Why Option Traders Focus on Vega

Options are derivatives. They derive their value from how the underlying actually moves as well as the market’s perception of how much they will move. So there’s a realized and implied component to the value of an option. When people start using options they are usually attracted to them as an inherently levered way to hedge or speculate on a stock. In other words, they are interested in options as a bet on direction.

In the course of trading options, directional players tend to acquire a solid understanding of delta and gamma.

  • Delta is the option’s sensitivity to the stock price

The more OTM the option is the less sensitive it is to the stock price. Simply the option’s “moneyness” drives it’s delta

  • Gamma is the option delta’s sensitivity to the stock price

Formally, gamma is the second derivative the option’s value with respect to the stock price. Intuitively, it is a measure of how the option’s delta changes as the stock’s moneyness changes. If a call is 20% OTM it may have a low delta. Say 5%. But if the stock suddenly surged 20%, the call would be ATM or 50% delta. It is now highly sensitive to the stock price. That increased sensitivity was the visible effect of gamma.

The movement of stocks is driving the value of options by pushing a giant universe of options in and out of the money at all times. The directional players are getting their fix whether its hedging or punting. This creates a robust ecosystem of buyers and sellers who are able to make very specific bets targeting the size and timing stock moves.

Enter Vol Traders

As the directional traders sling option prices around based on their outlooks for stocks, a much smaller segment of traders will notice a relative lack of attention on the other significant driver of an option’s price — it’s implied volatility. The perception of how much a stock will move in the future sets the price of the option today. In fact, it’s the largest unknown in an option price. With continuous bid/ask prices for stocks, a highly liquid interest rate market, and well-estimated dividends the other inputs into listed option prices are trivial.

So this smaller group of professional traders is actually buying and selling levels of a derived value — implied volatility. This is not strange. A stock trader is dealing in implied levels too — forward earnings. They are converting those to multiples to make comparisons of risk/reward across stocks. Option dealers do the same. They compare levels of volatility to find bargains or to sell overpriced perceptions of future volatility.

So in addition to delta and gamma, option pros are focused on vega — the change in an option price due to changes in implied volatility.

A Basic Example of Vega

Vol traders sometimes think in terms of straddles. To be long a straddle is to own the call and put on the same strike. If you own an ATM straddle you are agnostic on direction, you are just rooting for a large move. Straddles, since they are just the sum of a call and put, can be used to bet on implied volatility changing as well.

If a straddle is worth $10.00 and has a vega of $.30 then we can say for every 1 point move in the vol the straddle will change by $.30. So if vol increases 1 point, the straddle will appreciate to $10.30

This should remind you of delta. If the straddle had a delta of 30% then for a $1 increase in the stock the straddle would increase by $.30, also to $10.30. Delta describes how an option responds to the stock while the vega describes how the option responds to the vol.

Vega As An Exposure

If you are a stock trader you will measure your risk in how many dollars you are long or short. This allows you to answer what your p/l is for say a 1% move. Long $1,000,000 worth of stock and it goes up 5% you make $50,000.

We can do the same with vega. If I own 100 of those $10 straddles then I can say I’m long 3,000 vega:

100 x $.30 x 100 = 3,000

              # of straddles x vega per straddle x option multiplier = 3,000


So if volatility increases by 1 point, the straddles increase to $10.30. Since I owned 100 straddles the value of my position goes from $100,000 1 to $103,000 for a net p/l of $3,000.

If vol started at 20% and actually increased 10 points to 30%, the p/l would have been $30,000:

3000 vega x 10 vol points


Vega Influences Everything

When a directional stock trader sizes their position, the volatility of the stock is a key input. So it follows that one of an option trader’s primary concerns is how volatile the implied volatility is. As we saw above, a shift in perceptions of future volatility can lead to significant gains or losses due to vega exposure.

There’s more.

While vega measures a direct exposure, namely the p/l of an option position due strictly to changes in implied vol, it also acts as an indicator that a position has additional sensitivities to implied volatility. Recall that delta and gamma are driven by moneyness (aka how far in or out of the money) a position is.

But moneyness depends on volatility!

If a stock is trading for $50 we might compute that the 1 year $60 strike call which is 20% OTM is 1 standard deviation away for a given vol. Perhaps it has a 15% delta. What if it’s volatility quadruples?

That strike which is $10 away in fixed dollar space is now much closer is standard deviation space. In fact, it’s delta could now be 50%! 2 So the size of the position’s vega indicates the potential for change in the entire portfolio’s Greeks.

An option portfolio’s dynamic properties can lead to very complex exposures quickly as sensitivity to volatility propagates thru every line item in a portfolio. Professionals will use many more types of Greek’s to measure individual sensitivities. How does your delta change as time passes? How does your delta change as implied vol declines?

You can get as nerdy and esoteric as you want in trying to flatten your exposure to every greek. In practice, nobody does this (well maybe the French), but because portfolios have complex dependencies on implied volatility it’s handy to remember that large gross and net vegas point to the possibility that a portfolio’s risk is quite dynamic under the hood.


Next Step: Vol convexity

The importance of vega warrants further discussion. In the next part, I will cover the “gamma of vol” — how vega itself responds to changes in volatility. Just like a directional trader might use option gamma to acquire convexity with respect to the stock price, the option trader is looking to acquire convexity with respect to volatility.

Pro’s call it volga, but in the spirit of Moontower we will build an intuition without calculus. Stay tuned…



Part Of The Solution

Protest. Riots. Justice. Change. It was hard to think about anything else this week. I have a lot of scattered thoughts. I keep fixing to them like stars in a black sky. I admit I cannot seem to find the constellation that connects them so I’ll just list the links that resonated. I’ll follow it with some of my own riffs at the end. I’ve picked up a lot more subscribers recently on the back of my financial posts. I probably don’t have enough goodwill to offend. If sorting my feelings here makes you uncomfortable you can always reach out. I don’t usually do posts like this but it felt a bit off-key to just write one of my typical posts. And of course, there’s always the “unsubscribe” button. I appreciate every reader but this is just a free email from a random middle-aged dude.

Ok, let’s ride.

My Favorite Links From The Week

1) Twitter thread of a fan describing how Dave Chappelle changed everyone in that room that night. 200+ people became part of the solution if they weren’t already. Even a privileged girl in a privileged hat with a privileged mindset. Point is, it doesn’t matter what you thought before. You can always change. (Link)

This Twitter thread pairs perfectly with Chappelle’s suggestions

@pickledmintTips on engaging in conversation with family about the BLM movement. From your local social worker who has dealt with extremely conservative, racist, bigoted, homophobic family members their entire life. A thread with examples. (Link)

2) Bob Seawright’s letter this week was bullet after bullet of insight. While I’ll mention my favorite parts, I encourage you to read the whole thing. (Link)

  • He was a criminal attorney in his younger years. He described himself as “generally conservative, law-and-order guy”. But he writes:I had to conclude that the system was rigged. The police had also determined that the system was rigged, but in a different way, and did what they deemed necessary to get what was, in their view, the proper result.

