Fixing Health Savings Accounts and High Deductible Health Plans

 Abstract:   The current rules governing health savings accounts and high deductible health plans favor the rich over the middle class, divert funds from 401(k) plans, and create an incentive for the chronically ill to forego prescription medicines.  These rules create a tradeoff — save for your retirement or take care of your health.   The tradeoff is most severe for middle class people with chronic health conditions.  This memo considers alternative rules for health savings accounts, which would lead to better financial and health outcomes.

Issue:   Health Savings Accounts coupled with high deductible health plans are gaining market share.   Proponents of this type of health insurance stress three advantages – (1) lower premiums, (2) incentives to economize on health care, and (3) a new source of retirement savings.

However, the increased use of health savings accounts has resulted in several problems.

First, the use of health savings accounts has resulted in low and middle income people with relatively low marginal tax rates paying more after taxes for health services.

Second, it appears that many mid and lower middle households have an incentive to contribute funds to a health savings account rather than a 401(k) plan.   All contributions from health savings accounts on qualified health care expenses are tax free.  After age 65, non health related expenses from health savings accounts are no longer subject to penalty and at that point health savings account and 401(k) health plans are fungible.   The creation of health savings accounts is funded in large measure by reduced contributions to 401(k) plans because of this fungibility in funds after age 65 and because many middle-income households can’t save more.  Moreover, most middle income taxpayers realize a modest tax savings from additional contributions to tax-deferred accounts.

Third, the high out-of-pocket expenses under high deductible health plans and the lack of funds in health savings accounts results in many people with chronic diseases choosing to forego needed prescription drugs. Studies have shown that 20% to 30% of prescriptions are never filled and that around 50% of prescriptions for chronic diseases are not taken as prescribed.   The research indicates that a lack of adherence to prescription drug prescriptions contributes to 125,000 deaths, at least 10 percent of hospitalizations, and increased annual health costs ranging from $100 billion to $289 billion.

Intuitively, the growing use of health savings accounts and high deductible health plans has exacerbated this problem.  Prior to the introduction of health saving accounts many insurance plans reimbursed expenses for prescription drugs prior to the deductible being met.  High deductible health plans generally do not provide any reimbursement for prescription drugs or for any service until health expenses exceed the deductible.

The greater use of health savings accounts and high deductible health plans will result in sicker people having lower levels of retirement savings than healthy people.   This occurs because sick people disburse more funds from health savings accounts and health savings accounts crowd out other tax deferred retirement accounts.   Some people may economize by foregoing use of prescription medicines.   This strategy may cause them to leave the workforce due to a chronic disease.

The increased substitutability of health care and retirement savings and expenditures insures that sicker people who cannot extend their careers are most likely to have insufficient retirement savings.

How should the rules governing health savings accounts and high deductible health plans be altered to reduce these unintended problems?

Alternative Rules:

The memo proposes modifications to current rules governing health savings accounts and high deductible health plans, which will maintain and strengthen existing positive incentives and will reduce the tradeoff between saving for retirement and spending to maintain health.

Modification One: Tax payers with family income less than 400 percent of the federal poverty line would be offered a refundable tax credit of $750 for individual plans or $1,500 for family plans to fund their health savings account.   Higher income households could continue to make untaxed contributions to their health savings accounts

Comments on modification one:

This modification directly reduces the economic disparities between high and mid or low-income households stemming from the greater ability of higher income households to place funds in health savings accounts.

The additional cash given to low-income households should encourage more people to adhere to their prescription drug instructions.

The tax credit would only be available to people who have active qualified plans.   The loss of the tax credit from a lapse in insurance coverage serves the same purpose as the recently repealed individual mandate for the state markets.

Modification Two:  Contributions to health savings accounts would be allowed for people with higher coinsurance rate plans even if their plan had a relatively low deductible.

Comments on modification two:

The partial payment for prescription drugs prior to the insured meeting the deductible will reduce the number of people who do not adhere to prescription instructions because they lack funds for their prescription.

High deductibles tend to be a highly effective way to reduce premiums.  In most cases the high-deductible plan will be less expensive than the high coinsurance rate plan.  The choice between a high coinsurance rate plan and a high deductible health plan may depend on who pays the premium.   When employers or government subsidies pay for the premium households are likely to prefer the more expensive plans.  Individuals may be indifferent or prefer the less expensive plan when they are responsible for premium payments.

