If you’re a grad student and your experience is like ol’ Prof. Elbow Patch’s, you probably don’t have a ton of extra cash lying around to invest in the market right now. That could and should change with the increasing trend toward grad student unionization, but if you’re already in school then your income is likely limited and doesn’t greatly exceed your expenses, if it even covers them. So why am I talking about investing in grad school?
Well, grad students have a financial superpower that PhD-holders don’t — the ability to apply for and receive federal student loans. Now, maybe you’re already taking out loans to make ends meet or because your PhD program isn’t funded. But if you are neither taking out loans nor investing in the market, my advice is to strongly consider taking out federal student loans to give you sufficient excess resources to max out an IRA account every year you’re in grad school. To see why with lots of nerdy details, read on!
Is This Legal and Ethical?
I would not recommend doing this to anyone without an income unrelated to student loans. First, doing so falls in a legal gray area if your loans are federal because you cannot claim you’re investing your income. Second, it’s ethically dubious, a clear example of moral hazard.
However, most students in PhD programs earn a stipend of some kind, and usually this will be enough to cover the annual IRA contribution limit. Under these circumstances, I see the question of whether to invest as a grad student as a much more flexible one. The reason is that money is fungible, meaning that the source doesn’t really matter once it’s in your checking account. Student loans are available to you as a graduate student even if you have an income to cover costs of living and studying for your degree. I’m not interested or qualified to offer you legal advice, but ethically there’s nothing stopping you in my book from also contributing to your tax-protected retirement accounts while receiving student loans if you are earning at least as much income as you’re investing.
How Student Loans Work for Grad Students
Next, you need to understand grad students’ student loan options. Most of us are familiar with undergraduates’ federal student loan options, but grad students’ options differ in a few relevant ways:
- Grad students aren’t eligible for subsidized student loans. In undergrad, you were probably eligible for subsidized student loans in which interest does not accrue while you’re in school. In grad school, you aren’t, so interest starts accumulating from the day you receive them.
- Grad students’ interest rates are higher than undergrads’. Studentaid.gov lists student loan interest rates at any given time, and explicitly lists higher rates for grads than undergrads.
- Your parents’ income doesn’t apply to your FAFSA application. So you’re likely eligible for a lot of support at grad student wages.
I recommend you primarily consider federal student loans rather than private loans. Federal loans offer a number of benefits that private loans don’t, such as income-based repayment plans, deferment opportunities, and the potential to have debt forgiven through programs like the broad-based federal loan forgiveness if it ever happens, the Public Service Loan Forgiveness program, and/or the NIH Loan Repayment Program, and more.
Considerations
The likely risks and benefits of taking out student loans to enable investment during grad school depend on a number of considerations you should keep in mind. Here I list three in decreasing order of importance:
Consideration #1: Interest Rates and Expected Returns
This is the #1 consideration. If student loan rates are higher than expected long-term returns on the stock market, then this plan may not make as much sense. The reason is that interest will be accumulating at the same time as your investments are hopefully accumulating value (with more randomness), so if you take out $6500 in loans at 10% interest, you’re unlikely to make much net profit in the stock market (which also averages a 10% long-run return, not adjusting for inflation), and are taking on considerable risk for this zero expected net profit opportunity. The lower student loan interest rates are, the more appealing it is to borrow to invest while in grad school.
Two things to keep in mind here, though:
- Remember that you only have access to a certain amount of tax-protected retirement investment opportunities per year. Every year you don’t use them is a lost opportunity. This may make a difference in how expected returns and interest rates balance out.
- You have some control over your expected returns based on your asset allocation. Assets like stocks have higher long-run expected returns than bonds at the price of higher risk. Investment diversification across companies, asset classes, market sectors, and geographic regions is also something of a free lunch in that you can lower your risk and potentially increase your expected returns. In other words, investing in a broad-based stock index fund carries very different expected returns than buying 10-year US Treasury bonds.
