Asymmetric Nature of Losses and Loss Aversion

Loss Aversion:

“In prospect theory, loss aversion refers to the tendency for people to strongly prefer avoiding losses than acquiring gains. Some studies suggest that losses are as much as twice as psychologically powerful as gains. Loss aversion was first convincingly demonstrated by Amos Tversky and Daniel Kahneman.”

For most people, losing $100 is not the same as not winning $100. From a rational point of view are the two things the same or different?

Most economists say the two are the same. They are symmetrical. But I think that ignores some key issues.

If we have only $10 to eat on today and that’s all we have, if we lose it, we’ll be in trouble: hungry.

But if we have $10 to eat on and flip a coin in a bet and double it to $20, we may just eat a little better. We’ll still eat. The base rate: survival.

They say rationally the two are the same, but that isn’t true. They aren’t the same. The loss makes us worse off than we started and it may be totally rational to feel worse when we go backward than we feel good about getting better off. I don’t like to go backward, I prefer to move forward to stay the same.

Prospect Theory, which found people experience a loss more than 2 X greater than an equal gain, discovered the experience of losses are asymmetric.

Actually, the math agrees.

You see, losing 50% requires a 100% gain to get it back. Losing it all is even worse. Losses are indeed asymmetric and exponential on the downside so it may be completely rational and logical to feel the pain of losses asymmetrically. Experience the feeling of loss aversions seems to be the reason a few of us manage investment risk and generate a smoother return stream rather than blow up.

To see what the actual application of asymmetry to portfolio management looks like, see: Shell Capital Management, LLC.

 

asymmetry impact of loss

Absolute Return: an investment objective and strategy

Absolute returns investment strategy fund

Absolute Return in its basic definition is the return that an asset achieves over a certain period of time. This measure looks at the appreciation or depreciation (expressed as a dollar amount or a percentage). For example, a $50 stock drifts to $100 is a 100% absolute return. If that same stock drifts back from $100 to $50, its absolute return is -50%.

Absolute Return as an investment objective is one that does not try to track or beat an arbitrary benchmark or index, but instead seeks to generate real profits over a complete market cycle regardless of market conditions. That is, an absolute return objective of positive returns on investment over a market cycle of both bull and bear market periods irrespective of the direction of stock, commodity, or bond markets. Since the U.S. stock market has been generally in a uptrend for 6 years now, other than the -20% decline in the middle of 2011, we’ll now have to expand our time frame for a full market cycle to a longer period. That is, a full market cycle includes both a bull and a bear market.

The investor who has an absolute return objective is concerned about his or her own objectives for total return over a period and tolerance for loss and drawdowns. That is a very different objective than the investor who just wants whatever risk and return a benchmark, allocation, or index provides. Absolute returns require skill and active management of risk and exposure to markets.

Absolute return as a strategy: absolute return is sometimes used to define an investment strategy. An absolute return strategy is a plan, method, or series of maneuvers aiming to compound capital positively and to avoid big losses to capital in difficult market conditions. Whereas Relative Return strategies typically measure their success in terms of whether they track or outperform a market benchmark or index, absolute return investment strategies aim to achieve positive returns irrespective of whether the prices of stocks, bonds, or commodities rise or fall over the market cycle.

Absolute Return Investment Manager

Whether you think of absolute return as an objective or a strategy, it is a skill-based rather than market-based. That is, the absolute return manager creates his or her results through tactical decision-making as opposed to taking what the market is giving. One can employ a wide range of approaches toward an absolute return objective, from price-based trend following to fundamental analysis. In the ASYMMETRY® Managed Accounts, I believe price-based methods are more robust and lead to a higher probability of a positive expectation. Through my historical precedence, testing, and experience, I find that any fundamental type method that is based on something other than price has the capability to stray far enough from price to put the odds against absolute returns. That is, a manager buying what he or she believes is undervalued and selling short what he believes is overvalued can go very wrong if the position is on the wrong side of the trend. But price cannot deviate from itself. Price is the judge and the jury.

To create absolute returns, I necessarily focus on absolute price direction. Not relative strength, which is a rate of change relative to another moving trend. And, I focus on actual risk, not some average risk or an equation that oversimplifies risk like standard deviation.

