller amount than it would be if the product used the mid-point account value. Using the end-of-year value

instead of the mid-point value allows Minnesota Life to provide a higher cap than its competitors without

necessarily incurring a higher cost to hedge or actually crediting more to the policy. In effect, Minnesota Life has

to purchase a wider call spread (0% to 15% vs. 0% to 13%) but less notional value. The cost of the hedge, then,

could be lower than a product using the mid-point method (therefore buying more notional) with a lower cap.

Table 6 illustrates the functional difference between using the mid-point and the end-of-year methods.

Pacific Life

Minn Life

Pacific Life

Minn Life

Pacific Life

Minn Life

Year 1 Year 1

Year 1 Year 1

Yr 20 (AV) Yr 20 (AV) Premium 20,000 20,000 65,000 65,000 1,000,000 1,000,000

Premium Load (1,320) (1,100) (4,290) (3,575) - - Policy Charges (9,099) (8,364) (9,099) (8,364) (1,083) (1,641)

End-Of-Year AV 9,581 10,536 51,611 53,061 998,917 998,359 Mid-Point AV 13,751 14,370 55,781 56,895 999,413 998,551

Marketed Current Cap 13% 15% 13% 15% 13% 15% Maximum Equity

Exposure (Notional x Cap) 1,788 1,580

7,252 7,959

129,924 149,754

Effective Mid-Point Cap 13.00% 11.00% 13.00% 13.99% 13.00% 15.00%

Effective End-of-Year Cap 18.66% 15.00% 14.05% 15.00% 13.01% 15.00%

The last two rows translate the marketed caps into their equivalent using the other method. For instance, in the

first set of columns, Pacific Life’s 13% mid-point cap is equivalent to an 18.66% using the end-of-year method. The

truism for comparing the two methods is that as policy charges become a smaller percentage of the total account

value, the difference between the two methods will shrink. Therefore, Minnesota Life can market a higher cap

using the end-of-year AV method than it would be able to under the mid-point method only in the early years of

the policy or in the event that the net amount at risk for the contracts stays high. In an overfunded scenario, as is

outlined in the right two columns, the effect of using the end-of-year method is virtually nothing. Minnesota Life’s

hedging costs will more or less match the equivalent cap on a mid-point product.

The potential effect on the client is twofold. First, underperformance will negatively affect Minnesota Life’s

product more than a competing mid-point product. Any unanticipated increase in NAR will not only cause more

drag simply from higher charges but it will also have an outsized effect on the interest credited to the policy.

Second, Minnesota Life is clearly offering a higher cap predicated, to some unknown degree, on the idea that it

can save costs by reducing the hedged notional using the end-of-year method. It only can cut costs compared to

its competitors if the block of business has a relatively high NAR, as noted in the table above. If we assume that

clients pay premiums on time and the products perform as illustrated, virtually all of the major sales designs will

have a thin NAR and Minnesota Life’s costs to hedge will equate its mid-point competitors currently offering much

lower caps. The result is somewhat paradoxical. If the block performs as illustrated, the cap may have to fall back

to market norms because the savings from the end-of-year method will vanish. If the block does not perform as

illustrated, the cap can stay higher than competing products. High performance is clearly better for clients than

underperformance, but the cap would fall in the former and potentially even rise in the latter. Using the end-of-

year AV method presents a somewhat perverse set of outcomes without any real benefit to the client. The end-of-

year method exacerbates underperformance without commensurate upside, except illustrated rate at sale.

Penn Mutual

Penn Mutual’s Accumulation Builder IUL product seems to offer the best of all worlds. It has an annual floor of

2%, a percentage point or less below Current Assumption UL products, and a current upside cap set at 13%. Like

Minnesota Life, Penn Mutual built exceptionally high policy charges into the product in later years to offset some

of the cost of additional upside. Also like Minnesota Life, Penn Mutual appears to be taking shortcuts in hedging

equity risk although in far more egregious ways. Schedule DBs for both the Penn Mutual Life Insurance Company

and the Penn Insurance and Annuity Company (where the Accumulation Builder IUL is written) did not contain any

call options prior to April of 2011. Penn Mutual representatives have confirmed that the company was internally

hedging its Indexed UL product against its Variable Annuity block of business until April of 2011. After that time,

PennMutual began to offload an unspecified amount of the risk to third parties via packaged call spreads.

