Averaging In And Averaging Out

One of my favorite techniques to buying and selling transactional assets (stocks being the prime example) is to dollar cost average on the way in and the way out.

I am doing this right now with Bitcoin. I want to buy enough bitcoin so I can make charitable gifts and political donations with it and generally transact in it as much as possible. I’m buying 1.5 bitcoin every week in my Coinbase account. I have a reminder in my calendar and I buy some every week at the same time (I bought some this morning). I’ll keep doing this until I feel like stopping. A lot depends on how much I spend I guess. But the point is I would not be comfortable going out and buying a bunch of bitcoin in one transaction. There’s too much market risk in doing that. By purchasing an asset in small amounts over a long period of time you average into your price and I like doing that.

When a stock is distributed to me from USV, I generally sell a little bit and then put some away permanently. And then I slowly sell the remaining amount over a long period of time, generally three to five years. I generally like to sell once a quarter at the same time. I like the week after the earnings reports, when all the information is in the market and the market has digested it. But that’s not the important thing. The important thing is to sell roughly the same amount in a regular rhythm.

The point of averaging in and averaging out is you never get the top or the bottom, but you get the average. And the average is just fine with me.

In some ways, building a position in an early stage venture fund is the same thing. We buy a bit at the seed stage, a bit more at the Srs A stage, a bit more at the Srs B stage, and so on and so forth. In some of our best companies, we have bought stock in five to ten rounds. Some of those rounds will turn out to have been bargains. Some will turn out to have been overpriced. But on average, if you get to invest in ten rounds, you will build a very good position at a very good price.

It goes back to optimizing versus satisficing. If you want to find the optimal entry price or the optimal exit price, you will drive yourself crazy. I prefer to find an acceptable price. And I think that averaging in and averaging out does that for you.


Comments (Archived):

  1. jason wright

    so you won’t be selling twitter stock this week?

    1. JimHirshfield

      I think they posted earnings yesterday.

      1. jason wright

        and the stock fell 10%. not enough new users was the market’s view on twitter’s trajectory.

        1. Chimpwithcans

          I find that a little harsh from the market – and missing the point of twitter as a deeper engagement platform than FB….what’s your view?

          1. jason wright

            i’m twitter twisting fred’s post this morning to indulge my love of data art;http://www.theguardian.com/

          2. Twain Twain

            Business Insider has an interesting transcript of FB’s earnings call too:* http://www.businessinsider….

          3. jason wright

            i was thinking about fb this morning in the context of fred’s sidechains post from the beginning of the week. i can’t find it, but last year (or maybe it was the year before) fred wrote a post about the possibility of a federated group of apps (was it ‘apps’, or another form?) that could challenge and chip away at fb. Then i read about sidechains, and then thinking about fb’s privatisation of personal data model (which i don’t approve of), and i wonder if i have now seen the future of social interaction, a dispersed pattern, nodal, and not centralised.I think twitter is a much more useful discovery tool than fb.

          4. jason wright

            bingo! :-)…and it was this year. ok, i’m losing it.

          5. jason wright

            on reading it again it isn’t quite what i have in mind, but its ‘shape’ approximates. thx.

          6. Twain Twain

            So the question is: “Which of the social media platforms is either in control of the block chain or has direct impact on the information transfer protocol itself?”The answer would be…Google because it owns Freebase which is a version of block chain and Google contributes to Schema which is a protocol for HTML itself.

          7. jason wright

            very informative.

          8. jason wright

            i see fb in terms of the life cycle of a star.

          9. Chimpwithcans

            Going Supernova….like it. Personally, I am less engaged than ever but that might have something to do with my smartphone being stolen, and now I am stuck in the 90’s with an old Nokia 🙂

    2. fredwilson

      Twitter announced earning this week

      1. jason wright

        stick or twist?

  2. Tom Labus

    The way everyone gets hammered after earning these days, it may be better to wait until prices snap back. FB saying they’ll spent for the future isn’t a bad thing.

    1. fredwilson

      Selling right after earnings sure doesn’t seem ideal

  3. Chimpwithcans

    Very nice clear writing on this post. I just invested in the complete opposite fashion last night – I had saved up a bunch of money and put it on a few stocks all at once. Love this approach though – especially with something like bitcoin. Learning.

  4. William Mougayar

    This works well if your assets keep appreciating, but what do you do if they start a downward trend. Do you have stop loss thresholds too?

    1. fredwilson

      Keep buyingAverage down

      1. Chimpwithcans

        How often would you recommend a reassessment of your macro investment strategy to guide the averaging up or down on specific investments?

