BUSI 683 Week 2 DB Forum 1 Example

Discussion Board Forum 1: Thread and Replies

BUSI 683 Money & Capital Markets, Discussion Board Forum 1 (thread and two replies)

Thread by [Student Name]

The forum prompt, the family and the classmates are composites standing in for the course's own; the market rates come from Federal Reserve Economic Data for September 2026, the projections are illustrative, and the textbook, Scripture and research cited are real; the requirements follow Liberty's public course guide for BUSI 683.

Thread

The prompt describes a composite couple, both 35, with $40,000 in savings beyond their emergency fund and a 30-year mortgage at 6.86 percent, the average 30-year rate in September 2026. They ask whether to prepay the mortgage or invest in a broad stock index fund. The question looks like a comparison of two returns, but chapters 4 and 5 show it is really a comparison of a certain return with an uncertain one.

Prepaying earns exactly the mortgage rate. Every dollar paid now removes a dollar of principal that would have accrued 6.86 percent interest, assuming the couple does not itemize the mortgage interest. Compounded for ten years, $40,000 at 6.86 percent grows to about $77,700 in avoided interest and principal. Cecchetti and Schoenholtz (2015) define risk as uncertainty about future outcomes and explain that risk-averse investors require a risk premium to hold a risky asset. By that standard, the prepayment is the safe asset here, and a strong one: it beats the 4.99 percent ten-year Treasury yield of the same month by almost two percentage points.

The index fund promises more on average but guarantees nothing. As an illustration only, assume a 7.5 percent compound annual return with an 18 percent standard deviation. At that rate the fund would grow to about $82,400 after ten years, only $4,700 more than the prepayment, and the spread around that figure is wide; under those assumptions there is roughly a 46 percent chance the fund ends the decade behind the prepayment. The extra expected gain is small relative to that risk. The comparison also ignores liquidity. Money sent to the mortgage cannot be withdrawn without refinancing or selling the house, while the fund can be sold in a day. Chapter 5's measures of risk do not capture that difference directly, but a family with young children and one income should count it, which is one more reason not to put the whole $40,000 into the house.

Research explains why reasonable people disagree about such choices. Mehra and Prescott (1985) showed that historical U.S. stock returns had exceeded the return on short-term safe assets by about six percentage points a year, far more than standard models of risk aversion could justify. If that premium persists, stocks look attractive. Yet in the experiments Kahneman and Tversky (1979) reported, losing a sum hurt their subjects more than winning that sum pleased them, which means a couple who would lose sleep over a 30 percent market decline may value certainty more than a model assumes. A return you will abandon in a panic is worth less than its average.

Scripture speaks to this uncertainty. The Teacher's counsel is to spread what one has among several ventures, since nobody can foresee which calamity is coming (English Standard Version Bible, 2001/2016, Ecclesiastes 11:2). Read in context, the verse counsels diversification under uncertainty, not fear. Proverbs also observes that debt places the borrower under the lender's power (Proverbs 22:7), a reminder that reducing debt has value beyond its interest rate.

My recommendation is to divide the money: $25,000 toward the mortgage, which captures a certain 6.86 percent and reduces the family's obligations, and $15,000 in the index fund through the couple's retirement accounts, where any employer match makes the investing return far more attractive. If their mortgage rate were 3 percent, I would reverse the weights.

Reply to Jordan

Jordan, you argued that the couple should invest all $40,000 because stocks have outperformed mortgage rates over every 30-year period you examined. The long-run evidence is real, and Cecchetti and Schoenholtz (2015) explain why: investors demand a risk premium for bearing risk, so riskier assets must offer higher expected returns. My concern is with the assumption that the couple will hold for 30 years without flinching. Benartzi and Thaler (1995) proposed that the equity premium puzzle can be explained by myopic loss aversion: investors who are sensitive to losses and evaluate their portfolios frequently, about once a year in their analysis, feel the stock market's bumps far more sharply than a decades-long chart would lead anyone to expect. A couple who checks their balance every month, as most people with an app now do, may feel each decline sharply and sell after a bad year, locking in the very loss they feared. That is not a reason to avoid stocks; it is a reason to match the investment to the investors. In 2022, for example, a broad U.S. stock index lost close to a fifth of its value, and investors who sold that year missed the recovery that followed. The couple's history with such a year matters more than any 30-year chart. If they held through 2022, your all-stock plan may suit them; if they sold, a split that guarantees part of the return could keep them invested in the rest. Proverbs 21:5 contrasts the careful planner, who ends with plenty, with the hasty person, who ends in want (English Standard Version Bible, 2001/2016); it describes steady, patient effort rather than a single bold bet. Would your recommendation change if the couple told you they sold their stock funds during the last market decline?

Reply to Sofia

Sofia, I appreciated your use of Proverbs 22:7 and your conclusion that the couple should put every dollar toward the mortgage. Debt does create obligation, and your point that a paid-off home gives a family freedom in a job loss is strong. I would test the rule, though, with the time value of money. Cecchetti and Schoenholtz (2015) show that the value of a future payment depends on the interest rate used to discount it, which means the cost of a mortgage depends on its rate. At 6.86 percent, prepayment is an excellent use of money; at 3 percent, it would be a weak one, because the couple could earn more than 3 percent in safe Treasury securities. A single rule cannot fit both cases. Lusardi and Mitchell (2014) survey research linking a grasp of how interest compounds with sounder choices such as planning for retirement, which suggests the couple is best served by understanding why prepayment makes sense now rather than adopting it as a rule. In the parable of the talents, the two servants who traded with what they were given are praised, while the one who hid his share in the ground is rebuked (English Standard Version Bible, 2001/2016, Matthew 25:14-30). Faithfulness, in that story, includes weighing returns. The servant who buried the money did protect it from loss, much as a rigid rule protects a family from debt, yet he was faulted for ignoring what the money could have done. Your instinct to reduce debt and the parable's call to use resources well can both be honored by setting the share of prepayment according to the rate. Would you keep your rule if the mortgage rate were 3 percent?

References

Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics, 110(1), 73-92. https://doi.org/10.2307/2118511

Cecchetti, S. G., & Schoenholtz, K. L. (2015). Money, banking, and financial markets (4th ed.). McGraw-Hill Education.

English Standard Version Bible. (2016). Crossway. (Original work published 2001)

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. https://doi.org/10.2307/1914185

Lusardi, A., & Mitchell, O. S. (2014). The economic importance of financial literacy: Theory and evidence. Journal of Economic Literature, 52(1), 5-44. https://doi.org/10.1257/jel.52.1.5

Mehra, R., & Prescott, E. C. (1985). The equity premium: A puzzle. Journal of Monetary Economics, 15(2), 145-161. https://doi.org/10.1016/0304-3932(85)90061-3