According to its 2nd Quarter of 2011 statutory filing, Penn Mutual started buying call spreads in April and, on June

3rd, bought call spreads to cover equity exposure through January of 2012. The notional value of the options was

approximately $112 million, less than its sales through the quarter and far less than its total block of business. The

call spreads were structured as a 2% floor and a 13% cap and the cost averaged 4.15% for the three months (April,

May and June) of one year options. The 2% guaranteed product floor is covered by the bond yield. The total cost

to hedge is the cost to option plus the guaranteed floor (which could have been spent on options), yielding an

average total cost of 6.15%. Over the same period, Minnesota Life’s 0%/15% options cost 5.64% and AXA’s

0%/12% options cost 4.92%. Penn Mutual does not appear to use the end-of-year AV method to cut hedging

costs. Penn Mutual is clearly still retaining a substantial amount of equity risk in order to reduce its reported

hedging costs because the cost of full, replicative hedging using options would be prohibitively high. Assuming a

general account yield of 5%, we can speculate that Penn Mutual could provide a 2% floor guarantee with a fully

hedged cap between 7% and 9%. The hypothetical look-back illustrated rate would be approximately 6.5% with a

9% cap and 2% guaranteed floor, meaningfully below the current illustrated rate of 8.36%.

Summary – Minnesota Life & Penn Mutual

By and large, Indexed UL products are constrained by crediting methodologies and market hedging prices that do

not change across carriers. Two carriers, Minnesota Life and PennMutual, have appeared to circumvent these

restraints and offer exceptionally competitive products with participation limits well above market benchmarks.

They both use high policy charges to subsidize high participation limits and both engage in potentially risky

hedging strategies, especially Penn Mutual, that could push the products rapidly back to or below their

competitors if they turn sour. Minnesota Life’s end-of-year AV crediting methodology is almost universally a

disadvantage for clients and only provides a benefit to Minnesota Life if the products do not perform as

illustrated, creating a perverse set of incentives. Producers should not sell PennMutual or Minnesota Life products

on the assumption that either carrier can actually support elevated participation limits over the long term that are

not predicated only on their relatively expensive product charges. Both products should be illustrated at rates

more in line with their closest competitors and producers writing Minnesota Life should be wary of the future

impact of the end-of-year AV method on underperforming contracts.

Long-Duration Account Options

Many carriers are starting to offer accounts with durations in excess of 1 year but not longer than 5 years. Long-

duration accounts are hedged identically to one year accounts.

Table 9 shows the cost of 5 year 100% participation rate options purchased by Pacific Life since 2008 as a

percentage of notional.

Month 2008 2009 2010

January 24.89% 15.80%

February 24.69% 15.97%

March 21.94% 23.54% 14.90%

April 18.95% 24.00% 15.42%

May 18.87% 20.29% 18.58%

June 20.45% 22.83% 18.86%

July 19.56% 19.29% 19.44%

August 19.25% 19.80% 17.55%

September 19.29% 19.15% 16.08%

October 22.77% 18.70% 15.72%

November 26.18% 18.76% 13.90%

December 27.41% 19.05% 14.20%

Average 21.47% 21.25% 16.37%

Figure 7 shows the value of the S&P 500 index versus Pacific Life’s 1 year options cost. Options costs are graphed

on the primary axis, S&P 500 on the secondary axis.

600

700

800

900

1000

1100

1200

1300

1400

1500

4.70%

4.90%

5.10%

5.30%

5.50%

5.70%

5.90%

3/14/2008 3/14/2009 3/14/2010

1 Year Option Cost S&P 500

Figure 8 shows the value of the S&P 500 index versus Pacific Life’s 5 year options cost.

Despite the superficial similarities, 5 year option costs differ from 1 year option costs in dramatic ways. The

analogy of a fat, unevenly weighted coin toss does not apply in this situation because the cap is unlimited.

Instead, 5 year options are theoretically tied more to the movements of the S&P 500 and the market’s

expectations about the yield of the index over the next 5 years. Long-duration, uncapped options prices should

move conversely to S&P 500. 1 year capped options should remain relatively steady due to limited upside. The

graphs below corroborate the theory. 5 year options appear to have almost perfect inverse correlation to the S&P

500 and 1 year options do not appear to be systematically correlated to the S&P 500.

