Time-Deposit Duration Choice Using Present Value and Rate-Curve Shape

# Determining the optimal duration of time deposits


# Determining the optimal duration of time deposits












Time deposits are popular among retail investors. I have proposed a forward-looking approach in order to determine the optimal duration of time deposits for retail investors (http://dx.doi.org/10.2139/ssrn.4988606). In a nutshell, my approach is to calculate the net present value of time deposits with different durations and to convert these net present values into constant annual payments during the durations of the time deposits, respectively. I consider the time deposit with the highest annual payment as optimal. In summary, the optimal duration has been three or four years on average over the last years.

1.) Do you think this is a good strategy to determine the duration of time deposits? What other approaches are you familiar with?

I have collected the highest interest rate offers on one- to five-year German time deposits on a monthly basis from January 2011 until December 2024. Although the data set suffers from minor data quality issues (that I need to correct), I run the following simulation experiment in six steps. First, I randomly select a starting month within the first five years. Second, I apply the strategy described above until the data set ends. The application of the strategy provides a sequence of time deposit durations. Third, I randomly shuffle this sequence as an alternative random strategy. The alternative strategy in step three has the same average duration as the strategy in step two. Thus, the two strategies approximately bear the same interest rate risk on average. Fourth, I calculate the sum of nominal interests and the compounded interests for both strategies, respectively. Fifth, I calculate the differences between the sum of nominal interests (respect. compounded interests) of the two strategies. Sixth, I repeat the steps one to five 100,000. I find that the strategy in step two outperforms the strategy in step three in about 56% of the simulation scenarios.

2.) Do these results support my theory-driven strategy from your point of view? Do you have any suggestions to improve this simulation experiment?

At the moment, I am searching for general reasons why three- or four-year time deposits are most attractive. To this end, I raise the question of what is the optimal duration of time deposits from the perspective of banks. A main task of banks in the financial system is maturity transformation (i.e. transforming short-term deposits into long-term loans). Let us assume that banks are willing to accept a certain maturity gap $\Delta$ (i.e. the difference in maturity between assets and liabilities). Furthermore, we assume that banks aim at maximizing the ratio of the difference between the investment rate (for the longer duration $m_b+\Delta$) and borrowing rate (for the shorter duration $m_b$) divided by $\Delta$ (as an approximation of interest rate risk). Let $IRC$ denote the interest rate curve. Then, $IRC(m)$ is the interest rate for maturity $m$. To sum up, we assume that banks seek to maximize the ratio of the difference of interest rates divided by the maturity gap: \begin{equation} \max\limits_{m_b}{\frac{IRC(m_b+\Delta)-IRC(m_b)}{\Delta}}\Rightarrow IRC’(m_b)=IRC’(m_b+\Delta). \end{equation} If I set $\Delta=3$ years based on Chart A.1 of this ECB report https://www.ecb.europa.eu/press/financial-stability-publications/fsr/special/html/ecb.fsrart202311_01~bbbe8e63be.en.html, I find that the optimal duration for borrowing is about 3.25 years. $\Delta=5$ years results in an optimal duration for borrowing of about 2.74 years. Do you think this (i.e. the shape of the interest rate curve) explains why the optimal duration from the perspective of retail depositors is three or four years?

3.) Do I have any errors in my thinking? I am very curious to read your opinions!