Of course, absolute return and the “All Weather” type portfolio sound great and seem to be what most investors want, but it requires incredible skill to execute. Most investors and advisors seem to underestimate the required skills and experience and most absolute return strategies and funds have very limited and unproven track records. There is no guarantee that these strategies and processes will produce the intended results and no guarantee that an absolute return strategy will achieve its investment objective.

For an example of the application of an absolute return objective, strategy, and return-risk profile, visit http://www.asymmetrymanagedaccounts.com/

Absolute Return as an Investment Strategy

Absolute Return Investment Strategy Fund Manager

In “Absolute Return: The Basic Definition”, I explained an absolute return is the return that an asset achieves over a certain period of time. To me, absolute return is also an investment objective.

In “Absolute Return as an Investment Objective” I explained that absolute return is an investment objective is one that does not try to track or beat an arbitrary benchmark or index, but instead seeks to generate real profits over a complete market cycle regardless of market conditions. That is, it is focused on the actual total return the investor wants to achieve and how much risk the investor will willing to take, rather than a focus on what arbitrary market indexes do.

Absolute return as a strategy: absolute return is sometimes used to define an investment strategy. An absolute return strategy is a plan, method, or series of maneuvers aiming to compound capital positively and to avoid big losses to capital in difficult market conditions. Whereas Relative Return strategies typically measure their success in terms of whether they track or outperform a market benchmark or index, absolute return investment strategies aim to achieve positive returns irrespective of whether the prices of stocks, bonds, or commodities rise or fall over the market cycle.

Whether you think of absolute return as an objective or a strategy, it is a skill-based rather than market-based. That is, the absolute return manager creates his or her results through tactical decision-making as opposed to taking what the market is giving. One can employ a wide range of approaches toward an absolute return objective, from price-based trend following to fundamental analysis. In the ASYMMETRY® Managed Accounts, I believe price-based methods are more robust and lead to a higher probability of a positive expectation. Through my historical precedence, testing, and experience, I find that any fundamental type method that is based on something other than price has the capability to stray far enough from price to put the odds against absolute returns. That is, a manager buying what he or she believes is undervalued and selling short what he believes is overvalued can go very wrong if the position is on the wrong side of the trend. But price cannot deviate from itself. Price is the judge and the jury.

Of course, absolute return and the “All Weather” type portfolio sound great and seem to be what most investors want, but it requires incredible skill to execute. Most investors and advisors seem to underestimate the required skills and experience and most absolute return strategies and funds have very limited and unproven track records. There is no guarantee that these strategies and processes will produce the intended results and no guarantee that an absolute return strategy will achieve its investment objective.

For an example of the application of an absolute return objective, strategy, and return-risk profile,  visit http://www.asymmetrymanagedaccounts.com/

Diversification Alone is No Longer Sufficient to Temper Risk…

That was the lesson you learned the last time stocks became overvalued and the stock market entered into a bear market.

In a Kiplinger article by Fred W. Frailey interviewed Mohamed El-Erian, the PIMCO’s boss, (PIMCO is one of the largest mutual fund companies in the world) he says “he tells how to reduce risk and reap rewards in a fast-changing world.” This article “Shaking up the Investment Mix” was written in March 2009, which turned out the be “the low” of the global market collapse.

It is useful to revisit such writing and thoughts, especially since the U.S. stock market has since been overall rising for 5 years and 10 months. It’s one of the longest uptrends recorded and the S&P 500 stock index is well in “overvalued” territory at 27 times EPS. At the same time, bonds have also been rising in value, which could change quickly when rates eventually rise. At this stage of a trend, asset allocation investors could need a reminder. I can’t think of a better one that this:

Why are you telling investors they need to diversify differently these days?

The traditional approach to diversification, which served us very well, went like this: Adopt a diversified portfolio, be disciplined about rebalancing the asset mix, own very well-defined types of asset classes and favor the home team because the minute you invest outside the U.S., you take on additional risk. A typical mix would then be 60% stocks and 40% bonds, and most of the stocks would be part of Standard & Poor’s 500-stock index.

This approach is fatigued for several reasons. First of all, diversification alone is no longer sufficient to temper risk. In the past year, we saw virtually every asset class hammered. You need something more to manage risk well.

But, you know, they say a picture is worth a thousand words.

Since we are talking about downside risk, something that is commonly hidden when only “average returns” are presented, below is a drawdown chart. I created the drawdown chart using YCharts which uses total return data and the “% off high”. The decline you see from late 2007 to 2010 is a dradown: it’s when the investment value is under water. Think of this like a lake. You can see how the average of the data wouldn’t properly inform you of what happens in between.

