Category Archives: Finance

Slow and Steady

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A widespread investing myth is the time diversification fallacy–the belief that young people should hold riskier assets than old people. People imagine a young person’s portfolio to be safer than an old person’s because it is somehow protected by time. This idea is a dangerous weed that cannot be easily uprooted. Here are my own arguments against it.

Seed Money

Suppose that the markets have been consistently earning 8% annually. Then one year there is a -50% crash. After that the markets return to their consistent 8% returns. The chart below shows how two investors would fare. Both start with the same $10,000 stake. The first was 20 at the time of the crash and the other was 59.


Age Early Crash Late Crash
20 $10,000.00 $10,000.00
21 $5,000.00 $10,800.00
30 $9,995.02 $21,589.25
40 $21,578.51 $46,609.57
50 $46,586.37 $100,626.57
59 $93,126.38 $201,152.98
60 $100,576.49 $100,576.49

The young investor lost half of his equity right away. Fortunately, there was plenty of time to make it back up. In the ensuing years, that portfolio grew by 2,000%. But since the seed money was reduced, the effects of that initial bear market were compounded over the next four decades. The final portfolio value was identical to the portfolio that lost 50% in its final year. Either way, whether the portfolio earns 2,000% first and then loses 50% at the end, or loses 50% at the beginning and then earns 2,000% afterwards, the investor retires with the same $100,000. The technical explanation is that “compounding is commutative.”

If someone advises you that you should hold a straight equity portfolio for the first 20 years of your career and then switch to more reliable bonds for the next 20 years, remind them of commutativity. Explain that your expected return would be the same as if you held the bonds for the first 20 years and then straight equities for the next 20 years. If you are going to change your asset allocation over time, the order of which portfolio you hold first is irrelevant. Young investors should only plan on becoming more conservative over time if they also believe it makes good sense to start conservative and get more aggressive every year until retirement.

Efficient Frontier

This argument is meant to appeal to the mathematicians. Every environment contains an efficient frontier, and the goal of portfolio management is to stay on the frontier. It’s easy to construct one portfolio that is aggressive and one that is conservative, although both are on the frontier. Suppose an investor held each portfolio, one at a time, for a certain number of years. The cumulative risk and return would be equal to the averages of those of the two portfolios. Graphically, the average would be a point midway between the two portfolios. Since the efficient frontier is a convex curve, the average itself would not be on the frontier. The investor’s cumulative lifetime portfolio would not be as efficient as if it had been consistently aggressive, or consistently conservative, or a consistent combination of the two.

Human Capital

An intuitive counter-argument exists. Over a lifetime, most people will save thousands of dollars from their steady income. So if they were to lose all their money at 20 years old, they could still recover by putting aside more savings in the future. A market crash would be more devastating at 60 years old when people can’t produce as much capital. This is a sound objection that ought to be factored into the model.

A young person with $10,000 savings and a $100 monthly savings plan actually commands about $25,000 in assets, if you count the present-day value of the expected savings. The $15,000 of expected savings could be risky, depending on how steady the income is. So the other $10,000 might need to be placed in assets that offset that volatility. If the income is reliable, then the accessible $10,000 could be placed in straight equities as an offset. At retirement, the same person would have $500,000 of investments and no more expected savings. Since the accessible investments are no longer offsetting anything, they would be allocated differently than before.

The human capital argument should not be interpreted to mean that a person’s overall portfolio grows more conservative over time. It means that a rational investor will target a consistent risk profile at all ages. As part of a holistic strategy, the value of human capital should be included in the portfolio. An investor who understands the value of consistency will be able to retire with larger and safer investments.

Guilt Money

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Almost everyone knows that they need to be saving more money for retirement. Good advice about budgeting is everywhere. People always feel like they need to be saving more, and they don’t always know how much is enough. That means that the motivator for most people is guilt or fear. But having a clear goal and knowing you are on the right track would be more effective than always combating feelings of inadequacy and dread.

The first steps are obvious. You need to get an income if you don’t have one. Then you need to pay down high-interest debt if you have it. Next put aside enough emergency cash for several months of necessities. After that is the time to seriously consider retirement savings.

You have to decide how big of a nest egg you want to build. There’s a formula that can take the guesswork out of it. Someone once taught me the following definition for wealth:

You are wealthy when your investment income is enough to cover your expenses.

When your investments earn enough to pay for your lifestyle, you are free from needing employment income. This strategy will bring more peace of mind than a strategy that allows you to live off of your retirement account for a certain number of years. The prospect of outliving your retirement money is nerve-wracking. The safe alternative is to plan well enough that you could live off of your investments forever. This doesn’t mean that you have to be super-rich. There are only two numbers that really matter–how much you want to save, and how much you want to spend. So if you want to be wealthy, you can get there by either saving more, or by scaling back your retirement spending. (Paradoxically, the people who learn to live with the least are also the wealthiest).