    I have no doubt that in the vast majority of cases, rough justice was done. But the dishonesty of the proceedings had to have a chilling effect on the people involved. Police, prosecutors, and judges lost sight of the oaths they swore. Defendants lost faith – if they ever had it – that justice was possible. The rule of law was honored only in the breach.

  • Vonnegut gave Seawright’s commencement speech in 1978. Teaser:

    Being stupid and full of myself – in other words, a new college graduate – I completely misunderstood it. At the time, what I heard was him telling us to hate more…


  • MLK on riots:

    Riots are “socially destructive and self-defeating,” the Rev. Dr. Martin Luther King Jr. said during the violent unrest in the 1960s. However, “[i]t is as necessary for me to be as vigorous in condemning the conditions which cause persons to feel that they must engage in riotous activities as it is for me to condemn riots.”

  • One of the best-articulated characterizations of Trump and his supporters:

    President Trump’s inaugural act was a petty and absurd lie about a meaningless fact, the falsehood of which was readily demonstrable…It was all ready-proof that President Trump is manifestly unfit for office…I screenshotted and highlighted what comes next. (Link)

Links That Stood Out To Me

On the insidiousness of racism:

  • Jowanza is a black software developer. The racism he deals with does not leave a smoking crater. I’d describe it as the 21st century, Nextdoor strain of racism. And this dude codes for a living. (Link to my tweet response and his post)
  • Ben Thompson usually writes about the chess game of big tech and media companies. Here he uses his sharp eye to deconstruct how institutionalized racism perpetuates. There’s a “crescent you can’t unsee” in Madison, WI. Read through the end to get to the tradeoffs in social media policies with respect to how they shape public discourse. (Link)

On Kaepernick:

  • First of all, the public can’t trade for a damn. (Link)
  • Malcolm Jenkins’s emotional rebuttal to Drew Brees who tried to die on the kneeling-dishonors-the-flag-hill (to his credit, he cut his losses). Jenkins’ pain, anger, disappointment and appreciation of history stands in very sharp contrast to Brees’ intellectually lazy stance. Jenkins’ pleas reflect skin-in-the-game. (Link)
  • If you watched Last Dance, you will recall that this tweet could have applied to Jordan too. I wouldn’t go so far as to condemn Jordan and Tiger. But the tweet accidentally reminds you how big Kap’s sacrifice actually was. (Link)
  • The flag idolatry arguments always felt a little dog-whistley to me. Let’s try this thought experiment: Kap was playing in SF, which has some of the most progressive gun restrictions. If he kneeled in protest of those un-American laws, would he have been “disrespecting the flag”? What if Kap was white and kneeling against gun laws that were “treading” on him?

    The Declaration of Independence’s “All men are created” comes before the Second Amendment. I mean it says it right there in the name — amendment. It didn’t even make the first draft. The way to honor the flag is by protecting our equal rights. Kap sacrificed his career to keep what our soldiers fought for sacred. Kneeling was never about dishonoring America. And if you think I’m an idiot at least I’m in good company. Check out Bill Burr in the first 60 seconds of this clip. (Link)

  • In a similar vein to my Kaepernick opinion, a buddy of mine wrote of all these protests:

    Please don’t be one of the people who claims that this all shows that liberals or democrats or whoever do not support the “rule of law”. This entire protest is about supporting the rule of law, because nothing is more damaging to “law and order” than law enforcement being above the law and untrustworthy. (emphasis mine)

On police:

  • David Epstein, who I’m a fan of, interviewed his brother who is a lawyer focused on justice reform. The history of the Minneapolis police and their “prone restraint” training makes Floyd’s homicide so much worse. But this interview goes into several embedded features of the police and union institutions that make reform so difficult. Interesting and disturbing. (Link)
  • When Springsteen remembered one of their victims, the NYC cops turned on him. It goes deeper. (Link)
  • The looters and opportunists suck. Not just because of their crimes. Because they provide cover to those who may want to delegitimize the protests. But many of the looters will hopefully face penalties. Many were arrested. Many will have their actions etched in their permanent records. But will we be able to say the same for the cops who were entrusted as agents of the state which is an agent of its people? I’m not talking about the cases where cops were earnestly defending themselves. I’m talking about the cops who confirm suspicions of sadism. Thread of awful videos. (Link)
  • Don’t get me wrong, I also have sympathy for the police. My view is best explained by an unexpected source — the “abolish the police” movement. It’s not what it sounds like. It’s rooted in the recognition that we ask too much of police. They are asked to be the mop for all society’s spills. Spills that we don’t take care of closer to the source. Police are asked to be social workers (anyone living in SF has seen this). They are asked to deal with the mentally ill. That shouldn’t be their job. The “abolish the police” movement is not so much about cutting the supply of police services as much as it’s trying to cut the demand for them. What can we fix upstream of the police? (Link)

On the press:

When I first saw this my head almost exploded. But it turns out this was a turduken of a headline sewed together by the AP to make Trump look like the pure spirit form of himself instead of the one that pretends to be a leader. But no, if you watch the clip he exercised enough restraint somehow to not actually link Floyd to the economy. This is just another piece of clickbait polluting the air and with no recognition of its negative externalities. If you wanted to make Trump look bad, you could just report on him honestly. By exaggerating, you cry wolf. You desensitize people to his nihilism.

Stream of Consciousness

Some of my own unorganized thoughts. Excuse the randomness. Much of it is open-ended.

  • Environments and culture are bigger than the self. The studies of bad behavior in police units with strong unions is both upsetting and unsurprising. Also wouldn’t you expect good cops to become reluctant accomplices in covering up for bad cops? We ask a lot when we ask them to choose between brotherhood and morality because their livelihoods and safety depend on the first. This is more of an indictment of the system than the individuals. But the system also attracts bad actors. Even if the Stanford Prison Experiment never replicated, I’m still scarred from learning about it in my first semester in college.
  • Mobs are scary. This is true in a physical sense. Just see this discussion of riots modeled as a coordination problem (h/t Taylor). But also in the groupthink sense. I’m just as wary of the warm embrace of mob acceptance. Validation without scrutiny usually precedes bonehead ideas.
  • You can be outraged at rioters that are attacking cops as well as the police brutality. It’s possible to hold both these thoughts in your head at the same time. The rioters are capitalizing on a moment when police have lost legitimacy as an institution. Their destruction is a despicable example of collateral damage. But this moment is screaming that the collateral damage of the status quo is far greater. Are you more angry at the rioters who are just idiots being idiots or the “civilized” people who stand for order while perpetuating injustice?

    Check out this graphic.

    It’s definitely too reductionist. In fact, if you find yourself analyzing the output rather than the assumptions you have already bought the premise. But you must also confront the possibility that cursing the looters with more passion than scolding the status quo could mean you have lost any sense of proportion. (H/t Joe for surfacing that graphic from this post).

