The Sluggish and Asymmetric Reaction of Life Annuity Prices to Changes in Interest Rates

• Published date: 01 September 2016
• DOI: http://doi.org/10.1111/jori.12061
• Date: 01 September 2016
• Author: Narat Charupat,Mark J. Kamstra,Moshe A. Milevsky

©2015 The Journal of Risk and Insurance. Vol.83, No. 3, 519–555 (2016).

DOI: 10.1111/jori.12061

The Sluggish and Asymmetric Reaction of Life

Annuity Prices to Changes in Interest Rates

Narat Charupat

Mark J. Kamstra

Moshe A. Milevsky

Abstract

Many assume that in the short run, annuity prices promptly and efficiently

respond to changes in interest rates. Using a unique database of quotes, we

show this is not the case. Prices are less sensitive to changes in rates than

expected, and responses are asymmetric. Prices react more rapidly and with

greater sensitivity to an increase than to a decrease in rates. The results are

robust, but there is a small degree of heterogeneity in the responses of dif-

ferent insurance companies. When rates increase, larger firms are slightly

quicker to improve prices. The opposite is true when rates decline. In sum,

we show that the microstructure of annuity dynamics is more complicated

than (simply) adding mortality credits to bond yields.

Introduction

It is well known in the literature that prices of life annuities depend on two major

factors—the concurrent term structure of interest rates and mortality probabilities

(e.g., Dickson, Hardy, and Waters, 2009). A change in the value of either factor will

cause prices to adjust. If the annuity markets were frictionless, arbitrage would ensure

that the price adjustment will be prompt and proportionateto the change in the factors.

In reality, however, there aremarket frictions such as the person-specific nature of life

annuity contracts and the inability to short sell them, and so the adjustment can be

slow and/or incomplete.

Narat Charupat is at the DeGroote School of Business, McMaster University.Charupat can be

contacted via e-mail: charupat@univmail.cis.mcmaster.ca.Moshe A. Milevsky is at the Schulich

School of Business, YorkUniversity. Milevsky can be contacted via e-mail: milevsky@yorku.ca.

Mark J. Kamstra is at the Schulich School of Business, YorkUniversity.Kamstra can be contacted

via e-mail: MKamstra@schulich.yorku.ca. Weare grateful for the helpful suggestions of the ed-

itor, Keith Crocker, and an anonymous referee, as well as Timothy (Jun) Lu, Sylvaini Benoit,

participants at the IFID Centre conference, Financial Management Association Asian Confer-

ence, Northern Finance Association 2013, Longevity 8 Conference, City University London and

seminar participants at the University of Vienna, York University, as well as Simon Dabrowski

and Yue Zhang for researchassistance. We thank the Social Sciences and Humanities Research

Council of Canada for financial support. Any remaining errors areour own. A previous version

of this article was titled “The Annuity Duration Puzzle.”

519

520 The Journal of Risk and Insurance

In this article, we use a unique database to examine the sensitivity of life annuity prices

to changes in interest rates. The database consists of over 3 million annuity quotes

from 25 U.S. annuity providers over the period from September 2004 to May 2012.

These are weekly quotes for single-premium immediate life annuities (i.e., ones whose

purchase prices are paid once at the start, and whose income payments start right

away), and are classified along several dimensions such as ages of annuitants, gender,

and guarantee periods. Toour knowledge, the database is the most comprehensive and

accurate collection of annuity quotes available. Since annuity providers can change

their quotes continuously or as conditions warrant, the weekly observations allow us

to track closely changes that occurred in the sample period.

Wecreate a measure for the sensitivity of annuity prices to changes in interest rates by

deriving an expression for the duration of life annuities. The logic for this expression

is akin to that for (modified) durations of bonds in the fixed-income literature, which

measures how sensitive bond prices are to changes in yields.1The expression is then

used to calculate theoretical durations of life annuities, which predicts how responsive

annuity prices should be to movements in interest rates in a frictionless market.2Next,

we empirically estimate the durations of life annuities, using regression analysis.

Finally, we compare the estimated empirical durations to the theoretical durations to

determine whether real-life annuity prices behave as predicted.