First, I show PIMCO’s own allocation fund: PALCX: Allianz Global Allocation Fund. I include an actively managed asset allocation that is very large and popular with $55 billion invested in it: MALOX: BlackRock Global Allocation. Since there are many who instead believe in passive indexing and allocation, I have also included DGSIX: DFA Global Allocation 60/40 and VBINX: Vanguard Balanced Fund. As you can see, they have all done about the same thing. They declined about -30% to -40% from October 2007 to March 2009. They also declined up to -15% in 2011.

Vanguard DFA BlackRock PIMCO Asset Allcation

Charts are courtesy of http://ycharts.com/ drawn by Mike Shell

Going forward, the next bear market may be very different. Historically, investors consider bond holdings to be a buffer or an anchor to a portfolio. When stock prices fall, bonds haven’t been falling nearly as much. To be sure, I show below a “drawdown chart” for the famous actively managed bond fund PIMCO Total Return and for the passive crowd I have included the Vanguard Total Bond Market fund. Keep in mind, about 40% of the allocation of the funds above are invested in bonds. As you see, bonds dropped about -5% to -7% in the past 10 years.

PIMCO Total Return Bond Vanguard Total Bond

Charts are courtesy of http://ycharts.com/ drawn by Mike Shell

You may have noticed the end of the chart is a drop of nearly -2%. Based on the past 10 years, that’s just a minor decline. The trouble going forward is that interest rates have been in an overall downtrend for 30 years, so bond values have been rising. If you rely on bonds being a crutch, as on diversification alone, I agree with Mohamed El-Erian the Chief of the worlds largest bond manager:

“…diversification alone is no longer sufficient to temper risk. In the past year, we saw virtually every asset class hammered. You need something more to manage risk well.”

But, don’t wait until AFTER markets have fallen to believe it.

Instead, I apply active risk management and directional trend systems to a global universe of exchange traded securities (like ETFs). To see what that looks like, click: ASYMMETRY® Managed Accounts

Sectors Showing Some Divergence…

So far, U.S. sector directional price trends are showing some divergence in 2015.

Rather than all things rising, such divergence may give hints to new return drivers unfolding as well as opportunity for directional trend systems to create some asymmetry by avoiding the trends I don’t want and get exposure to those I do.

Sector ETF Divergence 2015-03-04_11-24-54

For more information about ASYMMETRY®, visit: http://www.asymmetrymanagedaccounts.com/global-tactical/

 

Chart source: http://www.finviz.com/groups.ashx

 

 

This is When MPT and VaR Get Asset Allocation and Risk Measurement Wrong

This is When MPT and VaR Get Asset Allocation and Risk Measurement Wrong

I was talking to an investment analyst at an investment advisory firm about my ASYMMETRY® Global Tactical and he asked me what the standard deviation was for the portfolio. I thought I would share with you how the industry gets “asset allocation” and risk measurement and management wrong.

Most people have poor results over a full market cycle that includes both rising and falling price trends, like global bull and bear markets, recessions, and expansions. Quantitative Analysis of Investor Behavior, SPIVA, Morningstar and many academic papers have provided empirical evidence that most investors (including professionals) have poor results over the long periods. For example, they may earn gains in rising conditions but lose their gains when prices decline. I believe one reason is they get too aggressive at peaks and then sell in panic after losses get too large, rather than properly predefine and manage risk.

You may consider, then, to have good results over a long period, I necessarily have to believe and do things very differently than most people.

On the “risk measurement” topic, I will share with you a very important concept that is absolutely essential for truly actively controlling loss. The worst drawdown “is” the only risk metric that really matters. The risk is not the loss itself. Once we have a loss, it’s a loss. It’s beyond the realm of risk. Since risk is the possibility of a loss, how often it has happened in the past and the magnitude of the historical loss is the expectation. Beyond that, we must assume it could be even worse some day. For example, if the S&P 500 stock index price decline was -56% from 2007 to 2009, then we should expect -56% is the loss potential (or worse). When something has happened before, it suggests it is possible again, and we may have not yet observed the worst decline in the past that we will see in the future.

