Title: Financing guaranteed renewable health insurance

Author: Robert D. Lieberthal, PhD

Affiliation: Jefferson School of Population Health, Thomas Jefferson University

Telephone: (215) 503-3852

Fax: (215) 923-7583

E-mail: robert.lieberthal@jefferson.edu

Disclosure: This research was part of my dissertation. It was funded by an Agency for

Healthcare Research and Quality dissertation grant R36 HS018835-01.

Acknowledgements: I wish to thank my dissertation committee, comprised of Mark Pauly

(advisor and chair), Scott Harrington, Greg Nini, and Jessica Wachter for their feedback

on this work.

Title

Financing guaranteed renewable health insurance

Abstract Guaranteed renewable health insurance gives individuals long-term protection against

reclassification risk through a one-sided commitment. Insurers finance this risk,

managing the associated long-term liability through a contract reserve. The value of the

liability is uncertain because medical trend is highly stochastic. Insurers could manage

uncertainty about the value of the liability by investing contract reserves in correlated

assets to hedge medical spending growth. However, securities markets are probably

unable to fully hedge the risk of medical spending growth, and may not provide any

significant hedge for this important risk. A simple rule for investment of assets, utilizing

a diversified portfolio, is the best strategy for guaranteed renewable health insurance

reserves. New asset classes, whether created by public or private entities, may facilitate

risk management of stochastic medical trend for long-term health insurance contracts.

Keywords Guaranteed renewability; Medical spending growth; Cost curve; Healthcare finance;

Reclassification risk; Contract reserves

Introduction Individual health insurance coverage has long been guaranteed renewable, which

protected individuals against reunderwriting. Guaranteed renewable or ―time consistent‖

health insurance combined protection against current spells of illness and future

reclassification costs into one long-term contract (Pauly et al., 1995, Cochrane, 1995).

Consumers paid initial insurance premiums that are higher than the prevailing spot

premiums to get this extra protection. In return, insurance companies committed to

rerating based only on class experience, and to avoid individual reunderwriting.

Currently, the enactment of the Patient Protection and Affordable Care Act has

brought into question the use of required contract reserves for guaranteed renewability.

For example, insurers in North Carolina have been forced to refund reserves meant to

stabilize premiums that will not be needed after the PPACA comes into full effect

(Young, 2010). Insurers will continue to consider the effect of guaranteed renewable

insurance on their risk profile, as well as more general effects stemming from a risk pool

that ages, and becomes more expensive, over time. This is both because of the existence

of medical loss ratio (MLR) rules that may restrain the use of contract reserves, and

because of continuing demand for, and problems in, the long-term care insurance market

(Jost, 2010, Eldridge, Lynn, 2011). In these and other cases, insurers should charge front

loaded premiums, but the investment policy for those front loaded premiums has not been

well investigated. Determining how well front loaded insurance can be financed, as well

as determining which asset classes should be used to finance such insurance, is the

motivation of this study.

The actuarial mechanism for keeping low risk insureds in an insurance contract is

the contract reserve fund. Greater than spot market premiums flow into the reserve. The

reserve later cross-subsidizes the premiums of those who become high risk, allowing

them to pay actuarially favorable rates relative to the spot market without driving the low

risks out of the guaranteed renewable pool. To make the contract zero profit in

expectation, the reserve is calculated based on the shadow price of purchasing annual

renewal insurance for high types for the remaining term of premium protection specified

in the plan (Herring, Pauly, 2006). There have been also been allegations that high

premium growth for new insureds–duration rating–represents a violation of guaranteed

renewability and general protection against reunderwriting (Bluhm, 1993).

The value of the shadow benefits rises as future insurance becomes more

expensive and as medical trend becomes more unpredictable. The general level of

medical spending, or trend, is a key input assumption in determining the future cost of

medical spending (Bluhm, 2007). Health insurers could limit their exposure to rising

medical spending, for example through a pure indemnity arrangement, but in practice,

they do not because this exposes the insureds to more risk. It can be harder to limit future

benefits in health insurance contracts, since insured individuals want access to new

medical technologies. Retroactively removing previously allowable benefits could violate

the spirit or the letter of a guaranteed renewable or other long-term health insurance

contract. As a result, the value of the benefit in guaranteed renewable insurance is linked

to the rise in medical spending. However, insurers that charge adequately for prefunding

future spending growth could be charging rates that are unaffordable, or seem exorbitant,

when compared to spot rates.

