Tuesday, May 22, 2018

The path of returns and financial risk for 401(k) investors

The path of returns and financial risk for 401(k) investors

Question Eighteen:  A person has $200,000 in her 401(k) plan.   She contributes $500 per month to her plan. She is planning to retire in 15 years.  Investment scenario one involves 7 percent returns for 90 months followed by -4.0 percent returns to 90 months.  Investment scenario two involves -4.0 percent return for 90 months followed by 7.0 percent returns for 90 moths.

What is the difference in the FV of funds in the 401(k) plan between the two scenarios?  What does this result tell us about impact of path of returns on financial risk for 401(k) investors?

Methodology:   The final balance in the 401(k) plan can be calculated with the future value function.  It is a five-step procedure.

Step One:  Take the future value of the initial $200,000 to the end of the first period.

Step Two:  Take the future value of all first period contributions to the end of the first period.

Step Three:  Find funds available at end of first period (This is the sum of steps one and two.)  Take the future value of these funds to the end of the second period.

Step Four:  Take future value of all second period contributions.

Step Five:  Add results of steps three and four to get FV at retirement.

It is important to use monthly returns and monthly holding periods.   It is also important to input contributions and initial balances as negative numbers so you obtain a positive future value balance. 

Results:    The future value calculation for the two market scenarios is presented in the table below.

The timing of the bull market
401(k) balance at beginning of 15 year period
Monthly Contribution to 401(k)
Annual Return First Period
Annual Return Second Period
Length of First Period in Months
Length of Second Period in Months
FV of initial sum in 401(k) at end of first period
FV of monthly 401(k) contributions to end of first period
FV of funds at end of first period funds to
 end of second period
FV of second period contributions
FV all funds after 15 years

Observations about results:

The return in the overall market is R=(1.07/12)90 x (1-0.04/12)90 for both scenarios.

Even though market returns in the two scenarios are identical the final 401(k) balance is larger when the bull market occurs at the end of the period rather than the beginning of the period. 

The difference in portfolio outcomes is non-trivial.  The difference is around $42,000 or around 12 percent of the average of the two portfolio outcomes.

Analysis and Discussion:  The timing of the bull market matters for 401(k) contributors because more money is exposed to the market at the end of the holding period than at the beginning of the holding period.

Interestingly, timing or returns does not matter when the investment is a lump sum.   For example, the timing of returns does not alter the future value of the initial $200,000 investment.

Financial analysts argue that people need to invest in their 401(k) plan and place funds in equities at the beginning of a career because in the long-term stocks out-perform other asset classes.  However, the long-term performance of stocks will not protect investors from substantial losses when a bull market occurs near the end of a career.

Market timing is a significant risk factor!

Many financial analysts argue that end-of-career financial risk can be mitigated by investing in life cycle funds, which increase allocation of assets towards fixed-income assets as the investor ages.  But if returns are low after the first period should the investor maintain a risky position or reallocate assets as planned under the life cycle account.  

The rebound in the second ninety months is not a sure thing in advance.

 This is question eighteen in my Excel Finance tutorial:

Friday, April 27, 2018

Understanding the Adjusted Close Stock Price

Understanding the Adjusted Close Stock Price

Question:  The table below contains stock dividend payment information and stock closing price information for IBM.   Use this information to calculate the adjusted closing price for IBM on March 15, 2017.

Explain why the adjusted closing price concept is useful?  What does the difference between closing price and adjusted closing price measure?

When should analysts use the closing price concept and when should they use the adjusted closing price concept?

Dividend and Stock Close Price for IBM
1.5 Dividend
1.5 Dividend
1.5 Dividend
1.5 Dividend

Discussion:   The adjusted closing price accounts for payments of dividends and stock splits.   A comparison of price today to adjusted closing price in the past will accurately measure returns after stock splits and accounting for the reinvestment of all dividends. 

The adjustment of closing prices for dividend payments requires the analyst to multiply the actual close price by (1-D/SP).   Here D is Dividend and SP is stock price on dividend payment date.

The adjustment is made to all stock prices prior to the payment of the dividend.

The Calculation of Adjusted Stock Price on March 15, 2017:

March 15, 2017 is prior to all four dividend payment dates listed in the table.   We must adjust the actual closing price on March 15, 2017 by multiplying by the adjustment factor.

The adjustment factor is

ADJ = (1-1.5/153.85) x (1-1.5/151.57) x (1-1.5/143.47) x (1-1.5/155.05)

Multiplying the adjustment factor by the actual closing stock price I get 168.92 for the adjusted closing price.   This is in fact the value of ADJ closing price on March 15, 2107 listed in YAHOO FINANCE.

More Discussion: 

A person spends $100,000 on IBM stock on March 15, 2018

Actual shares purchased is equal to 568.8 ($100,000/$175.81)

Shares purchased on purchase date plus shares purchased through dividend reinvestment is equal to 592.0 ($100,000/$169.92)

The difference 592-568.8  or 23.2 represents the shares obtained through dividend reinvestment.

Concluding Thought:  The adjusted share price is very convenient when analyzing returns from stock when dividends are reinvested in the original asset.  However, when dividends are spent or invested in a different asset class the analyst must follow the money.   The process of calculating returns when an asset is held for a long time and dividend are invested elsewhere can be a bit complex.

Saturday, April 21, 2018

The Cost of Eliminating Subsidized Loans to Students

A Financial Model on Costs to Students from
Eliminating Student Loan Subsidies

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:

Subsidized Loans
No Subsidized Loans
Date of First Loan Payment
Subsidized Loan
Unsubsidized Loans
Interest Rate
Number of years In school
Date Repayment Starts
FV of subsidized loans
FV of unsubsidized Loans
Total Loans
Loan Maturity
Loan PMT
Lifetime Payments

·      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

·      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:  I will soon create additional Excel Finance problems involving the elimination of subsidized student loans.   The problems will involve students who borrow different amounts each year, take some time off from school, or obtain additional loan deferments to obtain graduate school.  

This problem is question 17 on the Excel finance tutorial.