Estimating Credit Risk and
Illiquidity Risk in Guaranteed
Investment Products
James X. Xiong, Ph.D., CFA®
Senior Research Consultant
Morningstar Investment Management
Thomas Idzorek, CFA®
Global Chief Investment Officer,
Morningstar Investment Management
October 10, 2011
Executive Summary
Guaranteed investment products, including stable value funds, Guaranteed Investment
Contracts (GICs), Synthetic GICs, Bank Investment Contract (BICs), Deferred Fixed Annuities,
etc., are offered in many defined contribution plans in the United States. These guaranteed
products can vary from product to product, but they all share some common characteristics:
× It is well known that asset returns often exhibit fat tails, negative skewness, time
× The volatility of the returns are lower than the volatility of cash (except in extreme
circumstances)
× There is a guaranteed minimum return (floor), e.g. 2%
× Liquidity constraints can exist from one year to 10 years
× Credit risk of the issuer(s) can not be ignored
Despite the popularity of guaranteed investment products, the literature offers little guidance in
the evaluation, risk estimation, and ultimately, the role in a diversified asset allocation portfolio.
This paper explores ways to estimate credit risk and illiquidity risk for guaranteed products, so
that their “true” risks are reflected in the inputs to asset allocation-oriented optimizations.
Ignoring or inaccurately estimating illiquidity risk and credit risk can lead to an unjustified
preference for guaranteed products.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
2
Estimating Credit Risk and Illiquidity Risk in Guaranteed
Investment Products
Guaranteed products include stable value funds, Guaranteed Investment Contracts (GICs),
Synthetic GICs, Bank Investment Contract (BICs), etc. They are offered in many defined
contribution plans in the United States. Many of these products seem to have low risk because
the returns are set based on certain rules, rather than marked to market. In order to evaluate
such products, compare them to one another, and to determine an allocation to a guaranteed
investment products, it is important to estimate the true risk of these products.
Despite the popularity of guaranteed products, the literature offers surprisingly little guidance in
the evaluation, risk estimation, and ultimately, the role in a diversified asset allocation portfolio.
An important and recent exception to this void is Babbel and Herce (2011). This paper
examines the performance of stable value funds since their inception in 1973. It analyzes the
performance of stable value funds using mean-variance analysis, Sharpe and Sortino ratio
analysis, stochastic dominance analysis, and optimal multi-period portfolio composition
analysis. All of these historical analyses suggest that stable value funds dominate short-term
government/credit bond funds and cash, and that stable value funds often occupy a significant
position in optimal portfolios across a broad range of risk-aversion levels. In this case, the
domination of stable value funds comes from a similar return but with a significantly lower
standard deviation.
While we believe it is clear to most people that comparing the volatility of a marked to market
asset to that of a rules-based product that is not market to market is an apples to oranges
comparison, there are some that continue to argue that the volatility of the guaranteed product
that is experienced by the investors should be used for asset allocation and / or portfolio
construction. We believe such a view fails to consider the true risk of the products to
investors, and makes meaningful comparisons between two rules-based products challenging.
For traditional GICs, credit risks are extremely relevant, especially in the case of a single issuer.
Traditional GICs are typically backed by the financial health of the insurance company issuing
the contract, not by the federal government. Therefore a GIC is only as good as the insurance
company that issues the contract. While there have been very few meltdowns of insurance
companies, the infamous failures of Executive Life and Mutual Benefit Life in 1991 forced
pension fund managers and 401(k) plan investors to re-think GICs and to re-evaluate the credit
risk associated with them.
In addition to credit risk, another type of risk associated with guaranteed products is illiquidity
risk. Some guaranteed products, but not all, have restrictions or penalties on withdrawals,
which limits immediate access to the investor’s money and limits the investor’s ability to
rebalance their overall portfolio toward their target strategic or tactical asset allocation. As a
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
3
result of this inability to rebalance (illiquidity), the effective asset allocation may be significantly
different from the target, and thus, the risk characteristics will be different from those of the
target. In other words, the inability to rebalance introduces uncertainty around the actual asset
allocation an investor might have at a given point in time; hence, there will be uncertainty in the
risk characteristics of the portfolio.
Leland (2000) shows that the “cost” of the undesired overall risk exposure due to the inability
to rebalance can be estimated as the present value of expected loss in utility. Systematically
rebalancing a portfolio toward a target is a type of investment strategy in which one
systematically sells assets that have appreciated in price and buys assets that have
depreciated in price. More specifically, it is a contrarian investment strategy that is expected to
earn a small liquidity premium because one is systematically supplying liquidity to the market.
Empirical studies, such as Buetow et al. (2002), show that disciplined rebalancing can enhance
returns and control risk.
Willenbrock (2011) demonstrates that the underlying source of the diversification return is the
rebalancing. If each individual asset in a portfolio has a geometric average return of zero, the
non-rebalanced or buy-and-hold portfolio will have a geometric mean return of zero. In contrast,
the geometric return of the rebalanced portfolio will earn a positive return. That positive
incremental return is the diversification return. On the other hand, Willenbrock (2011) argues
that the buy-and-hold portfolio can benefit from the fact that winning keeps winning. In other
words, buy-and-hold generally performs better in a trending market, while rebalancing performs
better in an oscillating market. More importantly, a rebalanced portfolio maintains a constant
risk profile, while a buy-and-hold portfolio can suffer from a varying risk profile. In this paper, we
treat the varying risk profile as a proxy for illiquidity risk.