The predictability of spending growth is a key driver of its effect on long-term

health insurance through the trend assumption. Guaranteed renewable premiums are

based on the expected future costs of insurance, which does include trend (Herring,

Pauly, 2006). While the trend is stochastic, the insurer still imputes the average expected

trend into the policy. The insurer may also factor the size of potential fluctuations into the

contract reserve. The economic fair price for the insurance could include a risk premium

for the additional risk the insurer is taking on, but in a competitive market with an

available hedge, this risk premium would not be added to the cost of the insurance.

In a setting with stochastic trend, the insurer also has to be concerned about the

credibility of the data used to predict future trends. The longer the time horizon for the

contract, the more the insurer wants to know about the longer term stochastic properties

of medical spending growth. The specific time series properties of spending growth

determine how to manage it with contract reserves. If each year's growth is a draw from a

distribution with noise, then gains and losses should balance out over time. The point of

reserves would be to cover shortfalls, especially if higher than expected spending

occurred in the early years of the contract.

If spending growth is serially correlated, then it is more likely that several years

of higher than expected growth could cause accumulated losses. In that case, the insurer

would be interested in above average asset returns, and would be willing to sacrifice

below average asset returns in the situation where spending growth was below trend for

several years. This could come from taking a long position in an asset that paid off more

when medical spending growth was unusually high, or a short position in an asset that

pays off less when medical spending growth is unusually high. Whether the correlation

between medical spending growth and returns is positive, negative, or zero, the time

series properties of trend should be factored into the reserve policy. Insurers should set a

policy that maximizes firm value or minimizes the probability of having a negative

reserve, i.e. ruin, rather than maximizing the value of the assets invested through the

contract reserve. The minimum probability of ruin that can be achieved may limit the

term of guaranteed renewable and other long-term forms of protection through health

insurance, making some risks uninsurable (Cutler, 1993).

Methodological background Separating trend from error is the first step in searching for a hedge for medical

spending growth. This means fitting the observed series of insured spending to a model. I

fit the spending growth time series to two models: a linear regression and an adaptive

expectations model. The linear regression model is designed to assess the predictability

of spending growth and the variables that might improve the fit of the regression model.

The adaptive expectations model separates the deterministic portion of trend, which is the

long run average trend assumption, from the stochastic portion of trend, which generates

risk for the insurer. The stochastic portion of the trend is then expressed as a prediction

error.

Prediction errors are used to determine if effective hedges exist. In the example of

commodities, an individual that enters into a futures contract that guarantees a set price

for the delivery of a commodity will not have an additional need to predict or reserve

against changes in the commodity price. Similarly for medical spending, if there were an

asset or group of assets that covary with the unpredicted portion of medical spending,

then they would be a useful hedge. The amount of reserves a health insurer would have to

set aside would be decreased toward the amount needed to prefund predictable increases

in medical spending. The higher the correlation between residual spending growth and

asset returns, the better the hedge. Such contracts have been attempted for insurance and

health insurance specifically, with limited success (Cox, Schwebach, 1992). There is no

similar model for asset returns, which are assumed to include all available information

(Fama, 1970).

The adaptive expectations model is specifically designed to generate prediction

errors and then find the correlation between errors and asset returns. The idea is that, for

medical spending growth, there is a long-term trend line and then errors around that trend

line. The errors arise as a disturbance term that is random and uncorrelated across time.

The size of errors around the trend line is not known, so deviations from the prior long-

term trend are factored into the long-term trend based on an updating factor. The

updating factor θ can range from 0 to 1, and is not known ahead of time. By estimating

the equation and varying the parameter θ, I can test the correlation between assets and

deviations from trend for a range of possible updating factors, giving the correlations

under different possible scenarios for how quickly the long-term trend in spending

growth is updated.

The underlying data generating function for medical spending growth has almost

certainly changed over time. The time since the last trend break is important for health

insurance risk because, aside from any particular model of medical spending growth is

the question of how long any relationship will persist. The problem is determining the

stationarity of the time series data, or whether there is a single consistent trend over time.

Whether the data available can answer these questions is an important part of how long

guaranteed renewable contracts could last. These issues are addressed further in the

Results section as part of the unit root test.