  • People are more scared of the threat posed to their self-interest. If you are on the right side of the tracks you fear disorder more than injustice. I live in a fancy white neighborhood. You think I wouldn’t be terrified if gangs were plotting to pillage our home Dark Knight Rises style? The rumors on Nextdoor of such plans are just rumors. Be honest. Part of the reason it’s so easy to dismiss them is a sense that the authorities would never let that happen to white neighborhoods with white kids. Feels gross to even say that but until we start playing with our cards face up we won’t make progress.  Meanwhile, black parents live in chronic fear that their sons may be pulled over by a caffeinated cop.
  • Is there a natural rate of racism? Is there a lower bound, like the natural rate of unemployment? Is human nature subject to a ‘law of conservation of conflict’? Does the fear that fuel racism shapeshift another set of group differences from a mere boundary to another “-ism”? Futile thought perhaps. Either way, as my Jewish friend Mike says, if you can’t eradicate the hate, he wants to know where it is so he can stay away. If you think there’s a baseline level of hate how does it change the mitigation strategies? Again, just thinking aloud.
  • White privilege as original sin is an ideological overreach. Self-denial feels like such a closed way to recruit people to your cause. The Catholic church does that. Perhaps they would have been even more successful if they didn’t push that idea. Social questions rarely have answers to such counterfactuals.
  • People are making lists of black-owned businesses to support. Others are countering that this non-merit based patronage is a long-run disservice to black owners. I ask, what is merit anyway? Unless you believe a white person was born endowed with superior ability, you can never escape the question of how the environment shaped ability. And if you cannot escape that, you cannot escape the question of racism. Disentangling this is complicated and since the problem is reflexive I don’t think studies are going to help. Economics has always posed trade-offs between equity and efficiency. In a showdown, whoever gets to define these terms will have won before the debate even starts.
  • If integration and education are the keys to fighting racism, then black business support can be considered a positive externality that is otherwise uncaptured by financial accounting. I could see this making its way into ESG discussions if it hasn’t already. It might even turn out to be a wise move in the narrow commercial sense that we are used to. I’m sure one can find studies of professional women or minority investors being better than white male counterparts. As social science goes you can find any kind of study, but conceptually that result still makes sense. Just consider Nassim Taleb’s argument that you do not want your surgeon to be handsome like they are on TV. All else equal, you’d expect the uglier surgeon to be better since it requires more merit to overcome the bias which may select for that role. In other words, it’s really hard for black people to become hedge fund managers, so when they do you’d expect them to be far more skillful than there more typical counterparts. I always think this when I see undersized NFL players. Pound for pound they are the baddest dudes on the field.
  • If riots and looting are the largest cost to having a moment of real change, I think we would be getting a bargain. I don’t think fixing the system would ever come that cheap. By the way, I really have no idea what fixing the system even means. What’s the bigger hurdle…agreeing there is a problem or having consensus on how to attack it?
  • I get nervous when talking about humans on the group level. I feel much more secure in how I think of individual interactions and relationships. I don’t really understand how to scale those relationships. I’m always hesitant to anonymize the members of a group which inevitably happens when we abstract. But such is the realm of policy. I foresee more misery comparisons and pop ethics trolley problems. I guess Covid prepared us for that.

Finally here’s my list of expressions that should make you brace yourself for idiocy

  • “All Lives Matter”

    A buddy said it best:

    Black Lives Matter is not that hard to understand. If I had a bumper sticker on my car that said “Unborn Lives Matter”, you’d understand that I was against abortions, not that I thought people already born didn’t matter. If I had a sign that said “Save the Whales”, you would understand that I thought whales were under threat. You would not angrily say to me “what about all the other animals?” Black Lives Matter is not in any way a statement that other lives do not matter. “All Lives Matter” is now used by racists and various other jerks primarily. Don’t do this.

  • “Not all cops are bad”

    While this is true this is a misdirection. It’s not the relevant question. That statement would be true if even half the cops were bad. For reference, defect rates in manufacturing are measured in PPM. Parts per million! We have high standards for widgets.

    What defect tolerance will we accept for our armed enforcers?

  • “Not all black people are bad”

    Um, this isn’t 1920. Racism is only that blatant behind closed doors. The problem of racism is when it’s been embedded in our institutions implicitly.

  • “Virtue signaling blah blah blah”

    Worrying about virtue-signaling seems like a problem only privileged people worry about. Who else worries about this? I think the concern stems from the zero-sumness of status. People who are concerned about it are feeling the loss of relative status. It costs little to say woke things and confer a benefit to yourself. So naturally, there will be some imposters looking for a status boost (NFL, cough). If you are concerned about this you are being kinda narrow. I’d guess you might also be kinda miserable. Lighten up. It seems like a petty thing to worry about.

    Actually, let me conjure a stronger case against this worry. Bear with me, it’s a bit recursive.

    If you see virtue-signaling wherever you look, this is worse than an even neutral stance. Your attitude can be contagious. Onlookers who now know about virtue-signaling suspect everyone is virtue-signaling which works to delegitimize the cause people are allegedly signaling about. So indirectly, by worrying about virtue-signaling you become the intellectual cousin of a rioter who undermines the protests. Now onlookers who are motivated against protests start using claims of virtue-signaling, warranted or not, to detract from the do-gooding.

    If you want to be part of what Chappelle calls the solution, stop worrying about virtue-signaling. Just focus on what can do to help. Actions > words.

Speaking of actions, I know I’m under-educated in this area. I rambled the thoughts I had this week. It just felt like the thing to write down. If not for you, then for me. You could probably live a thousand scholars’ lives and still be grasping for answers. But you don’t have that luxury anyway. You get 85 laps around the sun give or take. You are going to need to make decisions without all the information. If sharing what I saw this week provoked thought one way or another then I hope we both inched a little closer to our better selves.

If you are interested,2 organizations I’m a fan of both empower black or underprivileged through education in STEM and business respectively.

  1. The Hidden Genius Project (Link)
  2. Build.org (Link)

They can take money or time.

Lessons From The .50 Delta Option

I was chatting with a quant friend who was bouncing an options idea off me. In the course of the conversation, he was surprised I did not assume the .50 delta option was the ATM (at-the-money) option. My friend is much smarter than me on finance stuff but options aren’t his native professional language. So if this idea had him tripped up I realized I had a reason to write a post.

If I do this correctly you will gain a better understanding of:

  1. Delta as a hedge ratio, not a probability
  2. How volatility affects the mean, median, and mode of these returns
  3. The relationship of arithmetic to geometric returns in option theory
  4. What these distributions mean for the value of popular option structures

Some housecleaning:

  • Option math is known for being calculus heavy. If you are a layperson, you are in luck, this tour guide likes to stick to the roads he knows. You won’t find complex equations here. If you are a quant, I suspect you can still benefit from an intuitive approach.
  • We are going to ignore the cost of carry (interests and dividends). While crucial to actual implementation it is just distracting to the intuition.

Delta Is A Hedge Ratio Not a Probability

Often delta and “probability of finishing ITM (in-the-money)” are indistinguishable. But they are not the same thing. The fact that they are not equivalent holds many insights.

Before we go there, let us revisit the most basic definition of delta.

