The Whip Cracks Both Ways

The following is a guest post from Marotta Wealth Management.

Inherently volatile, the average daily fluctuation of the stock market is about 0.76%. If this movement were always up, the market would appreciate to more than six times its value in a year. If all the movement were down, you would have less than 15 cents for every dollar you invested at the beginning of the year.

Most of this fluctuation is like the beating of a hummingbird's wings--lots of movement but no progress. Every year after matching all the up days and down days, you are left with about seven days that represent the entire year's investment gain or loss. Thus daily movements are 97% noise and 3% direction.

Volatility, therefore, is a matter of perspective. Are you watching the hummingbird or its wings?

I've charted the movement of the S&P 500 total return since 1950 from eight different perspectives in what I call a "whip chart." Each measure of risk and return is analogous to a different part of the whip.

Out at the very end of the whip is a bit of thread called the cracker, or popper. As all the momentum of the heavier whip flows into this light thread, it curls back on itself. The snapping sound comes from the cracker accelerating beyond the speed of sound, creating a tiny vacuum and sonic boom as the air rushes back in.

We can compare the cracker to the six-month activity in the market. On average the six-month movement is up 6.4%, equivalent to a 13.2% annualized return. For the sake of just measuring speed, we convert all the market movements into how far they would have moved at that speed over a year.

On an annualized basis, six-month returns deviate wildly, about 23.7%. The standard deviation (SD) measures volatility statistically, or how much room it takes for the cracker to snap. Approximately 68% of returns will curl around within 1 SD (±23.7%), 95% will fall within 2 SD (±47.4%) and 99.7% will fall within 3 SD (±71.1%). Stock market returns are by nature capricious and exceed the statistical norms for returns that fall outside of three deviations.

In fact, the past six-month period was more than 3 SD above average, earning 40.5% (97.5% annualized). And the six months preceding that were below 3 SD, losing 41.8% (66.2% annualized). Because six-month returns are compounded, when annualized the positive side multiplies and the negative side is diminished. Therefore the 3 SD isn't exactly ±71.1%. The 3 SD return is compounded as +89.2% to -55.6%.

Unlikely ups and downs like these are sometimes labeled "black swan" events. Or they may be described by the number of SDs they fall within. For example, because these two recent events are slightly more than 3 SD, they are called "four-sigma" events.

Four-sigma events should occur less than 0.3% if market returns conformed to a Gaussian bell curve, but they do not. The markets are inherently volatile. Market returns are better described by a branch of mathematics known as power laws. Instead of a neat statistical bell curve, these formulas are used to describe fractals where the same patterns can sometimes be wildly larger or smaller than the one you are looking at. Having just experienced two four-sigma events, these are not simply academic musings.

Every time the cracker pops, and the news is talking about how good or bad the markets are doing, should signal you to rebalance your portfolio. Having just finished a four-sigma positive market run, now is an excellent time to take some money off the table. The cracker snapped up, and if you rebalanced at the bottom your asset allocation now tilts more toward stocks. By rebalancing your portfolio you will reset your portfolio to an allocation ready for the next move of the whip.

Annualized returns are slightly better behaved, more like the "fall," a bit of unbraided leather at the end of the whip. Annual returns within one sigma range from +29.2 to -5.2%. The two-sigma range is +46.4% to -22.4%. And the three-sigma range is +63.6% to -39.5%.

The leather fall attaches to the braided thong with a fall hitch. And a knot called a keeper holds the braided thong to the handle. Just as each of these parts of a whip experience smaller movements, so the SD continues to diminish for returns over a year and a half (fall hitch), 3 years (thong), 5 years (keeper) and 10 years (handle).

The handle of a whip, our 10-year horizon, is much more manageable. The one-sigma range for an annualized 10-year return is +16.2% to +6.33%. The two-sigma range is +21.1% to +1.40%. Not until a three-sigma event can a decade-long return for the S&P 500 turn negative. The three-sigma range is +26.1% to -3.5%. The past 10-year return has been -0.8%

The 10-year return (the handle) swings more than a 20-year return (the arm), which moves more than a 40-year return (the shoulder). Volatility begins to lessen as you move further and further away from the end of the whip. From the perspective of a whipping cracker, volatility is extreme, snapping faster than the speed of sound. But if you are a fly sitting on the shoulder of the person wielding the whip, you haven't moved.

At every stage of the whip, the average trend is more than 11% positive. Picture the person holding the whip as riding an escalator that is slowly but constantly ascending. Despite the whip cracking up and down, the general trend is upward.

Rebalancing frequently recognizes and takes advantage of the volatility of this trend. Staying invested during market gyrations takes advantage of the escalator.

Comments

[Eugene Krabs]

Very interesting and tightly-written. Good work.

[cmadler]

Excellent post!

[Old Limey]

I have found that one secret of successful investing is to avoid mutual funds and ETFs that have a track record of high volatility. The problem with high volatility is that it sometimes only takes 3 or 4 market days to wipe out a gain that may have taken weeks to achieve. With low volatilty investments you can ride them up and then when they finally roll over and go into a downtrend you have far more time to come to a decision on whether to Hold or to Sell.

The most widely known measure of volatilty is the Sharpe Index, named after Nobel prize winning, Professor Sharpe of Stanford. However two of his graduate students improved on his work by only considering 'Downside' volatility in the calculations, since investors are more than happy to have upside volatility. The two graduate students were Martin and McCann and they wrote a book, published in 1994, in which they provided the mathematical details of their variation of the Sharpe Index. They called their index the 'Ulcer Index', a very apt name. There is also a variation of the Ulcer Index called the Ulcer Performance Index which is a great measure of Risk Adjusted Return.

