Black-Scholes’ Dirty Little Secret

Tuesday, 6 September 2011 19:35 by The Lunatic

Back in 1973, two mathematicians named Fischer Black and Myron Scholes wrote a paper entitled "The Pricing of Options and Corporate Liabilities".  This became known as the “Black-Scholes option pricing model”, which earned them a coveted Nobel Prize in economics in 1997 (technically, Myron Scholes shared the prize with Robert Merton, another collaborator, since Fischer Black had passed away by that time).

The Black-Scholes option model serves as the benchmark for setting the price of a common stock option. All you need to know is the stock price, the strike price of the option, the time left to expiration, the current interest rate, and this tricky little thing called the volatility of the stock.

Ahhh, the volatility. There’s the rub. The volatility of a stock is calculated using an iterative process called a “cumulative normalized distribution function”. Basically, it looks at the variations of a stock’s up and down movement over a certain time period and offers up a percentage of the average movement. The volatility is an absolute measurement, which is different from a stock’s “beta” – the beta is a ratio of that particular stocks’ volatility as compared to the rest of the market, which is actually much easier to measure.

In my definition of volatility, I said that it relies on the variation of a stock price over a certain period of time. But what period of time should you use? One week? A month? Three months? Six months? A year? Maybe two years? The time period that you use can make a huge difference in the value of the option, but there’s no general recommendation for what period to use.

All of the other factors (stock price, strike price, time to expiration, etc.) are quantifiable values that can be specifically defined. The volatility, however, requires a bit of artistic interpretation.  If the stock was highly volatile nine months ago, but is more stable now, then measuring the historic volatility over the last six months is probably a good choice. Or not.

The chart below shows the stock price for Intermune (Symbol: ITMN), a small biotech company. In early March of 2010, an FDA review panel said that they would recommend approval for Intermune’s new drug and the price soared from around $15 per share up to the high $40’s. The FDA chose to ignore the recommendation of the review panel, and they decided not to grant approval in the first week of May, asking instead for additional information, which drove the price back down to under $10 per share:

image

Below the stock chart, you see another graph with three lines – the orange line is the volatility over the previous 30 days (one month) and the blue line is the volatility over the previous 60 days (two months). Anyone looking at the stock chart would agree that the stock was highly volatile throughout March, April, and May – but the “30 Day” measurement (orange line) shows that the volatility dropped down below 50% during most of April, as there wasn’t that big of a movement in the stock price over the 30 day window from about April 5 through the end of the month.

In contrast, the 60 day line (in blue) shows a more representative picture, as the period of high volatility lasted for almost exactly 60 days.

Note that the scale of the bottom graph tops out at 100%, which is normally considered a “high” volatility ... but both lines go up well over 100%, with the 30 day (orange line) volatility hitting a whopping 400% or so during May!

The red line shows the most interesting aspect of the Black-Scholes model: the “Implied Volatility”. This is a fascinating subject, and discovering all the nuances of the Implied Volatility has been a passion of mine for quite a few years now. Look at it this way: let’s say the Black-Scholes model says that an option should be worth $2.25 per contract, using a historic volatility of .55 for example (or 55%), but the option is really selling for $4.00 per contract. You can plug all the numbers into the formula backwards, and instead of solving for the price, you start with the price and solve for the volatility.

Suddenly you find that although the “historic volatility” of the stock is 55%, the current price suggests that the “implied volatility” is 90%. This means that the market thinks that the volatility in the future will be higher than it has been in the past. The market price is “implying” a higher volatility.

Again, there is no “time period” for calculating the Implied Volatility – but unlike using the historic volatility, you have an advantage. You can use different forward looking expiration dates to see when the market thinks the volatility will increase. So if you have options expiring in three weeks and again in seven weeks, you can see if the Implied Volatility is different between the two – which can give you an idea of the time period of expected increase in volatility.

In the above chart, the red line shows the implied volatility of the “near term” options. Note that leading up to the first week in March, the price of the stock is stable and the historic volatility is relatively low – but the price of the options went up steadily throughout the entire month of February. This is because the market anticipated the upcoming announcement – but no one was sure if the news was going to be good or bad. Again, in the month of April, as the 30 day historic volatility line went down, the implied volatility climbed back up as investors were looking forward to the final ‘yeah or nay’ vote from the FDA.