High coinsurance rate plans can in some circumstances provide a greater incentive to economize on health care plans than high deductible plans.   Consider the example in the box below.


Consider a simple example comparing incentives to economize for a high deductible health plan and a high coinsurance rate health plan.


The first plan has a $5,000 deductible and no coinsurance for expenses over $5,000.   The insured individual may be reluctant to spend anything on health care unless he believes that total expenses will go over $5,000.   Once expenses exceed $5,000 the person has no reason to economize of covered expenses.


The second health plan has a $0 deductible and a 50% coinsurance rate.    The person does not lose his incentive to economize on health care until or unless total health expenses exceed $10,000.


Modification Three:  Regulations governing prescription benefit formulas for high-deductible plans should be modified to require partial payment of prescription drug costs prior to the deductible being met.

Comment on modification three:

Patients who receive no prescription drug benefits until a very large deductible is met have a strong incentive to forego prescribed medicines.  This incentive is especially large for diseases like diabetes where the patient does not have immediate symptoms.  However, failure to control blood and failure to treat other chronic conditions can lead to bad health consequences in the long or medium term.

The disadvantage of modification three is that higher prescription benefits will increase premiums.

Cost Considerations:

The tax credit for contributions to the health savings account will result in a loss of tax revenue.  However, a tax credit that induces people to purchase less expensive health care plan could also reduce government subsidies for premiums.  The outcome may depend on whether and how the government subsidies for premiums both in state exchange markets and for employer-based insurance are restructured.

The cost of this proposal may also be offset by proposals designed to strengthen state market places created by the affordable care act.

Concluding Thoughts:

 There is something perverse about the movement toward health savings accounts and high deductible health plans when one considers the totality of the impacts.

The innovation makes health expenditures more expensive for low and mid income people with lower marginal tax rates.

This innovation creates an incentive for people to make contributions to health savings accounts rather than 401(k) plan.

People who are sick are more likely to spend funds in their health savings accounts than people who are healthy decreasing funds available in retirement.

People who have limited funds and high deductibles will have a large incentive to economize on all health expenses especially prescription drugs for diseases like diabetes.

The decision to forego necessary prescriptions and treatments will lead many individuals to get diseases that cause them to leave the workforce.

The current rules governing health savings accounts and high deductible health plans create a tradeoff — save for your retirement or take care of your health.   The tradeoff is most severe for the middle class and people with chronic health conditions.

Some Additional Readings:

Recent research has shown that a high deductible health plan coupled with a health savings account will be the only health plan offered by four of ten employers.

 Readers interested in empirical work on health savings account balances can go to the following study:

How Health Savings Accounts are Being Used Over Time:

Readers interested in learning more about failures to adhere to drug prescriptions can go here:

Some information on how diseases like diabetes affect workforce participation for people nearing retirement age can be found here.

Authors Note:  Please consider my book about ways to fix the student debt problem, available exclusively on Kindle and Amazon.



Diabetes and Employment

How Does Diabetes Influence the Impact of Aging on the Probability of Employment?

David Bernstein

Bernstein.book1958@gmail.com202 413 5492

Objective:   The purpose of this study is to evaluate how diabetes and complications from diabetes impact the relationship between age and attachment to the workforce for people nearing retirement age.

Research Design and Methods: The study uses data from the 2015 Medical Expenditures Panel Survey to examine how the relationship between age and attachment to the workforce differs across three health groups – (1) people without diabetes, (2) diabetics with no diabetic complications, and (3) diabetics with complications impacting either eyes or kidneys.   The sample covers 3314 people between the age of 58 and 66.  The dependent variable in the logistical regression models is whether a person was currently employed or attached to an employer during the survey period.   The coefficients of the logistical regression models are used to obtain employment probabilities for a specific worker at ages ranging between the age of 58 and 66.   These probability estimates allow us to examine how the impact of aging on employment probability is affected by diabetes and complications from diabetes

Results: The basic logistical regression model, estimated over the entire sample, reveals that diabetes and complications from diabetes lead to a substantial reduction in the likelihood a person nearing retirement age remains employed.  Separate logistical regression models reveal people without diabetes are better able to remain in the workforce until they become eligible for Social Security at age 62 and to remain in workforce additional years to increase their monthly Social Security benefit.   The tendency to exit the workforce early is especially pronounced for diabetics with complications.  The employment probabilities for a white college educated male at age 58-59 are 83.6 % for the non-diabetic, 76.4 % for the diabetic with no complications, and 32.3 % for the diabetic with complications. Employment probabilities at age 65-66 for the college educated white male are 57.0 % for non-diabetics, 40.1 % for diabetics without complications, and 11.5 % for diabetics with complications.

