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.







Survivor Bias and Stock Market Risk


Survivor Bias and Stock Market Risk


Shortly after the large stock price decline of Facebook on July 26,2018, CNBC posted an article with a chart of other large market-cap declines of U.S. stocks.   Every single company in the chart still exists as an ongoing company.   It appears as the chart was compiled from a database that only contain companies that are still listed.

What no longer actively traded companies might have made a list of the largest declines in equity value for large-cap companies?

Why does the exclusion of these companies from the chart create a misleading picture of the risk of investing in equity?

The chart lists three companies with large cap declines in 2018?  Why is the occurrence of so many recent large declines in big-cap equity a concern?

The article:

The Chart:

Market Cap Losses in Big Cap Stock


Date Decrease In Equity ($B)


Jul 26 2018 $114.50


sep 22 2000



Apr 3 2000


Apple Jan 24 2016


Exxon Mobile

Oct 15 2008


General Electric

Apr 11 2008



Feb 2 2018


Bank of America

Oct 7 2008



Apr 2,2018


Wells Fargo

Feb 5 2018



Jul 23 2002


JP Morgan Chase Sep 29 2008




What no longer actively traded companies might have made a list of the largest declines in equity value for large-cap companies?

Companies no longer actively traded, which experienced large one-day drops in equity value include   — Enron, Worldcom, the old General Motors, Lehman Brothers, Bear Stearns, and Merill Lynch.   There are probably many more.

Why does the exclusion of these companies from the chart create a misleading picture of the risk of investing in equity?

 First, this list suggests large drops in equity values occur less frequently than a chart composed from all firms that ever existed.

Second, a list of large declines composed of stocks that survived understates the potential loss of wealth from buying and holding stocks after a large decline.   In fact, all the stocks on the CNBC list have recovered nicely.

Third, an anaysis of risk, which includes bankrupt firms would encourage investors to seek greater diversification in terms of number of equity holdings, sector, and asset classes.

The chart lists three companies with large cap declines in 2018?  Why is the occurrence of so many recent large declines in big-cap equity a concern?

Facebook, Alphabet, and Amazon all had their large declines in 2018.   These are three of the four FANG stocks.   The smallest FANG company also has had a recent large percentage decline.

The most popular trendy sector of the stock market is now realizing extremely large one-day changes.   This appears to be happening with greater frequency.

The disproportionate number of 2018 large-cap declines in this chart convinces me that people who have made a lot of money in FANG and in other high-tech stocks need to take some money off the table when the stock prices reach new highs.

Of course, in the case of Facebook  this advise was more valuable prior to July 26.

The volatility of FANG names and other Tech stocks does not mean this is a good time to buy value stocks because the pending  increase in interest rates might hurt value stocks more than growth stocks

I would be alarmed by the large number of 2018 events even if the chart contained firms that were no longer actively traded.

The Democratic Split

Democrats are optimistic that the Russian and corruptions scandals will propel the party to victory in 2018.  Perhaps they are correct but I fear that they are wrong for two reasons.

First, President Trump continues to give weekly rallies to his enthusiastic base.  There are no figures on the Democratic giving large robust rallies.

Second, aside from Russia and corruption (admittedly two big asides) the entire debate today centers around Trump priorities – basically immigration, trade and low taxes.

The Democrats do much better when the conversation involves health care, student debt, pensions and Social Security.   The common theme linking these issues is that despite the currently strong economy many Americans are financially insecure and are having trouble saving for the future or for education.

Why aren’t Democrats out there rallying their base the way Trump is?

Why aren’t Democrats talking more about financial security — health care, student debt and retirement – issues of concern to working-class households?

The basic answer is that there is a huge split in the Democratic party both on economic priorities and appropriate policies.  This split is paralyzing the party and impeding the delivery of a viable progressive agenda.

 The liberal wing of the Democratic Party offers transformative radical change.  The centrists believe that the liberal wing’s policy proposals are unrealistic and could make many people worse off.