Is this just an academic exercise? Certainly not!  If a small pharmaceutical company has an upcoming decision by the FDA announcing whether their drug will be approved or not, or a small defense contractor is waiting for word of a large military order that will either make or break the company, then the implied volatility will almost always go up. Sometimes waaaaaaaay up. There is no other “traditional” technical indicator that can give you a heads up as to an upcoming move in a company’s stock price when it is up against a “binary event” like this.

So what is the “dirty little secret” of the Black-Scholes formula? Well, I’m not going to tell you.

Ok, I’ll spill the beans: the volatility and the implied volatility will almost always move in exact opposite directions from the calculations around the “Binary Event” date.  The Black-Scholes pricing model completely falls apart in this situation ... before the event, the historic volatility is low, and the Black-Scholes analysis (using the historic volatility) will say that that the option should be priced low – but as the market is anticipating a large movement in the price of the underlying security, the price of the option goes up (as measured by the “implied volatility”). Conversely, after there is a big change in the stock price and the historic volatility is very high, which would normally indicate a high price for the option going forward, the option price is low because the market does not foresee another big change in the near future.

What’s the bottom line?  What can an investor do with this information?

It’s a bit tricky. An astute options investor can monitor the Implied Volatility of all the stocks in the market and get a very good indication when a particular stock is going to have a big move in the near future – but there is no indication what direction the move will be. In a highly liquid market like we have with U.S. securities, the stock price itself would move if there was a reliable consensus of whether the news was going to be good or bad.

Buying or shorting the stock itself is not a viable strategy, since you don’t know what direction the stock will move and the odds are it will move quite far, so potential losses may be substantial.

In a “perfect market” the analysts following the company would project the potential high and low price of the stock after the news is announced (depending on whether the news was good or bad), and the stock would float almost perfectly in the middle of that range until the news was announced ... and the price of the “at the money” options would be one half of the expected move; meaning that the cost of an option straddle is expected to be the same as the anticipated movement of the stock. So if the stock was $50 per share, and the analysts expect the stock to move to either $35 or $65 (a $15 move in either direction) after the news is announced, the “at the money” options would most likely be priced at around $7.50 each for both calls and puts. 

This makes it difficult to use standard option strategies in this situation. Buying or selling straddles, covered calls/puts, or traditional spreads will almost always be unprofitable.

However, there are some multi-leg option strategies that can capitalize on the movement in one direction and minimize losses in the other direction. These trades are very complicated, and take a deep understanding of option dynamics – but they can be profitable if properly executed. You can also look at more obscure data like the “Volatility Smile”, the volume of calls vs. puts, or the ratio of ‘in the money’ vs. ‘out of the money’ option volume to try to glean some indication of what direction the other option traders think the stock will move.

The Black-Scholes pricing model is an amazing benchmark, used all over the world – but tread carefully if you find a situation where the historic volatility of a stock is fairly steady, but the option price (i.e., Implied Volatility) is rising dramatically. You can get in over your head quite easily.

 

Categories:   Economics
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Government Debt and Rising Interest Rates – A Dangerous Combination

Tuesday, 17 May 2011 18:41 by The Lunatic

Everyone knows that our national debt is completely out of control. But there’s an important issue that the press seems to be ignoring: the potentially devastating effect of rising interest rates.

The Federal Reserve is responsible for implementing our fiscal policy, but the Fed can not “set” interest rates – the overall market does that, based on supply and demand.  However, the Fed can influence rates by increasing or restricting money supply.  At the moment, just like in Louisiana and Mississippi, the floodgates are wide open. The bond market is awash in “virtually free” money, which is artificially keeping interest rates at historic lows.

But here’s the crux of the issue: with the floodgates open, the reservoir will eventually run dry – and the expectation is that interest rates will then rise. What happens to our federal budget when rates go up?  It could get really ugly really quickly.