        1. fredwilson

          i think about macro trends all the time. i obsess over them. but i don’t let them easily change a plan that is in place. i like to stick to plans until it is crystal clear that they are not the right thing to do.

          1. falicon

            The challenge is that sometimes you have to find yourself in check (or checkmate) before it’s crystal clear the plan isn’t right.Of course – I think that’s part of the fun 😉

          2. LE

            until it is crystal clear that they are not the right thing to do.To state the obvious by that time isn’t it to late?

    2. Mark Gavagan

      I think your idea of a stop loss threshold can make a lot of sense (Worldcom or Enron, anyone?).I’m certainly NOT an expert or professional, but people buying individual stocks might consider entering an automatic stop loss market sell order as soon as they enter a position, at whatever price they’d definitely want out at. This removes the need for constant monitoring and needing to be disciplined enough to enter a sell order to take your loss after its occurred. Note: this isn’t a perfect risk management tool because a stock might have a huge drop outside of market hours, for example.Another tool is to buy an out of the money put option, giving you the right but not the obligation to sell at a certain price and time, thus hedging your risk (for a price).

    3. Frank W. Miller

      The power of dollar cost averaging comes from buying both low and high. You allocate the same amount to purchase an asset periodically over time. By definition, when the price is high, you buy less. When the price is low you buy more. This buymorewhenitslow and buylesswhenitshigh dynamic is what yields exponential returns over time. Thats why people who kept their discipline after the 2008 crash have REALLY cleaned up.

      1. William Mougayar

        Discipline is key in any investment. Yup.

      2. Mark Gavagan

        Of course positive returns are only realized IF the average selling price is higher than the average buying price.I’m not suggesting averaging in or out is a bad idea, but if a buyer is fundamentally wrong, dollar cost averaging and discipline to hold though tough conditions won’t offset that fundamental wrongness.

        1. Frank W. Miller

          Personally, I typically only average in. I really only invest long and for downside protection, I’ve used protected puts when I’m worried. Something I learned the hard way after the dot com days.

  5. Matt Kruza

    Love the tie back to satisficing. That is an important concept for investors, but for entrepreneurs I think that may honestly be one of the 2 or 3 most important skill sets. The hardest part for us is we are working in a perpetually stressful, resource constrained environement, where we and our companies have to make an insane number of choices, and while each choice doesn’t have to be perfect, the next few choices have to happen to progress. I also think Mark Suster did some type of similar post of at least a similar ethos a while ago.. good minds at work 🙂

    1. Humberto

      Satisficing is the word.

  6. Twain Twain

    Whilst discussing high-frequency trading with a hedge fund friend the other day, we talked about optimization strategies and transaction speeds.We concurred that the trend over the multiple trades would be…averaging.

    1. fredwilson

      That’s funny

      1. Twain Twain

        The optimization matrix is collapsible into an average linear function — that’s what’s not obvious.Things which aren’t obvious are what and where Paul Graham might call “the fractal edges”.

    2. laurie kalmanson

      overheard a trader at dinner saying he isn’t trading anymore but is now writing algorithms to replace the trades he did, and that his next task after that is learning other trades and writing other algorithms for them

  7. Brandon Burns

    This smells of MBA Mondays, and I like it.Will it ever officially come back?

    1. fredwilson

      no. i am done with that. it was fun. but it is over.

      1. JimHirshfield

        “It’s not you, it’s me.”

        1. showmyhomework


      2. LE

        That makes a lot of sense to me. Back in high school I dropped out of cross country. I hated to be told to run every day.Yet ever since high school I’ve almost always been running. The last 16 or 17 years every day in fact. But nobody tells me to do it.Same with working. Nobody tells me to work the hours that I do. One of the things that I like is the fact that at any given moment I can work on anything I want to do at all. It all gets done but it gets done according to my schedule.

    2. jason wright

      I would like to see Future Friday as a periodic post theme.

  8. Russell

    Low transaction costs, and rebalancing the portfolio. On a different scale Norges, who run the Norwegian Sovereign Wealth Fund does the same, albeit with the $884B in loose change they found under the couch

    1. fredwilson

      yowza. that’s a lot of money

      1. Russell

        It is a big couchSent from my iPad

      2. LE

        I wonder how the structure of that is set up management and oversight wise?I think having a single entity managing something that large is a big problem risk wise. It would be fascinating to know what types of protections they have in place to make sure that the wrong thing doesn’t happen with something so big and complex. Imagine what types of crap could be hidden in a sofa that large. Not that it can’t happen with 100 billion or 20 million. (This is the type of shit I think about btw it fascinates me..)Compared to having 10 entities managing 1/10th the assets (even though that would invite competition which could, if not managed properly, cause it’s own risk problems).http://dealbook.nytimes.com

  9. Patrick Carey

    “October: This is one of the peculiarly dangerous months tospeculate in stocks. The others are July, January, September, April, November,May, March, June, December, August and February.” – Mark TwainBest to use DCA to catch the trend rather than try to time the market perfectly. ‘Speculating’ is usually a bad idea for the average investor.