The investment problem The investment problem is to find a hedge that is appropriate for the specific

insurance liability. It is the role of reserves to manage unhedged risk, specifically the

asset investments for the contract reserves set up by the insurer. The size of the forecast

errors informs the size of the contract reserves under guaranteed renewability. It might

also inform the investment policy of the insurer. Medical spending growth is a shock that

is common across all policyholders, so managing stochastic medical trend is also a

service provided to policyholders if the insurer can implement a hedging strategy that is

too complex or costly for individuals. The goal of the insurance company managers is not

to maximize the value of assets, but to maximize the value of the firm. Managers may be

focused specifically on minimizing the probability of ruin, which is the probability that

liabilities exceed assets (Hipp, Plum, 2000). Hedging serves this objective by allowing

assets to serve as a buffer against liabilities.

I search for hedges across a broad set of assets that are based on Fama-French

portfolios. Broad equity and bond asset classes make hedging assets results generalizable.

Popular, broadly available asset classes give data with a long enough history to test

against the spending data series. I also utilize specific return data on healthcare and

healthcare subsectors, which allows me to test the proposition that healthcare assets may

be a hedge for liabilities arising from medical spending growth (Jennings et al., 2009).

Almost no hedge is perfect, so there may be some gap between what predictions

and hedging can do and the size of medical spending growth risk. The size of the gap is

also important, as it would determine how important it is to try new assets, examine

policies that create new assets, or measure the size of risk that cannot be managed with a

hedging investment policy.

There is also a point where the risk becomes uninsurable to an insurer, and

possibly to any entity. One example would be investments with large transaction costs or

large leverage requirements. Contracts where the class average guaranteed extends for a

large number of years, or public insurance programs where a government commits to

keep a health insurance program unchanged for an extended period, are two examples.

The issue of insurability is tied to the availability of hedges, whether directly for the

insurance company or indirectly for the government that cannot bear too large of a risk.

Estimation methods In my model, insurance companies write contracts indexed to the total nominal

level of medical spending. As a result, the medical spending growth that I am explaining

with the regression is nominal medical spending. Insurance companies take trend as a

given, insure the portion that is attributable to guaranteed renewability, and pass the rest

on to insureds to the extent allowed through prospective pricing.

I consider two ways that insurance companies can utilize data from securities

returns to improve the management of risk arising from stochastic medical trend. One is

informational, as an explanatory variable that improves the prediction of trend. Then,

returns could be a hedge, or could simply be a tool to improve setting the deterministic

trend assumption when pricing insurance. I discuss this in the ―Returns as explanatory

variables‖ subsection below. Second, insurance companies could try to model the long

run average rate of trend, and see if securities returns can help explain forecast errors, or

variations from the trend line. In this case, securities are not used to improve the forecast,

but only to provide a hedge. I discuss this in the ―Adaptive expectations‖ subsection

below.

Returns as explanatory variables

I assess the year-on-year predictability of per capita insurer spending growth by

regressing current spending growth on lagged spending growth. My regression equation

with only lagged spending growth as an explanatory variable is:

1-t10t trendmedical trendmedical

Equation 1: Basic regression for medical spending growth

Given this model, insurance companies can then add variables that would improve

the predictability of medical spending growth. For example, general price inflation will

tend to increase nominal medical spending. The returns on securities could be one such

explanatory factor, either due to direct links (e.g. higher drug profits come from higher

spending and raise the price of pharmaceutical stocks) or indirect links (wealth effects

increase medical spending and are reflected in overall market returns). In that case, a

vector of variables v with an associated vector of coefficients Β can represent all of the

other explanatory variables.

v1-t10t trendmedical trendmedical

Equation 2: Forecast of medical spending growth with additional regressors

Adaptive expectations

I use a simple adaptive expectations model to determine the long-term expected

rate of nominal medical spending growth. The long-term rate of growth is equal to the

prior long-term rate of growth plus a linear ―adjustment‖ for the prior difference between

the expected rate of growth and the experienced rate of growth. The updating equation is:

ttD

tD

tDtDtDtD

at timegrowth of rate dexperience theis )(

tat timegrowth of rate termlong theis )(

where

))1()1(()1()(

Equation 3: Adaptive expectations updating equation

originally proposed by Bodie, 1976.

The updating factor θ for the adjustment ranges from 0 to 1. θ is not known a

priori. I calculate estimates of tD , the expected rate of growth, over a range of values for

θ. The choice of updating factor determines the time series of forecast errors in the

model. )()()( tDtDtd are the unanticipated shocks that result, and differ by choice of

θ. Therefore, this model shows the size of shocks for a range of possible updating factors.