The use of standard deviation is one of the very serious flaws of investors attempting to measure, direct, and control risk. The problem with standard deviation is that the equation was intentionally created to simplify data. The way it is used draws a straight line through a group of data points, which necessarily ignores how far the data actually spreads out. That is, the standard deviation is intended to measure how far the data spreads out, but it actually fails to absolutely highlight the true high point and low point. Instead, it’s more of an average of those points. However, for risk management, it’s the worst-case loss that we really need to focus on. I believe in order to direct and control risk, I must focus on “how bad can it really get”. Not just “on average” how bad it can get. The risk in any investment position is at least how much it has declined in the past. And realizing it could be even worse some day. Standard deviation fails to reflect that in the way it is used.

Consider that as prices trend up for years, investors become more and more complacent. As investors become complacent, they also become less indecisive as they believe the recent past upward trend will continue, making them feel more confident. On the other hand, when investors feel unsure about the future, their fear and indecisiveness is reflected as volatility as the price swings up and down more. We are always unsure about the future, but investors feel more confident the past will continue after trends have been rising and volatility gets lower and lower. That is what the peak of a market looks like. As it turns out, that’s just when asset allocation models like Modern Portfolio Theory (MPT) and portfolio risk measures like Value at Risk (VaR) tell them to invest more in that market – right as it reaches its peak. They invest more, complacently, because their allocation model and risk measures tell them to. An example of a period like this was October 2007 as global stock markets had been rising since 2003. At that peak, the standard deviation was low and the historical return was at its highest point, so their expected return was high and their expected risk (improperly measured as historical volatility) was low. Volatility reverses the other way at some point

What happens next is that the market eventually peaks and then begins to decline. At the lowest point of the decline, like March 2009, the global stock markets had declined over -50%. My expertise is directional price trends and volatility so I can tell you from empirical observation that prices drift up slowly, but crash down quickly. The below chart of the S&P 500 is an example of this asymmetric risk.

stock index asymmetric distribution and losses

At the lowest point after prices had fallen over -50%, in March 2009, the standard deviation was dramatically higher than it was in 2007 after prices had been drifting up. At the lowest point, volatility is very high and past return is very low, telling MPT and VaR to invest less in that asset. This is a form of volatility targeting: investing more at lower levels or historical volatility and less at higher levels.

In the 2007 – 2009 decline in global markets, you may recall some advisors calling it a “6 sigma event”. That’s because the market index losses were much larger than predicted by a standard deviation. For example, if an advisors growth allocation had an average return of 10% in 2007 based on its past returns looking back from the peak and a standard deviation of 12% expected volatility, they only expected the portfolio would decline -26% (3 standard deviations) within a 99.7% confidence level – but the allocation actually lost -40 or -50%. Even if that advisor properly informed his or her client the allocation could decline -26% worse case and the client provided informed consent and acceptance of that risk, their loss was likely much greater than their risk tolerance. When they reach their risk tolerance, they “tap out”. Once they tap out, when do they ever get back in? do they feel better after it falls another -20%? or after it rises 20%? There is no good answer. I want to avoid that situation. I prefer to reduce my exposure to loss in well advance.

You can see in the chart below, 3 standard deviations is supposed to capture 99.7% of all of the data if the data is a normal distribution. The trouble is, market returns are not a normal distribution. Instead, stock market gains and losses present an asymmetrical return distribution. Market returns experience much larger gains and losses than expected from a normal distribution – the outliers are critical. However, those outliers don’t occur very often: historically it’s maybe every 4 or 5 years, so people have time to forget about the last one and become complacent.

symmetry normal distribution bell curve black

Source: http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

My friends, this is where traditional asset allocation like Modern Portfolio Theory (MPT) and risk measures like Value at Risk (VaR) get it wrong.

These methods are the most widely believed and used . You can probably see why most investors do poorly and only a very few do well – an anomaly.

I can tell you that I measure risk by how much I can lose and I control my risk by predefining my absolute risk at the point of entry and my exit point evolves as the positions are held. That is an absolute price point, not some equation that intentionally ignores the outlier losses.

As the stock indexes have now been overall trending up for 5 years and 9 months, the trend is getting aged. In fact, according to my friend Ed Easterling at Crestmont Research, at around 27 times EPS the stock index seems to be in the range of overvalued. In his latest report, he says:

“The stock market surged over the past quarter, adding to gains during 2014 that far exceed underlying economic growth. As a result, normalized P/E increased to 27.2—well above the levels justified by low inflation and interest rates. The current status is approaching “significantly overvalued.”