A complete analysis of a guaranteed product must go beyond the artificially smoothed historical
returns, incorporating credit risk and illiquidity risk into the analysis. In an optimization setting,
the failure to incorporate these two additional risks will undoubtedly lead to an incomplete
analysis, and most likely, allocations to the guaranteed product that are too large relative to
their complete risk and return characteristics. This paper explores ways to estimate credit risk
and illiquidity risk for guaranteed products, so that their “true” risks are reflected in the inputs to
the optimizations.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
4
Overview of Guaranteed Products
Guaranteed products are prevalent in 401(k) retirement plans. Unfortunately, the guaranteed
product world is one in which the term “stable value fund” often serves as a catch all term for a
wide variety of guaranteed products, most of which are not mutual funds at all. Here we give a
brief introduction to the most common types of guaranteed products.
Stable Value Funds—Stable Value Funds typically offer smoothed returns that are at a level
similar to those of the BarCap U.S. Aggregate Bond Index. The funds invest primarily in
guaranteed investment contracts or GICs. Some stable value funds invest in collective trusts or
mutual funds, where the collective trusts or mutual funds are intern investing in GICs. In either
case, the primary underlying investment is a portfolio of GICs. In the Stable Value Fund
structure, counterparty risk is usually spread out over multiple GIC issuers.
Guaranteed Investment Contracts (GICs)—GICs are primarily offered by banks and insurance
companies. They are contracts, in which the issuer agrees to pay a predetermined interest rate
and principle. The interest payments and, more importantly, principal are subject to
counterparty risk. In theory, this is a spread product in which the issuer invests more
aggressively to earn a spread over time. The return of this type of traditional GIC should be
higher than a synthetic GIC (discussed below) due to the counterparty risk associated with the
principal. For details, see Kleiman and Sahu (1992).
Synthetic GICs—In this case, the investor retains ownership and control of the underlying
investment (usually high-quality bonds) and purchases a “wrapper” from an insurance
company. Most commonly, the wrapper guarantees that the principal will not go down and the
minimum return (floor) is above 0%.
Bank Investment Contracts (BICs)—BICs are similar to a GICs, but the underlying assets are
held in trust protecting them from other potential obligations of the issuer. In contrast, the
assets invested in a GIC are often part of a general account and thus could be impaired by the
well being of the general account. A BIC may or may not be covered by FDIC insurance.
Deferred Fixed Annuity—A deferred fixed annuity is an insurance contract, typically between an
individual investor and the insurance company. The invested money is placed in the insurance
company’s general account and invested as the insurance company sees fit, and is thus subject
to counterparty risk (ignoring any government guarantees). Each contribution into the deferred
fixed annuity will be credited with the current interest rate as declared by the issuer. The initial
interest rate is declared in advance and guaranteed for some length of time (e.g. one, three, or
five years). Following the expiration of the guaranteed period, most deferred fixed annuity
contracts will continue to be credited with a slightly lower than market interest rate, with
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
5
periodic adjustments. As with all deferred annuities, the holder has the right to annuitize the
contract value.
These guaranteed products can vary from product to product, but they all share some common
characteristics:
× The expected returns are set by rules, not marked to market
× The volatility of the returns are lower than the volatility of cash (except in extreme
circumstances)
× There is a guaranteed minimum return (floor), e.g. 2%
× Liquidity constraints can exist from one year to 10 years
× Credit risk of the issuer(s) can not be ignored
In this paper, to help generalize our analysis to a wide variety of guaranteed products we work
with a hypothetical guaranteed product (HGP). Our methodology can be applied to a broad
range of guaranteed products with varying levels of credit risk and liquidity constraints. For our
purposes, HGP is a guaranteed product that promises to preserve the principal value, to pay a
minimum guaranteed interest rate (with the opportunity for additional amounts), and to let
participants choose lifetime income payments when they retire.
Historical Analyses
We start by identifying the arithmetic mean return, standard deviation of realized returns, and
the minimum and maximum return for historical crediting rates of HGP in Exhibit 1. For
comparison purposes, we provide the equivalent summary statistics for the same time period
for the BarCap U.S. Government / Credit 1-3 Yr Bond Index, BarCap U.S. Aggregate Bond Index,
and the Citigroup Treasury Bill 3 Month Index. From Exhibit 1, we can see that the historical
mean return for HGP is comparable to the BarCap U.S. Government / Credit 1-3 Yr Bond Index
and it outperforms a typical short-term bond fund (with an expense of about 80 bps) by 57 bps;
however, the standard deviations for all of the vintages are about 2-3 percentage points lower
than the standard deviation of the BarCap U.S. Government / Credit 1-3 Yr Bond Index. As a
result, the Sharpe ratio of HGP is much higher than the short-term bond index based on
empirical data.
Exhibit 1. Empirical Analyses on HGP (Annualized Statistics)
HGP (1979.1-2010.12)
BarCap US Govt/Credit 1-3 Yr (1979.1-2010.12)
BarCap US Aggr Bonds (1979.1-2010.12)
Citi Treasury Bill 3 Mon(1979.1-2010.12)
Ari. Mean
7.17%
7.40%
8.71%
5.69%
Std. Dev.