Option delta is the change in option price per $1 change in the underlying

Consider the following example:

Stock is trading for $1. It’s a biotech and tomorrow there is a ruling:

    • 90% of the time the stock goes to zero
    • 10% of the time the stock goes to $10

First take note, the stock is correctly priced at $1 based on expected value (.90 x $0 + .10 x $10). So here are my questions.

  • What is the $5 call worth?

Back to the expected value:

    • 90% of the time the call expires worthless.
    • 10% of the time the call is worth $5

.9 x $0 + .10 x $5 = $.50

The call is worth $.50

  • Now, what is the delta of the $5 call?

$5 strike call =$.50

Delta = (change in option price) / (change in stock price)

    • In the down case, the call goes from $.50 to zero as the stock goes from $1 to zero.

Delta = $.50 / $1.00 = .50

    • In the up case, the call goes from $.50 to $5 while the stock goes from $1 to $10

Delta = $4.50 / $9.00 = .50

The call has a .50 delta

Using The Delta As a Hedge Ratio

Let’s suppose you sell the $5 call to a punter for $.50 and to hedge you buy 50 shares of stock. Each option contract corresponds to a 100 share deliverable.

  • Down scenario P/L:

Short Call P/L = $.50 x 100 = $50

Long Stock P/L = -$1.00 x 50 = -$50

Total P/L = $0

  • Up scenario P/L:

Short Call P/L = -$4.50 x 100 = -$450

Long Stock P/L = $9.00 x 50 = $450

Total P/L = $0

Eureka, it works! If you hedge your option position on a .50 delta your p/l in both cases is zero.

But if you recall, the probability of the $5 call finishing in the money was just 10%. It’s worth restating. In this binary example, the 400% OTM call has a 50% delta despite only having a 10% chance of finishing in the money.

I’ll leave it to you to repeat this example with a balanced distribution. Say a $5 stock that is equally likely to go to zero or $10. You will find the 50% delta call turns out to be ATM. Something you are used to seeing.

The key observation turns out to be:

The more positively skewed the distribution, the further OTM the 50% call will be. If a stock is able to go up 1000% and you sell a 400% OTM call on it you are going to need far more than a token amount of long stock to hedge.

The more positively skewed a distribution, the more the hedge ratio diverges from the “probability of finishing ITM”.


The Effect of Pure Volatility

Not to lead the witness too much, but an obvious feature of the binary example is the biotech stock is very volatile. That’s not a technical definition but a common-sense observation. “This thing is gonna move 100% or 900%!”.

Without math, consider how volatility alone affects a stock’s returns. If the stock price remains unchanged because we do not vary the expected value but instead inject more volatility what is happening?

  1. We are increasing the upside of possible payoffs.

In the biotech example, more volatility can mean the upside is not $10 but $20. 

  1. The counterbalance to the greater upside is a lower probability of rallying

If the stock is still worth $1 then the probability of the up scenario has just halved to 5% (95% x $0 + 5% * $20 = $1, the current price).

If we inject volatility into a price that is bounded by zero, the probability of the stock going down is necessarily increasing.

So volatility alone alters the shape of a stock’s distribution if you keep the stock price unchanged.

Let’s see how this works as we move from binary distributions to more common continuous scenarios.

How Volatility Affects Continuous Distributions

Let’s start with a simulation of a subjectively volatile stock.


  • The stock is $50
  • The annual standard deviation is 80%.

A basic presumption of option models is that returns are normally distributed but this leads to a lognormal distribution of stock prices 1.

Running the simulation:

  • I took a return chosen from a normal distribution with a mean of 0 1 and standard deviation of .80
  • I then ran that return through a simple log process to simulate continuous compounding. 2

S (T1) = S (T0) x e(random generated return)

  • I ran this 10,000 times.

Before we get to the chart note some key observations:

  • You get a positively skewed lognormal distribution bounded by zero. This is expected.
  • The median terminal stock price is $50 corresponding to a median return (aka the geometric mean) close to zero as expected.
  • The mean stock price is $68. corresponding to a mean return of 38%.
  • The modal stock price is $20 corresponding to a modal return of -60%.

Simulation Vs Theory

Let’s compare the simulation to what option theory predicts.

  • Median

As we stated earlier median expected return is 0 from theory and this lines up with the simulation.

  • Mode

The mode in the simulation lines up reasonably 3 with option theory which expects the mode to be:

S x e2 where σ is volatility

Note how volatility pulls your most likely outcomes lower. In this case, the most likely landing spot for the stock is $20 corresponding to a total return of -60%!

Average Arithmetic Returns

Look at the chart again. Note how the average arithmetic mean stock price is $68.89 in this sample. If the median return is 0, the positively skewed distribution has a mean arithmetic return of +37.8%! We don’t want to get excited about this since as investors we care about geometric returns which are zero here, but this 38% OTM strike is still very interesting.

It turns out it corresponds to the strike of the .50 delta option!

The equation for that strike:

S x e2/2)

That strike corresponds to 68.86 which is very close to the simulation result of 68.89.

This is the call that you must hedge with 50% of the underlyer.

The formula will look familiar if you remember that the geometric mean is pulled down from the arithmetic mean in proportion to the variance.

[This strike is special for option traders. This is the strike that has the maximum vega and gamma on the option surface. As implied vol changes the location of this strike can change, but it represents the maximum vega any strike can have for a given spot price. I’ll leave it to the reader to see how this relates to strategies that are convex in vol such as ratio’d vega neutral butterflies.]

Interesting Observations About Options

  • Even in a continuous distribution, the higher the volatility, the more positively skewed the distribution, the further OTM the 50d call strike lives.
  • The cheapest straddle will occur at the median outcome or the ATM4 strike. 
  • The most expensive butterfly will have its “body” near the theoretical mode. This makes sense since a butterfly which is just a spread of 2 vertical spreads is a pure bet on the distribution. If you chart the price of all the butterflies equidistantly across strikes you will have drawn the probability density function implied by the options market!

Enter Black Scholes

In a positively skewed distribution, the probability of finishing in the money for a call was lower than the delta. In the binary example where the stock had only a 10% chance of being worth $10, the probability of the $5 call was much lower than the delta of the $5 call.

What does this have to do with Black Scholes?

In Black Scholes:

  • The term for delta is N(d1).
  • The term for the probability of finishing in the money is N(d2).

What’s the relationship between d2 and d1?

  • d2 = d1 – σ√t

The math defines the relationship we figured out intuitively:

The higher the volatility 5 the more delta and probability will diverge!

Delta and probability are only similar when an option is near expiration or when it’s vol is “low”.

From Theory to the Real World

Markets compensate for Black Schole’s lognormal assumptions by implying a volatility skew. While a biotech stock might have a positive skew on steroids, a typical stock’s distribution looks more normal than positive. By pumping up the implied volatility of the downside puts and lowering the implied vols on the upside calls, the market:

  • Increases the value of all the call spreads.
  • Shifts the implied mode rightward.
  • Shifts the 50d call closer to ATM. Actually, it lowers all call deltas and raises all put deltas. This is important since deltas are the hedge ratios.
  • Fattens the left tail relative to a positive distribution and at least in index options even more than a normal distribution.

