[Editor's Note: This is a guest post submitted by Felix Chapovsky, MD, a physiatrist in Pennsylvania. In it he discusses the often misunderstood but important difference between arithmetic means (average annual return) and geometric means (compound annual growth rate or annualized return). We have no financial relationship. Be aware that I'm not a fan of active stock trading as an investment method.]
I first became interested in the stock market during residency, when the thought of finally having to pay off all my student loans hit me. It was a pretty daunting feeling know that I had to pay back over $200,000 for my education and I thought the market would be a great way to help make some quick money. Boy was I wrong.
I have been an active trader in the market for 6 years. By active trader, I mean that instead of utilizing a buy and hold strategy consisting of a diversified stock portfolio, I try to capitalize on intermediate term price movements in the stock market by investing in individual stocks that I feel offer the best opportunity for significant price appreciation. I have made many mistakes during my trading career, more than I could possibly discuss in this article, but I have learned something from each of them and this has made me a better trader.
Whether your goal is to learn how to trade individual stocks or to become a passive investor through asset allocation, there are certain rules that must be followed in order to achieve success, the most important of which I want to share with you today. What I am about to show you may seem very simple on the surface, but it took me 5 years to really put it into practice with my trading strategy and it has made all the difference.
The Stock Market Is Not A Casino
Last year, I had a good friend call me up and say “Hey. I hear the Facebook IPO is coming. Can I give you some money to invest for me?” I told him no but I get these types of phone calls rather frequently from colleagues of mine who think of the market is more of a casino and a way to make easy money. Nothing could be further from the truth.
Experienced Investors Concentrate on Risk
The problem is that most people spend 95% of their time trying to find the perfect strategy or the next “big stock” but this rarely leads to success. In other words, the majority of people focus most of their time on trade identification, but what they should be spending their time on is developing a risk management strategy. Even if you prefer a diversified asset allocation approach, it is critical for you to understand how to manage risk. We have had two 50% market declines in recent history, in 2000 with the internet stock bubble and during the 2007-2008 financial crisis. In 2008, 40 million 401(k) account holders lost a total of $1 trillion worth of assets, but if they had spent some time focusing on risk, they could have saved themselves a lot both in terms of time and money. [Editor's Note: I'm not sure what the author is suggesting these investors should have done to focus on risk, but a diversified stock/bond portfolio helped minimize losses in 2008, and rebalancing and using a buy-and-hold approach served many investors, including myself, very well to make up their losses in 2009-2011. An investing plan that requires me to be able to predict the future with any kind of certainty is a plan that is likely to fail.]
Remember, even if your only goal is to invest money in your 401(k) or some other retirement vehicle, it is up to you to determine how your money is allocated. You can seek all the counsel you want but the responsibility lies with you. You work very hard for your money and you must learn how to protect it.
Arithmetic Means Are Not Geometric Means
The lesson I am about to teach you can best be illustrated with an example. Say you are looking at 3 different mutual funds and are deciding in which one you would like to invest. Below are the yearly returns for each fund during the last 3 years. With no other information, take a moment to write down which fund you would invest in an why.
| Fund | 2010 | 2011 | 2012 |
| A | -18 | 20 | 6 |
| B | -30 | 25 | 16 |
| C | 8 | -10 | 10 |
Which mutual fund did you pick? If you calculated the average annual return for each fund, then you came up with the following table.
| Fund | 2010 | 2011 | 2012 | Avg Return |
| A | -18 | 20 | 6 | 3.33% |
| B | -30 | 25 | 16 | 3.67% |
| C | 8 | -10 | 10 | 2.67% |
If you are like most people, you picked mutual fund B since the table shows it offers the best return of the available choices. You would be wrong. Intuitively it doesn't make sense, math is math and you can't argue with results, but in order to gauge the value of the output you must first consider the relevance of the input. This is not regular math, it is stock market math, and there is a big difference.
