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Index Fund Millionaire4 min read

By Kyu Kim

In our Foundations of Finance class, we all learned about modern portfolio theory. In this brief article, I will summarize this famous theory we learned and how it’s implemented in the real world. I hope Sternies can understand this concept more practically, as it is essential for early retirement plans for young professionals.

According to modern portfolio theory, developed in the 1960s by Harry Markowitz, a Nobel Prize winning economist, risk-averse investors can create an optimal portfolio by holding both risk-free securities as well as risky assets. Given that higher risk is an inherent part of higher reward, this method maximizes expected return based on a given level of market risk.

When a company like Vanguard or Fidelity offers a fund with well-diversified funds that select different allocations of stocks and bonds, holding both risk-free assets as well as risky assets,  they are implementing the above theory.

Vanguard Target Retirement 2050 Fund

The Vanguard Target Retirement Funds are a type of fund with a diversified portfolio that adjusts its asset allocation throughout the year. This mutual fund compounds dividends quarterly and automatically reinvests. The funds provide broad diversification while incrementally decreasing exposure to stocks and increasing exposure to bonds as each fund’s target retirement date approaches. They offer target retirement years in five-years increments, so you can choose the appropriate retirement year for you: 2045, 2050, 2055 and so on.

For the sake of argument, let’s assume that investment began in 2020 with a plan to retire in 30 years, so we’ll use the Vanguard Target Retirement 2050 fund as our example. Using this fund, we will calculate what one can expect from saving $10,000 annually for 30 years with the intention of growing a nest egg so that one can retire in 30 years with the accumulated growth.

Before COVID, the annual rate of return was about 10% for this fund. However, I am unsure if this rate includes dividend payments as well. If the dividend is less than 1%, the difference could be negligible. If not, the total amount should also add this dividend payment in compounding on top of the below calculation. (The total amount should add this dividend payment regardless, but we assume the dividend rate is low, and therefore negligible for our calculation. We can assume anything under 1% is negligible, but that’s a judgment call. If the fund does well without calculating in dividends, then anything else is an added “bonus” on top of these numbers.)

I will use 10% as the expected return rate here. As you know, past results are not a guarantee of future performance. Here is the calculation we learned in class using this theory for this hypothetical situation:

10,000*(1.1)1+ 10,000*(1.1)2+10,000*(1.1)3…+10000(1.1)30 =1,809,434.25

You get an outcome of $1.8M in actual nominal terms, but the purchasing power of the $1.8M we might accumulate will be eroded since every $1 in 2050 will likely be worth less than $1 today due to inflation. So, I will divide this with (1.02)30 in order to factor in inflation and specify that we are using a constant 2% inflation rate. In reality, it changes every year.

$1,809,434.25 /  (1.02) 30 = $990,800. Ta-dah!

You get $990K when you account for inflation. In conclusion, according to the investment strategy developed with Markowitz’s theory, if you invest $10,000 yearly for 30 years in an optimal portfolio, which is a raw cumulative investment of $300,000 not accounting for inflation, the projected total amount of that outcome is roughly $990,800.

What’s next?

Target Retirement Funds are a great starting point, and many different companies offer them because you don’t need to allocate your fund until your retirement year — the fund adjusts its asset allocation by itself. However, if you are willing to adjust it by yourself, there are also other funds implementing the modern portfolio theory with even lower expense ratios. I hope this article inspired you to apply the theory we learned in class to your personal finance and retirement plan.

Disclaimer & Resources

Past results are not a guarantee of future performance. The information provided here is written by a student, not a financial professional, for general conceptual informational purposes only and should not be considered an individualized recommendation or personalized investment advice. The investment strategies mentioned here may not be accurate or suitable for everyone. Each investor needs to review an investment strategy for his or her own particular situation before making any investment decision.

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