These adjustments reconcile the desirability of a simple, easy to compute model like Black Scholes which uses lognormal distributions with empirically consistent asset distributions that we observe in markets.



The next time you hear delta used as probability, remember this is only really useful when options are near-dated. Since most option activity occurs in the front end of the term structure the assumption is typically harmless.

Taking the time to understand why they differ turns out to be a great exercise in building an intuition of investment returns and their distributions. 



The “No Easy Trades” Principle

My “No Easy Trades” Principle

A recurring theme here is the wisdom of markets. If you find yourself constantly disagreeing with prices visible to anyone with a smartphone you probably get invited to lots of poker games. This doesn’t mean markets are always right. It just means nobody can claim there is easy money in slanging investments around. It means your guess is not consistently better than the market’s. I highlight that distinction because it seems to be lost on efficient market detractors.

So my definition of markets being smart is not academic. It’s actually a survival heuristic — there are no easy trades. Today I will discuss 3 things.

1. What this heuristic looks like in the options market
2. The puzzle I stumbled into when applying this logic to stocks.
3. How the puzzle got cleared up.

Before I mosey into this we need to agree on a stylized fact.

Investment returns are driven by:

  1. Actual earnings (returned to shareholders or re-invested)
  2. Expectations (risk discounted of course)

So a stock’s return is driven by actual earnings (I call that the “realized”) and changes in the multiple (the forward-looking growth prospects is the “implied”). Same with real estate. If the cap rate is zero in one location and 10% in another it’s usually investors factoring in different growth rates. The actual rent is the “realized”.

As time passes, the market will pay attention to the fundamentals on the ground to revise the growth rates. Is this investment cash-flowing more or less than expected? So the “realized” earnings interact with the expected or “implied future earnings”.

Option Returns Are No Different

First, some reminders about options:

  • Volatility is the standard deviation of a stock’s return. The amount of volatility that transpires until an option expires is a large driver of an option’s value.
  • Nobody knows how much volatility a stock will experience during an option’s holding period.
  • We know the other inputs into an option price. Since the other inputs are known, we say the price of an option implies a volatility.

For somebody managing a hedged options book, the p/l is driven by:

1. The realized volatility of the underlying

If the market bounces around 2% a day and you purchased the option implying 1% per day you will “capture” p/l in excess of the option’s time decay. (The p/l due to “gamma” exceeds the losses due to “theta”)

2. The implied volatility baked into the option

If the market suddenly believes the future will be more volatile, it will bid up option prices. This will lead to profits for someone who owns options. (The sensitivity of the option’s price to the market’s vote on volatility is known as “vega”)

Option Markets Are Smart

Without getting into the nature of realized and implied volatility it’s sufficient to say that they are mean-reverting. If a stock becomes more volatile, say moving 2% per when a longer history pegs it as a 1%-per-day type stock the options prices will increase to price the extra volatility. But as the realized day-to-day volatility reaches extreme levels, say 5% per day, something we may have seen in March, the option implied volatility will likely not rise by as much (I’m hand-waving term structure and more, it’s not necessary to the point). Why does the implied volatility not keep up?

Expectations. The market understands the shock is temporary. So there is no easy trade. People that want to sell or short expensive options will be disappointed to find that they will experience negative gamma p/l during the holding period because the realized volatility will exceed the implied volatility they had shorted.

And option longs who may be enjoying the positive gamma p/l (or “carry”) know that they have bought a high implied volatility that is eventually going to recede.

When option volatilities get very low the inverse dynamic occurs. There are period when the SP500 will realize less than 30 bps a day but the market never sells you options at such a low implied volatility.

It’s simple. The market will not let you have a position that simultaneously:

  1. Carries well
  2. And has a tailwind in the direction of the mean-reversion

Classic dilemma. You enjoy one while fighting the other. Market implied parameters reflect expectations. But expectations do not vary as widely as what actually happens because volatility is a mean-reverting quantity. Net result: no easy trades.

The Puzzle: Is The Stock Market Smart?

I presume the stock market is smart and must follow a similar principle of “no easy trades”. By analogy, I mapped implied volatility to P/E and realized volatility to actual earnings. So if profits (earnings) were high, I’d expect forward P/E ratios to discount the elevated earnings. Otherwise, it would seem like an easy trade to take the other side of a market that extrapolated unusually high earnings into the future. Just because LeBron drops 50 points one night does mean the “point futures” market is “49 bid” for the next game.

Now earning themselves are not mean-reverting. I wasn’t quite naive enough to apply my cargo-cult thinking to that metric. Enter fund manager John Hussman. He argued that profit-margins, which have been extremely high, are both mean-reverting AND being extrapolated into the future via fat multiples.

This was to be the rare set-up of an easy trade — a bear case with a double tailwind. Luckily I didn’t trade in my PA based on this. For all the $20 bills on the ground I miss out on, my disbelief in their existence has also saved me from being short stocks for the past 5 years.

So what’s the deal with the stock market? Can it possibly be extrapolating mean-reverting metrics with straight lines?

Carry On, Nothing To See Here

Well, it turns out there is no puzzle. Profit margins aren’t a metric that matters. It’s return-on-equity that matters. Get all the details from @jesse_livermore in his paper Profit Margins Don’t Matter (Link with my highlights). It’s several years old but the thinking that permeates through this paper is better than 99% of finance stuff you might read today. And if you are weak on accounting like I am you’ll want to bookmark this one.

Extra observations on the options vs stocks analogy:

  • When an option has lots of time until expiration the implied expectations dominate its price. Conversely, as an option approaches expiration, the realized volatility will dominate. This manifests as the option’s vega decreasing while its theta and gamma increase.
  • Unlike options which have fixed expirations, real estate and stocks are more like perpetuities making them highly sensitive to expectations.


Moontower Money Wiki (Link)

Latest updates:

  • Risk Is Unavoidable, Let’s Get To The Good News (Link)
  • TANSTAFL (Link)

Preserving Habits From Covid

Last week I mentioned how the “great pause” has led many to re-prioritize. More sunsets, less commuting. Probably wishful thinking. As things open up you will slip back into old patterns.

Consider Zack Kanter’s story about “the mechanic” capturing the essence of returning from vacation (emphasis mine):

My moments near the ocean feel like they will stretch on forever; in that instant, I cannot imagine feeling any other way. And I find that it is this way with all epiphanies – coming to some realization during a long talk with a friend, reading a particularly insightful book, marveling at the clarity of mind brought by a just-organized workspace. Yet the moments are always fleeting; we quickly return to our pre-enlightened state within minutes, or hours, or days. (Link)

Well, this is no time to be defeatist. We are going to need all the positivity we can muster. If you had a moment of clarity in the quiet, it was a privilege. The feelings of discovery or rediscovery are fleeting. The way to give your realizations permanence is to change their forms.

