August 2021

Hanging With Leonardo

With the Volatility Index (VIX) going through the roof today, I think it is timely to remind everyone what it is.

At my advanced age, I have very few friends. Most of them are either puttering around some county golf course, or are dead.

By there is one who has stuck with me for my entire 50-year trading career, through thick and thin.

That would be Leonardo Fibonacci.

It always seemed like he could read my mind, as well as everyone else’s.

When a stock looks like it fell into a bottomless pit, it would bounce hard off of the precise price that he selected.

Similarly, he always knew high prices would rise before they topped out.

As a result, I think of Fibonacci as more of a magician than a mathematician.

I remember the 12^th century like it was yesterday.

In those days, the leading intellectuals used to get together and drink wine by the gallon, which then was really little more than rotten grape juice.

The problem was that we all used to pass out before anybody came up with a great idea.

Then someone started importing coffee from the Middle East, and thinkers stayed awake long enough to produce great thoughts.

Enter the Renaissance.

One of the guys I used to hang out with then was named Leonardo Fibonacci.

Good old Leo was a man after my own heart, a world-class nerd and geek, with a penchant for mathematics.

His dad was a diplomat from the Court at Pisa to the Algiers sultanate who had a nice little import/export business on the side.

It is safe to say that there was probably as little action in Algiers than as there is today. I know, because I’ve been there.

Instead of camping out in his dad’s basement and staying depressed like a lot of young men these days, Leo killed time trolling the local bazaars for interesting used books he could buy on the cheap.

Remember, this was before texting.

That was not hard to do since most people couldn’t read. He took the trouble to learn Arabic and translated them back into Latin. Ancient math books were his specialty.

It didn’t take Leo long to figure out that the Arabs had developed a numbering system vastly superior to the Roman numerals then in use in Europe.

Most importantly, they mastered the concept of zero and the placement of digits in addition and subtraction. The Arabs themselves, in fact, lifted these concepts from archaic Indian mathematicians as far back as the 6^thcentury.

If you don’t believe me about the significance of this discovery, try multiplying CCVII by XXXIV. (The answer is VIIXXXVIII, or 7,038).

Good luck designing a house, a bridge, or a computer software program with such a cumbersome numbering system.

Leo didn’t just stop there.

He also discovered a series of numbers, which seemed to have magical predictive powers. The formula is extremely simple. Start with zero, add the next number, and you have the next number in the series.

Continue the progression and you get 0,1,1,2,3,5,8,13,21,34,55…. and so on. It’s no surprise that the sequence became known as the “Fibonacci Sequence”.

The great thing about this series is that if you divide any number in it by the next one, you get a product that has become known as the “Golden Ratio”. This number is 1:1.618, or 0.618 to one.

Fibonacci’s original application for this number was to predict the growth rate of a population of breeding rabbits.

Then some other mathematicians started poking around with it. It turns out the Great Pyramid in Egypt was built to the specification of a Fibonacci ratio.

So is the rate of change of the curvature in a seashell, or a human ear. So is the ratio of the length of your arms to your legs.

Upon closer inspection, the Fibonacci formula turned out to be absolutely everywhere, from the structure of the tiniest cell to the swirl of the largest galaxies in the universe.

Fibonacci introduced his findings in a book entitled “Liber Abaci”, or “Free Abacus” in English, which he published in 1202.

In it, he proposed the 0-9 numbering system, place values, lattice multiplication, fractions, bookkeeping, commercial weights and measures, and the calculation of interest.

It included everything we would recognize as modern mathematics.

The book launched the scientific revolution in Europe that led us to where we are today and was a major bestseller. In fact, you can still buy it on Amazon, making it the longest continuously published book in history.

Enter the stock market.

By the end of the 19^thcentury, some observers noticed that share prices tended to move in predictable patterns on charts.

In particular, they always seemed to advance and pull back around the numbers forecast by my friend, Fibonacci, seven hundred years earlier.

These people came to be known as “technical analysts,” as opposed to fundamental analysts, who look at the underlying business behind each company.

By the 1930s, Fibonacci numbers had worked their way into mainstream technical analytical theories, such as Elliot Wave.

Today, most market tracking software and data systems, like Bloomberg, will automatically throw up Fibonacci support and resistance numbers on every stock chart.

Why am I talking about this?