To make a concrete goal, you need to come up with a number. First decide how much you are going to live off of. You can do that by adding up all your current expenses, for necessities like food, clothing, housing, transportation, and medicine. Alternatively, you can take your current income and subtract the amount that goes to taxes and debt and savings. Either way you should get a number close to how much you consume right now. Don’t include housing in the figure if you will have paid your mortgage before retirement. Then, you can adjust the number downwards if you know you will retire frugally, or upwards to retire extravagantly.

Suppose that you currently earn $36,000 annually, but you think you could live off of $12,000 after retirement. The first thing you should know is that you are going to need to put in the bank a little more than 20 times your estimated budget. So since $12,000 × 20 = $240,000, your savings target is around a quarter of a million dollars, before adjusting for inflation. Once you reach that goal, your investments will produce enough gains to support you forever. That’s going to be attainable as long as you start early. (Some of these calculations require guesses about the future, such as 8% returns, 13% volatility, 3% inflation, monthly periods, log-normal returns and some income elasticity).

The following chart shows the importance of starting your savings young. In the left column, find the number of years until you retire. Then look at the highlighted number across from that. That is the percentage of your retirement budget that you need to continuously save. For example, suppose you are going to retire in about 30 years. The highlighted number in the correct row is “43.3%.” That means that in order to live off of $1,000 per month, you need to save $1,000 × 43.3% = $433 per month.

Years Pessimistic Neutral Optimistic

-2 -1.5 -1 -0.5 0 0.5 1
5 462% 437% 412% 389% 367% 346% 326%
10 228% 210% 193% 178% 163% 150% 138%
15 145% 131% 118% 106% 95.8% 86.1% 77.3%
20 102% 90.9% 80.5% 71.2% 62.9% 55.4% 48.8%
25 76.4% 66.6% 58.0% 50.5% 43.8% 37.9% 32.8%
30 58.8% 50.5% 43.3% 37.0% 31.6% 26.9% 22.9%
35 46.2% 39.1% 33.0% 27.8% 23.4% 19.6% 16.4%
40 36.9% 30.8% 25.6% 21.2% 17.6% 14.5% 12.0%
45 29.7% 24.4% 20.0% 16.4% 13.4% 10.9% 8.84%
50 24.1% 19.6% 15.8% 12.8% 10.3% 8.24% 6.59%

The highlighted column is appropriate if you want to be conservative and assume that the markets will have moderately poor performance. If you feel like you want to be either more optimistic or more pessimistic, then you can choose one of the percentages in the other columns. The numbers from -2 to 0 to 1 in the column headings are a measure of how optimistic you are. Negative, pessimistic numbers are better, because they leave less chance that market conditions will force you to modify your plans.

As you can see, if there are only 10 years until your retirement, you would have to save a huge percentage of your income to meet your goals. One way to make that possible is to tighten your retirement budget to fit what you are capable of supporting. The only other solution is if you have already been contributing to a retirement fund. If you already have an investment account, then use the following chart to calculate how effective it will be. Find the highlighted number corresponding to the number of years until retirement, just like before. Multiple that percentage by the amount you have already saved. That’s the annual stipend that you’ll be able to draw, even if you don’t save any more. For example, suppose you already have $150,000 saved and you retire in 10 years. The table gives a percentage of “6.0%.” Since $150,000 × 6.0% = $9,000, your existing savings will earn you $9,000 annually after retirement. That’s equal to $750 per month. That means that for your total budget of $1,000, you only need to worry about how to get the remaining $1,000 − $750 = $250 per month. Going back to the chart above, you need to keep saving another $250 × 193% = $482.50 per month.

Years Pessimistic Neutral Optimistic

-2 -1.5 -1 -0.5 0 0.5 1
5 4.3% 4.7% 5.1% 5.5% 6.0% 6.6% 7.2%
10 4.7% 5.3% 6.0% 6.8% 7.6% 8.6% 10%
15 5.3% 6.2% 7.2% 8.3% 10% 11% 13%
20 6.2% 7.3% 8.7% 10% 12% 15% 17%
25 7.2% 8.7% 11% 13% 16% 19% 23%
30 8.5% 10% 13% 16% 20% 24% 30%
35 10% 13% 16% 20% 25% 31% 39%
40 12% 15% 19% 25% 32% 40% 51%
45 14% 18% 24% 31% 40% 52% 67%
50 17% 22% 29% 39% 51% 67% 88%

The important thing is to get started. Even if you don’t have a good idea of a realistic budget for your retirement, a rough estimate is better than nothing. The figures above are also only estimates, but they are accurate enough to be useful. Eventually you can talk to a financial planner to get more precise personalized recommendations, and to plan for other variables like a child’s education fund. Meanwhile, if you are following this formula, you know how much of your money is needed for savings and how much you can afford to play with. You can feel peace of mind knowing that you will be able to pay for your retirement plans and you will never outlive your savings.