The centrists offer relatively modest policy changes and appear to only reluctantly embrace left-wing proposals when they need votes.   The current message offered by the centrists will not rouse the base.

The liberals correctly believe the current centrist agenda would at best maintain the status quo and at worse could implement compromises with Republicans that will weaken the existing safety net.

This conflict can be illustrated by a discussion of three issues – health care, student debt and retirement savings.   These issues allow for the Democrats to create a theme for 2020.   The theme is how do we make Americans more financial secure and what party do you trust to do this?

This is a good place for me to state my bias.   I am a centrist not a liberal.  However, many of the current policy proposals offered by centrists are insufficient.

Here is an outline of some policy ideas, which could bridge the gap between centrists and liberals.

Policy Priorities

Discussion of Health Care:

It is hard to understand why Democrats aren’t spending more time talking about health care.   The number of uninsured Americans without health insurance rose by 3.2 million people during President Trump’s first year in office.   This issue and other problems with health insurance markets received more coverage in CNBC than by MSNBC.

The liberals want single payer health care.   The fact that single-pay works well in some countries, which have only known single payer, does not mean that the United States could transition from the current system to a single payer system.

The adoption of a single-payer system would make some people more financially secure but would make many people worse off than the current situation.   Many health care providers and doctors would have substantially lower compensations.   This would be a disaster for new doctors with substantial medical school debt.  The single-payer would be more generous than some private plans but might deny or provide insufficient reimbursement for expensive procedures.

Many centrists have endorsed and voted for a Medicare for all plan, even though their more detailed thoughts are more in line with ACA modification proposals.   They argue their vote is a symbolic one in support of universal coverage.   I would argue this vote is a pander.

The centrists want to repair the ACA but their discussions do not fully acknowledge that problems with the ACA existed even before the Trump Administration weakened the program. The ACA was a big step forward but also a disappointment compared to where we want to be.

Despite the enactment of the ACA, insurance premiums and out-of-pocket expenses have continued to rise.  There is some evidence that state exchange insurance has narrower networks and entail higher costs than some employer-based insurance.  Moreover, people who take ACA coverage are required to take employer-based insurance if they obtain a job with an employer that offers coverage.  Rules and tax incentives favoring employer-based insurance over state exchange insurance weaken state market places.

There is no doubt that Trump Administration polices – ending the individual mandate, reducing funds for ACA enrollment, potential new rules allowing alternatives to ACA policies and a freeze on ACA reinsurance payments – have weakened state exchanges and are responsible for the increase in the number of uninsured.

However, centrists need to do more than offer a patch to the ACA.   They need to offer a vision on how we can move to a system that provides more coverage, lower out-of-pocket expenses, and access to all procedures and drugs.

Authors Note: I am currently working on a health care proposal.   It will be published by the end of 2018.

Discussion of student debt:  It is hard to believe that the Democrats aren’t talking a lot more about student debt, especially given recent Trump Administration proposals.   Recent actions or positions taken by the Trump Administration on student debt include:

  1. The proposed elimination of the public service loan program,
  2. The proposed elimination of subsidized student loans,
  3. The end of compensation for student borrowers who are victims of fraud,
  4. The reduced enforcement of rules allowing enrollment in Income Based Replacement loan programs

Why aren’t Democrats talking more about these student debt issues?

The liberal wing wants free college for people attending public universities.   This does work in some countries.  However, free public college is very expensive and the transition would adversely impact private institutions.

The centrists need to come up with innovative pragmatic solutions to the college debt problem and incorporate these proposals in their standard speech.

I have published a working paper, which lists 12 pragmatic ways to reduce the growth of student borrowers with excessive student debt and mitigate debt burdens for overextended borrowers.

One of my proposals involves providing additional financial assistance and reduce student loans to first-year students who do not have an extensive credit history or proven academic record.

A second proposal reduces interest payments after 15 years.   This approach is likely to be more effective than current loan forgiveness programs, which are designed to discharge debt.

My student debt proposals are available in my working paper on Amazon.