Because I am frequently asked how I pick the precise strike prices for options in my own Trade Alert Service.

I use a combination of moving averages, moving average convergence-divergence (MACD) indicators, Bollinger bands, Fibonacci numbers, and a mumbling chant taught to me by an old Yaqui Indian shaman.

And I do all of this only after going over the underlying fundamentals of the stock or index with a fine-tooth comb. I can’t be any clearer than that.

Enter the high-frequency traders. Knowing that the bulk of us rely on Fibonacci numbers for our short-term trading calls, they have developed algorithms that seek to exploit that preference.

They enter a large number of stop-loss orders to sell just below a “Fibo” support level, then put up fake, but extremely large offers just above it which are usually cancelled.

Only 1% of these orders ever get executed.

When conventional traders see these huge offers to sell, they panic, dump their stocks, and trigger the stop losses. The HFTs then jump in and cover their own shorts for a quick profit, sometimes only for a fraction of a penny.

The net effect of these shenanigans is to make Fibo numbers less effective. Fibo support is just not as rock solid as it used to be, nor is resistance.

This is why the performance of several leading technical analysts has seriously deteriorated in recent years.

Although their importance is now somewhat diluted, I still enjoy Fibonacci numbers as I see them in nature all around me. They occasionally have other uses such as in cryptography.

When I watched The Da Vinci Code sequel, “Angels & Demons,” and listened to the clues, I recognized the handiwork of my old friend Leo.

The rest of the audience sat there clueless, except for the group in the next row wearing “UC BERKELEY” hoodies.

For the fellow geeks and nerds among you, here are the precise Fibonacci numbers indicating support and resistance, which you will find on a stock chart.

Fibonacci Ratios

Fibonacci ratios are mathematical relationships, expressed as ratios, derived from the Fibonacci sequence. The key Fibonacci ratios are 0%, 23.6%, 38.2%, and 100%.

The key Fibonacci ratio of 0.618 is derived by dividing any number in the sequence by the number that immediately follows it. For example: 8/13 is approximately 0.6154, and 55/89 is approximately 0.6180.

The 0.382 ratio is found by dividing any number in the sequence by the number that is found two places to the right. For example: 34/89 is approximately 0.3820.

The 0.236 ratio is found by dividing any number in the sequence by the number that is three places to the right. For example: 55/233 is approximately 0.2361.

The 0 ratio is :

Leonardo Fibonacci (Maybe)

August 18, 2021 - Quote of the Day

Diary, Newsletter, Quote of the Day

“Blue skies, nothing but blue skies. Never saw the sun shining so bright, things going so right, grey days, all of them gone. Nothing but blue skies from now on,” said the top musical lyric of early 1929, by Irving Berlin.

August 17, 2021

Biotech Letter

Mad Hedge Biotech & Healthcare Letter
August 17, 2021
Fiat Lux

FEATURED TRADE:

(EYES ON THE PRIZE)
(STAA), (UNH), (LLY), (AMZN), (V), (NKE), (MA), (GOOGL)

Eyes on the Prize

Biotech Letter

The investing world is filled with buzzwords, and one of the most widespread lately is “compounders” – aka stocks with the capacity to generate double-digit compound growth in terms of revenue and earnings.

They’re typically dubbed as the “next” Amazon (AMZN), Visa (V), or Nike (NKE), making them heavy favorites among growth investors aggressively looking for companies that can generate high returns in the next five to 10 years.

Ultimately, the goal is to find the next “10 bagger.”

Most investors are perfectly content with big and popular compounders like Mastercard (MA) and Alphabet (GOOGL).

Since the healthcare and biotechnology sector has its own well-known compounders, such as Eli Lilly (LLY) and UnitedHealth Group (UNH), it’s easy to miss the smaller lesser-known companies that are consistently generating high growth in their profits over the past years.

A good example of this is Staar Surgical (STAA).

Founded way back in 1982, this under-the-radar stock is up by over 243% over the past 12 months and more than 85% this year alone.

Saying that the company has had an impressive 2020 despite the pandemic is an understatement.

The company’s latest product is an implantable lens that works to correct myopia or nearsightedness.

This technology addresses a potentially massive market, taking into consideration the growing number of vision-related problems globally.

Staar anticipates the lens, which has already been made available across Europe and even Asia for roughly five years now, to enter the US market by the fourth quarter of 2021.