Conclusions:  Differences in how health conditions affect the impact of age on employment probability have important implications for the adequacy of retirement income and proposals to modify Social Security.  Relatively few people who leave the workforce early delay claiming Social Security to increase retirement income. Any increase in the age of eligibility for Social Security benefits would have harmful financial impacts on diabetics who already have a greater tendency to leave the workforce prior to age 62.  Medical expenditures that cure diabetes or reduce diabetes related complications would allow people to stay in the workforce longer and this expansion in workforce participation would stimulate economic growth.  Perhaps proposals to expand spending for improvements in health care outcomes should be evaluated based on dynamic scoring techniques to account for higher economic growth attributable to expanded workforce participation.


Previous research indicates diabetes has a statistically significant impact on employment or other work related productivity measures (1-6).  Diabetes is not the only disease associated with lower employment levels.   A recent blog post presented preliminary results indicated several diseases (diabetes, complications from diabetes, complications for diabetes, stroke, arthritis, asthma coronary heart disease, emphysema and cancer) reduced the likelihood a person nearing retirement age would remain employed.

Previous research has not examined how diabetes affects the impact of age on employment probability.   The exact age at which a person leaves the workforce has a large impact on household financial security, retirement income workforce participation and the Social Security system.

The financial incentives from Social Security on employment and on the decision of when to claim Social Security benefits are complex.  The maximum Social Security benefit can only be received by workers with an income history of 35 years.   62 is the earliest age where workers can claim Social Security retirement benefits but some workers may be eligible for a disability benefit prior to age 62.  The full Social Security retirement benefit for workers born between the years of 1943 and 1954 is 66 and workers who delay their retirement until 70 will further increase their retirement benefits.

Studies typically find that most people do not delay claiming Social Security after leaving work.  One highly influential study found that around 10 percent of men who retired before their 62nd birthday delayed claiming Social Security (7).

The relatively small percentage of people who are can delay claiming Social Security benefits after leaving the workforce suggests that the ability of people to remain in the workforce may be the most important determinant of financial security during retirement.  Furthermore, incentives designed to persuade people to work longer may be ineffective if a person is in poor health.  The empirical work presented here attempts to provide insight on how diabetes and complications from diabetes impacts attachment to the workforce as people age.

Research Design and Methods:

The study employs data from the 2015 Medical Expenditures Panel Survey (MEPS).  The MEPS survey contains detailed information on a wide variety of health topics including insurance, expenditures, and diseases of respondents. Data from the survey can be used to obtain estimates of national totals and averages.   The data can also be used to estimate relationships between economic variables and health variables.

The survey contains information on respondent employment status, whether the respondent has been diagnosed as having diabetes, whether diabetes has impacted eyes or kidneys, the respondent’s age and respondent’s education level.

The information on employment was obtained from questions EMPST53.  The dependent variable was set to 1 if the person responded she was employed at the time (option 1), had a job to return to during the round (option 2), or had a job at some point during the round.   This employment measure does not correspond to the concept of workforce participation used by labor economists.   People who are unemployed but actively looking for a position are considered workforce participants.

The key health related variables used in this study were obtained from variables DIABDX, DSKIDN53, and DSEYPR53. DIABDX asks whether a person has been diagnosed as a diabetic.  DSKIDN53 provides information about whether diabetes has ever caused kidney problems.  DSEYPR53 provides information on whether diabetes has ever caused eye problems.  The complications from diabetes variable used in this study is defined as having either kidney problems or eye problems caused by diabetes.