In mythology, the spirit sheds the body to find immortality. Here you must do the opposite. Maintaining the peace of clarity means transforming it from a feeling to physical actions. It’s not your mind that perpetuates the lessons from this “great pause”. It’s your habits. Be deliberate about how you will preserve what you found. Establish a new muscle memory. Turn the spirit into flesh.

How do you do this? Kanter has an answer:

And so I try to think in terms of process – that is, a specific action repeated on a regular basis, an improvement that stands the test of time. Try reframing one of your projects as a process: get in shape becomes go to yoga every day, declutter becomes put away one thing every time you enter the room, read more books becomes read for 15 minutes each morning. The truth is that all of your thoughts, wishes, and goals amount to nothing if they do not make the leap into your daily life.

The distractions are roaring back. If you go back to all of your old ways as the world re-opens make sure it was your active choice. These chances are rare.

After reading that “mechanic” post by Zack Kanter I read most of his blog.

Some of my favorites:

  • Why Your Kid Hates School (Link)
  • 10 Killer Negotiating Tactics [or, how I got $125,000 for nothing] (Link)
  • 8 Simple Philosophies That Changed My Life (Link). #1, #2, and #5 are in my top 5 as well. #6 is very wise and I think the most underappreciated.
  • 5 Steps To Creating A Product (Link). This is part of his “How I Make Money” series and this has really interesting business info in it.
  • What I’ve Learned About Love (Link). This short post has a beautiful reduction: “I have since thrown away my list and replaced it with a simple philosophy. Find someone who you feel lucky to be with, and who feels lucky to be with you. Someone who you admire, someone who you want to become more like.”

It’s a dope blog. Happy yakshaving.

Felder Makes It Count

For much of the past year my guitar lessons have focused on solos. My instructor considers where I am then assigns challenging but makeable solos that will “unlock” a new technique or concept. I like learning about the background of the songs and guitarists whose solo I’m studying. I’m currently learning the solo for One Of These Nights by the Eagles. With disco being popular, the Eagles took a stab at a song in that style.

From Wikipedia:

“We wanted to get away from the ballad syndrome with One of These Nights…While they were recording the album in Miami, the band also shared a studio with the Bee Gees, and according to Henley, the “four-on-the-floor” bass-drum pattern is a nod to disco.”

The solo, recorded separately in LA, is a sharp departure from the rest of the song’s vibe. The solo is “composed of blues-based licks and sustained string bends using an unusually meaty distortion tone”

Doug Frey said “With Don Felder in the band now, we can really rock…[we] wanted One Of These Nights to have a lot of teeth, a lot of bite—a nasty track with pretty vocals.”

My teacher, Patrick, is friends with Felder. He added some more color. At this time the Eagles were writing their 4th album and Felder just joined the band. They were already very popular in the US (they wouldn’t reach international stardom until Felder writes Hotel California a couple of years later). Felder comes into the studio and his first assignment is to lay down a solo for One Of These Nights. The solo has a tight, highly compressed tone. As I am trying to learn it it’s very clear as the technique requires choking off the sustain on the notes to mimic the staccato attack. It’s strangely aggressive given the song’s style. Patrick explained how he could hear the nervous energy that drove it.

It turns out it was the first take. It could have been a brainstorm. But context is everything. To the band, a first take counts for nothing but to Felder, the new guy stepping up to the plate, it counted for everything. He had something to prove. The whole “you never get a second chance to make a first impression” type thing.

The mindset of something mattering to you if it doesn’t “matter” is powerful. In Last Dance, someone argues that, even more than innate ability, Jordan’s greatest gift was his ability to be present. It made regular-season games matter. If you can fabricate meaning when there is none you have a superpower. It’s an answer to nihilism. You naturally channel Eminem’s “Lose Yourself” as you walk out to mow the lawn.

So that first Felder take was the final take you hear on the track. Sometimes nobody cares about a moment but to you it’s everything. But the meaning you give it can turn out to matter to everyone.

Fwiw, I was never a huge Eagles fan but the History Of The Eagles doc on Netflix is outstanding. Although, I hear the contentious parts are just one side of the story…

WFH: Deus Ex Machina

Money is an important driver of what jobs people take. Especially at the level where basic needs are at stake. But at some point, flexibility in location, hours, and benefits gain relative importance. The more negotiable the mix the better chance we have of creating sustainable work situations for people. Sustainable means less burn-out, less disability, less dissatisfaction, and more productivity.

The growth of remote work shades in a fuller menu of points along the efficient job frontier. It creates more shots at sustainability. You can choose to work for less cash if it means a better overall life fit. (I know of a few people, moms to be precise, who were thrilled when employers allowed them to work 4 days a week for a 20% pay cut).

Why Is Sustainability So Important?

When I introduced the Moontower Retirement Model, I mentioned “how destructive I think the whole vision of retirement is as portrayed by Charles Schwab commercials. The fact that it takes a moment to figure out if it’s a financial commercial or a Viagra ad is enough of hint that drugs are being sold in both cases.” The entire notion of retirement is unsustainable.

The average American’s savings are inadequate to even cover an emergency. Forget having enough savings and social security to survive with dignity from 65 to 85 or 90. The presumption that investment returns will make up the shortfall even if everyone invested is fragile at best and quite likely nonsense.

The classic idea of retirement has outlived its usefulness. It is a vestige of a bygone era and was targeted to people who did back-breaking work. The cost of this charade is staggering. Underfunded pensions even after a 10-year bull market. Politicians needing to kick all cans lest they be forced to do arithmetic that doesn’t work in plain view. Too many lonely, poor senior citizens.

What Is The New Retirement Look Like?

More working years. But of a different type. Working years that don’t just feel like a thing to get-over-with. The future of work has the chance to be more sustainable. The subject is vast, beyond the scope of this post. But an emerging efficient frontier trade-off between salary and location offers a promise of better-centered lives. We should agree that matching ourselves to our environments is a public good. A sustainable balance means we can work more years. A double bonus. We save for more years and withdraw for fewer years. It is the only viable solution to the pension crisis.

If remote work means more sustainable working lives then WFH will be the pension crisis’ deus ex machina. And that’s a bigger cause for hope than the short-run sprint of getting paid SF wages while Zooming from a lakeside cabin.

To learn more:

  • I’ve summarized the roots of the pension crisis as told by Charley Ellis. (Link)
  • Once Facebook tells you how much they’d pay you if relocate to Boulder, Asheville, Nashville, Summerlin, or wherever you’d like to be, check Atmos to see what you can rent or build. Find your own efficient frontier. (Link)
  • Matt Mullenweg, founder of WordPress, explains Distributed Work’s 5 Levels of Autonomy. What does it mean to jump from remote to remote-first? How about from asynchronous to autonomy? (Link)

For remote-work to truly sustain us, we should, when practical, aspire to the pinnacle of the pyramid — autonomy. Daniel Pink identifies autonomy as 1 of the 3 pillars of human motivation (the other 2 are mastery and purpose). If we can grease the rails of motivation maybe we can scrap the retirement parties that in hindsight turn out to be death sentences.