  10. TroyHenikoff

    I like your approach, but would suggest a tweak to the purchasing strategy. If you always purchase the same $$ worth of stock/BitCoin, then you get better averaging. When the price is low you get more units, when the price is higher you get fewer units. At the end of the purchasing period you will have a better cost basis than purchasing the same number of shares/coins each time…

    1. fredwilson

      That true if you think in dollars. But what if you think in Bitcoin?

      1. TroyHenikoff

        If purchasing BitCoin, I would purchase the same dollar amount each time ($500 / week for example) if purchasing other things with BitCoin, then purchase the same BitCoin worth (2 BTC each time for example) and at least you will be optimizing for getting the most per BitCoin, but you are still exposed to the volatility of BitCoin…

        1. pointsnfigures

          yup. without a futures mkt, no way to hedge. No hedge=more vol. http://mjperry.blogspot.com… This article shows the dampening volatility effect of futures on commodity prices.

  11. nnutter

    It’s not really averaging though is it? Sampling a signal at periodic intervals can lead to aliasing. I agree it’s unlikely to be the best or lowest price and that for most people it would be an acceptable price. I guess maybe you can assume a long-term, semi-smooth signal to be guiding the real signal in which case periodic sampling might still reveal that signal?

    1. Frank W. Miller

      Aliasing would require the input and output signals to be harmonic and phased such that you happen to keep hitting non-representative points in the sampled signal. While the sample frequency will be periodic, the sampled signal is not so its unlikely that any aliasing effects will occur, especially over a long duration.

    2. sigmaalgebra

      Ah, someone else who worked with the FFT,the Nyquist sampling theorem, canonical interpolation, second order stationary stochastic processes, power spectralestimation, etc.!

  12. falicon

    I have always struggled with ‘when to sell’ and had never really thought of it like this before (though I do ‘buy’ things in this fashion)…so LOVE it. Thanks. I’m stealing this strategy (and in a few years will probably claim to have invented it myself) 😉

    1. fredwilson

      I took it from someone too

    2. LE

      had never really thought of it like this beforeThat’s because it’s a mind trick to make an investor feel better and not based on rationality.

  13. Richard

    It’s interesting that the expense side of the ledger seem to be playing havoc on the stock prices of both Twitter and Facebook. (Twitters is also getting hit on the revenue side as well).

  14. pointsnfigures

    buying in bits allows you to keep dry powder for adverse events. For example, suppose you were bullish a stock. You want to build a position. Then one day out of the blue, the stock moves way against the position you want to have. If conditions that you used are the same, you aren’t worried about a one time event-you can reel in a lot of stock at a much lower price. In the recent market downdraft, if you were bullish, you could have bought with both hands and helped your return.

  15. leeschneider

    How do you decide when to flip from buying to selling?

  16. Kirsten Lambertsen

    At what point will you apply the selling method to your Bitcoin?This is a very nice explanation by the way. Almost makes me feel like trying it, heh.

  17. JLM

    .Want to advance the cause of bitcoin?Make political donations with it. Hell, politicians will make it the official currency of the United States.JLM.

    1. Kirsten Lambertsen

      Politicians will make it the official currency when GE tells them to.

      1. JLM

        .Well isn’t that all really the same thing?JLM.

        1. Kirsten Lambertsen

          I love it when we agree 😉

    2. LE

      Make political donations with it.Yeah I was really impressed with that as well.Another idea is finding publicly visible events (like children dying in Africa from Ebola ) and pledging money in bitcoins instead of USD as part of the press release which the press will then talk about as a story angle. [1] Kind of like how they talk about a guy who shows up to pay his taxes in pennies because it’s a fish out of water event.[1] Doesn’t matter if people figure out it’s a ploy btw.

    3. ZekeV

      Ugh. When the legislature starts making laws to promote bitcoin, that’s when I know it’s time to convert my bitcoin into federal reserve notes and ammunition. Bitcoin benefits from skepticism.

  18. Frank W. Miller

    The eighth and ninth wonders of the world: compound interest and dollar cost averaging

    1. Druce

      But then, instead of buying 1.5 bitcoins per week as Fred is doing, you buy e.g. $500 worth of bitcoin per week. Then you will tend to buy more when the price is lower.

