Apr 18

Stock Diversification and Coin Flips

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: ,

Nov 24

Can the Market Make You Rich?

This was the question posed on a Morningstar article a couple weeks back. It begins by offering the fact that the bull market of the eighties set the stage for high expectations, specifically that the market would make you rich even with a small sum invested. It closes with this punchline; “Here’s the reality: Your contributions matter much more than investment returns.” Within the article appears the following chart. It assumes an annual deposit of \$10,000 invested monthly over the stated time horizons and given rates of return.

The logic behind the article centers around the ratios calculated above. With an annual return of 6%, (I’ll ignore the 12, as I don’t expect to see 12 long term) you can see that over a ten year period, the value of the account is 73% from deposits, and 27% from growth, the market’s return. Over a 20 year period, with the initial deposits having longer to grow, the ratio is now 48% from gr0wth. This is where the article stops and concludes with the “control what you can” advice. I am 47 years old, and have been working since I’m out of college, 25 years now. Even if I retire early, my money is still invested, so at 62, I’ll have a 40 year investing history, and after retirement a couple more decades, I’d hope. So, why not extend this chart a bit?

Note, I took out the potential 2%/yr loss. It stands to reason that with zero or less return, all of your return is from deposits. I did add a column for 8% and 10% as the long term stock returns fall closer to this range. A thirty year time horizon really starts to change things, doesn’t it? At 30 years you can see that 64% or nearly 2/3 of the ending account value is from growth, and only 1/3 from deposits. The numbers are even more skewed at higher returns or longer time horizons.

What to conclude from this? First, whenever you read anything regarding a long time span, take it with a grain of salt. Second, even a small difference in returns, just 2%, will dramatically affect your returns over a sufficiently long period. Last, and most important, you need to understand your own risk tolerance, I included the 12% column as it was part of the original article, but with reward comes risk, don’t count on that kind or return when you plan your retirement 30 or 40 years hence.

(If the link to Morningstar doesn’t function, the article is available from Invesco Aim)

Joe

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