2.06%
4.53%
7.04%
3.54%
Min
3.75%
0.55%
-2.92%
0.13%
Max
12.00%
21.65%
32.62%
15.05%
As an experiment, we performed a traditional mean-variance optimization based on historical
inputs that included HGP, Citigroup Treasury Bill 3 Month Index, BarCap U.S. Government /
Credit 1-3 Yr Bond Index, BarCap U.S. Aggr Bond Index, and equities. As one would expect
given its superior Sharpe ratio, HGP dominated the safe or fixed income allocations of the
efficient frontier. Again, as we pointed out earlier, the artificially low standard deviations of the
historically credited returns belies the true risk of HGP. To perform a meaningful mean-variance
analysis, we need to adjust the standard deviation number to account for both credit risk and
illiquidity risk.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
6
Forward-Looking Analyses
Historical mean returns provide limited use because they are not likely to be repeated in the
future. Instead, we use forward-looking capital market assumptions to perform our analyses.
Exhibit 2 shows the assumed composition of our HGP portfolio. Experience tells us that this is
not that different from how an actual deferred fixed annuity might invest with in an insurance
company’s general account and that historically this mini-portfolio of sorts has produced a
superior return at a slightly lower risk level than a portfolio consisting of 100% BarCap U.S.
Aggregate Bond Index.
Exhibit 2. Composition of the HGP Portfolio
General Fixed Income
Domestic Equities
Institutional Real Estate
Cash
Total
BarCap U.S. Aggregate Bond TR
S&P 500 TR
NAREIT-Equity TR
CG U.S. Domestic 3 Mo Tbill
89.2%
4.4%
4.0%
2.4%
100%
Panels A, B, and C of Exhibit 3 show an example of Ibbotson forward-looking capital market
assumptions for five assets: large cap, mid-small cap, international equity, bonds, and HGP. The
mean and standard deviation of HGP are inferred based on the underlying asset allocation of
HGP from Exhibit 2 and coupling those weights with the appropriate forward-looking capital
market assumptions. Our analyses are performed at the asset-class level, not at the fund or
product level. The expenses and management fees must be considered at the fund level. The
top part of Panel A shows the unconditional mean and standard deviation while the bottom part
of Panel A shows the modified mean and standard deviation after adjusting for the 2.0%
guaranteed minimum return floor.1 As a result of applying the floor, the standard deviation of
HGP is significantly reduced from 6.58% to 3.35%. Panels B and C of Exhibit 3 show the
correlation matrix before and after the floor was properly applied to the HGP.
1
More specifically, a Monte Carlo simulation, in which the underlying asset classes of HGP were assumed to follow
a multivariate Truncated Lévy Flight distribution (Xiong, 2010), was used to generate a return series with the
appropriate starting summary statistics, and then returns below 2.0% were automatically set to 2.0%. The returns
are also capped so that the expected return remains 4.85%. Finally, the modified summary statistics were
calculated.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
7
Exhibit 3 – Panel A. Ibbotson Forward-Looking Capital Market Assumptions
Before Floor
Mean
Std. Dev.
Skewness
Kurtosis
LC
10.06%
20.26%
0.36
5.98
MSC
13.08%
26.48%
0.50
5.79
International
11.03%
24.79%
0.41
3.95
Bonds
4.44%
6.57%
0.78
6.54
HGP
4.85%
6.58%
0.72
6.24
Mean
Std. Dev.
Skewness
Kurtosis
10.06%
20.26%
0.36
5.98
13.08%
26.48%
0.50
5.79
11.03%
24.79%
0.41
3.95
4.44%
6.57%
0.78
6.54
4.85%
3.35%
0.52
2.00
After Floor
Exhibit 3 – Panel B. Correlation Matrix Before the Floor is Applied
LC
MSC
International
Bonds
HGP
LC
1
0.9001
0.5991
0.2923
0.4786
MSC
0.9001
1
0.571
0.2767
0.4624
International
0.5991
0.571
1
0.2237
0.3438
Bonds
0.2923
0.2767
0.2237
1
0.9722
HGP
0.4786
0.4624
0.3438
0.9722
1
Bonds
0.2923
0.2767
0.2237
1
0.852
HGP
0.4318
0.4204
0.3126
0.852
1
Exhibit 3 – Panel C. Correlation Matrix After the Floor is Applied
LC
MSC
International
Bonds
HGP
LC
1
0.9001
0.5991
0.2923
0.4318
MSC
0.9001
1
0.571
0.2767
0.4204
International
0.5991
0.571
1
0.2237
0.3126
As shown in Panels B and C of Exhibit 3, the correlation between HGP and bonds are 12
percentage points lower after the floor is applied, while the correlations between HGP and
equity asset classes are about 3-to-4 percentage points lower after the floor is applied. While
the proper application of the floor is a necessary first step at eventually arriving at appropriate
capital market assumptions for HGP, we have yet to account for credit and illiquidity risk.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
8
Estimating Credit Risk
Examining a debtor’s ability to repay its financial obligations is a crucial endeavor for lenders
and investors. Answering the question, “How likely is it that my loan will be repaid on time,” is
critical to the valuation and asset allocation of debt portfolios.
