Mind Your Decisions

The Calculating Guru Asks: When Should I Care about Market Swings?

The Calculating Guru is Presh’s alter ego—a cold, number-crunching force. TCG is not a financial professional–use your own judgment or consult a professional before implementing any ideas. Read more about TCG here.

Special thanks to Glenn B. for the idea.

Does it matter when a stock has a good year or a bad year?

I will illustrate how market swings affect investment value through two examples. For the sake of illustration, I am going to focus solely on the annualized return. This is one of the most important parts of a stock investment, as it heavily affects your return on investment.

Investments involve other factors like dividends, taxes, and trading/expense fees. And no investment should be made without assessing risk. I’ll discuss these factors in more detail in future articles. For now, I want to illustrate how the timing of returns affects your investment value.

I’ll present two examples. The first will analyze a one time (lump-sum) investment. The second will consider periodic investments. The second is a more realistic example and it suggests why investors should curb risk as they get older.

One time (lump-sum) investment

Let’s say you make a one-time investment and elect to buy and hold two stocks, A and B, for two years. Suppose the stocks provide the following annual returns:

	Stock A	Stock B
Year 1	-10%	20%
Year 2	20%	-10%

Which stock outperformed the other?

Without running the numbers, I bet most of you would think stock A. This is because the stock lost money early on, but made it up later. It’s often said that early losses are better.

The truth is that it doesn’t matter mathematically. Your original investment would end up with the same value in either case.

To see this, let’s track the return of $1 (the logic scales for larger amounts like $1,000)

	Stock A	Stock B
Year 1	$0.90 = $1 * (1-10%)	$1.20 = $1 * (1+20%)
Year 2	$1.08 = $0.90 * (1 + 20%)	$1.08 = $1.20 * (1 - 10%)
Ending	$1.08	$1.08

Despite the difference in timing of the returns, the two stocks yield the same result.

In fact, any time you invest in only one time period, and you hold for a fixed number of years, the timing of returns does not mathematically matter to the ending investment value.

(Mathematically, this is because multiplication is commutative.)

Periodic Contributions

The lump sum example is extreme and unrealistic. Most of us contribute regularly since we don’t have cash lying around. We often cut money directly from our paychecks, as the case is for 401(k) contributions.

What happens in this more realistic case?

Let’s suppose you invest $1 at the start of each year. Would it be better to invest in stock A, with the early loss, or stock B?

Now, conventional wisdom holds true that stock A with the early loss will be better. Let’s go through the numbers by tracking the value of each investment:

	Stock A	Stock B
Year 1 (invest $1)	$0.90 = $1 * (1-10%)	$1.20 = $1 * (1+20%)
Year 2 (add $1)	$2.28 = ($1 + $0.90) * ($1+20%)	$1.98 = ($1 + $1.20) * ($1-10%)
Ending	$2.28	$1.98

Now stock A is the better investment. With regular contributions, it is therefore better to have the loss earlier in the investment pattern.

The reason is that an early loss affects less of the money you have contributed.

More specifically, in stock A, the -10% return only hurts the initial $1 contribution. In stock B, the -10% return hurts both of the yearly $1 contributions.

From a practical perspective, it also matters when you want to withdraw the money. For instance, in stock A, the early loss gives you an opportunity to save and contribute more to “make up” the loss. This is a very important consideration when you’re planning for long-term goals like retirement.

The examples illustrate why investors close to retirement give up higher returns for lower risk. The potential for high negative returns near retirement would be quite unpleasant—the impact would be felt on all contributions and all compounded returns.

As a general rule, any time you invest the same amount regularly (called monthly/quarterly/yearly contributions or sometimes called dollar-cost averaging), it’s better to have negative returns early on.

You can’t control the timing of returns, but knowing this can help you assess how much risk you should take.

Tool to play around with

I think that experimenting is the best way to solidify understanding. To that end, I’ve added a spreadsheet called “Timing of Returns” to the Financial Tools section. You can understand the impact of late losses to your portfolio by playing around with the numbers.

I’ve lately been humbled by many smart comments, especially in the article about dividing a restaurant bill (mentioned in Lifehacker).

So I know there are improvements to be made. If you have ideas, please send them along to me.