The test of the ability of assets to hedge medical spending growth is the effect of

spending shocks on excess return. I use the following specification:

)()(

where

)()( 10

(t)DtRtR

tdtR

e

e

Equation 4: Test of effect of spending shocks on securities returns

originally proposed by Bodie, 1976. In my case, )(tRe is the excess return, that is, the

return to assets in excess of the long-term trend in medical spending.

I use this method as a test of the use of securities to hedge spending growth. If the

coefficient on 1 is significant, then the return index used to calculate )(tRe is a good

hedge. The sign of the coefficient indicates whether the hedging position is long or short.

There may be positive coefficients for some assets, such as healthcare stocks, if there is a

positive correlation between above trend spending growth and returns to healthcare

securities. There may be negative correlations, say to the overall market, if above average

healthcare costs depress profits of most public companies.

Data The National Health Expenditure Survey tabulates data on total and per capita

medical spending. CMS also surveys health plans to tabulate medical spending per

insurance plan enrollee. The data includes per capital spending by private plans and

Medicare, and further splits the data into all benefits and common benefits provided by

both plans (for example, Medicare did not offer drug benefits until 2003 (Centers for

Medicare and Medicaid Services, 2011)). The data for per capita insurer expenditures is

similar, growing at rates of 7-8% over the period 1982-2008 (see Table 1).

Private insurance growth rates are substantial with a high degree of variance.

There is not a single year of negative spending growth in the data. The advantage of the

data is that it focuses on the spending for insured lives, which will allow me to evaluate

hedges for health insurers. Part of the risk I want to measure is the portion of trend due to

with general changes in the type and quantity of medical care delivered, which is

reflected in the insured spending time series. One disadvantage is that it the measure of

average spending is aggregated across many types of private health insurance plans. The

goal is to measure and find a hedge for a common shock that should affect all types of

individual health insurance.

All benefits Common benefits

Insurance type Medicare Private Medicare Private

mean 7.08 7.91 6.08 7.33

sd 3.50 3.56 2.83 3.22

skewness 0.07 0.35 0.59 0.16

kurtosis 3.76 2.22 4.19 2.09

min -1.50 1.87 0.08 2.18

max 15.21 15.33 14.1 13.69

p25 4.90 4.89 4.38 4.84

p75 8.96 10.39 7.37 9.62 Table 1: Per capita nominal insurer expenditures 1982-2008, rate of change (%)

I show initial statistics on bond returns in Table 2. For the risk-free rate, I use one-

month Treasury bills. These are a standard in the literature because they are U.S.

government securities of short duration, which eliminates default risk and inflation risk.

The data comes from the Fama/French factor for risk-free rates (the factors are described

in Fama, French, 1993, and are available from Fama, French, 2010). The return on bonds

that I use as investments to hedge growth comes from ten-year government bonds and

Moody‘s index of AAA rated corporate bonds. Both are total return indices, and so

contain interest and principal payments. The data come from the Global Financial Data

Total Return database (Global Financial Data, 2011).

I use the Fama/French factors to generate returns for the stock market, health care

stocks as a whole, and health care subsectors stock returns (Fama, French, 2010). The

Fama/French returns are value weighted and cover stocks on the major U.S. exchanges.

The negative skews show the fact that shocks in the distributions of stock returns are

often negative (Campbell, Hentschel, 1992). Health sector returns may have a high beta–

they have higher mean returns than the market but also higher variance (see Table 3).

Bond class

Returns 10 Year

Government Bonds

AAA Corporate

Bonds

Risk-Free Rate

mean 0.84 0.88 0.42

sd 2.42 1.91 0.21

skewness 0.22 0.52 0.43

kurtosis 3.75 5.54 3.22

min -6.94 -4.73 0.02

max 8.64 8.55 1.13

p25 -0.65 -0.13 0.28

p75 2.35 1.87 0.54 Table 2: Bond monthly nominal returns (%, continuous log basis)

Equity class

Market Health Health

services

Medical

equipment

Drugs

mean 0.91 1.12 0.83 1.05 1.21

sd 4.48 4.83 6.92 5.29 5.01

skewness -0.91 -0.19 -0.36 -0.50 -0.10

kurtosis 6.21 4.24 4.75 4.85 3.84

min -22.54 -20.47 -31.50 -20.56 -19.10

max 12.85 16.54 20.49 16.31 16.37

p25 -1.70 -2.03 -3.51 -1.82 -1.89

p75 3.91 4.00 5.11 4.46 4.38 Table 3: Stock monthly nominal returns, 1982-2008 (%, continuous log basis)

Results

Modeling of spending growth

Both total spending and insurance premium growth are strongly serially

correlated. The growth rate in total medical spending is correlated from year to year in a

way that GDP growth is not (see Figure 1). Premium growth per enrollee in private plans

is also serially correlated. Using prior year trend alone explains 51% of the variation in

the next year's spending, using only data from 1970-2008, as shown in Figure 2. The

predictability in annual data suggests that it may be possible to forecast future medical

spending growth. If the data were predictable enough, a hedge would not be needed.