The correlation between 5 year options prices and the level of the S&P 500 may be a temporary phenomenon

spurred by recent market volatility. The sentiment in the 5 year options prices appears to be that the S&P 500 is

going to remain flat as it was over the past decade. In order to maintain make options prices match the flat yield

assumption, options prices must be inversely correlated to the S&P 500. But it is irrational to think that options

prices would continue to fall indefinitely as stocks rise. In fact, it is reasonable to believe that a strong market

sentiment about future equity returns could actually create positive correlation between 5 year options prices

and the S&P 500. The point is not that long-duration options prices are correlated to the S&P 500 in a particular

way. Rather, it is that long-duration options prices are estimates of future S&P 500 returns and that it is unlikely

for an options purchaser to consistently beat the options writer due to the linkage with market expectations for

S&P 500 returns. Furthermore, we may also conclude that 5 year options are substantially more volatile than 1

year caps and that policyholders may see drastically different caps or participation rates (whichever floats) in the

future than today.

Long-duration accounts make sense is when a client is extremely bullish about future equity returns. Whether the

client is right or wrong is irrelevant. The 5 year bucket accommodates those who think that the next 5 years holds

substantially more promise than the options writers (and, by extension, the market) have priced. It is also the

riskiest option because the long-duration nature of the bucket means fewer flips of the coin. Some clients will

profit madly (on a risk adjusted basis) from 5 year accounts. Some will merely receive protection of principal. The

average return, however, is unlikely to deviate far from the market expected return for the bucket adjusted by

any future decreased participation limits. The 5 year bucket simply allows for the traditional understanding of

options as a leveraged bet on the market. The 1 year capped bucket is less about leverage and more about

opportunity cost of capital.

600

700

800

900

1000

1100

1200

1300

1400

1500

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

22.00%

24.00%

26.00%

28.00%

30.00%

3/14/2008 3/14/2009 3/14/2010

5 Year Option Cost S&P 500

Hindsight & Other Esoteric Options

International, “hindsight rainbow” options used for products such as ING Global Index UL and AIG Elite Global IUL

follow the same general logic as the above. Prices are logically most correlated to the expected return of the

strategy. The strategies may themselves have higher yields but the price of the options balances against the

higher return of the strategy. Evidence of this is that participation rates are substantially below 100% for

hindsight, multi-index accounts whereas current S&P 500 5 year accounts are at 100% or above. The hindsight

strategy has higher expected yields than point-to-point but the cost of the options forces the participation rate

well below 100%.

Hindsight products are often illustrated at the highest rates in the industry. ING has released a Monte Carlo based

calculator that uses historical data to build simulations for product performance over thousands of historical

blocks of time. Monte Carlo suffers from the same problems as traditional historical analysis by making the same

poor assumptions about the similarity in size and shape of previous equity returns and the stability of

participation limits over time. Nonetheless, ING proactively uses the percentile simulator to substantiate

illustrated rates in excess of 9%. The real source of the elevated returns is the discrepancy between the

immediate past performance of the product and its historical estimated performance. There is little reason to

believe that hindsight rainbow options are structurally priced to deliver a higher yield than American options over

the same duration. The ING and AIG products can illustrate elevated performance by applying pricing based on

today’s “low” options prices to historical periods of extreme returns, especially in the Hang Seng. This analysis is

useless for projecting future returns unless ING and AIG can provide empirical analysis for the reason behind

these options being loss-leaders for the writers over the long term.

Carriers have created a litany of one year indexed account options that do not conform to the typical capped

annual point-to-point account used for the vast majority of the analysis in this paper. Most carriers admit that

non-standard account options receive a sliver of the premium that standard account options do. Accordingly,

many carriers choose to retain the risk of low-volume account options on their balance sheets or to loosely hedge

with futures and other non-replicative methods. It is difficult to trace third-party hedging activities for these

accounts because carriers often do not include sufficient detail in the options trades.

Observations on Options Profit Models

Since 2006, options have been a relatively profit-neutral proposition for Pacific Life policyholders. The past 4 years

have certainly been abnormal for the market as a whole but, for the Indexed UL strategy, the magnitude of the

volatility of the index is irrelevant. The past 4 years have simply contained two increases and two decreases. Total

and annualized returns are skewed towards the later years due to increasing amounts of premium. The arithmetic

mean shows the average of the yields in each individual year and points more towards the expected return in any

given year for this strategy. The geometric mean for the options is 0 due to the occurrence of a total loss in the

data. In short, this strategy has an exceptionally high level of risk and volatility and an uncertain arithmetic

average outcome. This data set is too short to glean meaningful answers about long term performance. Note also

that Pacific Life’s profitability is not directly affected by the profitability of the options in the short or long term.