For more than a century, the big three bond-rating agencies—Moody's, Standard & Poor's, and
Fitch—have been the unchallenged arbiters of corporate creditworthiness. Rating references
are embedded in hundreds of guidelines, laws, and private contracts that affect a broad range
of financial concerns. The financial crisis in 2008, however, revealed a weakness in the creditrating agencies' models: their ratings are backward-looking because they are predicated on
historical data that is observed at a discrete point in time. Given this constraint, the agencies
have not been able to react quickly to rapid changes in a creditor's financial health. Hence,
evidence of accounting fraud in a company's financial statements may elude their scrutiny.
Also, the agencies have demonstrated that they remain ill-equipped to assess the risks of some
complex, structured products.
There are a number of ways to estimate the credit risk of a guaranteed investment product. In
this paper, we choose to use Morningstar’s Distance to Default (DTD) to model the issuer’s
credit risk (see Appendix for more details). Our goal is to adjust the guaranteed product’s risk
for the credit risk by using the DTD measure.
Next, we need to know more about the guaranteed product. In particular, we need to estimate
the expected loss to investors should the issuer default. The default loss is unlikely to be 100%
because holders of guaranteed investment products usually come before the equity holders. If
no data is available, we assume that the default loss is 30% for the guaranteed investment
product.2 This loss will be used to adjust the guaranteed product’s risk for the credit risk.
Returning to our simplified example given in the appendix where the DTD for the issuer is 2.5,
let’s assume an investor had purchased a guaranteed product with a value of $10. Coupling this
with the expected loss in a default of 30% along with the probability of a default of 0.62%, the
expected loss for the investor is about 2 cents.
Now the question becomes how to find a risk level for the guaranteed product so that it has a
0.62% chance to lose 30%. This can be solved as long as a distribution is assumed and the
other three moments are known. To do this, we treat the guaranteed product as a type of fixed
2
According to the GAO-11-400 June 7, 2011 report on page 38 and footnote 67, entitled “Retirement Income:
Ensuring Income throughout Retirement Requires Difficult Choices,” Executive Life Insurance Company had high
ratings from certain rating agencies—A.M. Best, Moody’s, and Standard & Poor’s—prior to its insolvency. They
reported that 44,000 retirees with Executive Life had received only 70
percent of their promised monthly annuity payments for almost 13 months after California regulators seized control of
the company.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
9
income investment. The distribution of the fixed income is assumed to follow a truncated Lévy
flight model (Xiong, 2010). We run Monte Carlo simulations to establish the relationship
between the probability of 30% loss and the risk (second moment) by fixing the mean,
skewness, and kurtosis. This relationship is used to infer the risk associated with the credit risk
of the issuer. The mapping table for a 30% default loss and a typical distribution for the fixed
income asset class is shown in Exhibit 4.
Exhibit 4. Mapping Table between the Distance to Default and Risk Level of Guaranteed
Product
Distance to Default
5.20
4.25
3.25
2.93
2.78
2.63
2.50
2.20
Probability to Default
0.00001%
0.001%
0.06%
0.16%
0.27%
0.42%
0.62%
1.33%
Risk Level
4.66%
5.66%
6.66%
7.66%
8.66%
9.66%
11.66%
13.66%
From Exhibit 4, we see that in our example the DTD of 3.25 corresponds to a risk level of
6.66%. When the DTD is less than 2.5, the probability of default (0.62%) should not be ignored.
If the DTD is greater than 6, the default is remote. Since the DTD is calculated every month, we
can dynamically adjust for the credit risk.
As we mentioned earlier, the default loss is an important parameter to estimate. If the default
loss is less (more) than 30%, the risk level in Exhibit 4 will be correspondingly lower (higher).
A lower (higher) default loss indicates that a lower (higher) adjustment for the credit risk is
needed.
If the DTD value is not available, we can use the average of the credit ratings from the three
agencies (Moody's, Standard & Poor's, and Fitch) for the issuer in question, and use the credit
migration matrix from Schuermann (2007) to estimate the probability to default
(See Exhibit 5).
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
10
Exhibit 5. One-year Credit Migration Matrix Using S&P Rating Histories (1981-2003).*
T
AAA
AA
A
BBB
BB
B
CCC
D
AAA
92.29
0.64
0.05
0.03
0.03
0
0.1
0
AA
6.96
90.75
2.09
0.2
0.08
0.08
0
0
T+1
A
0.54
7.81
91.38
4.23
0.39
0.26
0.29
0
BBB
0.14
0.61
5.77
89.33
5.68
0.36
0.57
0
BB
0.06
0.07
0.45
4.74
83.1
5.44
1.52
0
B
0
0.09
0.17
0.86
8.12
82.33
10.84
0
CCC
0
0.02
0.03
0.23
1.14
4.87
52.66
0
D
0
0.01
0.051
0.376
1.464
6.663
34.03
100
* Source: Schuermann, 2007. Estimation method is cohort. All values in percentage points. The final column, the migration to default, deserves special attention.
Exhibit 5 shows that a current credit rating of AAA has a 92.29% chance to stay in AAA and a
0% probability of default in next period. However, this should be viewed cautiously. For
example, AIG had a credit rating of AAA until Sep 19, 2008. Had it not been for the U.S.
government bailout, AIG would have been forced to file for bankruptcy protection. In practice,
we assign a small but non-zero probability (0.00001%) of default to AAA.