Here’s why:

If you look at the chart in my earlier post, Trying to Make Sense of the Federal Budget, (the second chart, with the Social Security and Medicare numbers removed), you will see that interest payments on the federal debt clocked in at $218 billion in 2010, or 11% of our federal budget:

image

The weighted average interest rate of all the US debt currently runs about 2.07%.  Shorter term debt has a lower interest rate – less than .25% – and longer term debt has a higher interest rate – approaching 4.375%. When longer term debt is more expensive than short term debt, we have what is referred to as More...

Trying to make sense of the Federal Budget

Wednesday, 6 April 2011 17:00 by The Lunatic

Pop quiz: What percent of our federal budget goes to the military? 

If you look at the “official” budget numbers, the White House reports that Defense spending takes up just over 19% of our budget.

Here is what our government spent in 2010, as reported by the Office of Management and Budget and the Department of the Treasury:

Budget5_thumb3

At first glance, this looks like a reasonably balanced chart, without any single slice of the pie taking up too much of the available dough (the pun was intended, although the joke was – admittedly – kind of crusty).

However, there’s been an unfortunate trend which started sometime around the Reagan era, where they try to “de-emphasize” the amount we spend on Defense by including More...

The Worst Investment Ever Made

Tuesday, 15 March 2011 16:54 by The Lunatic

The height of the “dot com” boom was a pretty crazy time for investors; venture capitalists were investing huge sums of cash with any entrepreneur who could type the word “internet” without using a spell checker. People made some really BAD investments and only a few of the startups from that period are still operating today.

But there’s one deal that really takes the cake. This acquisition was so absurd in its reasoning and so insidious in scale that I’m surprised the story hasn’t been made into a Hollywood feature film.

Let’s back up a few years, to 1996. This was the year that yours truly joined a small internet startup called VXtreme, an early pioneer in streaming video on the web. VXtreme had actually developed a viable technology and we created what was arguably the best streaming video platform (codecs, encoder, player, server) in the world at the time.

Remember that in 1996, people were connected to the internet with 28.8Kbps modems – or if you could afford it, you might have one of the spanking new 56K modems.  Whoo-Hooo! Blazing fast internet it was, indeed. Delivering real time streaming video over such a connection was problematic at best – but it was SO exciting to see a media player embedded in a web page, rendering real time video with a resolution of 160x120 pixels at a whopping 15 frames per second refresh rate! We were truly on the bleeding edge.

In just over ten months, we built the company, produced the product, engaged a bunch of high profile customers, and sold the whole thing to Microsoft for about $74 Million (and to set the record straight, I was not one of the founders or shareholders – just a “late hire” marketing manager, with options that were only worth about 1/10th of 1% of the company).

It was a fair valuation for VXtreme.  Our technology was merged in with the “NetShow” product that Microsoft had been struggling with, and the platform was eventually renamed “Windows Media”. Even today, the Windows Media Player, Windows Media Audio/Windows Media Video file formats, Silverlight, and the More...

Categories:   Economics | Miscellaneous | Science
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Tackling the Healthcare Issue

Monday, 25 October 2010 19:10 by The Lunatic

Newsflash: The cost of healthcare in America has been out of control for many years and we really need to do something about it!

Ok, so this isn’t news. And we already have the all-new healthcare reform legislation which fixes all our problems, right?

Unfortunately, this new law – officially called the “Patient Protection and Affordable Care Act” (PPACA) but more affectionately referred to as “Obamacare” – has some problems, and now a few people are lobbying to ditch this plan so they can come up with something different.

Part of the problem with baking up a new healthcare plan is that there are so many fingers in the pie, all with vested interests – you have the healthcare insurance companies, malpractice insurance companies, pharmaceutical companies, hospital owners, nurses unions, lobbyists, medical licensing boards, government agencies (FDA, HHS, CDC, VA, CMS, etc), the politicians (who love to shoot down whatever their opponents propose, no matter what it is) ... and let’s not forget the doctors and the patients themselves.  It really is fundamentally IMPOSSIBLE to implement any reform that won’t upset someone in the chain. It’s a political nightmare, and everyone knows it – but something has to be done. More...

