Investing Math

As a homeschooling mom, I am in the middle of teaching my daughter about the intricacies of addition and subtraction of simple numbers. She is starting to realize that math takes effort. Sometimes she looks at a complicated problem and just takes a wild guess. I have to stop her and say, “No, you don’t have to guess. You know how to figure this out.”

As I learn about investing, the same advice applies to me. One of the investing mindsets I have had to adopt is:
 

Good investors are always open to learning math
and calculation methods.

 
I know some readers are groaning at this point. They don’t like math or think they are terrible at math or some other rationale. But if you want to learn how to invest, you must learn math. It is not optional.

As an example of how we take wild guesses as inexperienced investors, we might be filling out a savings calculator and it might say, “Enter your estimated rate of return.” “I have no idea,” we might think. Then we might remember reading something about how the stock market averages around 8% each year so we put in 8%.

I read an article recently by Jason Zweig of The Wall Street Journal titled “Are Pension Forecasts Way Too Sunny?” that challenges us not to guess on these return calculations and tells us to figure it out. In the article, Mr. Zweig says that pension managers used to forecast around 12-16% returns. Now, after many difficult years in the stock market the managers have revised their return estimates to around 8%.

But Mr. Zweig argues that this is still an unrealistic guess and that “you [would have to be] a better stock picker than Warren Buffett” to pull this off. When I read this, I was surprised but his explanation was rooted in easy-to-understand math.

His example:

You want to earn 8% per year and your portfolio is 50% in bonds and 50% in stocks. Bonds are currently earning about 2.2% per year.

His calculation: 50% * 2.2% = 1.1% estimated contributions from bonds to the portfolio

If you want to earn 8% per year, your stocks must contribute at least 6.9%. To a naïve investor like me, this doesn’t sound impossible. But though more math, Mr. Zweig demonstrates that it is unrealistic.

His calculation: 50% * 13.8% = 6.9% estimated contributions from stocks to the portfolio

In order for the portfolio to earn 6.9% from stocks, the stock portion of the portfolio needs to be earning at least 13.8% per year. The pension plan being overseen by Berkshire Hathaway is estimating a return of around 7.1% with about 30% in bonds (i.e. Mr. Buffett thinks he can earn about 9.2% on his stocks). Stocks in general have averaged 3.9% – 8% over the last 20 years. So, the portfolio managers estimating 8% with a 50/50 mix would more realistically estimate a 5.7% return (if they assume they can equal Mr. Buffett’s stockpicking talent).

The lesson: when it comes to your own portfolio, use a reasonable rate of return based on math:

For example, a typical investment portfolio for a younger person is 90% stocks and 10% bonds. If you use Mr. Zweig’s formula, you come up with:

90% *(3.9% – 8%) = range of 3.5% – 7.2% return from stocks

10% * 2.2% = 0.22% return from bonds

Total estimated portfolio return = 3.72% – 7.42%

So, if you are estimating how much you might earn on your investments in this “aggressive” portfolio, you might guess somewhere in the middle, say around 5.5%. As you can see, this is far less than 8%. These calculations could change each year based on changes in the stock and bond market so you will have to recalculate periodically but you don’t have to just give a wild guess. I will have to update my own planning accordingly.

Was the above example as eye-opening to you as it was for me? What other simple math formulas do you rely on to steer your investments in the right direction? Please share in the comments.