Inasmuch as the human eyes are considered powerful organs, they are definitely far from perfect. That’s why eyeglasses and even contact lenses have been in the market for decades.

Aside from its new product, Staar’s bread and butter is its Visian implantable collamer lenses, which are designed to deal with various vision issues including myopia (nearsightedness), presbyopia (an incapability to focus on nearby objects), and astigmatism (blurred or distorted vision).

Although they are quite different, many people confuse Staar’s solution with LASIK.

The key difference is that LASIK surgeries necessitate trimming of the cornea using lasers to correct the vision of the patient.

In contrast, what Staar does is to implant the corrective lenses directly in the eye, specifically behind the patient’s iris but right in front of the cornea.

This makes Staar’s solution reversible and, of course, less invasive compared to LASIK.

To date, Staar’s surgery is more expensive at $3,500 per eye, while LASIK costs roughly $2,246 for each eye.

However, this cost is expected to go down as more doctors eventually choose Staar implants over other options.

Looking at its trajectory, Staar could lead to LASIK becoming obsolete in the same way that radial keratotomy stopped being the norm before.

So far, Staar remains profitable and continues to grow its quarterly profits by 18.3% year over year. However, it’s the long-term revenue that shareholders would stand to gain most.

At this point, roughly 30% of the world is diagnosed as nearsighted. By 2050, over half of the population may require vision for myopia alone.

Meanwhile, 75% to 80% of adults between ages 45 and 74 are already struggling with presbyopia.

These figures spell massive opportunities and lucrative markets for Staar’s vision lines, with the annual spending on cheaper alternatives like eyeglasses projected at $48 billion.

Silently growing companies in the seemingly humdrum market are often pretty sneaky.

Vision correction doesn’t appear to be a white-hot investment sector that calls for urgent investment.

Only a handful of investors possess the foresight to view mundane products and services, like eye surgeries, as lucrative investments.

However, there’s usually a flicker of greatness in the most unlikely markets.

Trade Alert - (FB) August 17, 2021 - BUY

Tech Alert

When John identifies a strategic exit point, he will send you an alert with specific trade information as to what security to sell, when to sell it, and at what price. Most often, it will be to TAKE PROFITS, but, on rare occasions, it will be to exercise a STOP LOSS at a predetermined price to adhere to strict risk management discipline. Read more

Trade Alert - (SPY) August 17, 2021 - BUY

Trade Alert

When John identifies a strategic exit point, he will send you an alert with specific trade information as to what security to sell, when to sell it, and at what price. Most often, it will be to TAKE PROFITS, but, on rare occasions, it will be to exercise a STOP LOSS at a predetermined price to adhere to strict risk management discipline. Read more

August 17, 2021

Diary, Newsletter, Summary

Global Market Comments
August 17, 2021
Fiat Lux9

Featured Trader:

(IS AIRBNB YOUR NEXT TEN-BAGGER?),
(ABNB), (WYNN), (H), (GOOG), (PYPL)

Is Airbnb Your Next Ten-Bagger?

Diary, Newsletter, Research

When the pandemic hit in February, I figured Airbnb was toast. Global travel had ground to a halt, and competitors like Wynn Resorts (WYNN) and Hyatt Hotels (H) saw their share prices plunge to near zero.

Instead, the opposite happened.

While the big hotels continue to roast in purgatory, Airbnb catapulted to a new golden age, and how they did it was amazing.

They turned all travel local. Instead of recommending that I visit Cairo, Tokyo, or Rio de Janeiro, they suggested Carmel, Monterey, or Mendocino, all destinations within driving distance. It worked, and the company is now moving from strength to strength.

My neighborhood in Incline Village, NV was almost always deserted outside of holidays. Now it is packed with Airbnbrs awkwardly moving in every Friday only to flee on Sunday.

How would you like to get a 90% discount on all of your luxury hotel accommodations?

During my most recent trip to Dubrovnik in Croatia, I rented an 800-square foot, two-bedroom, two-bath home inside the city walls for $300 a night.

A single, cramped 150 square foot room in the nearest five-star hotel was $600 night.

All that was missing was room service, a hand out for a big tip, and a surly attitude.

Sounds like a massive, game-changing disruption to me.

Thank you, Airbnb!