The purpose of replicative hedging is that the options exactly replicate the liability, allowing PacLife to offload risk.

Table 10 shows the options premium and consideration at maturity from 2006 to 2009. Pacific Life began the

Indexed UL line in mid-2005 but the data was not available for this analysis. It would have almost certainly been a

yield on the order of 2006 but with a substantially smaller premium number, perhaps even under $1.5 million.

Pacific Life Options P/L

Pur. Year Premium Consideration Return

2006 2,117,482 3,616,603 70.80%

2007 5,717,383 - -100.00%

2008 11,060,565 5,061,683 -54.24%

2009 13,912,306 28,225,291 102.88%

Total 32,807,736 36,903,577 12.48%

Annualized

2.38%

Arith. Mean

4.86%

The other piece to the options pricing puzzle is opportunity cost of capital. Assuming Pacific Life pays premium at

the beginning of the year and the investment bank can invest it at will over the period, the bank earns the yield

that Pacific Life would have earned had it internally hedged. Pacific Life likely considers its opportunity cost to be

its general account yield or earned rate for specific product block assets (see Appendix). Opportunity cost for the

bank is a little bit stickier. Strictly speaking, opportunity cost is the yield on a 1 year Treasury note. The reality,

however, is that the bank most likely pushes the money into theoretically higher yielding assets or hedges its own

exposure. If one assumes the AAA composite is a fair proxy for opportunity cost for both Pacific Life and the

investment bank, the cost of the options to Pacific Life (and the return for the investment bank) gets markedly

higher. Average raw options costs for Pacific Life since 2006 was 5.45%. Accounting for opportunity cost at the

AAA composite rate, the average cost was 5.75%. Carriers paying more for options to support higher cap rates will

be affected more by opportunity cost losses than carriers with lower caps.

Accounting for opportunity cost drastically changes long-term options profitability models for options purchases.

Assuming that annual profits are a coin toss of either 0% or 12%, Pacific Life’s options purchases would have had

an average expected yield of 20.82%. Accounting for opportunity cost at the AAA composite rate drops the

average expected yield to 9.45%. Changing the generic coin toss assumption to the fat, unevenly weighted coin

toss analogy espoused in this paper, profit models would change dramatically depending on the assumed metrics

of the coin. Further complicating the problem is the reality that, in the real world, the coin constantly changes

shape and weight.

Table 11 shows options premiums with and without opportunity cost and the expected profit under a coin toss

assumption of 0% and 12% sides. Expected profit is calculated as the difference between maximum gain (12%-

Options Premium/Options Premium) and maximum loss of 100%. Opportunity cost is calculated as the AAA

composite index at each data point.

Pacific Life PL Premium Coin Toss Coin Toss

Date Option Premium Plus Opp. Cost Profit Profit w/ Opp. Cost

1/14/2006 5.50% 5.79% 18.182% 7.338%

3/15/2006 5.35% 5.65% 24.299% 12.505%

7/14/2006 5.95% 6.30% 1.707% -9.405%

9/14/2006 5.71% 6.03% 10.158% -0.949%

11/14/2006 5.50% 5.79% 18.182% 7.200%

1/14/2007 5.62% 5.92% 13.531% 2.571%

3/15/2007 5.63% 5.93% 13.144% 2.454%

7/14/2007 5.78% 6.12% 7.612% -3.806%

9/14/2007 6.07% 6.42% -2.468% -13.103%

11/14/2007 5.96% 6.29% 1.342% -9.190%

1/14/2008 5.68% 5.98% 11.268% 0.520%

3/15/2008 5.55% 5.85% 16.216% 4.983%

7/14/2008 5.50% 5.80% 18.182% 6.729%

9/14/2008 5.61% 5.92% 13.904% 2.637%

11/14/2008 5.70% 6.06% 10.526% -2.044%

1/14/2009 5.52% 5.79% 17.403% 7.367%

3/15/2009 5.25% 5.55% 28.567% 16.241%

7/14/2009 5.22% 5.50% 29.885% 18.045%

9/14/2009 5.10% 5.36% 35.288% 23.806%

11/14/2009 5.04% 5.30% 38.095% 26.240%

1/14/2010 4.84% 5.09% 47.934% 35.746%

3/15/2010 4.82% 5.07% 48.963% 36.544%

7/14/2010 5.47% 5.73% 19.378% 9.410%

9/14/2010 5.31% 5.55% 25.989% 16.236%

11/14/2010 5.04% 5.30% 38.095% 26.606%

Average 5.47% 5.76% 20.22% 8.99%

Implications for Indexed UL Illustrated Rates

Profit model sensitivity raises the larger question about long-term assumed profitability of options trading.