Look at the table below and see if you can figure out why fund B is actually the worst possible choice above.
| % Loss | % Gain Needed To Get Back To Even |
| 1 | 1.01% |
| 5 | 5.26% |
| 10 | 11.11% |
| 15 | 17.65% |
| 20 | 25.00% |
| 25 | 33.33% |
| 30 | 42.86% |
| 35 | 53.85% |
| 40 | 66.67% |
| 45 | 81.82% |
| 50 | 100% |
| 75% | 300% |
| 90% | 1000% |
Losses Matter More Than Gains
There is a stock market saying that says “Winners take care of themselves, losers never do.” Say you put on a trade and it shows you a 1% loss. This is not a big deal and you only need to return 1.01% of the next trade to get back to even. Your second trade shows you a 5% loss, also manageable as you only need to earn 5.26% on the next trade to get back to your initial trading capital. If you go down the table, you will notice that winners and losers are not correlated in a linear fashion. In other words, losses work exponentially against you and the more significant your loss the harder it is to recover from. This may seem like a simple concept to understand, but the importance of this can't be overstated.
Lessons Learned
There are 2 important points to be gained from this information.
- The greatest traders of all-time were right at most 50% of the time, even during bull markets. Let's assume for this discussion that you can replicate their success and you have a 50% batting average on your trades. The size of your winning trades must be bigger than the size of your losing trades or you will lose money overall. Look at the table above; if you take a 20% loss on a trade, you must make 25% on your next trade just to get back to even. If you only get back 20%, you are not even getting back to your initial trading amount. If you repeat the same cycle 10 times, you have lost a lot of money.
- For you mutual fund investors out there, the key point is that average annual return is meaningless when it comes to calculating the actual growth rate of your money. Looking at our 3 choices of mutual funds, if you were to calculate how much $100 invested in 2010 would be worth at the end of 2012 you would get the following results.
| Fund | 2010 | 2011 | 2012 | Avg Return | Annualized Return | Dollar Value |
| A | -18 | 20 | 6 | 3.33% | 4.30% | $104.30 |
| B | -30 | 25 | 16 | 3.67% | 1.50% | $101.50 |
| C | 8 | -10 | 10 | 2.67% | 6.90% | $106.90 |
Look At The CAGR
It can't be stressed enough, losses have a more significant impact on your portfolio than gains so even though fund B had a great 2011 and 2012, this still was not enough to overcome the 30% loss experienced in 2010. Also consider that this only encompasses 3 years of data. Mutual funds report their average 1, 3, 5 and 10 year returns. You should realize now that you must take these numbers with a grain of salt and that making investment decisions based solely on average returns is a mistake. [Not to mention making investment decisions based on past performance of any type- ed] The best way to use average returns is to see how your fund performed relative to the stock market in general. For example, if the market was down 15% and your fund was down 10%, you are not losing as much as the market so that is good. This also means that if the market was up 15% you probably would be up less than the market as well. This is not necessarily a bad thing because everything should be seen in terms of risk and reward. Preservation of capital is most important, so even if you are not making as much you are losing less during a bear market. The most important number you need to look at is the compound annual growth rate of the fund you are interested. If you don't see this number, ask for it.
To sum it up, it is not stock market gains you should be worried about, it is losses. This is very relevant to our current market situation. During the financial crisis, the S&P 500 suffered over a 50% decline from its highs in late 2007. At the time this post was submitted, the S&P was about 1% away from those previous highs and since that time has eclipsed that mark. This means that if you had money invested in the market in 2007, it has taken you almost 6 years just to get back to even! Forget about all the average returns you have seen in your statements over the years, if you haven’t put any additional money in your account you are just now getting back to where you were before.
Have A Plan For The Next Bear
What I really want you to take away from this is to understand that you must take risk into account when making investment decisions. What if you were of retirement age in 2008? You were toast. You lost 50% of your entire net worth in the span of 1 year, all because you spent too much time focused on growing your money, and not enough time on protecting your money. You would never give a patient medication without first considering what potential side effects there could be and what you would do should they occur, right? Shouldn’t you treat your investment portfolio the same way? [Editor's Note: An investor nearing retirement probably shouldn't have an asset allocation consisting of 100% stock, which would have led to a 50% loss in the 2008 bear market.]