The Crazy Price of Video Cables

Thursday, 16 September 2010 04:02 by The Lunatic

In years past, when you purchased a VCR or a DVD player, it would come with a video cable so that you could go home, connect your new player to your TV, and immediately start watching.  It was usually a cheap combination audio/video cable – not very sturdy, but it would get the job done.

If you purchase a new Blu-Ray player today, however, you will find that not a single cable is to be found in the box. A high tech Blu-Ray player should really should at least come with an HDMI cable (High Definition Multi-media Interface, the preferred method of connecting any HD video source to a digital television).

 A decent quality cable costs less than fifty cents to make. Are the manufacturers just getting cheap?  Trying to cut corners?

Nope.  They’ve stopped including cables because More...

Categories:   Economics | Miscellaneous | Science
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Energy, Efficiency, and the long road to SBSP

Saturday, 3 April 2010 14:29 by The Lunatic

Here’s an old high school physics puzzle, let’s see if you can get the right answer:

You have perfectly insulated room (i.e., no heat can escape).  Inside the room is a refrigerator, plugged in and running – but the refrigerator door is left wide open.

As the refrigerator runs, does the room:
A – get colder
B – get warmer
C – stay the same temperature

Think about it for a minute ... (and yes, I first heard this from my high school science teacher back in the late 70’s)

The answer is ... (drum roll please!) ... More...

Categories:   Economics | Science
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The Bigger Chill

Sunday, 31 January 2010 02:10 by The Lunatic

The star studded 1983 movie "The Big Chill” was about a weekend reunion of a bunch of old college friends – now in their early 30’s – who all get together for the funeral of Alex, one of their classmates who committed suicide.

The movie is poignant, intelligent, very funny, and somewhat disturbing all the same time. It’s about rekindling old friendships, coping with the shock of their friend Alex’s death, and wondering what happened to the social idealism that they all shared when they attended the University of Michigan in the late 60’s. They were all anti-establishment, idealistic, smart, enthusiastic, with a vocal desire to change the world and make it a better place.

Alex, now deceased, was a charismatic science major. Everyone thought he was the most intelligent one of the bunch – and their mutual friendship really survived through the years because of him. He was the glue that kept them all together, but he was never able to get his own life straightened out.

Now, in 1983, they realize they are becoming the conservative “establishment” that they protested against in college.  More...

Hey, let’s blame it all on Obama!

Monday, 5 October 2009 12:43 by The Lunatic

 

A good friend of mine forwarded the following email to me the other day.  Now, before I begin, this friend is one of the smartest people I know.  He is the CEO of a rapidly growing company, introducing successful new products into the marketplace even in this economy. He is a vocal Republican, so all I ever heard from him for about 20 years was that “it’s the Democrats fault” when referring to ANY problems in the world.  I’m neither democrat nor republican, so it's never bothered me any.

But then, halfway through the second term of the Bush administration, he swung around and admitted that maybe it’s not ALL the Democrats fault, the Republicans need to take some part of the blame for the state of the world’s affairs. And horror of horrors, he hesitantly (accidentally?) said some positive remarks towards Obama during the election (but really, I think it was more of an anti-McCain sentiment than anything, in one email he said “clearly McCain is an even worse war monger than Bush, very scary.  I bet he never met a weapon he didn't buy.”)

However, he’s back to his lovable More...

Categories:   Economics | Politics
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AloeControl – New from USAloe

Thursday, 28 May 2009 15:38 by The Lunatic

 

AloeControlBottle_Cutout Following the hugely successful launch of AloeBoost and AloeRest, I am happy to announce that USAloe is now shipping their third product, AloeControl.

AloeControl™ is your unfair advantage in the struggle to maintain a healthy weight.

In each healthy 2oz serving you'll enjoy a unique blend of the world's finest fruits, vegetables, and natural ingredients designed to help you control your appetite, efficiently burn calories, and provide you with the essential vitamins and minerals that are MISSING in today's typical American diet.

The four core components of AloeControl™ include Appetite Control, Metabolic Enhancers, Digestive Aids, and Core Nutrition. Get all the details and the ingredient list at:
http://shop.usaloe.com/products-aloecontrol.aspx

I don’t mean to brag, but More...