Figure 1: Growth rate of nominal GDP and nominal medical spending per capita

Hedging growth with asset returns requires a separating medical trend from

prediction errors. To the extent that growth predictably increases, insurers prefund future

medical losses with actuarially fair premiums. Simple correlations of nominal asset

returns and total medical inflation are instructive. In Table 6, I show the correlations for

the high frequency time series and securities returns over the 1982--2008 period. The

correlations show that medical inflation is most correlated with the risk-free rate (short-

term Treasury bills), general inflation, and health care services companies. It also shows

that stocks are not highly correlated with inflation, despite stocks‘ known relationship

with inflation (Bodie, 1976). This analysis shows the finding a hedge with the proper

relationship. By partialling out the predictable portion of medical spending growth, the

forecast errors, or surprises, remain. It is buffering against these surprises that hedging is

important. For that reason, I analyze regression results in addition to raw correlations.

The time series properties of medical spending growth suggest that there is not

one consistent trend rate1. For example, a unit root test for the period 1971-2008 shows

that there is almost certainly a unit root in the insured spending data, while there may or

may not be a unit root in the change in spending time series (see Table 4 and Table 5). A

unit root test for the period 1982-2008 shows that there is almost certainly a unit root in

the total spending data. This may be because of U.S. specific factors, such as the

managed care revolution (Strunk et al., 2002), or a common factor across developed

countries such as Baumol‘s ―cost disease‖ (Hartwig, 2008). While I can reject the

possibility of a unit root in the Medicare change series, I cannot strongly reject the

possibility of a unit root in the private spending change series. As a result, I will use the

errors in forecasting the change in privately insured spending as the goal for hedging.

1 That would make a hedge more valuable if the nonstationarity in medical trend matched the

nonstationarity in asset returns, but that is a consideration beyond the scope of this study.

Figure 2: Nominal insured medical spending per capita, year on year rate of change

Time series Test statistic p-value

Spending per enrollee

Medicare

All benefits 5.97 >0.99

Common benefits 5.60 >0.99

Private insurance

All benefits 7.96 >0.99

Common benefits 8.65 >0.99

Change in spending

Medicare

All benefits -3.08 0.03

Common benefits -2.37 0.15

Private insurance

All benefits -2.34 0.16

Common benefits -2.11 0.24 Table 4: Unit root test of per capita nominal insurer expenditures, 1971-2008

Time series Test statistic p-value

Spending per enrollee

Medicare

All benefits 3.79 >0.99

Common benefits 2.69 >0.99

Private insurance

All benefits 4.34 >0.99

Common benefits 5.04 >0.99

Change in spending

Medicare

All benefits -3.63 <0.01

Common benefits -3.54 <0.01

Private insurance

All benefits -2.56 0.10

Common benefits -2.34 0.15 Table 5: Unit root test of per capita nominal insurer expenditures, 1982-2008

Variables Stock

market

Health

stocks

Health

services

stocks

Health

equipment

stocks

Drug

stocks

1 month

govt

bonds

10 year

govt

bonds

AAA

corp

bonds

General

inflation

Medical

inflation

Stock

market

1.000

Health

stocks

0.805 1.000

Health

services

stocks

0.032 0.032 1.000

Health

equipment

stocks

0.719 0.772 0.024 1.000

Drug

stocks

0.781 0.993 0.030 0.714 1.000

1 month

govt

bonds

-0.012 0.012 0.654 0.003 0.014 1.000

10 year

govt

bonds

0.105 0.146 0.136 0.119 0.146 0.126 1.000

AAA corp

bonds

0.188 0.171 0.150 0.148 0.168 0.102 0.595 1.000

General

inflation

0.009 -0.034 0.204 -0.007 -0.037 0.259 -0.069 -0.108 1.000

Medical

inflation

-0.036 -0.087 0.263 -0.074 -0.087 0.431 0.032 0.035 0.342 1.000

Table 6: Correlations of monthly inflation and nominal returns, 1982-2008

First, I examine the amount of spending growth I can explain. Over the entire

period my data covers, 1971-2008, one year lagged spending growth explains roughly

half of the variation in current year's spending growth. Over the more recent period 1982-

