I wrote about this five years ago, in my pre-blog days, time to revisit and share with new readers.

Today, we’re going to look at a complex topic, how diversification helps reduce your risk when investing in stocks. I’m going to use an analogy, coin flipping, to simulate stock returns in a way that should help simplify the concept. We’re going to start with a simple idea, a game in which you flip a dollar coin and if you bet right, you gain 30 cents, if wrong, you lose 10 cents. It’s an exaggerated way to simulate the stock market, either +30% or -10% on a dollar bet.

The above summarizes the results for one flip. For sake of easy math, -10% is listed as .9, and +30% is 1.3. The average is 1.1, a 10% return, not too far from reality, and a simple standard deviation calculation shows .283 quite a bit higher than the S&P standard deviation. For annualized return I take the geometric mean, the square root of .9 *1.3. Bear with me. It gets better. The next step is to split the bet. After all, the odds are in your favor, right?

You can see that a loss requires two heads, a one in four event. Half the time you will get the average 10% return, and a one in four chance at 30%. The important thing to note is that while the average didn’t rise, the standard deviation dropped quite a bit. And the geometric mean of the 4 results gives us an annual return of 9.1%. We can continue this process following the pattern of Pascal’s Triangle

The third row here helps us understand the three coin scenario, of 8 possible outcomes, one is all heads, three is two heads one tail, etc, a pretty cools chart to understand the odds involved.

The math gets a bit more complex with each added coin, but it’s easy to see that the more flips the bets are spread across, the lower the standard deviation, in other words the results cluster more closely to the average, and the geometric mean also improves in the process. That’s my thought for today, the math of stock diversification is similar, yet far more complex to explain as each stock has its own set of risks. I hope this made the process a bit easier to understand.

written by Joe \\ tags: Investing, stock returns

Every so often, it’s time to look at the terms that we use when discussing financial matters. I’d like to take a look at the terms ‘Average Return’ vs ‘Compound Annual Growth.’ These two phrases sound similar, yet the results can be quite different.

The math isn’t complex, so we’ll start with a simple example. Two years, the first year is up 20%, the second, down 20%. It’s pretty obvious that the average of +20 and -20 is zero, no surprise there. But the compound annual return is a bit different, as 1.2 * .8 = .96 and this results in -4% over a 2 year period or a true return of -2%/yr CAGR. I know that too many numbers make your eyes glaze over, so an image:

This comes from the site Money Chimp, where you can check the market return between the end of two years, and adjust for inflation if you wish. It’s one thing to see random numbers trying to illustrate a point, and quite another to see how it would actually impact your money using real data. You can see that the Compound Annual Growth of “True CAGR” as the Chimp calls it, lags the Average by a full 2%. This is a result of the volatility of returns, as in my exaggerated example, a -20 cannot simply be averaged with a +20.

I don’t know what the market will do in the future. No one can know, really. But I do know how to look at the past, and to look at this specific period, 1926-2011, and suggest it returned 12% is simply incorrect. Had we actually seen 85 years of 11.84%, the result would have been a $13,513 return, four times the final return. Lest you think that the difference of 2% was a result of the 85 year time horizon shown, head over to the site and just enter 2001 and 2010 as the beginning and final years. You’ll learn the disparity is formed by both volatility as well as time, so even short periods are affected.

I was recently reminded of Dave Ramsey’s 12% ongoing market claim, and re-read his article The 12% Reality. In his article Dave confuses simple with compound average and stands his ground. He even discusses the so called Lost Decade; From 2000–2009, the market endured a major terrorist attack and a recession. S&P 500 reflected those tough times with an average annual return of 1%. Last I checked, ten years of 1% returns would grow your money at least 10%, no? The calculator shows us a True CAGR of -.99% for a cumulative loss of 9% over the decade. Let me spell that out – You started the decade with $10,000, and ended with $9,100, a bit less after expenses. Dave’s claim that you’d have $11,000 or so misses the true number by 20% for the decade.

I’ve always loved math, and find that it’s tough to argue with facts. Next time someone starts quoting market returns, remember, knowledge is power, and you’re now armed with the knowledge to help you understand the numbers and educate others.

written by Joe \\ tags: CAGR, dave ramsey, Finance, investment, stock

Blogging at A Young Investor, Tony shares his investment strategies and his thoughts on the financial markets -

Investing is an extreme game: when you lose, you feel like crap, but when you make money and outsmart the market, you feel like you’re king of the world. So how should you emotionally deal with both situations? Do you bang your fist against when table and scream insults when you lose a chunk of money? Should you party for a week after making a huge profit? The answer to both is no.