The MEPS database had a variable SEX used to create a dummy variable set to 1 if the respondent was male. The dummy variables ba_deg (has a BA degree or higher) and no_college (has not attended college) were created from responses to question EDUYRDG.

The first model considered in this paper involves using the entire sample to estimate the impact of diabetes and complications from diabetes on employment probability.  This approach implicitly assumes that the impact of aging on employment probability does not depend on whether the respondent has or does not have diabetes or diabetic related complications.

The second model considered in this paper involves the estimation of logistical regression models for three samples – (1) people without diabetes, (2) people with diabetes but no complications, and (3) people with diabetic related complications.   This approach allows us to contain separate estimates of the impact of age on employment probabilities for the three groups.

The regression coefficients obtained from logistical regression models can be used to examine the employment probability of an individual with specific characteristics at different age levels.   These probability estimates are generated by the following formula.


In this formula X is the vector of variable values and B is the vector of coefficients.

This formula was used to estimate the employment probability for a specific individual (a white male with a college degree) at the five age groups (58-59, 60-61, 62, 63-64 65-66). These estimates provide insight on when people with and without diabetes with and without complications from diabetes tend to leave the workforce.

In this model, employment probability estimates for females and people with educational background different than college educated would simply be a shifted version of the results for males with a college degree. The model specification used here does not allow for the impact of age on employment to vary with gender or sex.   The parsimonious model was selected due to the limited sample size in the MEPS database.

There is always room for additional sensitivity analysis of the model to alternative specification.  Am happy to look at specific suggestions from reviewers.


Most of the previous research motivating this paper involved an examination of how a disease impacted employment variables over a sample covering people in an age range.

The results of this approach for a model on how diabetes and diabetes related complications impacted employment based on people between the age of 58 and 66 from the MEPS database is presented below.


Logit Model of Disease on Employment, Entire Sample Age 58 to 66
Variable Coef. P>z
age5859 0.511 0.000
age6061 0.228 0.092
age6364 -0.225 0.101
age6566 -0.857 0.000
male 0.413 0.000
ba_deg 0.627 0.000
no_college -0.007 0.949
diabetes -0.505 0.000
complications -1.186 0.000
_cons 0.064 0.668
Number of obs 3314
LR chi2(9) 330.59
Prob > chi2 0
Pseudo R2 0.0722

The coefficient of the full-sample employment logit regression model reveal that both diabetes and complications from diabetes significantly decrease the likelihood that a person is employed.   This is consistent with other literature on the relationship between disease and employment.

The reported coefficients on the age variables are reflective of the difference in employment at specified age and the base group, which is people who are 62 years old.  The age coefficients for the model estimated with the full sample, people with and without diabetes, reveals that increases in age are generally but not always related to a decreased likelihood of being employed.

  • At age 58-59 the employment probability is significantly higher than at age 62.
  • At age 60-61 the difference in employment probabilities is not significant if one employs a one-tailed test with alpha equal to 0.05.
  • At age 63-64 the difference between employment probability at age 62 is not significant with a one-tailed test at alpha equal to 0.05.
  • At age 65-66 the employment probability is significantly lower than at age 62.

The impact of age on the employment probability may differ for people with diabetes and for people without diabetes.  Similarly, the impact of age on employment may differ between diabetics with no complications and diabetics with complications.   This issue can be considered by comparing logistical regression models for the three groups.   The results from the three logistical regressions are presented below


Employment Equation for Three Groups
No Diabetics Diabetics No Complications Diabetics with Complications
Variable Coef. P>z Coef. P>z Coef. P>z
age5859 0.585 0.000 0.248 0.458 0.014 0.985
age6061 0.274 0.069 0.118 0.726 -0.359 0.625
age6364 -0.190 0.212 -0.343 0.312 -0.470 0.551
age6566 -0.761 0.000 -1.327 0.000 -1.285 0.131
male 0.367 0.000 0.725 0.000 0.191 0.667
ba_deg 0.690 0.000 0.339 0.400 0.137 0.899
no_college 0.042 0.727 -0.307 0.277 -0.005 0.994
_cons -0.015 0.926 -0.138 0.714 -1.081 0.188
#  obs 2635 535 145
LR chi2(7) 181.58 53.98 4.43
Prob > chi2 0 0 0.729
Pseudo R2 0.05 0.0734 0.0305


The results presented here indicate that the impact of aging on employment probability differs sharply for the three groups of people.