- You can also affect your expected returns through your own behavior. If you’re the type to get scared the first time a recession hits and you pull your money at the bottom, you’re going to have much lower expected returns than someone who rides out these inevitable storms.
Consideration #2: Expected Ability to Repay
Obviously, you shouldn’t take out student loans if you don’t think you’ll be able to repay them in your likely range of career trajectories. However, you should also consider how repaying these loans after you earn your PhD will affect your subsequent investment behavior. As you’ll see below, the consequences of this strategy will depend a lot on whether you’re likely to reduce your retirement account contributions to pay off your loans.
Consideration #3: Traditional vs Roth
This actually isn’t much of a consideration — if you’re a grad student and want to follow this advice, you should invest in a Roth IRA. There are income limits for Roth IRA eligibility, but as a grad student you almost certainly qualify. Plus, student loans are not taxed as income, so you’ll only have to pay the taxes you owe on any grad school stipend or other income your household has. Being able to invest in a Roth at your current likely low tax rates is an absolute steal.
Consideration #4: Federal vs Private Loans
I would be much more likely to consider this strategy if my student loans were federal rather than private. The reason is that federal loans offer a much wider range of repayment and forbearance options and, for many academics, the potential for public service loan forgiveness. Private loans don’t have most of these benefits.
Simulation Time!
Ok, let’s get down to it. I ran a simulation generating wealth accumulation trajectories under several different scenarios, each of which were varied independently:
- Different expected investment returns. These ranged from 1-12%.
- Student loan interest rates. These also ranged from 1-12%.
- Investment behavior during loan repayment period. I simulated three different scenarios:
- You reduce your retirement contributions by your full loan repayment amounts during your repayment period.
- You reduce your retirement contributions by half your loan repayment amounts during your repayment period.
- You do not reduce your retirement contributions during your loan repayment period.
I made a number of assumptions while generating these simulations:
- Market returns and student loan interest rates were constant throughout your investment/loan period. Obviously that’s unrealistic since markets fluctuate and you can sometimes refinance your loans for lower rates, but it won’t matter for the main conclusions and simplifies things considerably.
- You attend graduate school ages 23-29 and repay any loans over a ten-year period ages 30-39.
- You invest a constant annual amount except for the loan repayment adjustment variations noted above — $6500 during graduate school (the current IRA contribution limit), $15000 post-graduate ages 30-65.
- Those who do and do not take out student loans to invest during graduate school are otherwise identical.
This simulation generated a lot of output. You can see the Stata program I wrote to conduct the simulation at the bottom of the post — feel free to play with the code and assumptions yourself. I’m sure the biggest nerds among you will want to dig through that (and there is some explanatory text to help you understand what you’re looking at), but for the rest, let me skip to the takeaways for your retirement nest egg’s prospects at age 65.
Simulation Findings
This simulation leads to a number of very clear findings:
- Interest rate vs expected returns matters a lot — if you’re going to reduce your 30-39 investments by the amount of your loan payments. In this repayment scenario, taking student loans to invest during grad school was profitable when expected returns exceeded the student loan interest rate, and was still slightly profitable if the two rates were the same. However, if the student loan interest rate exceeded the investment expected return rate, borrowing to invest was a losing strategy.
- Interest rate vs expected returns matters a lot less for your retirement-age nest egg if you do not reduce your 30-39 investments based on your loan payments (or only do so by half those payments). In the repayment scenarios where investment was unaffected by loan repayment amounts or when investment was reduced by half the loan payment amount, the borrow-to-invest strategy was a big winner. The only exception of the scenarios I examined was when you were reducing retirement contributions by half and the student loan interest rate exceeded the expected market return by 10+ points. So, in that unlikely scenario, I don’t recommend this strategy. However, if you aren’t going to reduce your retirement contributions at all during the loan repayment period, your nest egg comes out ahead at 65 even in these extreme scenarios.
- Roth always beats traditional IRA. I already told you that it obviously would, but it’s important to note that the simulation shows that too, in case you didn’t trust good ol’ Prof. Elbow Patch.