I programmed the two indexes and have used them successfully ever since to perform my fund selection. Since retiring in 1992, my only losing year out of the last 17 was a 10% loss in 1994, the year that Alan Greenspan surprised the market by raising interest rates very sharply.

With low volatility issues you can get rich slowly (and keep the gains), with high volatility issues you can make money fast but lose it even faster.

[Eugene Krabs]

Interesting, Old Limey, and I think it's good advice for most everyone.

Just for the sake of the conversation though, volatility in itself isn't a bad thing. It just needs to be appropriate relative to the investor's investment objective and risk tolerance. A young'un in his early 20s can and probably should take on higher volatilities, whereas someone in their 60s and older should not.

The Sharpe ratio is the Dow Jones of risk measurements, and while it provides a simple, direct feedback, it does not provide a risk-adjusted picture. So, I do try to lean towards the Sortino ratio whenever I can. I trade stocks, and therefore am interested in the possibility of risk-adjustment, but perhaps this is not necessary for others....

As for this article, I think it could be summed up very simply with a lay rule such as, "If my asset allocation deviates by 2%, then I'll rebalance." or even "I'll rebalance once a year." Still, it's good to see the numbers being posted to provide a more technical view of when rebalancing appears statistically advantageous.

[Old Limey]

Eugene:
There's an old saying, "You can't put an old head on young shoulders" and few people in their early 20's have the knowledge and experience to be good investors. My three children have entrusted me with managing their money by giving me trading authorization on their accounts. My two 51 and 49 year old daughters now have 7 figure portfolios and my 45 year old son is well on his way to his first million. They jokingly call their portfolios "Black Holes" because once they put money into their accounts and especially for IRAs they know what my response will be if they try to touch it before they reach 59 1/2 at the very earliest.

The first rule of investing for the very young is to put the maximum possible into IRAs and 401Ks and to start at the earliest possible age. Dollar cost averaging is a great strategy for very young people.

When I am selecting a fund to buy I first pick a time period somewhere between 6 and 12 months. I then sort by 'maximum drawdown' during that period, with low values at the top. Right away all the very volatile funds will have dropped to the bottom. Starting at the top I then make a note of the 3 or 4 candidates with the highest returns that have the lowest volatilities and drawdowns. Then I start comparing these candidates over different time periods, varying from 2 months to many years in order to get a feel for both recent performance as well as long term performance. The winners are usually very obvious. I gave up on individual stocks decades ago - too many 'disasters de jour' during the earnings reporting season. I had one NYSE stock many years ago that was suddenly delisted and went to $0 after fraud was discovered and the CEO fled the country, fortunately I only had $4K in it.

In my younger days I took more risk which involves market timing and consequently a lot more trading, now at 75 I take as little risk as possible, do very little trading, and investing has become a whole lot easier.

[Eugene Krabs]

Your "children" are very fortunate to have you as their father. :D

I maintain that I do not believe volatility is inherently a bad thing, especially for younger people in their 20s and even 30s. But I also fully agree that simply taking on risk blindly is and will always a bad idea, regardless of age, and therefore, it does require some effort on our part to make the most intelligent decisions possible... even if that means to hand the money to someone else.

Cheers.

[Eric N.]

I love what you have to say Old Limey.

Can you please start your own blog? Or perhaps guest posts on this one? :)

[Mike]

Old Limey, keep posting. I like your posts!

[Eugene Krabs]

Limey, I too would be interested to know your children's asset allocations, and also whether you did anything differently for them last year (2008) and this year (2009)?

Thanks in advance!

[Old Limey]

Eugene:
Even though my children are much younger I have always used the same fund choices and allocations for their accounts as I do my own. Consequently they have had the same kind of positive returns that I have had both for 2008 and 2009. I haven't drunk the coolaid regarding the green shoots appearing in the economy primarily because I read some amazing, detailed, articles from some of the best minds in the business. If I was optimistic about the economy, the employment picture, the debt, the deficit, the dollar etc. I would have some of our family's money in stock funds - but I am not. We own only municipal bonds (purchased in 10/2008, average yield 4.84%, tax and AMT free, in our taxable accounts), a municipal bond fund (YTD return=24.12%), FDIC insured CDs (purchased in 10/2008, yielding as much as 5.5%, in our IRAs), and a fund holding mortgage securities backed by the US government, also in IRAs (YTD return=19.36%). The two funds are where I invest the interest from the CDs and muni bonds.

If you google 'John Mauldin newsletter' he has a free weekly newsletter called 'Outside the Box' that contains very informative, well written, articles from experts that provide the truth about what's going on and not just the internet and newspaper spin that those with vested interests want you to believe. If you subscribe you will receive his weekly e-mail report - your e-mail address is kept private and is not given out to advertisers.

The single most important rule of investing that I have always followed is "Don't Lose Money". Big losses like the ones that many people took in 2000 and again in 2008 are devastating to the compounding of your money. A 50% loss requires that you double your money just to get even again. Doubling your money is very difficult. Taking a 50% loss is very easy - there were millions of them in 2000 and again in 2008.

[Eugene Krabs]

Thank you for the response, Limey. I really do appreciate the glimpse into your asset allocations.

Indeed, it is very conservative, although I am not saying that there's anything wrong with it, especially in your case.

On the other hand, I think it's also worth noting that the saying, "Don't Lose Money" also means "Don't Lose Money to Inflation". Principle risk is one of many investment risks that we still have to consider. So, I don't disagree, but I would like to add that perhaps there is a place for other types of securities as well for other investors and their asset allocations.

I assume the munis are taxable accounts and the CDs are tax-deferred?