The age589 coefficient is a measure of differences between employment probability at age 58-59 and age 62.   It is positive and significantly different from zero for people without diabetes but insignificantly different from zero for both diabetics with no complications and for diabetics with complications.   The lesson here is that diabetics with or without complications tend to leave the workforce early, often before they are eligible for any retirement Social Security benefits.

The age6566 coefficient is a measure of differences between employment probability at age 65-66 and age 62.      The point estimates are negative for all three groups.   The difference is significant for people without diabetes and for diabetics without complications.   The difference is not significant for people with diabetic related complications

Aging is not a statistically significant explainer of the employment probability for diabetics with complications.  None of the coefficients for the age variables are statistically different from zero (at alpha equal to zero) for the sample of 145 individuals with complications related to diabetes.   This occurs partially because the smaller sample size reduces the power of the statistical tests and possible because the employment probability is already lower at an earlier age.

Economists and health professionals could also benefit from information on the magnitude of differences in employment probabilities at different ages for different health profiles.

Separate employment probability estimates are presented for a male with a college degree for the three health condition groups.

Employment Probability Estimates for a

 College Educated Male

Age Not Diabetic Diabetic No Complications Diabetic with Complications
58-59 83.6% 76.4% 32.3%
60-61 78.8% 74.0% 24.8%
62 73.9% 71.6% 32.0%
63-64 70.1% 64.2% 22.8%
65-66 57.0% 40.1% 11.5%
% Change 58-59

 to 62

-11.6% -6.2% -0.9%
% Change 62

to 65-66

-22.9% -44.0% -64.0%

Results for a college-educated male.   Estimates for females and people with different education backgrounds would be a shifted version of this chart.

The estimates reveal that employment probability at age 58-59 is 7 percentage points higher for people without diabetes compared to people with diabetes and no complications.   The employment probability gap between people without diabetes and people with diabetic related complications is over 51 percentage point at age 58-59.

The decrease in employment probability from age 58-59 to age 62 is 11.6% for people without diabetes, 6.2 percent for diabetics with no complications, and -0.9% for diabetics with complications.   The lower decrease in employment probability for the two diabetic categories stems from the fact that many diabetics had already left the workforce at age 58-59.

The estimated employment probabilities at age 65-66 is 17 percentage points higher for people with no diabetes and diabetics with no complications.  The employment probability gap between diabetics with no complications and diabetics with complications at age 65-66 is around 29 percentage points.   Only 11.5% of diabetics with complications are employed at age 65-66.

The decrease in employment probability from age 62 to 65-66 is 22.9% for non-diabetics, 44.0% for diabetics with no complications, and -64.0 percent for diabetics with complications.

The examination of magnitudes in the shift of employment probability variable is especially important to better under the diabetes with complications group.   The age variables are not statistically significant.   However, the age 65-66 employment probability is only 11.5 percent, very low compared to other groups at this age.


Diabetes substantially reduces the ability of people to stay in the workforce as they age.   The impacts of aging on employment are especially large for diabetics with complications impacting eyes or kidneys.  A substantial number of diabetics especially those with complications leave the workforce before becoming eligible for Social Security Retirement benefits.   Diabetics especially those with complications appear unable to prolong employment to increase their Social Security benefit.

Diabetes is not the only disease impacting the relationship between age and employment.  A recent blog post using the same database employed in this paper found that a 10-factor disease index also affects the impact of aging on employment probability (7).

Many financial economists are fearful that improvements in health which increase life expectancy could worsen the finances of the Social Security system.   The results presented here indicate that improved health could increase workforce participation and spur economic growth.



