Download Fixed Index Annuity Return and Risk Analysis with an Enhanced

Fixed Index Annuity Return and Risk Analysis with an Enhanced Model
Executive Summary
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This paper examines the risk and return of fixed index annuity (FIA) with an enhanced
model framework which takes into account correlations among market variables and a
changing participation rate fluctuating with the market moves.
The FIA business model is discussed to explain the participation rate model
Sensitivity analysis of FIA returns is performed for key model assumptions.
The risk and return profile of the mix (30/70, 40/60, 50/50, 100/0) of the S&P 500 Index
and the 1-year Treasury bills is compared with that of the FIAs.
This study focuses on 2 hypothetical contracts: (10-year) annual reset Point-to-Point
(PTP) and Monthly-Averaging (MA) contracts with participation rate but no cap or yield
spread.
PTPs outperformed MAs. They together outperformed the mixes of stock/treasury with
comparable risk. Simulated stock index shows higher returns than FIAs most of the time,
but FIAs has much less volatilities and much lower tail risk.
The inherently unstable and unpredictable stock market has given rise to an endless search for
safe investment products. Hybrid features of fixed indexed annuity (also known as equity
indexed Annuity) draw interests of many risk-averse investors: the product provides investors
potentially high return from the stock market while protecting them from downside risks. In
1995, the first FIA product was introduced by Keyport Life. FIA didn’t attract many investors
when the stock market soared in the 1990s. However, many early FIA investors saved their
needing retirement savings from the stock market crash after the dot-com bubble burst at the
beginning of the 21st century and more investors started purchasing FIAs in the following years.
According to a report from Towers Watson (2012), FIA sales skyrocketed from approximately
1.5 billion in 1995 to over 32 billion in 2011. During the recent financial crisis 2008-2009, FIA
again proved itself as a safe investment choice when the financial market is depressed.
Despite its dramatic growth in sale figures, FIA’s long-term performance is still being
questioned, mainly because historical crediting rates and policy data are not publicly available.
FIA’s actual returns as well as comparison between FIA and other alternative investment choices
have been the subjects for many published studies and researches (e.g. Kuhlemeyer, 2001;
McCann and Luo, 2006; Collins, Lam and Stampfli, 2009). Most studies create hypothetical FIA
contracts and analyze their performance by simulating the market variables like stock market
returns. One study by VanderPal, Marrion and Babbel (2011) criticized some major limitations
of model assumptions from those model-based studies and offered an empirical examination of
FIA returns based on some real policy data from participating insurers.
The authors of this paper studied the assumptions in previous analysis taking the modeling
approach and built an enhanced model framework hoping to improve the model assumptions
such as constant participation rates and constant interest rates. This framework includes
distribution models for key market variables which are stock index return, stock option implied
volatility, 10 year and 1 year US treasury rate and credit spread; a separate model for
interdependencies among market variables; the option pricing models and the participation rate
model. Sensitivity tests are performed for all major assumptions to reveal the impact and to
check the robustness of the framework.
Note: Conditional tail expectation 5% (CTE 5%) is defined as the average return of the worst 5%
scenarios.
Figure 7: S&P 500 Index Price Return
Figure 8: Simulated Total Returns for S&P500 /1-year T-Bills Mix
Risk and Return
Simulation Historical SPX Base
Average 10yr Return
7.1%
6.8%
9.1%
Standard Deviation
5.6%
5.3%
5.6%
CTE (5%)
-2.5%
-3.0%
-2.5%
Sharpe Ratio
1.27
1.28
1.63
SPX+2% SPX-2% Div +1% Div -1% 30/70
11.4%
6.9%
10.1%
8.1%
3.6%
5.7%
5.5%
5.6%
5.6%
1.9%
0.3%
-4.5% -1.5% -3.5% -0.02%
2.00
1.25
1.81
1.45
1.85
40/60
4.5%
2.4%
-0.3%
1.86
50/50
5.3%
2.9%
-0.6%
1.83
Note: Base dividend yield is 2%. Div +1% assumes 3% for dividend yield in the total return calculation. 30/70 represents 30%stock index
and 70% treasury bills portfolio.
Figure 12: Summary of Simulated 10-Year Total Returns
Simulated Data
Average 10yr Return
Standard Deviation
CTE (5%)
Sharpe Ratio
Outperform PTP
Outperform MA
PTP
5.0%
2.2%
1.8%
2.26
N/A
81%
MA
4.0%
1.6%
1.6%
2.47
19%
N/A
SPX
9.1%
5.6%
-2.5%
1.63
85%
86%
30/70
3.6%
1.9%
-0.02%
1.85
13%
37%
40/60
4.5%
2.4%
-0.3%
1.86
36%
59%
50/50
5.3%
2.9%
-0.6%
1.83
58%
74%
Note: PTP and MA are simulated total return data for Point-to-Point and Monthly-Averaging annuities
respectively. SPX is simulated S&P500 Index total return data. 30/70 is the mix of 30 % stock index and 70 %
of T-bill. Outperform PTP is the percentage of the simulations of other assets (e.g. SPX) outperforming PTP.
Author:
Zhixin Wu, Ph.D, Associate Professor, ASA
602 South College Ave,
Math Department, DePauw University,
Greencastle, IN 46135
Email: [email protected]
Phone: 765-658-4488
Co-Authors:
Lei Liang, Ph.D, CFA, CAIA, FRM
40|86 Advisors, Inc.
CNO Financial Group
535 College Dr., Building # K
Carmel, IN 46032-5622
Email: [email protected]
Phone: 317-817-4752
Fax: 317-817-4115
Huong Dao (Undergraduate student)
Math Department, DePauw University, Greencastle IN 46135
Email: [email protected]
Phone: (317) 403-4191
Linh Phuong Nguyen (Undergraduate student)
Math Department, DePauw University, Greencastle IN 46135
Email: [email protected]
Phone: (405) 428-2531