At the same time, we shouldn’t be surprised to eventually see rising interest rates drive down bond values at some point. It seems from this starting point that simply allocating to stocks and bonds doesn’t have an attractive expected return.

I believe a different strategy is needed, especially form this point forward.

In ASYMMETRY® Global Tactical, I actively manage risk and shift between markets to find profitable directional price trends rather than just allocate to them.

 

Mike Shell is the Founder and Chief Investment Officer of Shell Capital Management, LLC, and the portfolio manager of ASYMMETRY® Global Tactical.

The observations shared on this website are for general information only and are not specific advice, research, or buy or sell recommendations for any individual. Investing involves risk including the potential loss of principal an investor must be willing to bear. Past performance is no guarantee of future results. The presence of this website on the Internet shall in no direct or indirect way raise an implication that Shell Capital Management, LLC is offering to sell or soliciting to sell advisory services to residents of any state in which the firm is not registered as an investment advisor. Use of this website is subject to its terms and conditions.

 

VIX® gained 140%: Investors were too complacent

Several months ago I started sharing some of my observations about the VIX ( CBOE Volatility Index). The VIX had gotten to a level I considered low, which implied to me that investors were too complacent, were expecting too low future volatility, and option premiums were generally cheap. After the VIX got down to levels around 11 and 12 and then started to move up, I pointed out the VIX seemed to be changing from a downward longer term trend to a rising trend.

As I was sharing my observations of the directional trend and volatility of VIX that I believed was more likely to eventually go up than down, it seemed that most others were writing just the opposite. I know that many volatility traders mostly sell volatility (options premium), so they prefer to see it fall.

As you can see in the chart below, The VIX has increased about 140% in just a few weeks.

VIX october

Chart courtesy of http://www.stockcharts.com

For those who haven’t been following along, you may consider reading the previous observations:

A VIX Pop Then Back to Zzzzzzzz? We’ll see

Asymmetric VIX

VIX Shows Volatility Still Low, But Trending

VIX Back to Low

The VIX is Asymmetric, making its derivatives an interesting hedge

Is the VIX an indication of fear and complacency?

What does a VIX below 11 mean?

What does the VIX really represent?

The VIX, my point of view

The VIX, as I see it…

Volatility Risk Premium

Declining (Low) Volatility = Rising (High) Complacency

Investors are Complacent

 

Asymmetric VIX

In The VIX is Asymmetric, making its derivatives an interesting hedge I explained how the CBOE Volatility Index (VIX) tends to react with sharper and with greater magnitude than stock indexes. There is an asymmetric relationship between stock index returns and the VIX. Below includes yesterdays action when the S&P 500 stock index was down 2% and the CBOE Volatility Index (VIX) spot gained 27%. The chart is a good visual of how, when the stock index falls, implied volatility spikes up.

 

asymmetric vix

source: http://www.stockcharts.com

I have been sharing some observations about the VIX recently because it had gotten do a low level not seen in many years. It’s an indication that investors have become complacent about risk. When a trend gets to an extreme, it’s interesting to observe how it all plays out.

 

 

Volatility Risk Premium

Following up from “VIX Back to Low” I wrote last week, sure enough: the volatility index has gained 20%. Since last week it has been a good time to be long volatility and a bad time to be short volatility. Many professionals who trade volatility as their primary strategy mostly sell it to collect the Volatility Risk Premium. To do that, they have to be willing to experience gaps like this.

VIX CBOE VOLATILTY INDEX JULY

 

The VIX is Asymmetric, making its derivatives an interesting hedge

Asymmetric payoff VIX

The VIX is asymmetric, its distribution is non-symmetrical, it is skewed because it has very wide swings. The volatility of volatility is very volatile. There is an asymmetric relationship between stock index returns and the VIX. This asymmetric relationship is what initially makes the VIX interesting for hedging against S&P 500 volatility and losses.

Since I started the series about the extremely low VIX level Monday, like The VIX, as I see it…, The VIX has gained 17% while the S&P 500 stock index has lost about 1%. The VIX is asymmetric. While the VIX isn’t always a perfect opposite movement to the stock indexes, it most often does correlate negatively to stocks. When stocks fall, the implied (expected) volatility increases, so the VIX increases. Asymmetry is imbalance: more of one thing, less of the other. For example, more profit potential, less loss or more upside, less downside.