Takeaway Advice
So, is there a positive expectation for grad students taking out student loans so they can afford to invest? Generally, I think yes, if the following statements apply to you:
- You have a strong likelihood of a well-paying job after you graduate. This will affect your ability to repay your loans while continuing to invest in your retirement accounts, which as we just saw, is a big factor in how this strategy plays out. Plus, if you happen to take a loss using this strategy, you’ll better be able to handle that.
- Student loan rates are less than 7-10%. The S&P 500 returns 10% (unadjusted) over the long run, so the chances you come out ahead are pretty good if student loan rates are <7%. Plus, even if rates are high now, there’s a good chance they’ll come down later so that you can refinance at a lower rate.
- You are comfortable with stock market risk. Beyond the diversification premium, according to the influential efficient markets hypothesis, investment assets with higher expected returns come with higher risk. You can goose your investment expected returns higher by investing in a higher percentage of stocks rather than bonds, and riskier / higher-yield stock classes like small-cap value, but these decisions increase the variance in your annual returns at the same time as they increase the expected return. If you’re a grad student in your 20s, you have decades for those stock market swings to even out and the long-run expectation to work in your favor, but not everyone is comfortable with that, especially if they’re taking on debt to do it, which compounds the risk. If you don’t feel comfortable with this idea, I don’t recommend this strategy.
Stata Code for the Nerds
/*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*
--------------------
PROF. ELBOW PATCH
4-29-2023
--------------------
GOAL: Examine what combination of expected market returns and student loan interest rates would lead to positive expected value if you effectively borrow
student loans to invest them in a tax-protected (roth and traditional IRA) or brokerage account.
ASSUMPTIONS:
- We're ignoring any other loans they may take and assuming they won't invest if they don't take out loans.
- Set it and forget it in index funds investment in some mix of stocks and bonds
- Constant growth rate in investments' value at the expected rate
- Grad student earns $23,250/year, is single, and in the 10% tax bracket for income >$10,275. Income figure is lower bound for 12% tax bracket minus
standard deduction for simplicity (can assume all income over deduction taxed at the same rate).
- Retiree lives on $60,000/year is subject to 22% tax bracket
- All taxees take the standard deduction ($12,950)
- Individual is in graduate school ages 23-29, so the decision is simulated over 7 years
- Will just compare wealth at age 65 by taxing non-Roth wealth at 22%
- Borrower pays off loans over a ten-year period and reduces their post-graduation investments correspondingly. Assume baseline investment post-grad
is $15k/year.
VARIATIONS OF INTEREST:
- In each sim, the grad student who borrows an additional $6500 to put equivalent share of stipend into investments is compared to one who does not do so.
- Different simulations are conducted for those investing in a traditional IRA, Roth IRA, or taxable brokerage.
- Expected returns from investments and interest rates are varied independently 1-12%
NOTES:
- Loans accrue interest while in grad school because grad students can't get subsidized student loans in the US.
*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*/
clear all
set more off
capture log close
version 17
global date "230429"
global logs "<fill in output directory>"
log using "${logs}/simlog_${date}.log" , text replace
postfile simresults str9(acct dec) int(exp_ret int_rate) ///
double(asset_noinvest swr_inc_noinvest asset_invest swr_inc_invest asset_diff asset_diff_perc swr_inc_diff swr_inc_diff_perc) ///
using "${logs}/borrow_to_invest_simulation_${date}.dta" , replace
//Setting assumed investment accounts during and after grad school
local inv_20_29 = 6500
local inv_30_65 = 15000
//Examine accounts with different tax exposures - traditional IRA vs Roth IRA
foreach acct in trad_ira roth_ira {
//Set tax rakes for each account type:
if ("`acct'" == "trad_ira") {
local tax_rate_20s = 0 //Top marginal tax rate your invested $ is subject to while in grad school
local tax_rate_60s = .22 //Top marginal tax rate your invested $ is subject to when withdrawn in 60s
local pretax_inv = 6500 //Traditional contributions are pretax so $6500 investment = $6500 pretax
}
if ("`acct'" == "roth_ira") {
local tax_rate_20s = .12
local tax_rate_60s = 0
local pretax_inv = 6500 * (1 / (1-`tax_rate_20s')) //Roth contributions come on a higher pretax basis = $7386 @ 12% tax rate
//does this matter? I don't think so actually. You're borrowing the money, it's not taxed.