2008, prior growth is less predictive of current growth, with an adjusted R2 of 39% (see

Table 7 and Table 8). The lower predictability is not a function of the variance of

spending growth, which has remained constant relative to the rate of spending growth

(which has fallen constantly over the last 40 years). However, for the more recent period

adding spending growth from two years ago improves the prediction of recent spending

growth (adjusted R2 of 43%) while slightly reducing the adjusted R

2 for the entire time

horizon. Dropping lagged spending growth leads to much less predictability. This

suggests that a large portion of the annual growth in medical spending cannot be forecast.

With multiple years of trend necessary for guaranteed renewable health insurance,

accurate forecasts beyond the long run require additional political or social factors or

general equilibrium models2.

Variable Coefficient SE t-statistic p-value 95% CI

min

95% CI

max

constant 2.50 1.30 1.92 0.06 -0.14 5.14

Spending

lag 1

0.72 0.12 6.07 <0.01 0.48 0.96

N 38

F-test <0.01

Adj R2 0.49

Root MSE 3.26 Table 7: Per capita nominal insurer expenditures regressed on lagged expenditures, 1971-2008

2 For examples of how to produce longer term forecasts, see thee Society of Actuaries technique for

modeling long run healthcare cost trends (Getzen, 2007), or the estimates produced by the CBO for their

budgeting purposes (Congressional Budget Office, 2010).

Variable Coefficient SE t-statistic p-value 95% CI

min

95% CI

max

constant 2.58 1.29 2.00 0.06 -0.08 5.24

Spending

lag 1 0.64 0.14 4.50 <0.01 0.35 0.93

N 27

F-test <0.01

Adj R2 0.43

Root MSE 2.70 Table 8: Per capita nominal insurer expenditures regressed on lagged expenditures, 1982-2008

I can improve the prediction of current spending by using lagged medical inflation

and physician office employment. Using either variable in concert with two lags of

medical spending produces an adjusted R2 of 49% in the recent period. The coefficients

on lagged employment growth and inflation also have lower p-values. The best model for

predicting spending growth for the entire period is the model with two lags of spending

growth and current medical inflation and physician office employment growth. While

physician office employment is not significant, it improves the fit of the model, so I

chose to continue to include it as a predictor. The best model in the more recent 1982-

2008 period is the one with two lags of spending growth and lagged physician office

employment growth (see Table 9). There is a substantial remaining error term to be

hedged using this model.

Variable Coefficient SE t-statistic p-value 95% CI

min

95% CI

max

constant -0.09 1.57 -0.06 0.96 -3.35 3.17

Inflation 1.10 0.40 2.73 0.01 0.26 1.93

Premium growth

Lag 1 0.62 0.16 3.84 <0.01 0.29 0.95

Lag 2 -0.35 0.15 -2.26 0.03 -0.67 -0.03

MD office

Lag 1 0.66 0.42 1.59 0.13 -0.20 1.53

N 27

F-test <0.01

Adj R2 0.63

Root MSE 2.16 Table 9: Per capita nominal insurer expenditures regressed on multiple variables

As a first pass approach, I added asset returns to try to improve the fit of these

models as part of vector B in Equation 2. Asset returns do not improve the prediction of

current spending growth. Adding the risk free, the market return, health sector and

subsector returns, one or two period lagged asset returns do not improve on the prediction

of spending growth. The results hold across all of the asset classes I use for the recent

period 1982-2008. There are two asset classes with significant results (p-values between

0.01 and 0.05) with lags: drugs and medical equipment. The results are insignificant over

the longer 1973-2008 time horizon. All of these results point to the need for more

sophisticated methods that focus on errors to try to hedge aggregate medical spending

growth.

There are two main takeaways from this approach. One is that, significant work

has been done to identify predictors of medical spending growth. My work builds on that

prior literature, and finds that these previously identified predictors, and models, produce

potentially useful forecasts of medical spending growth. The second takeaway is that

securities market returns do not contain additional information that is not already

included in other macroeconomic regressors for predicting medical spending growth.