Discussion of retirement security issues:   Retirement security entails Medicare, Social Security and 401(k) plans.

The discussion on this issue should start with a recognition that under current law there will be automatic cuts to Social Security and Medicare benefits unless Congress acts.   Democrats need to ask whether Republicans can be trusted to act given their performance on ACA repeal or replace.

In the 1980s, President Reagan and Democrats in Congress came together to fix Social Security.   The Democrats need to ask whether the current Republican party can be trusted to compromise on this issue.

The other aspect of the retirement security problem is that many workers have insufficient retirement savings. Today few companies provide workers with traditional pension plans.   Many 401(k) plans have high fees and most lack an annuity option during retirement.   Many workers are unable or unwilling to maximize their contribution to 401(k) plans and often the money in these plans is disbursed prior to retirement.

The Democrats then need to provide detailed proposals on how to improve retirement security.   These proposals should recognize two important goals – (1) Social Security needs to be placed on a sound finance system and (2) the entire retirement savings system needs to be improved.

The Democrats need to advance policies that achieve both these goals and must reiterate opposition to Social Security benefit cuts that worsen retirement security.   The proposed solution is likely to include either additional revenue or use of some general tax revenue to maintain current Social Security income.

The Best Dialogue for Democrats

The current political dialogue is being set almost entirely by Trump and the Republicans.   Their focus is on trade and tariffs, immigration, and standing for the national anthem.

My thesis in this essay is that Democrats need to put financial security — health care, student debt, and retirement income at the center of the national discussion.

Centrists must move forward with a pragmatic progressive approach to these issues.  Many key centrists are spending more of their time either pandering to liberals or bashing liberals for being too radical than proposing polices that solve problems.

Some Democrats, both progressives and centrists, are more focused on tax issues and/or inequality.  The centrists are concerned that proposals by liberals will explode the deficit.  They should be more focused on revenue losses from the recently enacted Trump tax cut.

Elizabeth Warren recently pointed out the America was more prosperous when marginal tax rates were over 50 percent.  This defense of high tax rates is a losing argument both substantively and politically.  The decrease in prosperity or the increase in inequality was more likely caused by loss of jobs from factories moving overseas and from technological changes which reduced wages of low-skilled workers.

Tax policy is complicated.   A case can be made for changes in the tax code to obtain more revenue.   However, economists have found that high marginal tax rates change distort behavior.   Most notably, high marginal tax rates can decrease work, especially in two-worker households.

An economic agenda stressing reforms that will improve household financial security will resonate more with voters than an agenda focused on taxes and income inequality.

We live in a world where every one of Trump’s utterances and farts dominates the news cycle. Democrats seem totally incapable of prioritizing the farts.   In my view, Trump’s treasonous approach to Russia and separation of children from parents at the border are more important than Stormy Daniels

Democrats must respond to the moral dilemma created by the Trump Presidency.   However, at the end of the day a person struggling with student debt, worried about health care coverage for her family, and worried about whether she will be able to retire with decent income is more concerned about financial security than the scandal of the day.

Democrats need to get out there and reset the nation’s agenda.  To modify Bill Clinton said it was the economy stupid.   My view is that the economy must be broadly defined to include financial security.

Holdings of Ten Emerging Market Funds

Holdings of Ten Emerging Market Funds

This post started with a list of emerging market funds found at the site below.

I examine and describe the holding and recent returns on the 10 largest of these funds.

I comment on the holdings of these funds, the risk of these funds and the risk of some of the holdings.