After estimating the probability of default for each of the various credit ratings for our base case
expected loss during a default of 30%, we rerun our Monte Carlo simulations to find the
estimated risk level of the guaranteed products. These risk levels are summarized in Exhibit 6.
For example, a guaranteed product with single-carrier credit risk from a AA-rated private insurer
has a 0.01% probability to default, which corresponds to a risk level of 6%. We believe a strong
argument can be made that these implied risk levels based on creditor risk are significantly
better estimates of true risk in a forward-looking context. In almost all cases the estimated risk
levels are significantly higher than the realized standard deviation of the past.
Exhibit 6. Implied Risk Level of the Guaranteed Products
Credit Rating
AAA
AA
A
BBB
BB
B
Probability to Default
0.00001%
0.01%
0.051%
0.376%
1.464%
6.663%
Risk Level
4.66%
6.00%
6.50%
9.25%
14.0%
20.0%
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
11
Estimating the Illiquidity Risk
Next, we turn to illiquidity risk. While clearly illiquidity risk involves the haircut one must receive
for demanding immediate liquidity (should liquidity even be available), our estimate of illiquidity
risk focuses on the change in overall portfolio risk characteristics that results from the inability
to rebalance the portfolio across time. In the presence of rebalancing restrictions—the type of
restrictions embedded in many guaranteed income products—assets with relatively poor past
returns will see their weights fall, while the ones with relatively high returns will increase in
weight. The implication is that both portfolio composition and portfolio total risk will change
across time and will not necessary equal those of the desired target asset allocation.
To illustrate, consider the impact of the 2008 financial crisis. During the crisis, fixed income
asset classes dramatically outperformed equity asset classes. If one is unable to rebalance, the
realized or effective asset allocation drifted away from the target, overweighting fixed income
asset classes and underweighting equity asset classes. As a result, the total risk level of the
portfolio will be much lower than the target risk at the end of the crisis.
Withdrawals make the problem even worse because the withdrawals must come from liquid
assets, thus the portfolio will deviate from the target asset allocation further. Lu and Mitchell
(2010) examines the withdrawal behavior in 401(k) plans. They find that most withdrawals are
less than 20% of the maximum allowable withdrawal. Additionally, they find that participants
are most likely to take loans between ages 35 to 45.
Illiquidity risk is widely noted in the literature; however, the literature offers little guidance on
how to estimate it. We discussed earlier that the illiquidity risk is associated with the risk
uncertainty resulting from the inability to fully rebalance. We can estimate the illiquidity risk by
computing and comparing the differences in the risk profiles of two portfolios at the end of the
liquidity-constrained period: one with full rebalancing allowed and another partially allowed. As
we mentioned earlier, disciplined rebalancing allows one to maintain a target risk profile.
To estimate the impact of liquidity constraints in altering the risk profile we use Monte Carlo
simulation. For a given starting asset allocation, we assume that withdrawals can not be made
during the first seven years of an investment in HGP. To establish a reasonable starting asset
allocation we create a mean-variance efficient frontier using the assumptions in Exhibit 3 (the
top section of Panel A).3 Recall that the standard deviation of HGP in top part of Panel A does
3
Optimization constraints are 1) no shorting is allowed; and 2) maximum allocation to each asset class is 50%.
Because the returns of the assets are not normally distributed, one may also want to consider a higher moment
optimizer, such as the mean-conditional value-at-risk optimization that incorporates fat-tailed and skewed returns
presented in Xiong and Idzorek (2011).
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
12
not reflect the floor. Six of the optimal asset allocation mixes from a resampled optimization
are shown in Exhibit 7.
Exhibit 7. Asset Allocation Mixes – Ignoring HGP Floor
Mix (Exp. Ret.)
Large Cap Stocks
Mid/Small Cap Stocks
International Stocks
Bonds
HGP
1(5%)
2.31%
1.31%
2.93%
47.00%
46.44%
2(6%)
5.16%
7.52%
6.73%
40.66%
39.93%
3(7%)
7.08%
14.99%
9.93%
37.08%
30.93%
4(8%)
8.69%
22.69%
13.08%
31.96%
23.58%
5(9%)
10.54%
30.24%
16.51%
26.11%
16.60%
6(10%)
13.71%
36.86%
20.47%
18.08%
10.89%
In these starting asset allocation mixes, the allocations to HGP are slightly lower than the
allocations to bonds due to its relatively higher correlation with equities. To demonstrate our
Monte Carlo simulation method for estimating illiquidity risk, we focus on Mix 5 with an
expected return of 9%. Of the mixes in Exhibit 7, the overall stock-bond split is closest to the
prototypical 60 / 40 mix.
Based on the starting asset allocation of Mix 5, we ran two Monte Carlo simulations—one with
no withdrawals and one with 10% withdrawals during the first four years of the simulation. The
simulated returns for HGP incorporate the floor shown in the bottom section of Panel A of
Exhibit 3. Each Monte Carlo simulation consisted of 5,000 trails, or paths, lasting seven years.
Furthermore, we assume that HGP is not rebalanced during the seven-year horizon due to
liquidity constraints, while the other four assets (the liquid assets) are annually rebalanced
based on their rescaled target asset allocations. Thus, based on the simulated returns, different
withdrawal scenarios, and rebalancing restrictions/rules the asset allocations evolved
accordingly.
