Investing an SU loan

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During education it is possible to take an SU loan (Danish student loan). If one takes an SU loan solely for investing, what can one then expect after the loan has been repaid? This will be investigated in the following model.

Model description

For the model, the underlying historical data follows the S&P500. The data is retrieved from www.econ.yale.edu, 16-11-2020. See SP500.csv for the processed data.

Two different lengths of loan-taking, with a loan taken every month, are simulated: 3 years and 5 years. 5 years is representative of a bachelor’s plus master’s degree. In practice there is 1 month between the bachelor’s and master’s where one is not in education, and should pay the interest rate applying after education. This period is neglected in the model, and it is treated as if the 5 years were one long education.

During education the interest rate is 4%, after which it is X% in the model. Currently the interest rate on SU loans after education is 1%, but the loan does not have a fixed rate, so the rate can in principle change in the future.

The repayment of the SU loan is computed so that the loan is exactly repaid by the end of the given repayment period (which depends on the size of the loan).

A 27% interest deduction applies to the interest on the SU loan.

For all X% interest rates, a best-case and a worst-case situation are simulated. The best case is where the entire progression limit for share taxation is available for the invested amount from the loan. The worst case is where it is assumed that the entire progression limit is used up by other investments, so that the amount from the SU loan is taxed at 42% share taxation. In the model it is assumed that the investment is in a mark-to-market taxed ETF.

Discussion of results

The results of the model can be seen in the graph below.

The graph above shows the expected return after repayment of the SU loan. The ‘solid’ lines are where the full progression limit (for share taxation) is available for the SU loan. The dashed lines are where the entire progression limit is used elsewhere. The different colors represent the interest rate on the loan after education has ended.

Given that the investment period is ~20 years, and that those who choose to invest an SU loan probably also have other investments, the following discussion will focus on the dashed lines.

For both education lengths, it would historically always have paid off to take an SU loan for investing, given an interest rate of 1% after education has ended.

Note that the shorter the education, the greater the risk, since the repayment period will be shorter. This can be seen from the fact that if the interest rate rises to just 3%, there is a ~20% risk of a loss from investing the SU loan over a 3-year education. Whereas investing the loan over a 5-year education will only carry a risk of loss for interest rates above 3%, given that the stock market behaves as it has historically.

Given the long investment horizon that comes with investing an SU loan, the biggest risk is interest rate risk. Even if interest rates do not look set to rise in the coming years, it can be hard to know what will happen just 5 years into the future. This can matter a great deal, since SU loans do not have a fixed interest rate.

The code used to make the graphs can be found here: sulaan_investering.py

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