List of Funds, Discussion of Geographic Diversifications, and YTD returns:

Some Information on Ten Emerging Market Funds
Symbol Fund Geographic Concentration YTD Returns
VWO Vangarud FTSE Emerging Market 7 of top ten holdings are in China -7.32%
IEMG I Shares Core MSCI Emerging Market 7 of top ten holdings are in China -6.95%
EEM I Shares MSCI Fund 7 of top ten holdings are in China -7.44%
SCHE Schwab Emerging Markets Fund 6 of top ten holdings are in China -7.34%
FNDE Schwab Fundamental Large  Firm Emerging Market Index Largest holding is from Korea and second and third largest holding are Russian.  Top 10 holdings also include companies from China, Brazil and Taiwan -6.71%
DEM Wisdom Tree Emerging Markets Equity Income Fund Top two holdings are Russian.   Most other top ten holdings are form China or Taiwan. -4.54%
RSX Van  Eck Vectors Russia ETF All holdings appear to be in Russia. 4.36%
GEM Goldman Sachs ActiveBeta Emerging Markets Equity ETF 7 of top ten holdings are in China -6.75%
SPEM SPDR Portfolio Emerging Markets ETF 6 of top 10 holdings are in China -6.54%
DGS Wisdom Tree Emerging Markets Small Cap ETF Top 10 holdings are less than 9 percent of all holdings.   Highly diversified, smaller companies. -7.34%


Some Observations:

Many of the funds have a very large share of their funds in China.   In fact, some of the emerging market funds could accurately be called China plays.

Three of the funds have substantial issues in Russia.  Also, most but not all, of the Russian holdings are in the oil and gas sector.  Important to research holding If concerns about corruptions and sanctions would deter you from investing in Russia.   Energy funds that are not in Russia may be preferable to Russian energy plays.

Nine of the Ten funds have negative YTD returns.  The fund that exclusively invests in Russia has a +4.36% return. This fund performed really poorly in prior years.  The YTD return on U.S. large cap stocks is around 6.0%, largely because the market has been up for the past week or so.

Can investments in emerging market ETFs provide insurance against a major downturn in the U.S. market?

 Short answer is probably not:   The downturn in emerging markets in the 2007 to 2009 crisis was larger than the downturn in large-cap U.S. stocks.

Go here for discussion of emerging market funds during the financial crisis

Thoughts on specific holding of emerging market funds:

Emerging market funds have some well know reputable holding and some firms with dubious reputations, and some firms with little name recognition.

The most successful holdings of the funds in this sector include: (1) Alibaba, (2) Tencent and (3) Baidu Inc.

Investors who want a taste of advanced emerging markets or China may be better off directly investing a small fraction of their wealth in these companies.

Emerging Markets During the Financial Crisis

Emerging Markets During the Financial Crisis

True or False:   During the 2007 financial crisis emerging market funds outperformed U.S. large Cap funds?

Answer:  False:

Evidence:   The chart below compares peak price in 2007 prior to stock market collapse and trough price in 2009 prior to the recovery.   The peak price for VLACX was on October 1, 2007.   The peak price of VWO, the largest emerging market fund, occurred a bit later, on October 22, 2007.   The trough price for both funds was realized on March 2, 2009.

U.S. Large Cap versus Emerging Market During the Financial Crisis
Funds Peak Before Crash in October 2007 Trough at End of Crash in March 2009 % Decline
VLACX U.S. Large Cap 28.1 12.6 55.3%
VWO Emerging Markets 57.5 19.0 67.0%

The collapse in the Vanguard emerging market fund was larger than the collapse in the Vanguard large-cap U.S. equity market.

Perhaps some other emerging market fund did better but I doubt it.

Asset Allocation for Twelve Sector Funds

Asset Allocation for Twelve Sector Funds

Issue:  Under an asset allocation investment strategy, an initial allocation is assigned to all assets in a portfolio and the portfolio is rebalanced from time to time to maintain the original composition of assets.   The rebalancing can be at scheduled dates or whenever the portfolio manager observes large changes in relative asset prices.

The original allocation of assets is maintained by selling assets that do well and buying assets that do poorly.   This approach can backfire.   A hedge fund manager who bought horse and buggy stocks and sold car stocks after the introduction of the car would not have done well.  However, asset allocators who sold internet firms prior to the tech bubble in the late 1990s did quite well.

Question:   Table one below has stock price information on 12 sector ETFs offered by Vanguard for three dates – 7/1/13, 7/1/16, and 6/29/18.