One thing I can tell you with absolute certainty is that we will get another bear market in the future. Trying to predict when this will happen or how deep the correction will be is impossible so it is not even worth the effort to try. All you can do as a market participant is develop your own risk management strategy so that when the eventual market downturn comes, you have a plan to protect your capital. Spend at least a little time thinking about risk. It is well worth the effort.
What do you think? What methods do you use to deal with market risk? Comment below!
In response to this line, “…if you haven’t put any additional money in your account you are just now getting back to where you were before.”
The author is only looking at index levels and not including dividends. Buy and hold investors would have been back above their peak levels much earlier when dividends are factored in. Rebalancing every year would’ve helped even more by adding more to equities near the bottom.
Managing risk with active investing (mainly through hedging with options) has its place in many of the portfolios I manage, but that doesn’t mean I can change the facts of the benefits of buy and hold.
I also agree with the editorial comments, no semi-smart investor near retirement should be 100% in stocks. I understand some were, but they aren’t the type of people who read this blog.
Great article! The author highlights an extremely crucial lesson that most investors and traders who remain actively involved in managing their investments learn the hard way – by experience! Risk management is the answer to making money in the markets. Familiarity with Gaussian (bell curve) distribution explains why – if one can minimize the negative return (downside of the bell curve), the average return automatically increases.
Unfortunately, most retirement accounts (401k, etc) only allow participants to invest in mutual funds, where an active risk management strategy is not possible. In personal brokerage accounts (including retirement accounts), the active trader can hedge their positions (manage risk) by use of options trading strategies. Hence, the active investor/trader needs to be cognizant of both how to diversify and balance their retirement portfolio as well as how to minimize the risk in their actively managed accounts.
A must read article for anyone investing in markets. The guest author got it right. Instead of focusing too much on high return, take into consideration the variability of returns year over year. Lower the variance, more consistent is the return.
Dear Alex,
I was not trying to bad mouth the “buy and hold” strategy that has essentially become the accepted philosophy by most people who refer to themselves as investment professionals.
By “facts” you are no doubt referring to the numerous studies that show a well-diversified portfolio has never decreased in value when the average holding period is 20 years or later and thus “buy and hold” is the way to go. Here are some other things for you to consider.
1. Buy and hold is risky during certain market environments. It is “fact” that 3 out of 4 stocks follow the general trend of the market. If we are in a bear market, the upside reward of holding stocks does not justify the potential down side risk. Buy and hold means you need to be invested during all markets, whether the market is going up, down, or sideways.
There have been and always will be bear markets as well as extended periods where the market moves sideways. Just closing your eyes and accepting buy and hold does not fit with the inherent reality of investing. The fact is that nobody knows what the market is going to do next week or next year. The average length of bull markets is 4 years and we just eclipsed that. If we enter a new bear market over the coming months do you think it makes sense to “buy and hold” even when the market is going down? This makes no sense, in my opinion.
I am not saying you need to be “all in” or “all out.” The point I was trying to make is that you need to take risk into account and act accordingly during bad market environments which will occur. Some people have mentioned using options. Another way to manage risk is just to decrease your exposure to the markets during downtrending periods, this is the approach that I take. The more the market goes down, the more I decrease my exposure. What this does is ensure that I am least invested when the market is going down. Conversely, I also re-enter incrementally which means that in order for me to be fully invested the market must be going up, thus ensuring that I am most invested when the market is rising.
In this way, I can say with absolute certainty that my account will never suffer a drawdown of 50% because I would have been out of the market way before then.
