PLUS Loans for Parents and Parent Income

PLUS Loans for Parents and Parent Income

Question:  How has the use of PLUS loans for parents changed over time for parents of student attending undergraduate institutions and for students attending graduate schools?   What is the share of PLUS loans taken out by parents with income in the bottom quartile?

Does it appear that parents taking out PLUS loans for students have adequate income to repay their obligations?

Why this issue is important:  Parents who have problems repaying PLUS loans are not allowed to default on the loan.   Increasingly, many parents with PLUS loan obligations have had problems repaying and in some cases the government has garnished Social Security benefits from these borrowers.   It is possible that many of the financial problems caused by use of PLUS loans could have been prevented if lenders had considered the adequacy of parent income prior to making the loan.

Data and Methodology:

I addressed this issue with TRENDSTATS from the NCES DATALAB.

TRENDSTATS allowed me to get data on use of parent plus loans by income quartile for five different survey years  — 1996, 2000, 2004, 2008 and 2012.

I created separate analysis for parents of undergraduate students and parents of graduate students.

The table on PLUS loans for undergraduates only involves parents of dependent students.

The table on PLUS loans for graduate students uses the combined income of the student and the parent.

Results:  Two tables on PLUS loan use and income quartiles over time are presented below.

Percent of Dependent Parents with PLUS Loans by Income Quartile
Year Lowest 25th  Percent Lower Middle 25th  Percent Lower Upper 25th  Percent Upper 25th  Percent Total
1996 2.96 5.56 6.38 5.65 5.06
2000 3.56 5.48 8.61 6.76 6.07
2004 3.92 6.53 9.34 8.34 6.98
2008 4.33 6.73 9.37 8.86 7.25
2012 6.22 9.17 11.33 10.87 9.27
Percentage Growth 1997 to 2012 109.91% 64.96% 77.57% 92.49% 83.27%

Sample is all parents of dependent undergraduate students

Parent Plus Loans for Graduate Student by Quartile of

Sum of Parent and Student Income

Year Lowest 25th  Percent Lower Middle 25th  Percent Upper Middle 25th  Percent Upper 25th  Percent Total
1996 6.83 3.94 2.36 0.80 3.48
2000 7.37 5.75 4.14 2.90 5.07
2004 7.98 6.18 3.44 3.87 5.51
2008 9.82 8.14 5.48 3.88 6.76
2012 11.47 7.87 5.23 3.27 7.13
% Change 67.85% 99.63% 121.73% 308.91% 104.82%

Analysis of Percent of Plus Loans Across Income Quartiles:

Undergraduate Students:

The lower upper 25th percentile had the highest share of students dependent on PLUS loans for parents in all years.

Growth rate in use of PLUS loans for parents is highest in the lowest 25th percentile.

Graduate Students:

The lowest 25th percentile consistently had the highest percent of people dependent on PLUS loans for parents.

The upper 25th percentile had the highest growth rate in the use of PLUS loans for parents; although, the PLUS loan share for this quartile remained lower than all other quartiles in 2012.

Share of PLUS Loans Taken Out by Parents in First and Second Income Quartile:

Above I discussed the percent of students in each quartile that used a PLUS loan.

Here I look at the percent of students using PLUS loans that are in particular quartiles in each income quartile.

PLUS Loans for Parents Usage
Number out of 1,000 per income quartile
Q1 Q2 Q3 Q4 Total
Undergraduates 62.2 91.7 113.3 108.7 375.9
Graduates 114.7 78.7 52.3 32.7 278.4
Share in Each Quartile
Q1 Q2 Q3 Q4 Total
Undergraduates 16.5% 24.4% 30.1% 28.9% 100.0%
Graduates 41.2% 28.3% 18.8% 11.7% 100.0%

Calculations above are for 2012

Observations on use of Parent PLUS Loans Across Income Quartiles:

Lower-income people take out a lot of PLUS loans.

16.5 percent of PLUS loans taken out by parents of undergraduates are in the lowest income quartile.

41.2 percent of PLUS loans taken out by parents of graduate students are in the lowest income quartile.

Methodological Note:

I wanted the software to provide numbers of students in each income quartile based on population weights.   I would have obtained contingency tables based on population weights in SAS or STATA if I had access to the raw data files.  TRENDSTATS does not appear to have this capability.   Alas, I don’t have access to the raw data so this could not happen.

I attempted to switch the row and column variables in TRENDSTATS but the TRENDSTATS software does not allow for automatic creation of income quartiles when parent income of dependent variable is the column variable.

How then did I get the share of loans for all income quartiles?

By definition, each quartile has the same number of observations so I assumed each group had 1000 students.   I multiplied 1000 by share of students using PLUS loans for each quartile to get PLUS loan use per 1,000 students.