The results of the two Monte Carlo simulations are shown in Exhibit 8, where Panel A contains
the results for the no-withdrawal scenario and Panel B contains the results for the scenario that
included 10% withdrawals during the first four years. Within each panel, the top row shows
the allocation to HGP at the end of the sever-year simulation for a variety of percentiles, where
the 5th percentile corresponds to good “market” performance and the 95th percentile
corresponds to bad “market” performance. The bottom row, labeled as “Risk Uncertainty,”
identifies the difference in total risk of the portfolio in question at the end of the simulation
relative to the total risk of the target asset allocation. Recalling that the target asset allocation
to HGP in Model 5 is 16.6%, we can see that in the good market environment of the 5th and 10th
percentiles the allocation is considerably less than the target, while for the bad market
environments of the 90th and 95th the allocation is considerably greater than the target.
Correspondingly, in good market environments the risk of the portfolio is higher than the risk of
the target, and in bad market environments the risk of the portfolio is lower than the risk of the
target.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
13
Exhibit 8. Risk Differential and Allocation Drift
Panel A. No Withdrawals
Percentile
HGP Allocation
Risk Uncertainty
5%
9.23%
-1.24%
10%
10.57%
-0.75%
50%
16.92%
0.77%
90%
27.33%
1.71%
95%
30.68%
1.91%
50%
26.36%
-0.61%
90%
43.68%
0.95%
95%
50.77%
1.28%
Panel B. 10% Withdrawal for the First Four Years
Percentile
HGP Allocation
Risk Uncertainty
5%
13.47%
-4.14%
10%
15.76%
-3.12%
In Panel B of Exhibit 8, the divergence from the target is less symmetrical than Panel A. With
the withdrawals, the main risk is that the allocation to HGP will be too high at the end of the
seven-year horizon, thus the portfolio’s total risk will be too low relative to the target. At the
10th percentile, the risk of the portfolio is 3.12 percentage points below that of the target. At
the 90th percentile, corresponding to a bad market environment, at the end of the seven years
the risk is 0.95 percentage points above the target. In general, a longer horizon or a larger
withdrawal will increase the illiquidity risk. Conversely, a shorter horizon or a smaller withdrawal
will decrease the illiquidity risk.
Based on this type of analysis, we can now adjust the starting standard deviation (with the
floor) of HGP to reflect illiquidity risk. The illiquidity-adjusted risk for HGP is the sum of the risk
uncertainty shown in Panel B of Exhibit 8 and the starting risk with the floor (3.35%). For
example, at the 10% level, the illiquidity-adjusted risk for HGP is 6.47% (=3.35%+3.12%). This
additional risk (3.12%) can be interpreted as the unwanted or uncontrolled risk taken over the
liquidity-constrained period. Admittedly, the illiquidity-adjusted risk calculated in this way might
be subjective, but it is intuitive in capturing the relationship between the illiquidity risk and
withdrawals, and between the illiquidity risk and the length of locked horizons.
Intuitively, the size of the initial starting HGP allocation impacts the potential risk uncertainty
caused by illiquidity—larger starting allocations to HGP require a larger illiquidity adjustment,
while smaller starting allocation to HGP require a smaller illiquidity adjustment. Exhibit 9 shows
the dependence of illiquidity-adjusted risk on the size of the starting HGP allocation. It plots the
total estimated risk of HGP (including the varying illiquidity-risk adjustment) as a function of the
size of the initial HGP allocation relative to the initial allocation to bonds. The vertical axis shows
the size of the starting HGP allocation relative to the starting bonds allocation. The horizontal
axis shows the illiquidity-adjusted risk as calculated in the last paragraph. When the lines are
above zero, the starting HGP allocation is greater than the starting bonds allocation. When the
starting allocation to HGP is higher, the illiquidity-adjusted risk for HGP is higher, and vice versa.
The pink, green, and blue lines correspond to three potential (and subjective) illiquidity
adjustments to HGP, the 5th percentile, the 10th percentile, and 15th percentile, respectively.
Whether to choose the 5th or 10th level depends on an investor’s risk tolerance. A lower
percentile corresponds to a lower risk tolerance.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
14
Allocation Difference (HGP less Bonds)
Exhibit 9. Size of Illiquidity-Adjusted Risk Relative to Starting HGP Allocation
8%
4%
0%
5%
6%
7%
8%
9%
-4%
-8%
-12%
Illiquidity Adjusted Risk for HGP
15% Level
10% Level
5% Level
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
15
Putting the pieces together
Thus far in this paper, we have developed two very different methods for estimating the risk of
HPG. In the first part, “Estimating Credit Risk,” we developed a method based on Morningstar’s
distance to default, or agencies’ credit ratings, to infer the credit risk of HGP. In the second
part of this paper, “Estimating Illiquidity Risk,” we used Monte Carlo simulation to quantify the
amount of illiquidity risk—the potential difference between the total risk of the target asset
allocation and that of the actual portfolio caused by liquidity constraints. In this section we
bring these two separate pieces together in a process designed to determine an appropriate
allocation to HGP.