I was not surprised to hear that the home-sharing app, Airbnb, was given a $31 billion valuation in the latest venture capital funding round.

The big question for you and me is: Will the valuation soar tenfold to $300 billion, and how much of a piece of that will you and I be allowed to get?

To answer that question, I spent six weeks traveling around the world as an Airbnb customer. This enabled me to understand their business model, their strengths and weaknesses, and analyze their long-term potential.

As a customer, the value you receive is nothing less than amazing.

I have been a five-star hotel client for most of my life, with someone else picking up the tab much of the time (thank you, Morgan Stanley!), so I have a pretty good idea on the true value of accommodations.

What you get from Airbnb is nothing less than spectacular. You get three or four times the floor space for one-third the price. That’s a disruption factor of 7:1.

The standards are often five-star and at the top end depending on how much you spend. I found out I could often get an entire three-bedroom house for the price of a single hotel room, with a better location.

Or, I could get an excellent abode in rural settings, where none other was to be had, whatsoever.

That’s a big deal for someone like me who spends so much of the year on the road.

You also get a new best friend in every city you visit.

On most occasions, the host greeted me on the doorsteps with the keys, and then introduced me to the mysteries of European kitchen appliances, heating, and air conditioning.

Pre-stocking the refrigerator with fresh milk, coffee, tea, and jam seems to be a tradition the hosts pick up in their Airbnb orientation course.

One in Waterford, Ireland even left me a bottle of wine, plenty of beer, and a frozen pizza. She read my mind. She then took me on a one-hour tour of their city, divulging secrets about their favorite restaurants, city sights, and nightspots. Everyone proved golden. Thanks, Mary!

After you check out, Airbnb asks you to review the accommodation. These can be incredibly valuable in deciding your next pick.

I had one near miss with what I thought was a great deal in London, until I read, “The entire place reeks of Indian cooking.”

Similarly, the hosts rate you as a guest.

One hostess in Dingle, Ireland shared a story about picking up her clients from town after they got drunk and lost in the middle of the night. Then they threw up in the back of the car on the way home.

Guests forgetting to return keys are another common complaint.

Needless to say, I received top ratings from my hosts, as fixing their WIFI to boost performance became a regular and very popular habit of mine.

After my initial fabulous experience in London, I thought it might be a one-off, limited to only the largest cities. So, I started researching accommodations for my upcoming trips.

I couldn’t have been more wrong.

Just the Kona Coast on the big island of Hawaii had an incredible 50 offerings, including several bargain beachfront properties.

The center of Tokyo had over 300 listings. The historic district in Florence, Italy had a mind blowing 351 properties.

Fancy a retreat on the island of Bali in Indonesia and tune up your surfing? There are over 197 places to stay!

Airbnb has truly gone global.

Airbnb’s business model is almost too simple to be true, involving no more than a couple of popular applications. Call it an artful melding of Google Earth, email, text, and PayPal.

While no one was looking, it became the world’s largest hotel at a tiny fraction of the capital cost.

The company has 4 million hosts in 100,000 cities worldwide, and 150 million users. That supply/demand imbalance shifts burden of the cost to the renters, who usually have to fork out a 12% fee, plus the cost of the cleaning service.

Hosts only pay 3% to process the credit card fees for the payment.

The tidal wave of revenues this has created has enabled Airbnb to become San Francisco’s largest privately owned “unicorn”,

To say that Airbnb has created controversy would be a huge understatement.

For a start, it has emerged as a major challenge to the hotel industry, which is still stuck with a 20^th century business model. There’s no way hotels can compete on price.

One Airbnb “super host” in Manhattan at one point managed 200 apartments, essentially, creating out of scratch, a medium sized virtual “hotel” until the city caught on to them.

Taxes are another matter.

Some municipalities require hosts to pay levies of up to 20%, while others demand quarterly tax filings and withholding taxes. That is, if tax collectors can find them.

Airbnb may be the largest new source of tax evasion today.

In cities where housing is in short supply, Airbnb is seen as crowding out local residents. After all, an owner can make far more money subletting their residence nightly than with a long-term lease.

Several owners told me that Airbnb covered their entire mortgage and housing cost for the year, while paying off the mortgage at the same time.

Owners in the primest of areas, like mid-town Manhattan off of Central Park, or the old city center in Dubrovnik, rent their homes out as much as 180 days a year.