Typically, this question isn’t relevant to options buyers for two reasons. First, options buyers who are hedging only

care about offloading the risk at a reasonable cost. Second, options buyers who are speculating are taking a short

to medium-term position on market movements and only care about being in-the-money during the duration of

the option. Long-term estimates of options profitability are relevant to the life insurance market for the simple

reason that life insurance contracts are shown to clients with assumed rates of return that stretch up to 120 years

into the future. Current industry practice is to illustrate Indexed UL at rates between 200 and 550bps above

comparable Current Assumption UL crediting rates. Carriers support illustrated spreads between Indexed UL and

Current Assumption UL with spurious “hypothetical historical” analysis. However, given that options are the only

differentiator between IUL and CAUL assets, we believe that long-term beliefs about options profitability verses

general account assets is more indicative of real future performance spreads between the two lines.

The math is straightforward. The net premium is discounted by the general account rate (assumed, in this

example, to be 6%) to obtain the options budget. The remainder of the net premium is placed in the general

account and will equal the full net premium at the end of the period. The options return will depend on the

performance of the external equity index. For the policy to yield 8% in a 6% general account rate environment,

the options would have to return 41.33% over the year. An illustration at 8% shown in a 6% environment implies a

constant options profit of 41.33% for the duration of the illustration. An 8% illustration in a 5% general account

rate environment implies a 68% annual rate of return. Options yield in any given year may be high, but over the

long term that options purchases will be profit-neutral to the buyer. The importance in this situation, given the

long-term nature of the illustration, is the long-term options profit model. The possibility of earning a high yield in

any given year is largely irrelevant to long term nature of the profit projection shown in the illustration. Note that

the importance of long-term yields is a function of the long-term illustration used in the sales process.

As a rule of thumb, Current Assumption UL and Indexed UL should be illustrated at the same long-term rate after

adjusting for differentials in policy charges if one is comfortable with the assumption that options purchases will

not be profitable to the buyer in the aggregate. If options have a 10-20% expected average return, Indexed UL

should be illustrated at 25-50 basis points over Current Assumption UL. Conversely, if Indexed UL is shown at a

rate far in excess of Current Assumption UL, the reasoning should be that historical CAUL yields are substantially

higher than current CAUL yields and Indexed UL will hold some predetermined spread over historical CAUL yields.

Recommendation for Indexed UL Illustrated Rates

The essential point is that long-term options profit models are largely irrelevant to all market participants except

for life insurance companies yet not a single life insurance carrier has laid out a mathematical model to support

the assumed annual options yields in excess of 40% commonly shown in Indexed UL illustrations. Hypothetical

historical analysis falls woefully short for more than the obvious reasons that interest rate environments clearly

affect options prices and that assuming a constant cap since the beginning of time ignores the natural bias that

makes options prices increase at precisely the moment they are expected to be most profitable. The more

problematic assumption is that equity returns will not only match historical aggregate returns but also that the

shape of returns will be identical. Options prices are the best immediate guess at any given year’s return

regardless of historical long-term performance. Until life insurance companies can come up with a reliable,

mathematical model for consistently beating options writers at their own game, Indexed UL should be illustrated

at the same rate as Current Assumption UL after adjusting for the caveats addressed in the Technical Appendix.

Technical Appendix

Policy Charges – Current Assumption UL & Indexed UL

Direct comparisons between Current Assumption UL and Indexed UL are complicated by the fact that the charge

structures for the two product lines can be wildly different in shape and size. Policy charges play a role in

determining the assumed asset yield for policy crediting rates and, by extension, options budgets. Contracts with

high policy charges may allow a carrier to pass more investment earnings to policyholders and vice versa. On

average, Indexed UL contracts are substantially more expensive in every metric than Current Assumption UL

policies.