The sum of these numbers is total PLUS loan use across all students.   I divided PLUS loan use by income quartile by total PLUS loan use in the population to get quartile shares.

I am very interested in understanding the advantages and limitations of the POWERSTATS and TRENDSTATS education department software and will continue to make comments that might lead to improvements in the on-line databases.

Concluding Thought:

Barring really exceptional circumstances, student debt including PLUS loans obtained by parents is not forgiven or discharged even in bankruptcy.   Lenders happily give PLUS loans to lower-income parents because the loans are guaranteed even if the lender cannot make repayments.

The combination of government guarantees for loan payments and a prohibition on discharge of loans in bankruptcy has led to a thriving debt market geared towards people with little chance of repayment.

The Elimination of Subsidized Student Loans

The Trump Administration is proposing the elimination of subsidized student loans.  This post provides estimates of the additional costs of this proposal based on the number of years students stay in school.

Introduction:   Currently, low-income undergraduate students can take out a total of $31,000 in federal student loan.  Subsidized student loans are only available to people in low-income households.  The main difference between subsidized and unsubsidized student debt is that the government pays all interest costs on subsidized debt when the student is in school while interest accrues on unsubsidized loans.

The current limit on subsidized student loans is $23,000.  The total limit on undergraduate federal student loans is $31,000.

The Trump Administration is proposing to eliminate all subsidized student loans.

The purpose of this post is to model and analyze the  impact of this policy change for a student who is planning to take full advantage of subsidized student loans.  I also examine how this financial cost depends on the number of years it takes for the student to graduate.

Methodology:   I set up a spread sheet where the key model inputs are number of years it takes for a student to graduate, the interest rate on the student loan, and the maturity of the student loan.

Key Assumptions:

In this model, I assume the student borrows $31,000/n each year where n is the number of years it takes for the student to graduate.  When subsidized loans exist the annual total borrowed for subsidized loans is $23,000/n and total unsubsidized loans for the course of the person’s undergraduate career is $8,000.

(An expanded version of this model will consider uneven borrowing scenarios, where student borrows a different amount each year or perhaps drops out from school for a few years.)

Student remain in deferment until six month after graduation or leaving school.

Student does not apply for loan deferments for economic hardships or when unemployed.

The interest rate is 5 percent.

Student loan maturity is 20 years.

The procedure to calculate lifetime costs involves two steps.

Step One: Calculate the total loan balance on the day the student borrower starts repayment.  The subsidized loan at time of repayment is equal to the balance when issued since all interest is paid for. The FV of the unsubsidized loan is determined at time of graduation and multiplied by (1+0.05)0.5 to account for the six-month delay in repayment after graduation.

Inputs of FV function:

INT interest rate 0.05 or some other assumption.

NPER number of periods in this case number of years in school.

PMT is payment in this case the annual loan amount.

PV in this case 0

Type is ! for end of period.

The FV gives the value of the loan at graduation.   Repayment is six months later.   The value of the loan at repayment is FV0.5

The total loan balance is the sum of the subsidized and unsubsidized loan balance at time of repayment.

Step Two:  Calculate total payments over the lifetime of the loan.  This is done by using PMT function to get monthly payment and then multiplying by the total number of payments.

Spreadsheet for person who graduates in four years:

row Subsidized Loans No Subsidized Loans
2 Date of First Loan Payment 9/1/10 9/1/10
3 Subsidized Loan $23,000 $0
4 Unsubsidized Loans $8,000 $31,000
5 Interest Rate 0.05 0.05
6 Number of years In school 4 4
7 Date Repayment Starts 3/2/15 3/2/15
8 FV of subsidized loans $23,000 $0
9 FV of unsubsidized Loans $9,275 $35,940
10 Total Loans $32,275 $35,940
11 Loan Maturity 20 20
12 Loan PMT -$213 -$237
13 Lifetime Payments -$51,120 -$56,925
  • The elimination of subsidized loans increases lifetime repayment costs of the loan by $5,805 when the person graduates in four years and starts repayment six months after graduation.  (The other key assumptions are a 5% student loan interest rate and a 20-year student loan.)

Impact of delays in finishing schools:

The addition cost stemming from the loss of the subsidy can be obtained by changing line 6 of the spreadsheet number of years in school.   Below we present results for # of years in school for 4, 5, and 6.

Calculations are below:

# of Years in School Payments with Subsidized Loans Payments with No Subsidies Difference
4 $51,119.83 $56,924.81 $5,805
5 $51,496.04 $58,382.62 $6,887
5 $51,884.94 $59,889.61 $8,005
  • The elimination of subsidized loans leads to even higher costs for the person who spends more years in school.   Additional lifetime costs of loans are $6,887 for the person who graduates after 5 years and $8,005 for the person who graduates after six years.