  1. Tunceli, K, Bradley C. Nerenz D, Williams L., Pladevall, M and Lafata, J The Impact of Diabetes on Employment and Work Productivity
  2. Kahn ME: Health and labor market performance: the case of diabetes.J Labor Econ 16:878–899, 1998
  3. Bastida E, Pagan JA: The impact of diabetes on adult employment and earnings of Mexican Americans: findings from a community based study.Health Econ 11:403–413, 2002
  4. Kraut A, Walld R, Tate R, Mustard C: Impact of diabetes on employment and income in Manitoba, Canada.Diabetes Care 24:64–68, 2001
  5. Mayfield JA, Deb P, Whitecotton L: Work disability and diabetes.Diabetes Care 22:1105–1109, 1999
  6. Ng YC, Jacobs P, Johnson JA: Productivity losses associated with diabetes in the U.S.Diabetes Care 24:257–261, 2001
  7. Bernstein D, The Impact of Disease on Employment for People Nearing Retirement Age,
  8. Courtney, C., Diamond, P, Gruber, J,. Jousten, A.  Delays in Claiming Social Security Benefits, Journal of Public Economics, 84: 357-385, 2002



Short Term Stock Trends 8/17/2018


Question:   The chart below has information on number of times stock price has increased in the past 10 days for six ETFs.   The chart also has the median number of up days for a 10-day period over the past year for the six funds.

What funds have streaks that are above or below average?

Are there any obvious buy or sell signals?

The Data:

Short Term Stock Trends
Up days over last 10-day period Median Stock Up Days
Fund Sector 8/17/18 2017-2018
VDE Energy 6 5
VDC Consumer Staples 4 5
VFH Financial 6 6
VHT Health Care 6 6
VIS Industrials 5 6
VGT Information Technology 7 6


The Discussion:

Current number of stock wins out of 10 days is lower than median by 1 day for consumer staples and industrials.

Current number of stock wind out of 10 days is higher than median by 1 day for energy and technology,

I do not see any obvious buy or sell signals based on the analysis of number of recent up days.

This post relies on a previous Excel post on the use of the frequency function in Excel.




Impact of Market Changes and Interest Rates on Four Stocks

Question:   To what extent have the stock prices of four companies – Duke Power, Bank of America, IBM and Proctor and Gamble – moved with the overall stock market?   Do lagged movements in the overall stock market also impact the current period stock price?

How have changes in the 10-year government bond interest rate impacted the stock price for the four companies?

The Data:   The analysis presented here is based on monthly data starting with the fourth month of 1980 and ending with the seventh month of 2018.   N=456.

The Model:   The dependent variable is stock price at period t divided by the stock price at time t-1.   The explanatory variables are S&P 500 at period t divided by S&P at time t-1, three lags of this S&P ratio, and the ratio of the current 10-year government bond interest rate to the lagged 10-year government bond interest rate.

Results:   The results for the return equations for the four companies are presented below.

Duke Power
dukror Coef. P>t
spror 0.33556 0
lag1spror 0.0365767 0.546
lag2spror 0.058777 0.335
lag3spror -0.0211995 0.725
tenyrch -0.1645325 0.001
_cons 0.7624648 0
Bank of America
bacror Coef. P>t
spror 1.392815 0
lag1spror 0.0396445 0.68
lag2spror 0.1671838 0.085
lag3spror -0.0386275 0.686
tenyrch 0.1329733 0.079
_cons -0.6889676 0
ibmror Coef. P>t
spror 0.9212106 0
lag1spror -0.051747 0.444
lag2spror -0.0875875 0.199
lag3spror -0.0776229 0.248
tenyrch 0.0725273 0.172
_cons 0.2299272 0.089
Proctor & Gamble
pgror Coef. P>t
spror 0.5961397 0
lag1spror -0.0131834 0.844
lag2spror 0.0276608 0.682
lag3spror -0.0264788 0.692
tenyrch -0.0543051 0.173
_cons 0.4844197 0


Observations on Beta or Systematic Risk

The short-term beta is the coefficient of the current mark variable.

The long-term beta is the sum of the coefficients for the current market variable and the three lagged market variables.

Below is a chart comparing betas (both short and long term) from this model to betas published by yahoo finance.

Different Measures of Beta
Yahoo Finance Beta One Period Beta from Model Long Term Beta from Model
Duke 0.03 0.336 0.410
BAC 1.67 1.393 1.561
IBM 1.04 0.921 0.704
PG 0.43 0.596 0.584


The order of betas from this model and from Yahoo finance across the four companies least to highest are identical.

Both estimates reveal that Duke Power has the lowest beta and BAC the highest one.

Even though Duke Power still has the lowest beta, the estimates presented here indicate that Duke Power has far larger systematic risk than the Yahoo finance beta estimates.

