# Don’t Pay Off Your Student Loans?—A Commentary by Ian Ayres ’86 and Barry Nalebuff

*The following commentary was posted on Forbes.com on November 4, 2010.*

**Don’t Pay Off Your Student Loans?**

By Ian Ayres ’86 and Barry Nalebuff

Here’s a deceptively easy personal finance question. Imagine you are 26 years old and you owe $40,000 on student loans. You’ve managed to save $10,000. Should you use that money to pay off part of the loan balance or should you invest the money in the market?

If the student loan carries a 5.5% interest rate and you expect the stock market return to be 5%, this question seems like a no-brainer. You should use your savings to pay off the student loan and implicitly earn 5.5% on your money (by saving that amount in accrued interest) rather than invest the money in stock and just earn 5%. Indeed, by paying off part of your student loan, you are guaranteed a 5.5% return, whereas with a stock investment you’re taking the risk that your return might be much smaller.

But it turns out that there is a third option, another way to invest in stock that may be more attractive that either of the foregoing alternatives. You can use the $10,000 as collateral and invest $20,000 in stock by buying on margin at 2:1 leverage. Today, it is possible borrow (directly at Interactive Brokers or indirectly through ProShares UltaS&P500 or Barclay’s leveraged ETNs) at less than 1.7% interest. The market return only needs to exceed 3.6% [= (1.7 + 5.5)/2] in order to produce a better result than paying off your student loan. When you buy stock on margin, you incur two different kinds of cost. The opportunity cost of not paying down your student loan is 5.5% on first 10k and the margin interest cost on the 10k that you borrow is 1.7% (or less!) – so that the average or blended cost of investing on margin is 3.6%.

Perversely, this means that while it may not be worthwhile to invest in stock on an unleveraged basis, it may be prudent to invest in stock on a 2:1 leveraged basis instead of paying down your student loan. The same logic applies to home mortgages. Instead of paying down your home mortgage, you might do better by investing on margin in stock. However, as we emphasize in our book, you should almost certainly pay off your credit card before using any extra cash to invest in stock on margin. If you have a revolving credit card balance with even with a 14% interest, the blended cost of investing on margin would be 7.85%. It’s just not credible to expect the stock returns to beat this hurdle rate, never mind the added risk.

One way to think of this about this “don’t pay down your loan” result is in terms of the expected equity premium. A young investor with a student loan might not expect an unlevered stock investment to produce a sufficient risk-premium over the implicit risk-free return that she could earn by simply paying down some of her student loan. But there can be an expected risk-premium to investing in stock on a leveraged basis – because the expected risky return on stock can exceed the certain blended costs (which is a mixture of reduced student loan interest and the margin loan interest).

This result is driven by the fact that the interest rate demand by margin lenders is much less than the interest rate demanded by student loan lenders. This result is not a fluke of the current post-crisis world (where TIPS can sell with negative interest rates). In our recent book, Lifecycle Investing (and in this new academic paper), we show that margin interest rate has averaged just a few basis point over the interest rate on government treasuries. While investing on a margin basis increases investing risk, there is nothing unexpected about competitive margin lenders offering very low interest – because margin loans are highly secured and callable. The supra-competitive rates charged by otherwise reputable intermediaries like Vanguard and Fidelity obscure the increasing opportunities for small investors to cheaply invest in stock on a leveraged basis.

Another way to see this result comes from the adage “It takes money to make money.” If you have $10,000 to invest, that also creates $10,000 of collateral with which to borrow. While no bank will lend you money against your future income, brokers will lend you money using the stock you buy with the $10,000 as collateral. Because you can borrow at low cost, that allows you to come closer to achieving the level of equity exposure you’d like to have if you had access today to more of your future wealth.

More formally, “don’t pay down your loan” result is easily related to a central equation from our book (which can be found on p. 138 of Lifecycle Investing and is inspired by the seminal articles of Samuelson and especially Merton (equation 25)) which estimates the share of your retirement portfolio that you should invest in stock:

Merton-Samuelson share = Equity Premium/(Risk2 * Risk Aversion),

where “Risk” is the standard deviation measure of future stock return volatility, “Risk Aversion” is a quantitative measure of your relative risk aversion. Usually the “Equity Premium” is defined as the extent to which the stock returns are expected to exceed the opportunity cost of investing in risk-free government bonds. But when analyzing the leveraged investing by an investor with a student loan, the “Equity Premium” should be defined as the extent to which expected stock return exceeds the blended (average) of student loan and margin rates.

To be precise, imagine that the expected future volatility of stock is 20%. (The VIX is currently about 21%). And imagine that our young investor has relative risk aversion equal to 2. Then the Merton-Samuelson share to invest in stock on an unleveraged basis would be negative because the expected stock return of 5% is less than the certain student loan interest cost of 5.5%. But the equity premium of investing on a leveraged basis would be 1.4% (5% – 3.6%). Plugging in this equity premium value (along with the assumed Risk and Risk-Aversion of 20% and 2 respectively) produces an estimated Merton-Samuelson share of 17.5%. [You can easily calculate Merton-Samuelson shares for alternative assumptions using our widget.]

Following the central argument of Lifecycle Investing, a young investor should want to invest in stock not just 17.5% of her current retirement savings, she should endeavor to invest in stock 17.5% of her future retirement savings as well. If we imagine that the present value of future retirement savings for our young investor is $190,000, this means our young investor should try to invest 17.5% of $200,000 (her $10,000 in cash plus $190,000 of her future savings) or $35,000. Our young can’t cheaply borrow enough to immediately invest $35,000 in stock. But by buying stock on margin, she can expose herself to $20,000 of stock and thus come closer to achieving her desired level of equity exposure.