Also, by the comment “no semi-smart investor near retirement should be 100% in stocks” I assume you are meaning that their portfolio should be more invested in bonds. This may have been true in recent decades but I don’t believe that is true now. The subject of bonds has been discussed here before and I am of the opinion that if you are heavily overweight bonds in your portfolio, you are asking for trouble. This is another situation where the upside reward does not justify the risk.
Let me clearly say that I have no idea where bonds are going or when. However, with regard to this discussion, I am only implying that if a reader on this site has a high percentage of their portfolio invested in bonds they should understand that they may be putting themselves and undue risk.
2. Mutual funds don’t buy and hold. Do you know that most mutual funds have turnover rates over 100%. They preach for you to buy and hold but they don’t put their money where their mouth is, they put your money where their mouth is.
As JonLuc correctly stated above, “Unfortunately, most retirement accounts (401k, etc) only allow participants to invest in mutual funds, where an active risk management strategy is not possible.”
This is because if one were to practice proper risk management, this means they would not be invested at all times and at some points would have to decrease their market exposure. If you pull your money out, they make less money because they charge you many fees based on a percentage of assets under management. This is one of the reasons that funds tell you to buy and hold for the long term, they don’t want you to pull your money out.
3. If you shorten your holding period to 15 years, buy and hold will show you losses. Even more importantly, your “average holding period” is much different from you actual investment period. In practical terms, a person’s true average holding period may be much shorter than 20 years because for most people the majority of savings come later in life. This means their actual holding periods may be shorter than that required to show a net return.
Most people, especially physicians, don’t have a large amount of money to invest at age 30 or 35 and then hold it for 20 to 30 years. The commonly reported “average return” of 7% to 10% is meaningless when it comes to real world investing. Do you know that if you look at over 100 years of data examining the Dow Jones from 1900 to 2002, only 5 of these years showed returns between 5% to 10% (Fooled By Randomness, Taleb). One shouldn’t expect average returns on an annual basis, doing so does not take into account the inherent volatility of investing.
There are simple steps you can take that are statistically proven to match market returns while decreasing your downside risk. In other words, your risk adjusted returns would far outperform the averages. This is not rocket science or terribly difficult and is something a busy physician could easily implement. Maybe I will make this the subject of a future post.
I am not telling anyone not to “buy and hold”, and for most doctors given their time constraints it makes sense. The point I was trying to make was that by doing so you may be taking excessive risk when the rewards don’t justify them. By thinking of risk first, you go from a totally passive approach to a semi-active approach in that you are practicing the most important rule on investing, preservation of capital.
Thank you for your comment.
Felix
I follow these principals in dealing with risk:
Remember that there is almost nothing that is sure, and today those things that are sure pay so little that you really need a large investment to produce enough income for your retirement.
The single most important thing about any investment is the price. If the price is reasonable or low then the risk of losing is reduced. When you purchase stock at a market high your risk is very high in the short term and your prospects for gains are reduced in the long term.
Know something about the industries that you are invested in, including management. I don’t generally like any managed mutual fund since a person who I don’t know and really don’t trust is making the decisions for me. I have been burned by these folks enough that I want any mistakes (and I have made a few) to be mine.
In a low yield environment there is a risk that your money will not produce income, so this is offset by having a large portion of your investments in stocks.
Reduce your needs and therefore your risk by living a somewhat cheap life. If you are lucky or just make a good investment then you can splurge.
I am retired and keep a very large portion of my investments in dividend paying stocks. I was fortunate that I purchased almost all of them at good value during the recession. I now can live off the income for as long as I might live and leave most of the principal to my children.
No annuities – They pay way too little. No Nursing Home insurance – I am still young and it costs way too much. No travel around the world or even the US, it is not in my budget.