}
//Vary market expected returns 1-12%
forval exp_ret = .01(.01).12 {
//Vary student loan interest rate 1-12%
forval int_rate = .01(.01).12 {
//Establish starting values of debt and wealth (0)
local debt_invest = 0
local asset_invest = 0
local debt_noinvest = 0
local asset_noinvest = 0
//Play out the scenarios for grad school ages 23-29
forval age = 23/29 {
//Appreciate previous investments & debts by applicable expected returns / interest rates
local debt_invest = `debt_invest' * (1 + `int_rate')
local asset_invest = `asset_invest' * (1 + `exp_ret')
//Add new investments and debt for this year after appreciating previous ones
local debt_invest = `debt_invest' + `inv_20_29' //Take out additional $6500 to indirectly fund investment
local asset_invest = `asset_invest' + `inv_20_29'
}
//Quick pause to calculate borrowers' monthly loan payments assuming pay 120 installments at fixed rate
//Formula is P = a ÷ { [ (1 + r) n ] - 1 } ÷ [ r (1 + r) n] - see amortized section of https://www.moneygeek.com/personal-loans/calculate-loan-payments/
//Breaking it into parts to debug...
local r = `int_rate' / 12 //converting to monthly interest rate
local x = ((1 + `r')^120) - 1
local y = `r' * ((1+`r')^120)
local loan_pmt = `debt_invest' / (`x'/`y')
di "r=`r', x=`x', y=`y', debt_invest=`debt_invest' loan_pmt = `loan_pmt'"
//Ok, that looks right
//Three new locals for alternative ways loan repayments affect retirement contributions
foreach dec in zero half full {
local asset_invest_dec`dec' = `asset_invest'
}
//Play out the scenarios for 10 year loan repayment period (ages 30-39) if applicable
forval age = 30/39 {
//Appreciate previous investments & debts by applicable expected returns / interest rates
local debt_invest = `debt_invest' * (1 + `int_rate')
local asset_noinvest= `asset_noinvest' * (1 + `exp_ret')
//Add new investments and debt for this year after appreciating previous ones
local asset_noinvest= `asset_noinvest' + `inv_30_65'
local debt_invest = `debt_invest' - (12*`loan_pmt') //Subtracting annual loan payments
//Alternative ways loan repayments affect 30-something retirement contributions
foreach dec in zero half full { //3 diff ways loan repay impacts invests: no effect (zero), lose half debt repay (half), lose full repay (full)
if ("`dec'"=="zero") {
local d=0
}
if ("`dec'"=="half") {
local d=0.5
}
if ("`dec'"=="full") {
local d=1
}
//Appreciate previous investments & debts by applicable expected returns / interest rates
local asset_invest_dec`dec' = `asset_invest_dec`dec'' * (1 + `exp_ret')
//Add new investments and debt for this year after appreciating previous ones
local asset_invest_dec`dec' = `asset_invest_dec`dec'' + `inv_30_65' - (`d'*12*`loan_pmt') //Grad school investors reduce annual investments by 0x (zero), 0.5x (half), or 1x (full) annual loan payments
di "local asset_invest_dec`dec' = `asset_invest_dec`dec'' + `inv_30_65' - (`d'*12*`loan_pmt')*****"
}
}
//Play out scenarios for post-loan repayment period (ages 40-65)
forval age = 40 / 65 {
//Appreciate assets
local asset_noinvest= `asset_noinvest' * (1 + `exp_ret')