Our findings show that annuity prices do not promptly and fully respond to changes

in interest rates. Annuity prices are very insensitive to interest rate movements,

especially when price responses are measured over a short time period such as 1 or 2

weeks. More interestingly, we find that the responses are asymmetric. Annuity prices

react with greater sensitivity to an increase in interest rates than to a decrease in

interest rates. That is, when rates increase, insurance companies reduce their annuity

prices by a larger magnitude than what they do in the opposite direction when rates

declined.

One possible explanation for the observed sluggish responses is that insurance com-

panies may want to smooth out the price changes and/or wait in order to get a better

sense of the trend of interest rates. It is also possible that insurance companies from

time to time have unbalanced books (i.e., mismatches of durations of assets and liabil-

ities). These companies may deliberately offer uncompetitive annuity prices or delay

price adjustments to allow themselves time to rebalance their books, resulting in the

sluggish responses that we observe.3

1The concept of duration for life annuities is not new, and insurance companies have been

using duration measures in their risk management process for decades (see Reitano, 1992, for

additional information and references). However, to our knowledge, this article is the first to

estimate empirical durations of life annuities and compare them to their theoretical values.

2Since changes in mortality probabilitiesoccur very gradually, in the short run, it can be assumed

that changes in annuity prices are explained exclusively by movements in interest rates.

3This explanation is based on our conversation with insurance companies. We note, however,

that it is difficult to verify this information because it would require detailed knowledge of

insurance companies’ holdings, which are not public information.

Annuity Price Reaction 521

The observed asymmetric responses can be due to the providers’ reluctance to raise

their prices for fear of negative reactions from annuity buyers. The negative customer

reaction hypothesis of Rotemberg (1982) suggests that customers prefer relatively

stable prices and will react more negatively to unfavorable price changes than to

favorable ones.4As a result, insurance companies will try to delay a price increase as

long as they can. In the meantime, they absorb the loss through the profit margin that

they build into the annuity prices.

The results are robust with respect to annuitant purchase ages, lengths of guarantee

periods, proxies for interest rates, subsets of annuity providers, and the subperiods

of the sample.5As a by-product of our robustness tests, we uncover a small degree of

heterogeneity in the responses of differentindividual annuity providers. For example,

when interest rates increase, larger firms are slightly quicker to adjust (i.e., reduce)

their prices than smaller firms do. The opposite is true when interest rates decline. In

addition, firms with higher credit ratings are slightly quicker to adjust to changes in

market interest rates, regardless of the direction. Also, lower-rated providers adjust

their prices in a more complete manner only when measured over longer periods.

Nevertheless, these cross-sectional differences are not largeenough to affect our over-

all findings.

Our findings have implications for previous studies in the literature. For example,

the sluggish response suggests that the timing of an annuity purchase can affect the

individual’s optimal allocation decisions and the magnitude of welfare gains from

annuitization. This is particularly important considering that an annuity purchasing

decision is irreversible and typically involves a substantial portion of an individual’s

wealth. Also, caution should be exercised when attempting to infer mortality expec-

tations from observed annuity price as the timing of the calculations matter. Finally,

if a pension from a defined benefit plan is to be properly valued as if it were a life

annuity, then the lag and asymmetry we identify will affect the valuation. Our focus

here, however, is to demonstrate how annuity prices behave in response to interest

rate changes. That is, our findings are a first step in an attempt to understand the

microstructure dynamics of annuity prices—a subject that, to our knowledge, has not

been examined before.6

4The customer reactionhypothesis is proposed by Rotemberg (1982) in the sticky price literature.

Rotemberg also develops a model of sticky prices and tests this model on microeconomic data.

5Recently, Koijen and Yogo (2012) report that insurance companies sold life insurance policies

and life annuities at “fire sale” prices during the financial crisis of 2008 in order to raise capital.

Weshow later in the article that our results are not qualitatively affected by the unusual pricing

during these few months.

6The closest mention that we can find is in Cannon and Tonks (2009) who use monthly data

to calculate the correlation between UK annuity rates and the UK government 10-year bond

yields. They report that the correlation was very high (i.e., 0.98) during the period from 1994

to 2000, but declined substantially to only 0.57 during the period from 2001 to 2007. The low

correlation in the latter period (which overlaps with our sample period) is consistent with our

findings here.