Authors Note:  My student debt book looks at existing student debt and financial aid programs and proposals offered by both the Trump Administration and candidates in the Democratic party.   I then offer my own solutions to the problem.

The book is available on Kindle.

Innovative Solutions to the College Debt Problem


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.

Are Tech Stocks Overvalued?

Are Tech Stocks Overvalued?

Issue:   Professor Jeremy Siegel maintains that the stock market and tech stocks are still fairly value.

He supports this argument with the observation that the PE ratio of Tech stocks in the S&P 500 is still under 20.

What are the limitations of using the PE ratio for a basket of stocks to measure the valuation of the portfolio when some stocks in the portfolio have negative earnings?

Does an analysis of the PE ratios of the stocks in the Vanguard Information Technology ETF support or contradict Professor Siegel’s view on the valuation of Tech stocks?

Is Professor Siegel correct in his assertion that tech stocks are valued correctly?

Discussion of ETF PE Ratios: 

Professor Siegel pointing to a PE ratio for a basket of tech stocks in the S&P 500 has argued that the sector is valued fairly.   My problem with this argument is that published statistics on ETF PE ratios often fail to accurately include information on firms with negative earnings.

Firms with negative earnings have negative PE ratios.  These firms often have a lot in common with high PE firms.   Often startups have negative or low earnings.   If earnings are negative the PE is negative.  If earnings are slightly positive the PE is large.

It would be incorrect to average negative PE firms with positive PE firm because the result would be to reduce the PE of the portfolio even though the negative PE firms have high valuations compared to their income.     Some web sites including yahoo finance report and include negative PE ratios.   Most analysts omit negative PE ratios from their calculation of the portfolio PE.   However, this procedure will also understate valuation relative to income because firms with negative PE ratios have high valuation compared to earnings.

PE ratios have no clear economic interpretation when earnings are negative.  When earnings are slightly below zero (a small loss) the PE ratio is a very large negative number.   When a company has a larger loss the PE ratio is a smaller negative number.

Why PE ratios make no sense for firms

 with negative earnings

Earnings per share

Price per share PE ratio


3.00 (30.00)
(5.50) 3.00


In short, PE ratios incorrectly rank firm valuation when earnings are negative.

It would be incorrect to average negative PE firms with positive PE firm because the result would be to reduce the PE of the portfolio even though the negative PE firms have high valuations compared to their income.     Some web sites including yahoo finance report and include negative PE ratios.

Most analysts omit negative PE ratios from their calculation of the portfolio PE.   However, this procedure will also understate valuation relative to income because the firm with a negative PE ratio has a high valuation compared to earnings.

I am not the first to write about the problem of measuring ETF PE ratios.  Here are some additional resources.

Why ETF Price/Earning Ratios Lie.

Understanding Negative PE Ratios for ETFs

Data used in this study:

I obtained a list of stocks in the VGT mutual funds from Zachs guide at the link below.

Vanguard Technology Fund VGT has a total of 356 firms.  This study examined the PE ratios of all firms where the equity investment was greater than or equal to 0.1 percent of the value of the VGT portfolio.     There were 109 such firms.

Results:   The frequency distribution of dollar share values invested and number of firms for five PE categories – less than zero, 0 to 15, 15 to 30, 30 to 40 and over 40 – are presented below.


   Shares of Firms in VGT by PE category

PE Category

Dollar Share Invested by PE Category

Percent of Companies

<0 6.31 17.43
0-15 5.74 6.42
15-30 36.19 34.86
30-40 31.16 12.84
40< 13.12 28.44
Total 92.52 100

Sample consists firms in VGT where the equity position was greater than or equal to 0.1 percent of the total value of the VGT portfolio.   There were 109 firms meeting this criterion.   These 109 firms represent 92.5 percent of the value of the VGT Portfolio.


Around 6.3 percent of dollars invested in the 109 positions of VGT are in firms with negative earnings.  Around 17.4 percent of the 109 firms had negative earnings.

Over 13 percent of dollars invested in the 109 VGT positions had PE ratios over 40.   Over 128 percent of the firms in this group had a PE ratio over 40.


 What can we conclude about the question of whether tech stocks are overvalued after examining the distribution of stocks in VGT?

The large number of tech stocks with high PE ratios or worse yet negative earnings is consistent with a bubble.   Perhaps the bubble is in the early stages and some people can buy, sell, and make money before the crash.   However, there are a lot of overtly optimistic analysts and a lot of inaccurate or misleading information out there.

This is not going to end well.