In two cases, (Duke and BAC) the long-term beta is smaller than the short-term beta. The long-term beta for IBM is lower than the short-term beta.   The long and short term betas for PG are similar.

Need to do more research on reasons difference in companies that might cause this result.

Observations on the Interest Rate Coefficient

The 10-year interest rate is negatively related to stock price for only one company Duke Power.   This coefficient is significantly different from zero for a two-tailed test with alpha equal to 0.05.

The interest rate coefficients for the other three companies are positive but not significantly different from zero at a two-tailed test with alpha equal to 0.05.

Concluding thoughts:   The impact of interest rates on firm returns can be very complicated.  First, the direct impact on the S&P 500 should be modeled.  Changes in short rates could have a much different impact on rates than changes in long rates but this impact could be difficult to separate because of collinearity.

More empirical work on how interest rates impact stock prices will follow.



Flatting Yield Curves, Mortgage Rates and Choice of Mortgage

Flatting Yield Curves, Mortgage Rates and Choice of Mortgage

Question:  Short and intermediate term government bond rates have risen substantially more than long-term bond rates in recent months.   This pattern of rates is called a flattening yield curve.

To what extent has the government bond yield curve flattened between January 4, 2018 and July 26, 2018?

Has the yield curve for the mortgage market also flattened between January 4, 2018 and July 26, 2018?

Calculate mortgage payments for a 15-year and 30-year Fixed Rate mortgages on these two dates.  Calculate equity after five years for the 15-year and 30-year mortgage rates on the two dates.

Most market analysts at the beginning of the year were advising clients to take out a 15-year mortgage rather than a 30-year mortgage if the client could obtain the necessary down payment.

Have changes in market conditions warranted a change in this advice?

Descriptive Statistics on Government Bondn and Mortgage Market Interest Rates

Below are calculations on government bond yields and mortgage market rates for the two dates.

Government Bond Yields
4-Jan-18 26-Jul-18
2-year U.S. Bond Rate 1.931 2.686
10-year U.S. Bond 2.463 2.975
30-year U.S. Bond 2.786 3.101
10-year minus 2-year 0.532 0.289
30-year minus 10-year 0.323 0.126
Mortgage Market Yields
4-Jan-18 26-Jul-18
5/1 Year ARM 3.45 3.87
15-year FRM 3.38 4.02
30-year FRM 3.95 4.54
15-Year mins 5/1 ARM -0.07 0.15
30-year minus 15-year 0.57 0.52


The gap between 10-year and 2-year bond rates and the gap between 30-year and 10-year bond rate narrowed considerably between 1/4/2018 and 7/26/2018.

The spread between the 15-year FRM and the 5/! ARM went for negative to positive from January to the end of July.   This spread remained low.

The spread between the 30-year FRM and the 15-year FRM barely changed.

Below are calculations on mortgage payments and mortgage balance reduction after 5 years for the two mortgages on the two origination dates.

Mortgage Payments:

Mortgage 4-Jan-18 26-Jul-18
pmt 15-year loan $2,127.01 $2,222.07
pmt 30-year loan $1,423.61 $1,527.19
15-year pmt minus 30-year pmt $703.40 $694.88


Below are calculations on mortgage balance after 5 years of payments for the 145-year and 30-year FRM on the two origination dates.

Mortgage balance after 5 years of payments

Mortgage 4-Jan-18 26-Jul-18
15-year FRM $216,325.31 $219,268.50
30-year FRM $271,122.83 $273,639.10
Diff. ($54,797.52) ($54,370.60)


The gap between monthly payments on 15-year versus 30-year FRM went down between January and late July 2018 despite the slight flattening in mortgage rate yields.  (This occurred because the higher rates had a larger impact on 30-year payments than 15-year payments.)

The mortgage balance reduction obtained by taking the 15-year FRM over the 30-year FRM remains around $53 k.

Conclusion.  The government bond yield curve has flattened quite a bit. The mortgage market yield curve has not changed much.   The 15-year FRM remains the preferred mortgage option for those who can afford higher payments.


Interested Readers can go here for some articles on mortgage math and choice.