Moontower Money Wiki Update

I’ve completed the section Evergreen Beliefs That Work Together. It has 4 parts:

  1. The Gift Of Market Efficiency
  2. Investing Is A “Loser’s Game”
  3. Time And Human Capital
  4. Towards A Prescription

While the wiki is ultimately about investing your savings, this particular section goes nicely with the topic of today’s letter which is really about a chance to live our lives better by maximizing the returns to our human capital not our financial capital.

Check the wiki updates. (Link)

WFH: Be Excited Without Being A Sucker

Last week I riffed on geo-arbitrage. Twitter, Visa, Square, Spotify, Alphabet are all pushing their chips in on remote work. Lots of people are excited about a remote work future. Ramp Capital’s post The Death of Cities lists data points suggesting the TAM for remote work is a wide blue ocean. Less than 5% currently WFH but 80% want to. (Link)

I’m not going to make predictions. My understanding of remote work is a mix of hearsay and personal impression. So that’s what you’re getting this week. Opinions and a semi-rant in The Money Angle.

First, my take on remote work in advice format: Be excited without being a sucker.

Don’t Be Pollyannish About Remote Work

  • Sahil Lavingia, founder of Gumroad, tweets: Everyone loves remote work until they realize 7 billion people will soon be competing for the job they have.
  • If you choose to work remotely somewhere especially somewhere remote, you need to appreciate its full costs. This Wall Street Playboys post was terrific when it was published pre-covid. Now it’s a must-read. One of the reasons why companies are allowing people to work remotely is so they can’t move, get paid less and they know they are stuck and can’t do much about it! I will add that this is valid not just for remote workers but for anyone who chooses to work for a company that’s far away from the center of their industry. The I-banker in Denver has limited opportunities if he loses his job. Don’t think his boss isn’t aware of that. (Link)
  • Zuckerburg nixed the pure geo-arb. The SF salary requires you live in the Bay. Byrne Hobart explains Facebook plans to adjust salaries based on cost of living. He also thinks the effect on expensive cities to be muted. Superstar cities will be less affected since many are dual income and it pays to be close to the office. (Link)
  • Working remotely can also be awful. I have a relative with a bird’s eye seat in a major CRE brokerage. One of his clients is a Fortune 50 company with a WFH culture. He describes it as “truly backwards. The culture causes bureaucracy and weird politicking. You have people trying to assert their domain virtually and put as many traps and stops around their domain as possible.”

So working from home isn’t just work-without-pants. It has its share of downsides. It’s crucial to be aware of them and how the negatives compound over time by compromising your negotiating position and limiting your options.

But if you can be honest about the negatives you deserve to be honest about the positives. Not commuting, living where you want. All great. These are the details of something even greater which excites me about remote-work.

Why I’m Excited About The Impact of Remote-Work

I’m excited about choice and its downstream effects. Geo-arbitrage is the wrong model for how to think about an explosion in remote work. Sure in the near-term there might be low-hanging geo-arbs. But arbs never persist. Hobart explained that Facebook is a price-setter. As a large and growing employer their behavior leads. There’s no economic basis for employers to allow the employees to capture all the surplus in a geo-arb.

Instead as Hobart wrote:

tech workers will be teleported back about half a century, to a time when your standard of living was the same whether you lived in the Midwest or California, but you could choose CA because the weather was better.

Instead of geo-arb, I recommend thinking of the new world as an efficient frontier of combinations of job and location. Make $150k in SF or $100k in Raleigh. There’s no magical arbitrage point available beyond the envelope of the frontier but there are many more points lying on the efficient curve. When many of you were designing your life you used to feel like there were just a few choices. NYC, SF, DC, Boston. Maybe Austin. 5 cities. Now you have 50 states.

Even if this was a choice before, it might have been harder to find. The growth of WFH will lead to continued innovation in WFH practices to reduce the frictions. The experience will improve and that will feedback into even larger remote work menus. The more granular we can make location/comp tradeoffs the better.

Covid accelerated the growth of WFH. But more importantly, it accelerated our understanding of what it can mean.

WFH Is Not Just About Preferences. It’s About Priorities.

Covid has been a “great pause” (at least for office workers). You rediscover omitted joys. You redefine what is and isn’t essential. A moment to catch the sunset. The stillness where you notice the pebbles in your shoe. Their all-in costs are suddenly more legible.

Many people have created new habits they want to preserve (Yinh and I want to be less scheduled when “normalcy” returns). We all have a golden opportunity to affirm our priorities. It won’t be easy. During this timeout, your conscious mind decided you don’t want to slide back into all your old patterns. But muscle memory is strong like bull. You can’t re-program by words alone. It will take action. Turns out there is a big one available.

Where Do You Need To Be?

By disentangling work from location, we (are forced?) get to make choices that we felt were made for us. If I want to do X, I had to live here. Given the chance to be remote, you may suddenly find that simply maintaining one of these new-during-Covid habits is like buying a fern. It’s a half-measure at best. What you really want is a whole new scenery. Aligned with the values that you finally had a moment to reflect on.

Your actual desires are more apparent with the fog of FOMO lifted. Trying to decide if you want to build a pool when it’s 90 degrees out is not a good way to make decisions. Don’t waste this chance to think clearly.

When we are in the environment we want to be in, whether it’s in urban jungles or just jungles, we can live in closer accordance to what we need. As you’ll see this is much more than a personal victory…

Deus Ex Machina

This not a reference to that movie with the hot droid. It’s a reference to the meaning of that strange Latin phrase. From Google’s interception of Wikipedia, deus ex machina is a “plot device whereby a seemingly unsolvable problem in a story is suddenly and abruptly resolved by an unexpected and unlikely occurrence.”

In this week’s Money Angle, find out why WFH can be the deus ex machina to a wider American problem. (Link)

Origin of the Pension Crisis

Investor Charley Ellis is deeply concerned about pensions being underfunded as we approach peak boomer retirement years. He discussed it with Ted Seides on the Capital Allocators podcast which I summarize in full here.

The roots of our pension crisis can be traced back to 19th-century European rail workers! Here’s a summary of the problem, how we got here, and what to do about it.

The Pension Crisis

Scope of the Problem

Public pension plans are impossibly underfunded

If you look at what are the biggest problems we as a nation have in the investments world, it’s pensions or retirement security. You can see it easily in the state and city funds that are seriously underfunded. They need 7.5% rate of return which they’re not going to get because they’ve got 25% in 2.5-3% bonds. They’re just not going to get it.

Households are underfunded

If you look at individuals, half the population does not have a retirement plan. For those that do 401k is increasingly dominant, taking over from defined benefit system. The average person approaching age 63.5 which is the retirement age in this country is thinking:

“I’ve got 165,000 smackers in my account. Why my wife and I are going to Florida to play some golf, some tennis, have some fun. We’re gonna have great years. We’ve earned it. It’s been a long long working run, but we’ve earned it it’s going to work out just fine.”