Using this price data, calculate the average annual return between 7/1/13 and 7/116 and the average annual return from 7/1/16 to 6/29/18 for the 12 funds.

What do these annualized return statistics suggest about the likelihood of success of an asset allocation strategy, which starts out with equal shares of the 12 ETFs on 7/1/2013 and rebalances on 7/1/2016.

Adjusted Close Stock Price for 12 Sector Funds
Symbol Fund Description 7/1/13 7/1/16 6/29/18
VDC Consumer Stables 93.55 133.53 134.27
VDE Energy 103.12 88.25 105.08
VFH Financials 38.12 47.48 67.45
VHT Health Care 86.84 133.78 159.14
VIS Industrials 79.06 106.53 135.81
VGT Information Tech 73.07 112.61 181.42
VAW Materials 82.52 104.33 131.56
VNQ Real Estate 56.70 84.58 81.46
VOX Communications Services 68.28 94.02 84.92
VPU Utilities 72.52 106.33 115.96
GLD Gold 127.96 128.98 118.65
SLV Silver 19.14 19.35 15.15

A note on calculations:   The return between two dates is obtained from the formula (APt/ APt-n(1/n)-1

The first period is three years and the second period is two years.   (n is 3 for first period and 2 for second period.)

The table below sorts the funds from least to highest annualized return during the first period.

Annualized Rate of Return for 12 Funds
Symbol Fund Description July 2013 to July 2016 July 2016 to July 2018 Diff.
VDE Energy -5.1% 9.1% 14.2%
GLD Gold 0.3% -4.1% -4.4%
SLV Silver 0.4% -11.5% -11.9%
VFH Financials 7.6% 19.2% 11.6%
VAW Materials 8.1% 12.3% 4.2%
VIS Industrials 10.5% 12.9% 2.5%
VOX Communications Services 11.3% -5.0% -16.2%
VDC Consumer Stables 12.6% 0.3% -12.3%
VPU Utilities 13.6% 4.4% -9.2%
VNQ Real Estate 14.3% -1.9% -16.1%
VHT Health Care 15.5% 9.1% -6.4%
VGT Information Tech 15.5% 26.9% 11.4%


Information Technology, the best performing fund in the first period, was also the best performing fund in the second period.  This asset allocation strategy would have reduced holdings of an asset, which continued to out-perform all other assets in the portfolio.

Energy, the worst performing fund, in the first period, had a return 3 percentage points over average of the 12 ETF returns in the second period.

Four of the six worst-performing sectors in the first period realized improved returns in the second period.

Five of the six best-performing funds in the first period had worse returns in the second period.  (The only exception is the previously mentioned information technology fund.)

The median annualized return in first period was 10,9 percent.   Only four funds had annualized returns over this level in the second period.

Two sectors – financials and information tech – are positive outliers in the second period.  However, financials have underperformed in last few months.

Concluding Remarks:   Information Tech, the best performer in both time periods, did spectacularly in the second period.  Asset allocators sold the best fund.

Asset allocation strategies tend to work more consistently when the investor holds broader funds, including both the overall stock market and debt funds.  Subsequent research will look at situations where asset allocation provides better results.

Authors Note:  Interested in financial problems caused by student debt.   Take this quiz on student debt trends and proposed policy changes.

Review of Measuring Portfolio Valuation

My blogging ground to a halt the last few weeks because I was completing a paper “Measuring Portfolio Valuation. “  Will put link to paper here shortly.

My new paper looks at two issues.   The first issue involves correct and incorrect ways to measure the PE ratio of a portfolio of stocks.   The second issue involves the correct way to conduct statistical tests on valuation measures for groups of stocks.

The paper starts with a discussion of the limitations of the PE ratio, the most commonly used valuation measure for common stocks.   The PE ratio is undefined when earnings are negative and unstable when earnings are small. By contrast, the ratio of the difference between market cap and earnings to market cap (denoted (MC-E)/MC) has a clear economic meaning when earnings are negative and is not an outlier when earnings are low.  In addition, there is a one-to-one relationship between this ratio and the PE ratio.