Impact of Gender on Annuity Payments

Impact of Gender on Annuity Payments

 Introduction Females have longer life expectancy than males in virtually all countries.   Gender related differences in life expectancy make it more likely that females will out-live their retirement resources than will males. Females, because of their longer life expectancy, might choose to purchase a longer-term annuity.

Question:   A 75-year old person has $100,000 to spend on an annuity., which makes monthly payments for a fixed period.  She or he wants to reduce the probability of outliving the annuity to below 10 percent.

What annuity term would accomplish this goal for a male and for a female?

How does the longer life expectancy of the female affect the size of the monthly annuity payment?

Data Source: This analysis is based on the United States Life Tables, 2008 published on September 24, 2012 by the National Center for Health Statistics of the Centers for Disease Control and Prevention

Table Two of the report has life statistics for males and Table Three of the report has life statistics for females.   Both tables can be downloaded directly into an EXCEL Spreadsheet.The data in the Table below is from the CDC life tables. 


Age Total number of females alive at age x Proportion of 75-year-old females who survive to age X Total number of Males Alive at age X Proportion of 75-year Males surviving until age X
75 73,974 61,980
76 71,973 97.3% 59,531 96.0%
77 69,831 94.4% 56,962 91.9%
78 67,539 91.3% 54,268 87.6%
79 65,080 88.0% 51,437 83.0%
80 62,448 84.4% 48,469 78.2%
81 59,647 80.6% 45,390 73.2%
82 56,688 76.6% 42,227 68.1%
83 53,563 72.4% 38,994 62.9%
84 50,253 67.9% 35,694 57.6%
85 46,782 63.2% 32,360 52.2%
86 43,166 58.4% 28,996 46.8%
87 39,414 53.3% 25,650 41.4%
88 35,567 48.1% 22,372 36.1%
89 31,677 42.8% 19,213 31.0%
90 27,805 37.6% 16,223 26.2%
91 24,017 32.5% 13,448 21.7%
92 20,380 27.6% 10,928 17.6%
93 16,962 22.9% 8,691 14.0%
94 13,821 18.7% 6,754 10.9%
95 11,006 14.9% 5,122 8.3%
96 8,549 11.6% 3,783 6.1%
97 6,467 8.7% 2,719 4.4%
98 4,754 6.4% 1,898 3.1%
99 3,392 4.6% 1,286 2.1%
100 2,345 3.2% 844 1.4%


 Calculation the Annuity Term:

Based on this cohort of 100,000 females, 73,974 females have survived to page 75.   Around 90% of these females are still alive until somewhere between age 95 and 96.

In a cohort of 100,000 men 61,980 are still alive at age 75 and the 90% survival mark for these 75-year olds is reached somewhere between age 94 and 95.

Let’s interpolate to get an exact number of months for our annuity formula.

For females we get 96-75 (21) years plus (11.6-10)/(11.6-8.7) x 12 or (7) months.  The 75-year old female must buy an annuity of 259 months  to reduce the probability that she will outlive the annuity to 10 percent.

For males we get 94-75 (19) years plus (10.9-10)/(10.9-8.3) x 12 or 5 months (I am rounding up to fulfill the contract.)   The 75-year old male must buy an annuity of 233 months to reduce the probability that he will outlive the annuity to 10 percent.

Calculating the Impact on Annity Payments:

So now we calculate the annuity payments for the female and the male with the PMT function.   The only input that differs is the duration of the contract – 259 months for females and 233 months for males.

The annuity payment calculations were obtained from the PMT function in Excel.


Female Male
Rate 0% 0 0
Rate 3% 0.03 0.03
Rate 6% 0.06 0.06
NPER 259 233
PV $100,000 $100,000
PMT rate=0 $386.10 $429.18 ($43.08) -11.2%
PMT rate =3% $524.96 $566.77 ($41.81) -8.0%
PMT rate=6% $689.45 $727.62 ($38.17) -5.5%


Conclusions:   Females must buy a longer-term annuity to obtain the same reduction in longevity risk as a male.   This reduces their monthly annuity payment.

This annuity calculator on the web confirms that females receive lower annuity payments and or pay higher prices for a comparable annuity.  I am not familiar with the specific formulas used by this calculator or the product that it pertains to.   My sole interest here is to provide some insight on how gender determines longevity risk.