It sounds good but there’s a few issues with investing this way. First, as you well know you cannot predict the future. Just because the market has been going down recently doesn’t mean it won’t start going up tomorrow. Second, following a trend in a side ways market exposes you to a whipsawing effect. It is exactly the opposite of rebalancing a portfolio, and forces you to buy high and sell low. (Buy more as the market rises and sell it as the market falls.) Third, the more transactions you make, the more investment costs you incur, and in a taxable account, the more tax costs you incur. Those are all subtracted directly from your return. I agree that “Buy and Hold” has its issues. Like Democracy and Capitalism it’s the worst system ever, except all the other ones that have been tried. The turnover of the two largest mutual funds I hold in my portfolio last year was 3.2% and 2.7%. Just because some mutual funds have turnover higher than 100% doesn’t mean you have to buy those ones.
You seem to imply that bonds are somehow riskier than stocks. I agree that given low yields today that bonds may not be particularly attractive investments, but even at these yields, a reasonable bond portfolio of good quality bonds with short to intermediate durations still functions to lower the overall risk of a portfolio.
I think this was a great post and something that I really haven’t considered very carefully – how difficult it is to regain the value of a lost dollar. As a young investor, it seems like my greatest returns come from the amount I can currently contribute each year. As difficult as it is to see the overall value of my portfolio drop, I’ve been trying to train myself to see a drop in the market as ‘stocks are on sale,’ realizing that each dollar I invest will buy more shares when the market is down. With this mentality I looked at your mutual fund choices and thought I would have wanted to own Fund B for the three years from 2010 – 2012. Note I don’t mean I wanted to buy it at the end of 2012 based on the returns, but that I would have wanted to own it at the beginning of 2010.
As a simple exercise, I tried calculating the return of the three portfolios assuming I had invested $100 on the first of each year. At the end of 2012 the values of A, B, and C were $337.50, $362.50, and $315.92 with CAGRs of 6.00%, 9.75%, and 2.60%, respectively. (Feel free to check my math and let me know if I’m wrong. Part of my reason for trying this is to better understand where the numbers come from and what it means when they say average vs. annualized return! As a side note – does the column listing annualized return in the article actually state the total return? When crunching numbers I found the annualized return to be 1.41%, 0.50%, and 2.26% – even worse when we consider the investment was over three years and not one!)
This little exercise reinforced for me the idea of a young investor wanting a bear market followed by a bull market vs. a new retiree wanting a bull market followed by a bear market. As a young investor I think the best thing I can do is contribute more money with a greater percentage of my wealth in the risky investments. Based on your examples I should definitely make sure I turn to more conservative – or less volatile – investments as time goes on – each lost dollar will really be much harder to gain back. Again these ‘ideas’ are fairly common in investing, but I still think seeing the numbers is really driving the point home – so thanks!
With these ideas in mind I think your follow-up comment about decreasing risk when the market is dropping and increasing risk when it is rising is interesting – I would have thought the opposite to be a better approach, but I don’t really think I understand how to change my risk based on changing market conditions. I am hoping to learn more about optimizing dollar cost averaging, and just picked up ‘Value Averaging’ by Michael Edleson. I’d be interested to hear any thoughts on this approach if anyone is familiar with it.
Check out what John Bogle and Warren Buffett advises for the average investor. Both are in agreement that most people should “buy into the US economy” instead of trying to dance in and out of the market and gambling your money in the Wall Street Casino. PBS did a Frontline show couple of weeks ago showcasing the ignorance of Americans on what their 401k was invested in and the hidden cost of actively managed mutual funds.
This is important because people are always wanting to play Wall Street money manager and trying to decide how to invest in bear/bull markets or if they should buy more into this or that…and as I said below, there are people who gets paid 7 figures on Wall Street to pick stocks and investments all day long and in the end only a minority beat the market average and even then your return as an investor is cut down because of fees/cost of those actively managed funds.
In my opinion, the “safest” way is to invest in the US economy by getting things like index funds that tracks thousands of big US companies (or bonds, or REITs, or international stocks). The portfolio then can be risk-managed by allocating certain % into stocks/bonds/emerging markets/etc. and rebalance each year.