Many investment firms use a weighted average of firm PE ratios to measure the PE ratio of their ETFs or mutual funds.   The firms often discard observations from firms with negative earnings and cap the PE ratio of firms with high PE ratios.   These methods are arbitrary and often tend to understate the valuation of stock prices relative to earnings.

The ratio of the sum of market caps of firms in a portfolio to the sum of earnings of firms in the portfolio is the correct way to measure the PE of a portfolio.   This measure of PE can include all firms even firms with negative earnings.  Moreover, small changes in earnings for firm with high PE ratio do not have a large impact on the overall portfolio PE ratio.

A second way to measure the PE ratio of a portfolio, which relies on the weighted average of the statistic ((MC-E)/MC) is presented and shown to be equivalent to the ratio of the sum of market cap to sum of earnings.   This result is motivated in the following blog post.

Two Ways to Calculate a Portfolio PE Ratio:

The paper contains a formal proof demonstrating the two methods of constructing a portfolio PE are identical.

Often analysts conduct hypothesis tests on portfolio financial ratios.   Tests based on PE ratios often provide misleading results because of problems measuring the PE ratio when earnings are negative or small.   Firms with negative earnings are routinely omitted from the sample.  The standard deviation and skew of portfolio PE ratios are often large making it difficult to reject a null hypothesis.

By contrast, statistical tests based on (MC-E)/MC do not require the omission of firms with negative earnings.  Moreover, the distribution of (MC-E)/MC appears normally distributed with few outliers.    As a result, statistical tests using this ratio are more reliable than statistical tests using PE ratios.

Discussing Buy Versus Rent Calculators

  Discussing Buy Versus Rent Calculators

Realtor groups have created a number of on-line calculators that attempt to provide an objective view of the advantages of buying a home versus renting a home.  The link to one such calculator is presented below.

First, I describe the calculator.   Then I critique it.

Description of Calculator:

The simple version of the buy/rent calculator at allows one to put in an address and get financial estimates for renting or buying.  The more advanced and interesting version allows a consumer to select assumptions on costs of buying and cost of renting.

The key assumptions on the cost of buying involve home price, down payment mortgage term, buying costs, selling costs, house appreciation, real estate taxes and miscellaneous homeowner fees.

The most important renting costs include the initial rent and the yearly appreciation in rent.

Other key assumptions include the exemption of  $500,000 on capital gains in housing, an investment return, and an inflation rate.

Based on the inputted assumptions the model provides an estimate of the amount of time that it takes for buying a home to be cheaper than renting a home.

The model at assumes that buying costs are 4.0 percent of the purchase price and selling closing costs are 6.0 percent of the final sales price.   Due to transaction costs associated with home purchases, renting will be less expensive than buying for people who stay in a house for a short period of time.   The output of the model is the number of years it takes for buying to be less

Comments on the calculator at


Comment One:  Often realtors and bankers persuade young homebuyers to use available cash for a down payment rather than immediately retire consumer or student debt.  The model does not have an option to explicitly consider the impact of credit card debt or student debt on the buy versus rent outcome.   The model does require input on the assumption of investment returns.   One way to model the impact of keeping debt is to increase the investment return assumption so that it equals cost of credit cards and student loans.   It would be useful if the model allowed for separate assumptions on investment return and the cost of existing debt.

Comment Two:   I modified one example to consider the breakeven point of a transaction with a 15-year FRM at current interest rates.   I found that buying was preferable to renting after a 6-year period for the 15-year FRM compared to 8 years for the 30-year FRM.   Essay Four provides more information on mortgage choice and lifetime savings.

Comment Three:   The model cannot be easily modified to allow for interest rate uncertainty associated with adjustable rate mortgages.