It is doing nothing less than changing lives.

That has forced local governments to clamp down.

San Francisco has severe, iron-clad planning and zoning restrictions that only allow 2,000 new residences a year to come on the market.

It is cracking down on Airbnb, as well has other home sharing apps like FlipKey, VRBO, and HomeAway, by forcing hosts to register with the city or face brutal $1,000 a day fine.

So far, only 1,675 out of 9,000 hosts have done so.

Ratting out your neighbor as an off the grid Airbnb member has become a new cottage industry in the City of the Bay.

Airbnb is fighting back with multiple lawsuits, citing the federal Communications Decency Act, the Stored Communications Act, and the First Amendment covering the freedom of speech.

It is a safe bet that a $31 billion company can spend more on legal fees than a city the size of San Francisco.

The company has also become the largest contributor in San Francisco’s local elections. In 2015, it fought a successful campaign against Proposition “F” meant to place severe restrictions on their services.

An Airbnb stay over is not without its problems.

The burden of truth in advertising is on the host, not the company, and inaccurate listings are withdrawn only after complaints.

A twenty-something-year-old guy’s idea of cleanliness may be a little lower than your own.

Long time users learn the unspoken “code”.

“Cozy” can mean tiny, “as is” can be a dump, and “lively” can bring the drunken screaming of four letter words all night long, especially if you are staying upstairs from a pub.

And that spectacular seaside view might come with relentlessly whining Vespa’s on the highway out front. Always bring earplugs and blindfolds as backups.

Researching complaints, it seems that the worst of the abuses occur in shared accommodations. Learning new foreign cultures can be fascinating. But your new roommate may want to get to know you better than you want, especially if you are female.

In one notorious incident, a Madrid guest was raped and had to call customer service in San Francisco to get the local police to rescue here. The best way to guard against such unpleasantries is to rent the entire residence for your use only, as I do.

Another problem arises when properties are rented out for illegal purposes, such as prostitution or drug dealing.

More than once, an unsuspecting resident woke up one morning to discover they were living next door to a new bordello.

Coming out of the pandemic, my conclusion is that the travel industry is entering a hyper growth phase. Blame the emerging middle-class Chinese, who seem to be everywhere.

The real shock came when I left Airbnb and stayed in a regular hotel. Include the fees and the cleaning charges, and the service is no longer competitive for a single night stay. Total costs now regularly run double the posted one night price posted on websites.

In any case, most hosts have two or three night minimums to minimize hassle.

When I checked in at a Basel, Switzerland Five Star hotel, all I got was a set of keys and a blank stare. No great restaurant tips, no local secrets, no new best friend.

I spent that night surfing www.airbnb.com , planning my next adventure.

My New Best Friend

August 16, 2021

Tech Letter

Mad Hedge Technology Letter
August 16, 2021
Fiat Lux

Featured Trade:

(HOW TO BE A TECH ANGEL INVESTOR)
(FB), (PINS), (LYFT), (TWTR), (BTC)

How To Be A Tech Angel Investor

Tech Letter

It’s not easy to be the genius who doled out early seed money to Facebook (FB), Foursquare, GitHub, Pinterest (PINS), Lyft (LYFT) and Twitter (TWTR), among others.

These investments turned out to be highly successful. If someone even miraculously hit on one of these, your grandchildren would know about it.

This person even acquired a majority stake in Skype for $2.75 billion which was considered highly risky at the time and offloaded it to Microsoft in 2011 for $8.5 billion.

Not everyone can do this like Silicon Valley tech investment maestro Marc Andreessen.

Behind the public markets is angel investing and the data says that these investments fail over 50% of the time for the best of breed like Andreesen.

There are simply too many variables that can derail these profit models which nobody can predict.

To lose over half the time and claim to be an outsized winner means relying on those 10 or 100-baggers or might I even say 1,000-baggers to drag up the portfolio performance.

These are the guys who were buying bitcoin (BTC) at 10 cents on the dollar.

Truthfully, investing in startup companies is not for everyone considering there is over a 50% chance a company will end at a 0 or pennies on the dollar.

However, it can be highly gratifying if and when the investments do pay off and investors get a front seat to the forefront of the tech innovation cycle, which you simply don’t get by trading Facebook and Google from your Fidelity account on your computer screen.