Categories:   Economics | Social Issues
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PayPal for cell phones?

Tuesday, 21 April 2009 15:33 by The Lunatic

You normally don’t think of Kenya as being at the forefront of technical and financial innovation – but I was struck by this story I saw recently on CNN:

http://edition.cnn.com/video/#/video/world/2009/04/15/mckenzie.kenya.mobile.money.cnn

What started out as a way to transfer pre-paid cell phone credits to family and friends has turned into an entire micro-transaction commerce platform that is replacing banks in Kenya. And there’s no reason why it wouldn’t work elsewhere!

Think of it as PayPal for cell phones.  For example – you want to buy a magazine from a vendor on the street, but you don’t have change.  The vendor doesn’t take credit or debit cards. So you just enter their cell phone number, specify how much you want to transfer, tap in your security code, and hit send.  Just like sending a text message, but you’re sending cash.  The vendor’s phone beeps, notifying them More...

Categories:   Economics
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Yes, it’s outrageous

Sunday, 22 March 2009 02:38 by The Lunatic

Like everyone else, I’m completely outraged by the whole AIG bonus issue. Bonuses should reward exceptional performance and positive results.  Where’s the accountability?

This has been hashed to death in the press, so I’m not going to go into all the reasons why it’s just rotten to the core.

But let’s back up a little bit and see how this fits in with the bigger picture of executive compensation.  This has been an issue for many years, well before the economic downturn. It’s a big thorn in the side of many shareholders of large companies.

Executive compensation needs to be tied not only to performance, but also to their own personal risk.  For example – a hired CEO brought in to More...

Categories:   Economics | Social Issues
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What are we REALLY bailing out? Not mortgages ...

Monday, 23 February 2009 19:57 by The Lunatic

There is absolutely NO WAY that any kind of a mortgage bailout will be fair.  The people who would benefit from mortgage assistance are generally the ones least likely to deserve it.

Hardest hit are people who either bought a bigger house than they could really afford, and people who snagged one of those great “no money down” loans.  Are YOU willing to subsidize someone who is living in a luxurious home they shouldn’t have been able to afford in the first place?  Is that the kind of behavior that we are trying to encourage?

Absolutely not!

While I do have great sympathy for someone who is losing their home after 20 or 30 years, let’s look at the reality of who this might be:

Assume someone bought a house More...

Categories:   Economics | Politics
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AloeBoost and AloeRest - Two New Products From USAloe

Thursday, 19 February 2009 16:28 by The Lunatic

aloerest-final USAloe, a company in California that I've been doing some consulting work for, is launching two new products this week:  AloeBoost (an energy drink) and AloeRest (a relaxation and sleep aid). Both are made with Aloe Vera juice and other healthy, all natural ingredients.

What's interesting is that these products are going into a network marketing channel instead of a traditional retail channel, and I think people are going to make pretty good money from it.

Now, over the years, I've had plenty of people pitch me on different network marketing companies. All of them have said pretty much the same thing: "I'm going to be retired in two years!"  I've checked back with a few of them, and none of them had the financial success that I've had.

The truth is, a lot of people HAVE made a very substantial income with network marketing (or multi-level marketing, or whatever you want to call it) but these people are More...

Categories:   Economics
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Investing in stocks? Try options instead!

Friday, 9 January 2009 21:36 by The Lunatic

When people think about trading options, their first response is usually "too much risk". While it's true that options can be misused, they are often used to REDUCE risk by hedging other investments.  For example, buying a stock and selling a "covered call" is a substantially more conservative investment than just investing in the stock itself (less risk, but also potentially lower return).

And yes, I have learned the hard way what can happen if you lose your head.  After about ten years of successfully and profitably trading options, I entered into an overly aggressive position in 2006 that went south - and pretty much wiped out my entire gains of the previous ten years.  Lesson learned: stick to your strategy and stay within your limits!

But in general, even with that painful experience, I am still a firm believer that trading options is more prudent than buying stocks.

Admittedly, options are far more complicated.  More...

Categories:   Economics
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