Comment Four: The model requires an assumption of average annual growth in house appreciation over the entire period and does not consider issues related to the uncertainty of future house appreciation.  House prices do not appreciate in a steady or reliable fashion.   The realtor’s model would have severely overestimated the value of buying a home during the 2004 to 2009 time period and would have underestimate returns from purchasing in 2011 or 2012.  The argument that housing prices would continue to rise was made quite strenuously in 2007 and was used to motivate unrealistic price appreciation assumptions in the breakeven analysis.

The house price appreciation assumption is usually based on what the analyst expects will occur.   An alternative approach would involve basing this parameter on the certainty equivalent.   A certainty equivalent is the guaranteed return that someone would accept rather than take a risk on a higher but uncertain return.

Comment Five. Many people are forced to move because of a new job or divorce.   The rent versus buy calculator does not allow for economic costs associate with moving when house prices fall and house equity turns negative.   Nor does the buy versus rent calculator consider economic costs associated with negative equity that make it difficult for a home buyer to refinance should interest rates fall.


The more relevant question not answerable from this calculator is it better for a person to buy now or reduce debt and buy in a couple of years.

Comment Six:  Often realtors will expect home sellers to put additional investments into the property prior to selling the home.  (Most recently in many neighborhoods realtors are pushing home sellers to install granite kitchen tops.)   The model does not include an option to consider likely upgrade costs.  It may be able to correct for this problem by reducing the price appreciation assumption in the model.  However, the need for upgrades appears to differ widely across properties.

Comment Seven:: The buy-sell calculator can also be used to evaluate mortgage properties financed with FHA loans.   The FHA loan program is geared for relatively small mortgages.  The program has a loan limit that varies across counties and can change over time.   The FHA loan program allows for down payments as low as 3.5% FHA loan costs include mandatory mortgage insurance premiums, part of which is paid up front.  Due to the insurance premiums the cost of the FHA loan is often one percent point higher than the cost of conventional loans.  Most often, the number of years it takes for a home buyer to break even on an FHA loan program will be substantially higher than the number of years it takes to break even on a transaction financed with a conventional loan.   Not surprisingly, the use of real estate break- even calculators is usually illustrated with conventional loan examples rather than FHA loan examples.

Comment Eight: The assumption regarding the rate of appreciation of rents has a major impact on the buy versus rent decision.    A larger percent of people are choosing to rent rather than buy consequently more rents are continuing to rise often at a rate that exceeds the increase in the value of the home.   In some markets it may be legitimate to assume a higher increase in rents than home prices.  This alternative assumption might persuade more people to buy rather than rent.

Comment Nine:  Realtors often argue that a house purchase should occur now rather than later because macroeconomic conditions are about to change.   Over the last three or four years realtors have argued that people should buy because the FED is about to raise interest rates.  An increase in interest rates induced by Fed policy would increase the cost of interest on a home but might also lower house prices.

The Fed will eventually raise interest rates but even Nobel Prize winning economists are confused about when this will happen.  Potential homebuyers should not rely upon the interest rate forecasts of realtors when determining whether or not or buy or rent a home.

Concluding thoughts on the Limitations of Buy Versus Debt Calculators:  My comments suggest that for a wide variety of reasons buy versus debt calculators often overstate the case for buying rather than renting a home.    The approach relies on subjective assumptions on a wide variety of economic variables.   Assumptions on the most crucial variable – the future growth of housing prices have been grossly inaccurate in the past.

The one factor that favors buying over renting in the current environment is that stock prices are currently at historic highs and long term interest rates are at historic lows.   I suspect that based on the current market conditions returns on real estate will outpace returns on financial assets in the near future.  Hence an assumption of a low future return on financial assets might be justified at this time.

The buy versus rent calculator does not accurately measure the benefits of delaying a home purchase until consumer debt and student loans are substantially reduced or eliminated.   Nor does the model allow for active consideration of costs, which might be incurred if a young worker with little initial house equity is forced to sell a home in order to take advantage of a new job opportunity.  Usually younger households will be much better off by delaying the home purchase and using all available funds to retire student loans and consumer debt.