An advantage of the VIX for hedging is that it is asymmetric: it increases more than stocks fall. For example, when we look at historical declines in the stock index we find the VIX normally gains much more than the stock index falls. For example, if the stock index declined 5% the VIX may have gained 30% over the same period. That ratio of asymmetry of 6 times more drift would allow us to tie up less cash for a hedge position. Of course, the ratio is different each time. Sometimes it moves less, sometimes more.

When the VIX is at a low enough level as it’s been recently, the asymmetric nature of the VIX makes it an interesting hedge for an equity portfolio. The best way to truly hedge a portfolio is to hedge its actual holdings. That’s the only true hedge. If we make a bet against an index and that index doesn’t move like our positions, we still have the risk our positions fall and our hedge does too or doesn’t rise to offset the loss. I always say: anything other than the price itself has the potential to stray far from the price. But the asymmetry of VIX, its potential asymmetric payoff, makes it another option if we are willing to accept it isn’t a direct hedge. And, that its derivatives don’t exactly track the VIX index, either. None of the things we deal with is a sure thing; it’s always probabilistic.

This week has been a fine example of VIX asymmetry. The chart below shows it well.

The VIX is Asymmetric

Note: The VIX is an unmanaged index, not a security so it cannot be invested in directly. We can gain exposure to the VIX through derivatives futures, options, or ETNs that invest in VIX futures or options. This is not a recommendation to buy or sell VIX derivatives. To determine whether or not to take a long or short position in the VIX requires significantly more analysis than just making observations about its current level and direction. For example, we would consider the term structure and implied volatility vs. historical volatility and the risk/reward of any options combinations.

The VIX, as I see it…

The CBOE Volatility Index (VIX) reached a low point last week not seen since 2007 as evidenced by the chart below.

CBOE VOLATILITY INDEX HISTORY

To see a closer view of the last period, below I included the last time the VIX was at such a low value. I show this to point out that the VIX oscillated between 9% and 12% for about 4 months before it finally spiked up to 20. Such a trend reversal (or mean reversion if you prefer) can take time. Imagine if the VIX stays this low for the next 4 months before a spike. Or, it could happen very soon. You may notice the VIX reached the level it is now at its lowest level in early 2007. If we believed these trends repeat perfectly, that absolute level would matter. Trends are more like snowflakes: no two are exactly the same. But in relative terms, the fact that today’s level is as low as the lowest point in early 2007 is meaningful if you care about the risk level in stocks and the stage of the market cycle.

CBOE VOLATILITY INDEX VIX Low levels

The best way to examine a trend is to zoom in. Start with a broader view to see the big picture, then zoom in closer and closer. When people focus too much on the short-term, they miss the forest for the trees. Below is the last time the VIX was below 12. You may notice that is does oscillate up and down in a range.

VIX BELOW 12

The level and directional trend of the VIX matters because of the next chart. You may see a trend if you look closely. The black line is the S&P 500 stock index. The black and red line is the VIX CBOE Volatility Index. You may notice the two tend to drift in opposite directions. Not necessarily on a daily basis, but overall they are “negatively correlated”. When the stock index is rising, the volatility is often falling or already at a low level. When the stock index is falling, volatility rises sharply. It isn’t a perfect opposite, but it’s there.

VIX and S&P 500 correlation and trend

If you are interested in stock trends and the trend in volatility, and specifically the current state of those cycles,  you may want to follow along in the coming days. I plan to publish a series on this topic about the VIX, as I see it. Over the last week or so I have written several ideas that I intended to publish as one large piece. Since I haven’t had time to tie it together that way, I thought I would instead publish a series.

When a trend reaches an extreme level like this, it may be useful to spend some time with it.

Stay tuned…

if you haven’t already, you may want to click on “Follow” to the right to get updates by email to follow along. This will likely be several informal notes in the coming days.

 

 

 

 

Leading stocks are lagging

As another example of the observation I pointed out in Adapting to Change… and Volatility, below are today’s stock index price changes.

stock market losses 2014-04-04_15-15-53

Below are the price changes for the top 10 highest ranked stocks. Clearly, leading stocks are dropping more. And, such an increase in volatility is more common now days.

ibd 50 top ten losses 2014-04-04_15-15-31