These investors can also get direct access to the chatter while creating a rich network of tech know-how; and I do believe that’s half the value in it too, since it can propel angel investors to the next super app or guy behind the next super app.

I mean who could have ever predicted a global health crisis that’s going into its 3rd year soon? And who will be able to nail the knock-on effects of climate change.

That is why risking losing one’s shirt is a real possibility if they bet the ranch on an unknown entity.

Everybody wants the next Tom Brady to quarterback their team, but who knows who the next Tom Brady is at 18 years old?

Even though Andreessen hits on less than 50% of his ideas, the industry median is around 17%, showing how superior his performance is.

He definitely has this thing figured out on relative terms.

Let’s define Angel Investor.

An angel investor is a high-net-worth individual who provides financial backing for small startups or entrepreneurs, typically in exchange for ownership equity in the company.

The funds that angel investors offer could be one-off investments to help the business get off the ground or in drip injection form to support and carry the company through its difficult early stages, which means burning cash.

Most of these companies don’t make money for the first 10-years and that time is usually a referendum on the quality of the idea; very few stand the test of time.

The potential to make 100-baggers is out there with subsectors like fintech already worth half a trillion dollars in 2020 and with a predicted annual growth rate of 35%.

Angel investors typically require a 35-40% return on the money they invest in a company minus costs and inflation to call it a winner.

But Venture Capitalists may take even more, especially if the product is still in development. For example, an investor may want 50% of the business to compensate for the high risk it is taking by investing in a startup.

Angel investors do the jobs of banks.

Traditional banks would never lend to an entity based on a half-built product or even a genius idea.

Proof of income and debt to income ratios are realities at banks.

When net profits are negative, the balance sheet is too ugly for banks to even think about doing any business with these startups.

Therefore, there are limited pathways for entrepreneurs to find capital, and many turn to Angel investors to help startups take their first steps.

Who Can Be an Angel Investor?

Angel investors are normally individuals who have gained "accredited investor" status, but this isn’t a prerequisite. The Securities and Exchange Commission (SEC) defines an "accredited investor" as one with a net worth of $1M in assets.

Essentially these individuals both have the finances and chutzpah to provide funding for startups. This is welcomed by cash-hungry startups who find angel investors to be far more appealing than other, more predatory, forms of funding.

These private funds usually draw up opportunities for a defined exit strategy, acquisitions or initial public offerings (IPOs).

Liquidity events is what makes everyone happy at the end except for the investors who missed the boat.

It’s even possible that an angel investor only sees growth in the first 5 years and unloads the “idea” to another private investor for a profit.

Private market deals are common because of the excess of liquidity brought on by the U.S. Central Bank lowering interest rates for a prolonged amount of time.

What I do know is that America is the framework within which almost all unicorns prosper, and I do not envision any monumental shift to Europe or China, these other places simply have more problems than the U.S.

How does the normal Joe get it on the action?

Andreesen has said the only way he usually does business is with a “warm” introduction which can be hard to come by if one doesn’t rotate in the same social circles as these heavy hitters.

Scoring a warm introduction also means getting boots on the ground in California which is ebbing and flowing between its colossal wildfires and public health issues like many other places.

Honestly speaking, if might be difficult to get the best of the best angel opportunities even if the gunpowder is loaded.

It’s accurate to believe that probably guys like Andreesen get the best of the best ideas in front of them and if they pass on it, the likes of Sequoia, Benchmark, and Softbank have very smart people as well who get similar type of presentations and opportunities.

Like you correctly guessed, this private group of capital is quite incestuous and tight-knit. It’s a copycat league of the ages.

The one avenue that might be of interest is a platform that has democratized angel investing who on the last count had close to 1,000 companies looking for start-up capital.

This platform is called https://angel.co/angel-investing and some are even actively hiring on the same platform.

I won’t stand here saying this is the cream of the crop because it’s not, but I will say that sometimes companies are overlooked, or the industry consensus has shifted too far in one direction offering undiscovered dark horses a chance.

Lastly, this forum of angel companies on offer does give analysts insight into where money is funneled to and the current hot sub-sector of the tech industry.

This platform even offers an Angel index fund if a reader wants to take the aggregate performance of 150-200 companies with a $50,000 minimum.

If a reader wants access to facilitate angel investing by a deal-by-deal offer from the Angel list as a professional investor, then $500,000 is required.