The Case

Throughout this article, we will assume that a hypothetical individual, named Riley, is interested in building a retirement portfolio. Riley’s situation is as follows:

·      Age: 25

·      Desired retirement age: 65 (Time horizon = 40 years)

·      Annual salary: $55,000

·      Initial investment: $15,000

·      10% pre-tax contributions into a 401K + 4% employer match

·      Additional savings of $300 per month

·      Cost of desired retirement lifestyle: $40,000 per year (net, in today’s dollars)

 We further assume that the long-term rate of inflation is 2% per year, capital gains tax is 15%, and an income portfolio that pays out regular cash flows could reasonably payout 4.5% of total assets per year.

 In our base case, we assume that stocks generate, on average, 8.5% per year while bonds generate 4%. In our bear case, stocks generate 6.5% and bonds earn 3%. Our bull case assumes 10.5% for equities and 5% for bonds.

 Finally, we assume that a portfolio with a time horizon of more than 15 years is fully invested (100%) in equities and then gradually reduces its equity allocation to 40% (60% in bonds) as the start of retirement approaches.   

Financial Target

At 2% inflation, the $40,000 per year to fund Riley’s lifestyle in retirement would actually amount to $88,322 40 years from today. In other words, $88,322 in 40 years could afford you the same lifestyle you could afford today at $40,000. At 15% capital gains, the portfolio would therefore need to generate $103,908 per year to leave the investor with $88,322 after taxes. If an income portfolio can yield 4.5% per year, the total value of the portfolio would have to be at least $2.31 million to cover Riley’s desired lifestyle. Note that at $2.31mn the portfolio would generate enough income so that Riley would (in theory) never have to sell assets to fund her lifestyle, meaning that Riley is living entirely off of interest and the size of the portfolio remains approximately flat after entering retirement. One could also decide to retire with a lower portfolio value and sell a certain amount of assets each year to make up for the shortfall in interest income, gradually depleting the portfolio until its runs out of funds. This approach, however, risks the possibility of outliving your retirement savings and would either leave you in poverty if you live far longer than expected or force you to move in with your adult children or search for a new job to cover expenses. We, therefore, prefer to aim high (and save much) to maximize the odds of reaching the desired $2.31mn and mitigate this longevity risk.

Case 1: Simple 40-Year Horizon

First, we want to highlight the effects of compound interest and the advantage of starting to invest at a young age. Investments grow exponentially, not linearly. This means that the absolute dollar amount by which your portfolio grows increases each year, leading to rapid gains in absolute dollar amounts, especially in the later years of the investment. The below table attempts to illustrate the importance of time and compound interest in investing. Although the investment returns the same percentage amount each year, note that the dollar amount you are receiving changes dramatically for the last ten years compared to the first ten. In the first ten years, your investment returns $1,159 while it generates $54,355 for you between years 50 and 60($101,257-$46,902). In our case, if Riley could always earn 8% per year but decided to delay the start of retirement investing until 35, the initial investment would only increase 10.1-fold, while starting at 25 would result in a 21.7-fold increase. Most likely, even highly-skilled investment professionals could not earn a high enough return above 8% to make up for those ten lost years of compound interest. As Charlie Munger put it: “The first rule of compounding is to never interrupt it unnecessarily.”

To give another surprising example of the power of compound interest, consider Warren Buffet’s returns generate via his conglomerate holdings company Berkshire Hathaway since 1965 as shown in its annual shareholder letter. As of December 31, 2022, Berkshire has generated compounded annual returns of 19.8% compared to 9.9% for the S&P500. Berkshire exactly doubled the compound rate of the S&P500 over that 57-year span. However, it would be far from true to state that Berkshire’s total investment returns were only twice that of the S&P 500. The total gain on your initial investment with Berkshire in 1965 compounded at 19.8% would have amounted to 3,787,464% (that’s 37,874x your money back), while the S&P500 would have only returned 24,708% compounded at 9.9%. Although the 9.9% difference in the compound rate wouldn’t amount to a large difference over a year or two, it results in enormous differences over 57 years due to the power of compounding.   

Regarding the above-mentioned scenario, Riley starts with an initial investment of $15,000 that is 100% invested into a broad equity index, plus a 10% contribution from her pre-tax salary and a 4% employer match, as well as an additional $300 each month that are invested into the portfolio.  The chart below shows the potential results of this strategy over Riley’s 40-year investment horizon. In the base case scenario, Riley reaches the retirement target of $2.3mn at age 60, while the bull case scenario achieves this target at age 55. In the bear case, however, Riley never reaches the desired amount and is forced to gradually deplete the portfolio by selling assets (blue line) to secure the desired retirement lifestyle. In the bear case scenario, Riley is still able to enjoy the same retirement lifestyle that was set at the start, the difference is that Riley is depleting her portfolio, which means that it is declining in value and would eventually run out of money if Riley were to live too long. Note that this simple scenario assumes no salary increases throughout Riley’s career and no large expenses such as a down payment on a house. The Excel template attached at the end of this article will allow you to replicate our analysis and change the assumptions to flexibly adjust to other scenarios you wish to explore.

It is important to highlight that the smooth blue, orange, and grey lines are unrealistic and unobtainable results that give a false impression of security. Rather, they should be interpreted as ranges between which the actual portfolio value is likely to fluctuate. Although the long-term trend for equity and fixed income portfolios is upward-sloping over time, investors need to mentally prepare for the fact that their actual wealth will observe dramatic swings. To illustrate this, we added the black line which represents one hypothetical random portfolio path out of an infinite number of potential outcomes. This line more realistically represents the fluctuations investors will observe over their investment lifecycle, though the end-stage portfolio value may end up at entirely different levels with each simulation.

Case 2: Dynamic 40-Year Horizon - Salary Increases

This scenario is the same as described above except that Riley starts with a salary of $45,000 which increases by $5,000 every two years and then plateaus at $96,000 a year. We also assume that Riley is always able to save 5% of gross monthly income earned.  

The results are shown in the chart below and are similar to those of the first simple case, although more favorable as higher portfolio values at retirement are achieved in all three cases. In the bear case, Riley would still not quite reach the desired target but is closer to it which means that fewer assets will have to be sold and the portfolio will deplete at a slower rate.

We believe that this second case comes closer to the situation that our readers find themselves in and hope that our illustrations show that it is possible to secure a comfortable living standard in retirement without having to start with large sums of capital as long as one starts to invest early in life.

We also added a green line in this scenario. This green line represents the pure cash amount actually paid into the portfolio and is the total amount of savings you would have if you had kept your savings in a non-interest-earning bank account (or under your mattress) rather than investing it. At age 65, the total cash savings sum to $661,380 and would last Riley only 6 years into retirement before all of her life savings had been depleted. Contrast this $661,380 to the more than $3.5mn Riley has under the base case scenario. Riley had the same $661,380 at her disposal in both cases but invested it in one scenario and left it in a bank account in the other. Through 40 years of compound interest, the difference sums up to a staggering $2.9mn.