Reasons to expect that securities market data might be informative include the unique

incentives that traders have to find and utilize information that is predictive of future

economic trends, especially given the large share of the economic consumption for

healthcare. Reasons to doubt that securities market data might be informative include

prior results that show that the stock and bond markets may not reflect the real economy,

or may not do so in a way that is predictive (Harvey, 1989). It may also be that while the

securities market does not explain the growth rate, it explains unexpected changes in the

growth rate. This motivates my use of an adaptive expectations model in the next section.

Adaptive expectations results

The adaptive expectation results for a grid of updating coefficients ranging from

0.10-1.00 are in Table 10 and Table 11, and I summarize the prediction errors in Table

12. The expectation of long-term medical spending growth has come down as the rate of

growth in spending has decreased. For 2009, the predicted spending growth rates range

from 3-7% depending on the updating parameter θ3. The reason is the strong moderation

in spending increase rates from over 11% in 2002 to 4.5% in 2008. The smallest updating

parameter (θ=0.1) gives the smallest proportional variance.

3 The actual figure for 2009 was 6.9% (see

https://www.cms.gov/NationalHealthExpendData/downloads/tables.pdf).

θ

Statistics 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

mean 10.53 9.47 9.03 8.80 8.65 8.55 8.48 8.42 8.38 8.35

sd 2.19 2.57 2.72 2.85 3.01 3.16 3.32 3.46 3.60 3.73

skewness 0.22 0.42 0.42 0.36 0.33 0.32 0.33 0.34 0.34 0.33

kurtosis 1.59 1.86 1.97 1.89 1.80 1.76 1.79 1.88 2.02 2.19

min 7.52 6.32 5.49 4.98 4.64 4.47 4.38 3.50 2.66 1.87

max 14.19 14.35 14.37 14.34 14.35 14.44 14.62 14.86 15.16 15.49

p25 8.40 7.19 6.74 6.33 6.05 5.46 4.99 5.07 5.06 4.98

p75 12.22 11.61 11.71 11.21 11.28 11.63 11.29 10.96 10.66 10.57 Table 10: Adaptive expectations average rates for per capita nominal insurer expenditures, 1982-2008

θ

Statistics 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

prediction 7.12 5.88 5.24 4.72 4.32 4.04 3.84 3.7 3.6 3.53 Table 11: Adaptive expectations forecast rates for per capita nominal insurer expenditures, 2009

θ

Statistics 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

mean -2.62 -1.57 -1.13 -0.89 -0.74 -0.64 -0.57 -0.52 -0.48 -0.44

sd 3.21 3.29 3.27 3.22 3.16 3.10 3.05 3.01 2.99 2.97

skewness -0.23 -0.13 0.02 0.14 0.22 0.28 0.33 0.36 0.38 0.41

kurtosis 3.65 3.91 4.10 4.41 4.75 5.01 5.10 4.99 4.76 4.48

min -11.27 -10.51 -9.86 -9.34 -8.96 -8.66 -8.41 -8.19 -7.97 -7.73

max 3.70 5.48 6.76 7.60 8.10 8.33 8.33 8.13 7.76 7.21

p25 -3.94 -3.23 -2.64 -2.69 -2.45 -2.32 -2.27 -2.01 -2.31 -2.46

p75 -0.56 0.81 0.71 0.89 1.03 1.04 0.99 0.92 0.96 0.99 Table 12: Adaptive expectations errors for per capita nominal insurer expenditures, 1982{2008

I regress excess returns to the overall market, health care, and health care

subindustries on the error term for the entire and recent periods (see Equation 4). I used

the full range of updating factors from 0.1 to 1.0. I searched over ten possible updating

factors across eight asset classes (nine counting general inflation, which can be an asset

class via TIPS bonds). None of the coefficients were statistically significant when

factoring in multiple comparisons. The results show that unanticipated shocks in medical

spending either do not feed through into contemporaneous nominal asset returns, or these

effects cannot be detected using this data. I discuss the implications in the final section of

this paper.

I also used lagged asset returns, which are generally insignificant as well. Total

and excess returns to the market lagged one year for small θ (0.1 or 0.2) are both

correlated with errors, as are corporate bond returns both in total (all θ) and excess

returns (θ≤0.6). Excess returns to short-term government bonds (θ=0.1, 0.9, 1.0) and long

government bonds (θ=0.1, 0.2, 0.3) are also correlated with the shocks I generated for the

spending growth time series. All the correlations are also negative. This suggests that, as

in Bodie, 1976, above average medical spending growth may be bad for stock market

returns but with some lag. The results would also indicate that stock returns are a leading

indicator of the unpredictable portion of medical spending growth, which is important for

policy but does not make for a useful hedge.