      1. Frank W. Miller

        Correct. Averaging is a general concept that has as inputs the purchasing asset price over time, the purchased asset price over time, whether your long or short, and the duration. What I do is to hold the periodic amount of purchasing asset constant. If I read what Fred is doing correctly, he’s holding the amount of the purchased asset constant.By holding the amount of the purchased asset constant when you’re long, you don’t get the same exponential effects, i.e. your returns will not be as good. When the price is high you spend more of the purchasing asset and when the price is low you spend less. If you’re long this isn’t exactly what you want. By holding the amount of the purchasing asset constant, you get this whiplash effect that yields exponential returns when the purchased asset price bounces. You buy a whole bunch more when the price is low and then you get this acceleration in return when the price of the purchased asset rises, particularly when it shoots over the average. You can compare these approaches with some simple spreadsheets.

      2. Druce

        To be clear (and possibly beat it to death)If you buy 1 share day 1 at $301 share day 2 at $60 1 share day 3 at $120 after 3 days you spent $210 and bought 3 shares at average of $70.If you spend $70 day 1 for 2.33 shares at 30$70 day 2 for 1.167 shares at 60$70 day 3 and get 0.5833 shares at 120after 3 days you spend $210 and bought 4.083 shares at average of $51.43By buying a fixed dollar amount each period, the amount you spend is fixed in advance, and you get a better average price per share v. buying a fixed quantity of shares/bitcoin.If you buy n shares every weekday for a week at the closing price, your cost basis will be the arithmetic mean of the daily closing prices. The quantity of shares you bought will be 5, the amount you spent will be the average closing price * 5. The amount you spend depends on the fluctuations in the share price.If you buy $100 of shares every day, the amount you spend will be $500, and the cost basis will be the harmonic mean of the daily prices.Same math applies to the problem of running 1 hour at 30, 60, 120mph on the one hand, versus running for 70 miles each at 30, 60, 120mph, average speed will be 70mph v. 51.43mph.Instead of “buying 1.5 bitcoin every week in my Coinbase account,” which gives Fred the average execution price, he is guaranteed to have a better average price by buying $x every day, and in the case of a volatile asset like Bitcoin, possibly quite a bit lower.

        1. Frank W. Miller

          Its always possible to put together specific examples where buying a constant amount of the purchased asset (in this case Bitcoins) will do better. However, if you look at it from a formulaic pov, a specific amount of the purchasing asset (in this case dollars), should do better over time.

          1. Druce

            First sentence is not correct. Arithmetic mean never < harmonic mean.

  19. JLM

    .Once you reap your profits, then the fun begins.Invest in high quality — not junky crap — real estate that has a diversified rent roll to backstop the cash flow.Hold it for 20-30 years. Real estate never loses value over that period of time. The shoulders for every real estate crunch have been less than ten years, so you bridge the bumps.Then, don’t sell it — give it to your kids who get it at a “stepped up basis” — tax talk for cheating the tax man. This is the last meaningful tax strategy available to a thinking man — dying well.Every ten years get some “whip out” — which is a religious experience. Read about it here.http://themusingsofthebigre…Rinse, repeat.JLM.

    1. Salt Shaker

      You are so right about RE, particularly as it relates to the step up in basis and inheritance, which can have enormous tax implications. I invested fairly heavily in stocks when the market crashed and wish I had done the same w/ RE. Certainly less volatility, and if you’re a longterm investor, you have a very good shot at reward reaping, without the wide swing of equities (particularly of late). Of course, prop mgt is always a burden.

    2. LE

      real estate that has a diversified rent roll to backstop the cash flow.Interesting story either in the WSJ or NY Times the other day that the observation deck at both the Empire State Building and the World Trade Center contributes a large amount to the rent.http://online.wsj.com/artic…WTC:The owners of the skyscraper that cost $3.9 billion to build are expecting the observation deck—just three floors of the tower compared with 70 office floors—to bring in nearly one-fourth of the building’s annual revenue by 2019, or a projected $53 million, according to representatives of the ownership group.Empire State:Amid a growing trend of tourists clamoring for views, the Empire State Building now gets more than 40% of its revenue from its two floors of observation decks, bringing in $101 million in 2013, up from $78 million in 2010, according to filings by the building’s owner.Given the increased competition now that everyone and his uncle who owns a tall building is doing this there is apparently concern that this won’t last forever.

      1. JLM

        .Death and taxes. Hope the nation takes a crack at them on Election Day shortly.The observation deck angle is incredible. Who would have ever thunk it?JLM.