Table A1 summarizes the graphical data using cumulative charges and, more relevantly, Internal Rate of Return as

a calculation for the time value of money. IRR is a net present value calculation that solves for the rate of return

needed to get the net present value to zero.

CAUL IUL Differential

Cumulative Charges 1,449,446 2,212,455 763,008

Year 10 IRR 54.11% 46.91% -7.20%

Year 20 IRR 18.60% 15.88% -2.72%

A90 IRR 4.42% 1.76% -2.65%

A100 IRR -4.01% -10.13% -6.12%

Cumulative charges measure the total charges over the life of the contract without giving any indication to when

those charges occur. Obviously, the client would prefer to have more expensive charges at the end of the contract

for two reasons. First, the client may not be alive at the point. Second, lower policy charges in the early years

mean maximum opportunity to accumulate cash value at interest, thereby shrinking NAR and decreasing the

impact of high per $1,000 NAR charges in the later years. IRR captures the shape of the curve. High early IRR

figures indicate low charges and vice versa. Policies with high early IRR figures and low later IRR figures are best

for overfunding, narrow death benefit designs. Policies with lower early IRR and high late IRR are generally best

for level pay scenarios. There are exceptions to these rules of thumb, but the basic point for this paper is that high

IRR figures are better than low.

The data in Table A1 points to a structural difference between Indexed UL and CAUL that may account for

illustrated rate discrepancies. If Indexed UL products are more expensive than CAUL, illustrated rates may be

higher for Indexed UL simply by virtue of amplified policy charges. If this is the case, then using CAUL as a proxy

for Indexed UL returns misses part of the illustrated performance story. A CAUL with relatively inexpensive

charges should be run at a lower rate than an Indexed UL with higher policy charges. A fully educated consumer

would request that the IUL be run at the rate implied by the options purchases instead of the CAUL rate to

account for discrepancies in charge structures. Note that the actual cash-on-cash yield differential may be

negligible depending on the funding pattern and annual charge differences. The difference in crediting rates

simply impacts the illustration parameters, not the actual policy performance.

Even so, carriers have been less than forthcoming about why policy charges for different lines are so different.

Aviva has stated that its expected earned spread on assets is identical for its CAUL product, LifeStage UL, and its

Indexed UL lines, Accumulation Builder and Lifetime Builder. However, the policy charges for its IUL products are

substantially more expensive than LifeStage UL.

Figure A1 shows annual policy charges for the two Aviva Indexed UL products and the UL product.

AXA and Hartford products show the same phenomenon, as do several other carriers with Indexed UL and CAUL

products. One can speculate as to forthright reasons, such as expected funding patterns, and also reasons that

may be less honorable, such as the fact that higher illustrated rates effectively cloak higher policy charges.

Nonetheless, producers should be aware that using CAUL rates as a proxy for Indexed UL rates presents some

nuanced pitfalls due to policy charge differentials. We can reasonably expect the differences between CAUL and

IUL rates simply based on policy charges to be between 25 and 75bps.

Policy Charges – Indexed UL vs. Indexed UL

The phenomenon of discrepancies between charge structures in CAUL and IUL products and the implications for

crediting rates also exists within the Indexed UL universe. Some IUL products have exceptionally expensive

charges and, not surprisingly, high charge products also typically have the highest participation rates and/or caps.

Table A2 shows a representative sample of major IUL carriers sorted in descending order of highest participation

limits to lowest. Average rank calculated as average IRR rank.

Carrier Cap/Floor Year 10

IRR Rank

Year 20 IRR

Rank Age 90

IRR Rank

Age 100 IRR

Rank Av.

Rank

Minnesota Life 15.00% / 0% 41.97% 5 13.75% 6 0.81% 5 -9.74% 4 6

PennMutual 13.00% / 2% 46.70% 4 15.25% 4 0.20% 6 -14.68% 6 5

Pacific Life 13.00% / 0% 50.88% 2 17.31% 2 3.77% 1 -2.97% 1 2

Aviva 12.25% / 0% 41.14% 6 13.78% 5 2.02% 4 -7.96% 3 4

AXA 12.00% / 0% 49.79% 3 16.15% 3 2.72% 3 -7.79% 2 3

Lincoln Benefit 10.50% / 0% 61.37% 1 20.31% 1 2.74% 2 -11.34% 5 1

While this is not an exhaustive sample, there is evidence that the relationship between participation limits and

policy charges appears to exist. Policies with high charges have high participation limits. As such, producers should

be wary of illustrating all Indexed UL products at identical rates because some products are structurally designed

-

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

200,000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

Aviva LifeStage UL Lifetime Builder III Advantage Builder III

to provide a higher rate of return due to higher policy charges. Note again that the cash-on-cash yield inside the

products may be identical despite differences in crediting rates due to the difference in charge structures.