The steps are as follows:
1. Estimate the mean and standard deviation of the guaranteed investment products based
on forward-looking capital market assumptions and the issuer’s general accounts
2. Generate return series through Monte Carlo simulations, where the floor of HGP is modeled
appropriately
3. Estimate the standard deviation of the guaranteed products
4. Based on reasonable starting allocations, estimate the illiquidity risk coupled with
withdrawals using Monte Carlo simulations
5. Compare the two separately estimated risk levels of HGP—the total risk after adjusting for
illiquidity and the total risk after adjusting for credit risk—and select the larger one as the
adjusted total risk for the guaranteed products
6. Re-generate return series based on adjusted total risk, and perform the mean-variance
optimization.
Note that step 4 involves a trial-and-error process because the illiquidity risk depends on the
initial starting allocation of HGP. In practice, we start with an approximate risk estimate for HGP
and then use optimization (with real-world allocation constraints) to find a starting allocation for
the process. Iteratively, the starting allocation to HGP as well as the illiquidity-adjusted risk of
HGP are then refined. The process is repeated until a reasonable convergence has taken place.
This converging process can be demonstrated by Exhibit 10. The pink line is equivalent to the
pink line in Exhibit 9;once again it shows the tradeoff between the size of illiquidity-adjusted risk
and the size of the starting HGP allocation (relative to bonds). The new blue line in Exhibit 10
shows the optimal HGP allocation (relative to bonds) given the level of total risk of HGP
(adjusted for illiquidity), i.e., the lower the total risk of HGP, the higher the optimal HGP
allocation (relative to bonds). When the illiquidity-adjusted risk for HGP is approximately 6.5%,
the optimal allocation for HGP is 7% higher than that for bonds.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
16
The intersection between the diamond line and the square line indicates the optimal HGP
allocation at the 10th percentile level. It gives the illiquidity-adjusted risk of 6.6% for this optimal
HGP allocation. In this case, the optimal HGP allocation and bond allocation are approximately
equally weighted, each at 20%. At a more conservative 5th percentile level, the HGP receives an
allocation that is about 10 percentage points lower than that of bonds.
Exhibit 10. The Tradeoff Between the HGP Allocation and the Illiquidity-Adjusted Risk for HGP
Allocation Difference (HGP less Bonds)
40%
30%
20%
10%
0%
5%
-10%
6%
7%
8%
9%
-20%
-30%
-40%
Illiquidity Adjusted Risk of HGP
Optimal HGP Allocation Given the Risk
Illiquidity Risk Given the HGP Allocation
For step 5, we compare the illiquidity-adjusted risk to the inferred risk based on the credit risk
and move forward with the greater of the two estimates. Thus, following the procedure
described in “Estimating Credit Risk,” we estimate the credit risk for HGP. For example,
assuming HGP comes from a private company with a credit rating of AAA, the estimated risk
level at this credit rating is 4.66%, much lower than the illiquidity-adjusted risk (6.6%).
Therefore, we err on the side of caution and move forward with the more conservative risk
estimate, in this example, the 6.6% based on the illiquidity-adjusted risk.
As analogy, by choosing the more cautious estimate of true risk, we are focusing on the
weakest link in the chain. If the credit rating of the issuer for HGP is significantly downgraded,
the risk level for HGP adjusted for credit risk can exceed the illiquidity-adjusted risk, and thus a
lower allocation to HGP is warranted.
The same procedure can be applied to other asset allocation models. After that, the resulting
adjusted total risk measure reflects the greater of the illiquidity-adjusted risk estimate or risk
inferred from the credit risk.
It can be seen that the optimal allocation to HGP is sensitive to a number of variables. Our
framework provides a starting point to quantitatively assess the true risk of HGP. In practice, it
should be combined with other quantitative or qualitative judgments to make the process more
robust.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
17
Conclusion
Many guaranteed investment products are backed by the financial health of the single
insurance company issuing the contract, not by the federal government. Therefore their credit
risk can not be ignored. Another characteristic associated with some guaranteed products is
liquidity constraints, i.e. illiquidity risk. The illiquidity risk results not only from the haircut one
must receive for demanding immediate liquidity, but in our context the inability to rebalance the
portfolio across time, which leads to realized asset allocations that are different from those of
the target. Withdrawals can exacerbate this form of illiquidity risk.
Literature offers little guidance on how to estimate the credit risk and illiquidity risk for
guaranteed investment products. In this paper, we develop two methods for estimating the
total risk of a guaranteed product—one based on credit risk and one that starts with standard
deviation after incorporating the floor and then adjusting it for illiquidity risk. Arguably, both
methods lead to a better estimate of the “true” risk of a guaranteed product and are more
appropriate inputs in asset allocation-oriented optimizations. The search for the optimal
allocation to a guaranteed investment product involves a trial-and-error process because the
illiquidity risk depends on the initial size of the allocation. We provide a practical way to show
how the search is done. These hidden risks can have a significant impact on the optimal
allocations for guaranteed investment products.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
18
Appendix
Morningstar’s Distance to Default score is a slightly modified structural model (Miller, 2009)
similar to the option-pricing models created by Black and Scholes (1973) and Merton (1973)
and commercialized by KMV—now Moody’s KMV. Underlying the structural model is the
assumption that a company’s equity can be considered an option with a strike price equal to
the market value of assets (market capitalization) minus the book value of its liabilities. This
implies that a company is worth nothing, i.e. it has defaulted, when the market value of the
assets drops below the book value of the liabilities. Based on the current market value of a
company’s assets, the historical volatility of those assets, and the current book value of a
company’s liabilities, one can calculate the number of standard deviations, what we call the
“Distance to Default,” a company is away from bankruptcy using the slightly modified
Morningstar methodology. The Morningstar model is less intuitive than the Z-Score because it
does not specifically address the cash accounting values that are typically examined in a default
or bankruptcy scenario. In addition, the Distance to Default model does not examine the
financial covenants that would be the true determinants of whether or not distressed company
defaults on its obligations.