Anybody with any knowledge about investing knows right away — $165,000 if you take money out, from 63 years old to 85 or 90 is not enough. You’re not going to have anywhere near enough per year, cobbled together with social security to make anything like a decent connection.

Something over 65% of your life time health expenses are spent in your life six months. Well, that’s where half the bank for personal bankruptcies come from all kinds of trauma that goes with that as well assisted living expensive and dementia. So we’re going to have a real problem with old age, retirement security.

Political nightmare

So what are people gonna say?

“God damn it. I worked hard all my life I played by the game rules as everybody laid them out. And I was supposed to be able to retire at a decent age and enjoy retirement. That’s part of the deal.”

But the answer they will get back?

“Sorry, but nobody else understands that to be the part of the deal. And you’re on your own.”

So you will have a giant generation that is angry, focused, and motivated to do something about this false promise.

If you think we’ve had divisive politics in the past, imagine what it would be if you had millions of people and their relatives all saying “It isn’t fair. It isn’t right. These guys got screwed.” I think we’re going to have a terrible societal problem, political problem.

How Did We Get Here?

The retirement problem is rooted in an era of different needs and circumstances.

History of the retirement age

  • Age 65 came from Social security which dates back to 1935,

which came from:

  • Railroad Retirement act in 1923,

and even before that:

  • Churchill and Chamberlain jointly put forward in the United Kingdom retirement at 70, but people thought that was unfair because the Germans used 65.

And here’s where we get to the root…

  • German’s retirement age dates back to early 1880s

Baron Von Bismark tried to unify the German municipalities via technology namely the telegraph and the railroads. The telegraph combined with the post office allowed instantaneous communication anywhere in Germany.

We’re going to bring coal and iron ore from the rural and other areas to where the steel mills are and we’re going to build steel mills and have tremendous industry. And then railroads are going to be able to bring people from the cities out to the countryside for weekends, vacations  can be normal, and we will bring from the countryside, fresh fruit, fresh vegetables, all kinds of wonderful things that for people to eat, it’s going to make everything terrific. That’s great.

But where are you going to get the workers to work on the railroad?

Offer lifetime employment.

You get them to come out of the forest because they can get lifetime employment. That’s terrific. What do you call that? That’s guaranteed. This is a commitment. It’s the honor of Germany. Okay. Let’s go.

So what happened?

Well after a couple of years there were accidents on the railroads. Trains ran into each other, people were killed. Public outrage and scrutiny.

What’s going on?

Well, let’s send a study group and find out what the heck is going with these accidents. Well, we found out what the answer is in the work. Laying tiles, lifting heavy ties, brailles, shoveling coal, all kinds of heavy work. They’re saying to the older guys in their late 50s and 60s, your too old for this kind of work. You take the easy job. You’ll be in charge of the switches.

Then what happened?

So the switches are being manned by guys in their early 60s. A beautiful summer’s day and no trains coming in for the next couple of hours, why not take a little nap? And they’re just taking a nap, forget to wake up, and the accident happened. 

The solution?

Guarantees for life. Pay them not to work. To be cost effective find the min-max where it costs not too much to solve most of the problem. And the answer was 65. Most people don’t live to 65 in those days in Germany, but those who do are really doddering, so they will only last for another couple years after 65 anyway.

An obsolete model

We have inherited and retained a retirement model that is a poor fit for our post-industrial circumstances.

    • People live longer now. The ratio of non-working to working years has increased.
    • People are able to work longer as manual labor’s share of the economy has declined.

Dealing with the Crisis

Extend your savings

  • Take social security later…instead of 62 if you wait until 70.5 you make 76% more inflation-protected for the rest of your life. If you wait, you have fewer years in retirement, so they’re willing to give you a larger amount.
  • Continue funding your 401k in your 60s. These are the easiest years to save money. So you can ramp up your savings, dump it into the 401k as fast as you could. (also there are catch-up allowances)

Do all of these things and your chances of being in serious financial trouble in retirement go from awful to not too bad. So if we act soon, we could make a big, big difference in what could otherwise be one of the worst problems our society has ever faced.

Why has this been so challenging to solve?

The big problem is nobody’s paying attention to it. It’s too late. Congress is dealing with politically urgent issues. We need to agree to raise the retirement age to 70 but it’s easy to say that when you are not a ditch digger or coal miner.

Trying Too Hard

Excerpts from Dean Williams speech: Trying Too Hard

Effort to output in investing is weakly linked compared to other endeavors

“We probably are trying too hard at what we do. More than that, no matter how hard we try, we may not be as important to the results as we’d like to think we are.”

Worthless predictions

“One of the most consuming uses of our time, in fact, has been accumulating information to help us make forecasts of all those things we think we have to predict. Where’s the evidence that it works? I’ve been looking for it. Really…The
consolation prize is pretty consoling, actually. It’s that you can be a successful investor without being a perpetual forcaster.”


“Confidence in a forecast rises with the amount of information that goes into it. But the accuracy of the forecast stays the same. And when it comes to forecasting—as opposed to doing something—a lot of expertise is no better than a little expertise. And may even be worse.”

Related: Horse bettor example

Adam Robinson on the diminishing returns of data. Confirmation bias increases your confidence without increasing your accuracy

    • Study of horse handicappers found that the accuracy of their predictions did not improve from the original 5 variables they selected from a large menu of data. As they were given more variables there confidence went up (confirmation bias effect) although their accuracy did not!
    • In addition, the handicappers with only 5 variables were well-calibrated. They were close to 2x better than chance at predicting winner 20% vs 10% and they estimated their confidence as such. When they were given more variables their accuracy remained 20% but confidence grew to 30%!

Gather the right type of info — namely how to measure value (Me: this is how I trade)

We have security analysts. We get research reports from brokers. We get forecasts about the economy, interest rates, the stock market. We process that information and act on the basis of it. For all of that to make any sense, we all have to believe we can generate information which is unknown to the market as a whole. There is an approach which is simpler and probably stands a better chance of working. Spend your time measuring value instead of generating information. Don’t forecast. Buy what is cheap today. Let other people deal with the odds against predicting the future.

Sources of edge

“There are two ways we can try to gain an edge over the market. The one that most of us choose is to try to generate superior information. To know more than anyone else. The other choice is to be better at measuring value than others and not to care very much about what other investors think they know. To hold cheaper securities by today’s standards and to let the future speak for itself.”

Growth describes a phase not a category of company

“It is generally recognized that growth stocks produce a superior risk-adjusted rate of return. However, this is only true for stocks that are expected to grow in the future, and correlations between past growth and future growth are low”. There is no such thing as a growth stock. Only passing phases of growth in almost every company’s life. Phases whose beginning and end usually appear in disguise.”

Regression to the mean

The tendency toward average profitability is a fundamental, if not the fundamental principle of competitive markets. It is an inevitable force, pushing those profits and their valuation back to the average. It can be a powerful investment tool. It can, almost by itself, select cheap portfolios and avoid expensive ones. Its plain English equivalent is that something usually happens to keep both good news and bad news from going on forever.”