There are two main takeaways from this approach. One is that, significant work

has been done to identify deviations from trend in medical spending growth. Finding

when the trend will change, especially in an autoregressive time series, is important. It

may also be that a more complex, forward looking expectations setting process is needed

in order to admit data from securities returns. It may also be that the correct variables for

finding unexpected changes in medical spending growth are as difficult to model as

medical spending growth itself, such as unexpected changes in GDP growth, or difficult

to model entities such as the ―resistance point‖, when individuals in aggregate wish for

medical spending growth to stop (Getzen, 2007). In either case, securities returns will not

contain the information needed, and may even be lagging indicators of certain types of

macroeconomic variables.

Discussion If there are no good hedging assets for medical spending growth, then the ideal

investment allocation is a diversified portfolio. The portfolio would not differ from that

of any line of insurance where there is no available hedging asset, as is the case with

longevity hedges for annuities (Bauer et al., 2010).The characteristics of the investments

would then be determined only by the duration and convexity of the guaranteed

renewable liability. The timing of payments for guaranteed renewable insurance has not

been extensively studied (for an initial investigation, see chapter 4 of Lieberthal, 2011 or

Lieberthal, 2012). The basic actuarial idea is that expected payments will be made more

quickly for less healthy populations, while expected payments are more likely to be in the

future for more healthy populations. Otherwise, guaranteed renewable health insurance

looks like other lines of multiyear insurance; for example, lower interest rates increase

the duration of the liability. Financial arrangements should be used to match the timing of

premiums from the contract, which are generally frontloaded, with the claims, which are

generally back loaded.

The other general principle to consider is the risk appetite of the insurance

company. Insurers that are more risk averse may hold safer assets and have safer

portfolios, while other insurers may have riskier investment strategies. Guaranteed

renewable insurance as a particular product should not change that broad strategy. One

potential future implication of the Patient Protection and Accountable Care Act is to draw

more people into the insurance pool and induce less switching, or churn, in health

insurance. If that takes place, insurers may be able to increase their exposure to riskier

assets, whether through longer duration bonds or through equities in order to finance

guaranteed renewable health insurance.

Conclusion The newly enacted health reform law will have two effects that will change the

applicability of my results. First, the law may change the ability of insurers to create

underwritten pools of lives for the purposes of guaranteed renewability. It will also affect

the ability of insurers to price their premiums consistent with guaranteed renewable

principles. Other systems that have moved to a similar mandate based insurance scheme,

like Germany, have a significant, stable, market for guaranteed renewable health

insurance (Hofmann, Browne, 2010).

There is a second, indirect, potential effect of health reform. The law may change

the time series properties of spending growth, returns on financial assets, and the

relationship between these variables. Bending the cost curve was an explicit goal of

health reform, so the effect of the PPACA on future spending growth is an intended

consequence of the law. The effect of the law on healthcare asset returns is an anticipated

consequence, but there could be an indirect effect on other financial asset returns given

that healthcare is such a large segment of the entire economy. Finally, the relationship

between spending growth and asset returns is another unintended consequence of health

reform. It is possible that the PPACA will cause financial asset returns to become more

tied to the growth in medical spending. I consider the possibility a starting point for

future research in this area. Any new expansion by health insurers into the nongroup

market will have to consider this possibility, and set their investment policy for contract

reserves accordingly. Any required contract reserves may still be limited by new medical

loss ratio rules, which are still being developed.

Finally, I conclude that there is no ideal hedge for medical trend, because there is

no negatively, or positively, correlated asset. My next step, in future work, will be to

measure the gap between a diversified investment portfolio and the unpredictable

component of medical spending growth. One consideration I have not considered in this

paper is what the beta of that portfolio should be. In related work, I consider the effect of

the health of the population on the duration and convexity of claims (Lieberthal, 2012).

That work suggests that, for less healthy populations, the portfolio duration should be

lower in order to match the timing of claims, which would likely correspond to a lower

beta portfolio. Health insurers that wish to manage front loaded contracts, such as

guaranteed renewability and long-term care insurance, or have aging populations with a

higher spending profile, will be exposed to stochastic medical spending growth. They

will need to consider the effect of medical trend, asset returns, and the interaction with

population health variables such as the health of their insured populations in order to set

their investment policy.

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