As such, we use Morningstar’s Distance to Default (DTD) to model the issuer’s credit risk. Our
goal is to adjust the guaranteed product’s risk for the credit risk. In order to do this, we first get
the DTD value for the issuer from the Morningstar Direct database. We calculate the
probability to default as
p = NORMDIST(-DTD,0,1,TRUE)
where NORMDIST is an Excel function that calculates the probability that an observation from
the standard normal distribution is less than or equal to –DTD. Using a simplified example, let’s
assume that a company has a market capitalization of $100, a book value of liabilities of $75,
and a historical standard deviation of $10. Thus, the company in question is currently 2.5
standard deviations (DTD = 2.5) away from default and has a fairly high probability of default of
0.62%.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
19
References
Babbel, David F. and Miguel A. Herce. 2011. “Stable Value Funds: Performance to Date.”
Working paper.
Black, F., and M. Scholes, 1973, “The Pricing of Options and Corporate Liabilities.”
Journal of Political Economy, 81, 637-654.
Buetow, Gerald W. Jr., Ronald Sellers, Donald Trotter, Elaine Hunt, and Willie A . Whipple , Jr.
2002. “The Benefits of Rebalancing.” The Journal of Portfolio Management. Winter 2002, Vol.
28, No. 2: pp. 23-32.
Kleiman, Robert T., and Anandi P. Sahu. 1992. "The ABCs of GICs for Retirement Investing."
AAII Journal. March.
Lu, Timothy Jun and Olivia S. Mitchell. 2010. “Borrowing from Yourself: The Determinants of
401(k) Loan Patterns.” Working Paper.
Merton, R. 1973. “Rational Theory of Option Pricing.”
Bell Journal of Economics and Management Science. 4, 141-183.
Miller, Warren. 2009. “Comparing Models of Corporate Bankruptcy Prediction:
Distance to Default vs. Z-Score.” Morningstar Methodology Paper.
Schuermann, Til, 2007, “Credit Migration Matrix”, To appear in Ed Melnick and Brian EveriHGP
(eds.), Encyclopedia of Quantitative Risk Assessment, John Wiley & Sons.
Willenbrock, Scott. 2011. “Diversification Return, Portfolio Rebalancing, and the Commodity
Return Puzzle.” Financial Analysts Journal, Vol. 67, No. 4: 42-49.
Xiong, James X. 2010. Using Truncated Lévy Flight to Estimate Downside Risk. Journal of Risk
Management in Financial Institutions, 3, 3: 231-242.
Xiong, James X., and Thomas Idzorek. 2011. “The Impact of Skewness and Fat Tails on the
Asset Allocation Decision.” Financial Analysts Journal, Vol. 67, No. 2, 23-35.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
20
About Ibbotson
A unit of Morningstar Investment Management (a division of Morningstar, Inc.), Ibbotson
Associates is a leading independent provider of asset allocation, manager selection, and
portfolio construction services. The company leverages its innovative and ground-breaking
academic research to create customized investment advisory solutions that help investors meet
their goals. Founded by Professor Roger Ibbotson in 1977, Ibbotson Associates is a registered
investment advisor and a wholly owned subsidiary of Morningstar, Inc.
For more information, contact:
Ibbotson Associates
22 West Washington Street
Chicago, Illinois 60602
312 696-6700
312 696-6701 fax
www.ibbotson.com.
Important Disclosures
The above commentary is for informational purposes only and should not be viewed as an offer
to buy or sell a particular security. The data and/or information noted are from what we believe
to be reliable sources, however Ibbotson has no control over the means or methods used to
collect the data/information and therefore cannot guarantee their accuracy or completeness.
The opinions and estimates noted herein are accurate as of a certain date and are subject to
change. The indices referenced are unmanaged and cannot be invested in directly. Past
performance is no guarantee of future results.
This commentary may contain forward-looking statements, which reflect our current
expectations or forecasts of future events. Forward-looking statements are inherently subject
to, among other things, risks, uncertainties and assumptions which could cause actual events,
results, performance or prospects to differ materiality from those expressed in, or implied by,
these forward-looking statements. The forward-looking information contained in this
commentary is as of the date of this report and subject to change. There should not be an
expectation that such information will in all circumstances be updated, supplemented or
revised whether as a result of new information, changing circumstances, future events or
otherwise.
© 2011 Ibbotson Associates, Inc. All rights reserved. Ibbotson Associates, Inc. is a registered investment advisor and wholly owned subsidiary of
Morningstar, Inc. The information contained in this presentation is the proprietary material of Ibbotson Associates. Reproduction, transcription or other use,
by any means, in whole or in part, without the prior written consent of Ibbotson Associates, is prohibited.
21