Losing Money

1. I admit that I’m no novice when it comes to losing money. It feels like you’ve been punched in the guts and the wind’s been knocked out of you. Many investors dwell on the pain, unable to get out of the “losing psychology” trap. Here’s what you should do.
2. Stay calm and keep your emotions in check. A lot of money is lost when investors make investments solely based upon their emotions.
3. Many investors make the mistake of investing after they’ve been hit with a loss in hopes of making back what they lost. Doing so will definitely magnify your loss (hence why people say “losses beget more losses“). The important thing right now isn’t to make back the money you lost – the important thing is to rebuild your self-confidence. Confidence is key when it comes to investing, because you’ll have the conviction to stick to your position through rough times.
4. Do something to take your mind off the markets. In order to calm down and take measure of the situation, you need to step away from your investment. Do something fun that you enjoy.
5. Once you feel calm, take some time to think about why your investment lost money. What something in your original market hypothesis wrong? What can you do next time to prevent a similar mistake?
6. Like I said, it’s imperative that you regain the confidence you’ve lost. Instead of investing like you normally would, wait patiently for a golden opportunity, one of those investments that have a 95% chance of working out. Making some money (no matter how little) will help you rebuild your confidence.

On the other hand, booking a large profit is a totally different feeling. The thrill, the excitement… Here’s what you should do.

Profiting

1. It’s a common mistake among investors to become overconfident. Overconfidence leads to arrogance which leads to disaster. That’s why after every successful investment, I like to take some time to let the excitement wear off. Don’t jump right back into the markets – overextending a position can lead to disaster.
2. Now comes the hard part. Ask yourself (honestly) – did I make money because I was lucky, or because I was right? How do you tell the difference? Before you made the investment, you should have a list of reasons explaining why you believe this investment would work out. Now, count the number of reasons you wrote down that actually did happen. If more reasons on your list didn’t happen than those that did happen, than you were probably lucky as opposed to skillful.
3. Invest more heavily than you normally would when you’re on a winning streak. As they say “winning begets more winning” because you’re more confident about your decisions. Second-doubting is detrimental to successful investing.

written by Joe

While answering a question at StackExchange regarding backtesting of investing strategies, I came upon a web site, AssetPlay, which lets you test a variety of different asset class mixes over the last 36 years or so (currently 1972-2008). While tinkering to find the returns from 1980-2008 for different S&P and 5 year t-Notes I discovered the following returns;

This shows mixes from 100% S&P index, and adds 10% increments of 5 yr T-Notes, to show the different Compound Annual Growth Rates (CAGR) and Standard Deviations (SD).  I find a few things curious about these returns. First, the addition of the T-Notes reduces volatility dramatically, yet, the first two 10% increments actually increase growth. So the 70/30 mix lagged by only 2/100 of a percent, yet the volatility was fully 5% lower. Of course, this isn’t new, it’s the basis of the Efficient Frontier, the theory that proposes the optimal mix of assets based on risk. While I still find the concept fascinating, I’d warn that part of the success shown here is based on the fact that the 5 year note by itself had a return over 9% during this time. I’m not in possession of a crystal ball, but I’m willing to bet the next  decade won’t be so kind to the bond market. Regardless of bond returns, I suspect the stock/bond mix will continue to mitigate risk will little impact to one’s overall return.

written by Joe \\ tags: diversification, efficient frontier, Finance, Investing

A recent Forbes article led me to the author’s company site Portfolio Solutions. There I found an article The Portfolio Solutions 30-Year Market Forecast. The author presents a bit of an explanation of the relationship between risk and reward, and then we are presented a thirty year projection.

Before sharing a few highlights, I’d like to mention the past 30 year S&P return, the 30 years from Jan 1, 1980 through Dec 31, 2010. 11.39%. What’s curious about his number is that the first 20 years of that period saw a 16.53%/yr growth rate which came to a halt with a “lost decade.” It seemed that there was a strong reversion to the mean that made the 30 year period a bit closer to the 10% longer term growth. Portfolio Solutions believes the U.S Large Cap Stock return will average 7.8% over the next 30  years. This number comes with little further explanation, except that it’s the total return, inclusive of a 2.8% inflation rate, and a risk (standard deviation of annual returns) of 19%. To mention bonds as well, the 20 yr treasury is forecast to return 4.3% over the same period.

Before I went to the site and saw these numbers, I was skeptical, ready to disagree with whatever was forecast. But I must admit, as long term numbers go, this is probably close to the mark. Whether the next three decades mirror the past with a run of 15% growth mixed in with a flat period, or year to year randomness that produces three similar decades, I don’t know. Absent any global disasters of a long term nature, or on the positive side, a new set of discoveries/inventions that fuel worldwide growth, I’m good with 7.8%.

What do you think? Too high? Too low?

written by Joe \\ tags: Finance, Investing, stocks