My experience with Indexed UL pricing tells me that carriers will, on the whole, readily accept the proposition of a

higher options budget if they know it is possible to increase policy charges to cover the cost. Market caps have

been trending upwards while, as this paper has shown, options prices have remained relatively steady. The

increase in the value proposition for clients is questionable. High cap products are more appealing to more bullish

investors, low cap products appeal to more conservative investors who will perform better over the long term if

Indexed UL returns more closely mirror Current Assumption UL than the broader equity market.

Artificial Options Budget Return Leverage

Another important note is that policy charges allow immediate subsidization of crediting rates that far exceeds

the costs of options to support the hedging strategy. The core concept is that there is a material difference

between the marginal performance increase, in real dollars over time, between 5% and 6% and 7% and 8%.

Carriers using higher policy charges can afford larger options budgets that increase illustrated rates by at least as

much as the increase in the options budget. For example, if carrier A is purchasing options at 5% and illustrating

7%, carrier B could show many more dollars on its illustration by purchasing options at 6% and illustrating 8%

despite building higher policy charges that wholly offset the increase in options budget. This artificial leverage is

calculated as the difference between the dollars growing at 5% and 6% and 7% and 8% [(6%-5%) - (8%-7%)]. On a

$100,000 single premium, the artificial leverage created by this strategy over 25 years is $51,553 on $684,848

(7.5%) of cash value. Over 50 years, a common illustration length for younger Indexed UL buyers, the artificial

leverage increases to $1,049,183 on $4,690,161 (22.4%) of cash value. In short, subsidizing options budgets with

higher policy charges creates artificial value that is a function of the faulty illustrated rate calculation methods

employed today rather than real return potential. Compounding the problem is that fact that the higher policy

charges used to subsidize the options budget are cloaked excessively by higher crediting rates, serving to further

obfuscate the relationship between higher policy charges and higher participation limits. A fully informed agent

would illustrate products using the options budget to eliminate the artificial return bias of higher hypothetical,

historical look-back rates. This method would allow for meaningful comparison between products.

Caveats to Assumed Universal General Account Yields

The assumption in this paper is that the general account yield is known and universal across all product lines

within a carrier. However, in practice, many carriers will segregate general account assets to support different

types of product lines. For example, the general account assets backing a carrier’s CAUL product may be

fundamentally different than the assets backing its Indexed UL. Furthermore, the mixture of assets can change

over time as the block of business matures and grows or shrinks in the process. Profitability in Indexed UL and

CAUL products is determined not just by the cost of the liability of options budget or crediting rate, respectively,

but by how well that liability matches the supporting assets. One cannot assume that falling options costs for

Indexed UL products enhances profitability in the product line because the carrier does not specifically state the

performance of the particular general account assets backing the Indexed UL product.

Mitigating Factors to Opportunity Cost of Options Purchases

This paper makes an assumption that options premium is paid in advance and from premium dollars received to

most closely approximate the hedging strategy to what would be required on the open market. However, carriers

can avoid opportunity cost of capital for options purchases in at least two ways. First, carriers with outstanding

collateral balances with the same counterparties can simply use released collateral (opportunity cost of zero) to

purchase options for Indexed UL exposure. Variable Annuities often require large amounts of collateral often

posted at the same counterparties from which the carrier is purchasing call spread packages to support Indexed

UL products. As markets improve and collateral decreases, carriers can reposition newly released capital to

purchase options, effectively moving money with zero opportunity cost (posted collateral) to another instrument

with zero opportunity cost (options). The effect is to at least mute the opportunity cost argument, although

collateral fluctuates with market conditions and could be called back to the counterparty at any time. The second

way to reduce opportunity costs of options purchases is for carriers with significant clout to push counterparties

to accept options premium in arrears. This amounts to an effective discount on the options cost by the

opportunity cost of capital. Pacific Life has confirmed that it purchases options in arrears. One could also suspect

that other large options purchasers such as Aviva, Allianz and AXA have negotiated payment in arrears.