Checkout Bogleheads wiki, Buffett/Bogle interviews. I’m going to pick up David Swenson’s book on personal investment as well: Unconventional Success. He is also a well known proponent of having a “lazy” portfolio and investing in lost cost index funds. So in the end instead of trying to time the market or figure out what’s the best stock, you just adjust your risk by figuring out what asset classes you want in your portfolio.
Another very important point that I just learned about and I think is very relevant to this discussion is the difference between an actively managed mutual fund and a passive, or index, mutual fund (aka those offered by Vanguard). PBS Frontline did a show on America’s gamble on retirement just last week and how most people didn’t know how much fees they were being charged with their 401(k) investments. (Remember that 401k and IRA are simply how the IRS treats those sums of money, how the 401k/IRA money is spent is up to you yo a certain degree of course with 401k having limited options due to it being employer offered).
When the guest author mentions the case where his colleague calls him up to inquire about getting into the Facebook IPO, that is absolutely shocking to me. This is NOT the way for the average person (let alone someone like a physician with very limited free time on their hands) to invest in the stock market. There are professional money managers on Wall Street who get paid 7 figures to pick stocks all day long and only 24% of them beat the market in the last 10 years. (http://www.nerdwallet.com/blog/investing/2013/active-mutual-fund-managers-beat-market-index/)
So unless you’re the next Benjamin Graham, Peter Lynch, Thomas Rowe Price, or Warren Buffett, it’s really mind-boggling to me, at least, why individual investors try to pick out one stock or a very small amount of stocks and try to beat the market that way. Warren Buffett has been interviewed many times on his advice to individual investors and he repeatedly advises against trying to time the market and dance in and out of it.
After reading and listening to what Bogle and Buffet advises the individual investor (both recommend index mutual funds that tracks a very large asset class whether its domestic stocks, bonds, international stocks, etc.) it seems that a good way to invest is to get out of the Wall Street Casino, which is what it has become with the tens of thousands of mutual funds that have popped up and then also died over time, and basically you buy into the US economy as a whole by buying into index funds that tracks thousands of big US companies. Unless of course you don’t believe the US as a whole will continue to grow economically then that’s a different issue.
Here is a very insightful PBS Frontline documentary on the state of America’s retirement and the hidden cost of mutual funds: http://www.pbs.org/wgbh/pages/frontline/retirement-gamble/
Preach on brotha!
I agree with all you say.
A book that I think every doctor should read is “The Millionaire Next Door.” It profiles the millionaires of America and found that typically a millionaire does NOT live like what the average American imagines. They do NOT live in huge mansions, drive exotic cars, wear expensive clothing, and in general do NOT live a high consumption lifestyle. There has been a distortion of being wealthy and appearing wealthy.
Doctors, they profile, are one of the worst high-income earning group to have accumulated wealth. High annual wages is most certainly NOT a good indicator of wealth. Some reasons include doctors needing to live up to what “living like a doctor” is supposed to be. Anecdotal stories even showcased doctors who had multiple boats and cars but nothing in their retirement because they were burned by financial “advisors” before. And a NY Times piece recently did an article too on why doctors can be terrible at investing.
So with a lifestyle that is truly conducive to wealth-building and a good understanding of financial investment there is no excuse for doctors not retire early (if they want) and be able to live a very comfortable later years.
Great article BUT your “average return” for Fund A is incorrect.
You stated:
Fund A: -18 +20 +6 = +3.33% Average return
It should read +2.67% (8 divided by 3 years)
You’re right. Sorry about letting that slip through the editing process. Doesn’t change the conclusion of course.
Found this article and learned a lot! Have a question on compound annual growth rate.
Is this listed on individual mutual funds? Why is this not used for the 1, 3,5 ,10, since inception tables since it is more accurate?
Seems like it would be a better tool when fund shopping.
Would like to know how to find this on the funds I have. thanks
Here’s one funny thing about Vanguard. They call them average returns on their website, but they’re actually annualized returns, or CAGRs. So you can trust their 1,3,5,10, and since inception returns to be what you’re looking for. Can’t speak for other companies though.