//Add new investments
local asset_noinvest= `asset_noinvest' + `inv_30_65'
foreach dec in zero half full {
//Appreciate assets
local asset_invest_dec`dec' = `asset_invest_dec`dec'' * (1 + `exp_ret')
//Add new investments
local asset_invest_dec`dec' = `asset_invest_dec`dec'' + `inv_30_65'
}
}
//Output tax-adjusted wealth at age 65 in this scenario
//Express expected returns and interest rates as integers
local exp_ret_int = `exp_ret' * 100
local int_rate_int= `int_rate' * 100
//Round assets
foreach dec in zero half full {
local asset_invest_dec`dec' = round(`asset_invest_dec`dec'' ,1)
}
local asset_noinvest= round(`asset_noinvest',1)
//Let's tax this wealth now for traditional accounts assuming 4% SWR
foreach dec in zero half full {
local swr_inc_invest_dec`dec' = round( (`asset_invest_dec`dec'' * .04) * (1 - `tax_rate_60s') ,1)
}
local swr_inc_noinvest = round( (`asset_noinvest' * .04) * (1 - `tax_rate_60s') ,.1)
//Calculating outcome differences (investment advantage in absolute and relative % terms)
foreach dec in zero half full {
local asset_diff_dec`dec' = `asset_invest_dec`dec'' - `asset_noinvest'
local asset_diff_dec`dec'_perc = round( 100 * ((`asset_invest_dec`dec'' - `asset_noinvest')/`asset_noinvest') ,.1)
local swr_inc_diff_dec`dec' = round( `swr_inc_invest_dec`dec'' - `swr_inc_noinvest' ,1)
local swr_inc_diff_dec`dec'_perc = round(100 * ((`swr_inc_invest_dec`dec'' - `swr_inc_noinvest')/`swr_inc_noinvest') ,1)
}
foreach dec in zero half full {
post simresults ("`acct'") ("`dec'") (`exp_ret_int') (`int_rate_int') (`asset_noinvest') (`swr_inc_noinvest') (`asset_invest_dec`dec'') (`swr_inc_invest_dec`dec'') ///
(`asset_diff_dec`dec'') (`asset_diff_dec`dec'_perc') (`swr_inc_diff_dec`dec'') (`swr_inc_diff_dec`dec'_perc')
di `" acct=("`acct'") dec=("`dec'") exp_ret_int=(`exp_ret_int') int_rate_int=(`int_rate_int') asset_noinvest=(`asset_noinvest') swr_inc_noinvest=(`swr_inc_noinvest') asset_invest=(`asset_invest_dec`dec'') swr_inc_invest=(`swr_inc_invest_dec`dec'') asset_diff=(`asset_diff_dec`dec'') asset_diff_perc=(`asset_diff_dec`dec'_perc') swr_inc_diff=(`swr_inc_diff_dec`dec'') swr_inc_diff_perc=(`swr_inc_diff_dec`dec'_perc')"'
}
}
}
}
postclose simresults
use "${logs}/borrow_to_invest_simulation_${date}.dta" , clear
putexcel set "${logs}/key_output_tables_${date}.xlsx" , replace
foreach dec in zero half full {
putexcel set "${logs}/key_output_tables_${date}.xlsx" , modify sheet(`dec')
di "dec = `dec'..."
di "Roth..."
li exp_ret int_rate asset_diff asset_diff_perc swr_inc_diff swr_inc_diff_perc if acct=="roth_ira" & dec=="`dec'"
di "Trad..."
li exp_ret int_rate asset_diff asset_diff_perc swr_inc_diff swr_inc_diff_perc if acct=="trad_ira" & dec=="`dec'"
*set trace on
//Output to excel
preserve
keep if acct=="roth_ira" & dec=="`dec'"
drop acct dec
mkmat * , mat(A)
putexcel A1 = "Roth"
putexcel A2 = mat(A) , colnames
restore
preserve
keep if acct=="trad_ira" & dec=="`dec'"
drop acct dec
mkmat * , mat(A)
putexcel N1 = "Trad"
putexcel N2 = mat(A) , colnames
restore
*set trace off
}
log close