Wednesday, August 26, 2015

Some Truths about Compounding

Geometry Lesson

Is it me or does the teacher in the picture not look happy?

That's odd because we're going to talk about compound growth, which is a seemingly pleasant financial principle. Compounding is supposed to be a boon to investors and by the way, also mankind's greatest invention.

The idea is if you invest for long periods of time you'll get exponential returns. Exponential is a fancy word for bigger and bigger.

Maybe the teacher is frowning because this principle, while true on paper, is often exaggerated as to how it works in the real world...

What is Compounding?

Compounding is the process whereby reinvested returns result in the investment earnings increasing exponentially over time. A simpler definition might be: "when you earn interest on your interest." Over time, you earn not just on your original investment, but also on the earnings themselves.

This is the basis for the idea that if someone forgot about $5 in a bank account during the Civil War, today it would have grown to millions due to compound interest.

The chart below shows how geometric growth looks. Notice the line is not straight, but curved, and the curve becomes increasingly pronounced. This is called the "hockey stick."

Mark Zuckerberg opens the Facebook f8 conference with user growth numbers alongside major product launches.

Perhaps geometric growth worked for Mark Zuckerberg - but can it work for the rest of us?

The Amount of Capital Affects the Amount of Return

The rich do get richer. But not necessarily due to compounding. One reason is the more money invested, the more earned on the same positive percentage return.

If $10,000 invested earns 2%, that's $200. But if instead of $10,000, it's $1,000,000, the earnings would be $20,000. The percentage return stayed the same, but a greater gain resulted.

The simplest way to increase earnings is to have more invested. I find it interesting we so often focus on the return, when the easiest way to boost earnings is to increase the amount of capital put to work. Of course, having additional capital may not be an option.

Compounding and the Rule of 72

The “Rule of 72” is a rule of thumb. Divide a rate of return into the number 72, and this will tell how long it would take to double. For example, a 10% annual return means a double in 7 years (72/10 = 7). A 2% return means it would take 36 years (72/2=36).

 If you start inputting returns, you'll notice a small increase in the rate of return produces a big difference in the final product.

Consider someone, age 50, investing $10,000. This table shows what the Rule of 72 would imply with a return of 10% per year:

Hypothetical Investor: Age 50    

Rate of Return: 10% 

Time to Double: 7 Years
Investment Sum

Now compare the result if our only earned 2% per year. The time to double would be 31 years.

Hypothetical Investor: Age 50

Rate of Return: 4%

Time to Double: 18 Years

Investment Sum

After looking at these figures, it's easy to conclude compounding is a great deal. Investing in riskier assets would seem to be the way to go.

And there is mathematical truth to the idea. Investing for a longer period and earning a higher return will result in an exponentially higher sum.

Charts such as the above have shaped much of our investing philosophy. The key is to put the money in for a long period of time and to try to find investments which pay a higher incremental return.


Could Compounding be Overrated?

The problem is the concept lends itself to oversimplification. I believe many attempt to benefit from compounding and wind up losing.

While it's great when it occurs, I question how often this will be. Indeed, some of the arguments break down upon inspection.

You may have heard Albert Einstein once said compound interest is modern man's “greatest invention,” or something to this effect. In my line of work, I have heard it a thousand times.  However upon researching the matter, I can find no evidence he said this. It seems to be a statement that has been attributed to him to increase the idea that compounding is a magic elixir. It's modern day folklore.

Factors that Mitigate Compounding

First, compounding becomes a major factor only after the money is left untouched for an very long period of time. How many investors can afford to leave money untouched in an investment for 20, 30, or 50 years? A few, but not many. And probably not retirees. Most retirees need to draw income from their investments.

Second, to benefit from compounding an investor needs to earn a high return for a long period of time. This is difficult to do. It is hard enough to earn a high rate of return for a short period of time. Remember the arithmetic of loss? Losses disproportionately affect your rate of return.

Third, your investments are not the only thing compounding. Inflation, has averaged an annual rate of about 3% over the past 100 years. So while your investment may be growing at a
compounded rate, so is inflation. Inflation diminishes the value of your principal over time, much as compounding increases it.

Rip Van Winkle's Unhappy Discovery


There is an old financial joke.  An investor has $100 in his savings account and he falls asleep for a hundred years. When he wakes up, he rushes to his phone and calls to see the value of his account, since over the years it will have grown.

The investor is elated when he is told the value of his account has grown to $100,000. It seems a dream come true... everyone wishes they had a hundred years to be invested and to let their money compound. Then a voice comes on the phone and says the cost of the phone call is $500 dollars.

The idea is that while the savings compounded, so did inflation, and much of the effect was mitigated by the inflation.

Your interest or earnings may compound, but so does inflation!


Compounding may indeed be a positive factor if you are a long term investor. With a long term horizon, and if you are fortunate enough to earn a consistent positive return, the effect can be significant.
But be careful facile arguments. Don't let the hope of compounding draw you into unsuitable levels of risk.

Saturday, August 8, 2015

The Arithmetic of Loss

Rubik's Cube

If you played King of the Hill as a child, you'll remember the goal was to beat the other kids to the top. Not easy (at least it wasn't for me). But going down the hill was a breeze. The other kids and gravity were always ready to help!

It's easier to go down than up - this is the world of physics. The principle for how this applies to investments is called the Arithmetic of Loss.

The math: losses hurt more than gains help. For example, losing 5% is more negative than gaining 5% is positive.

Shouldn't the effect be equal? We'd think gaining 5% or losing 5% would have the same impact. But no.

To illustrate, consider a bigger percentage. Start with $100,000 and gain 50%, and you're $150,000. Great.

But as we know from the law risk equals potential return, where there's a chance for return, there's one for loss. Suppose the sword cuts the other way and you lose 50%. You'd have $50,000. Here's the rub: to get back to $100,000, you now have to go up 100%.

One more example: an investment of $100,000 earns 10% a year for three years. In the fourth year, it loses 10%. The ending value is $119,000. This computes to a return of just 4.6% per year. One down year disproportionately reduced the result.

You Can Only Lose All Your Money Once

Las Vegas in the 1950s

There is another important aspect to the arithmetic of loss. Gamblers in Vegas know
this - your capital is finite. Once it's all gone, it's gone.

When you lose, you may become more risk averse. Math is compounded by psychology - studies show losses hurt more emotionally as well. With capital depleted, you'll likely be less tolerant of further losses.

Risk Tolerance May Change with Market Conditions

Consider an investor who retires with what they figure is twice what they need to live comfortably. They take some risk. But if they suffer big losses, they will rethink their risk tolerance. They'll probably become more conservative and move what's left to safer instruments.

Daily Linear Chart of S&P 500 from 1950 to 2013 
When do investors lose money? During a market decline. Reallocating a portfolio to reduce risk during a market decline means selling the riskier assets in a down market, which is often bad timing.

Does Buy and Hold Protect Against Losses?

In the past, it was believed a buy and hold strategy would protect against losses. The value of an investment may temporarily decline, but the solution was easy: don’t sell. Just hold until the value came back.

This approach was based on the idea that the market and investments will always quickly go up after a decline. The problem is, that may not always be the case, especially during a shorter time frame. A better strategy is to accurately assess risk tolerance in advance.

Mathematically, just like in King of the Hill, it's much easier to go down than up. I don't know why it has to be this way. But kids -  and investors - have to live with it.