        1. LE

          The observation deck angle is incredible. Who would have ever thunk it?Well I never would have that’s for sure because I can’t for the life of me see what the big deal is about going up in an elevator and seeing essentially the same thing you see when you are up in an airplane.To me this is what I call “a jacuzzi”. It’s one of those experiences (and this is an important concept actually) that crowds of people claim to be so very wonderful but when you really boil it down it’s just “ok”.Same thing that causes idiots who never ever care about sports to go into the streets and get all excited when the local sports team wins something. It’s the lemming reflex. That’s a large part of it.Anyway what goes up must come down. I guess they figure that by the time the fad wears off the rents will increase so it won’t matter anymore. Or the guys who did the deal will be 6 feet under. Etc.

          1. awaldstein

            No airplane anywhere that gives you this view.I’m happy to be a tourist forever and I”m second generation New Yorker.This pic from opening day.

          2. LE

            Well you are in the majority and I am in the minority for sure judging by the visitor statistics.That said New Yorkers seem to have a thing about views of the city. Watching the re shows it’s amazing the value that is given to a view of a water tower or a bridge. Like “wow isn’t this great!”.In Philly my dad owned a building that had great view of the Ben Franklin bridge and water towers. Nobody gave it a 2nd thought.Later I rented an apartment (early 80’s) which had a huge deck and a view of the bridge as well. I currently have a small place down the shore which has a great view of the back bay and the ocean from a high floor and a balcony. In both places everyone raved about the views. I liked it for a short time then it didn’t matter to me anymore. I rent it now I’m totally over it at this point. (Used to have a boat at the dock within site of the balcony as well..)I’ve never like one time thrills like rides and amusement parks all of that stuff not for me. (I do like taking out a sail boat when I’m away of course that’s always fun but I control the boat and it doesn’t last 3 minutes either..)I like experiences that I can enjoy perpetually whenever I want at a whim.

          3. sigmaalgebra

            Gee, the Clean Air Act actually worked!I just paid my part: My car needed a little exhaust workand the bill was $800, mostly for just the catalytic converter, mostly due to platinum or some such.

          4. sigmaalgebra

            Gee, clearly the Clean Air Act worked in NYC!

          5. Chimpwithcans

            Dig the hat!

        2. awaldstein

          Next time you are in NYC, let’s grab Fred and rent a helicopter for 30 minutes and take some pictures.Amazingly affordable, freakin amazing to hoover over the Chrysler Building, to take a view of the East river across three or four bridges.Pretty cool.

          1. LE

            To risky to loose all three of you in a helicopter accident. What will become of AVC?

          2. JLM

            .I have a very spotty record in helicopters. There were complications and it wasn’t my fault.Still?JLM.

          3. LE

            My experience relates to crashing RC Gas Choppers. Boy you never saw something wack and chew itself to pieces like a 60 size gas chopper hitting the ground. (Some guy in Brooklyn was almost decapitated by a smaller one last year).http://7online.com/archive/http://www.youtube.com/watc…I wouldn’t get into a chopper. The state police had one that landed next to my office for years at the hospital. It would fly over my office on takeoff and landing some times.I could have easily walked over and gotten a ride if I wanted to. Never did. The paid’s no longer there the hospital relocated.

    3. sigmaalgebra

      Whip Out? These situations might be tricky to think of and, then, evaluate. And, a nagging question is, is that really the best that can be done, that is, optimal? Moreover, if there is some uncertainty involved, say, interest rates, how might we think of the best situation and analyze it?Well, fellow searchers for truth, justice, the American way, and financial security, there is a way. I credit R. Bellman, long at USC, and E. Dynkin, long at Cornell, R. Rockafellar, long at U. Washington, and others.So, suppose we set up a spreadsheet to analyze a situation, e.g., find ideas like whip out and more ideas and, net, the best possible, optimal things to do.So, we have, say, one spreadsheet column for each quarter, plan over 30 years, and, thus, have 120 columns.In that spreadsheet, for each line on the income statement and balance sheet we have a row. Also have a row for each loan outstanding. Also have a row for various candidate financial decisions.Then go to the end and describe the desired situation at the end of the last period, that is, in column 120.Then click on the button Optimize.Then the software considers all situations in period 119 and all decisions that might be made in that period that will result in one of the desired situations in column 120 and keeps the good situations and decisions.Then go back to column 118 and see how to get to one of the good situations in column 119.Continue in this way.It’s good that Intel likes making processors with several cores because some such problems can use several cores.That’s the baby talk case, the deterministic case.Actually, long it’s been common for spreadsheet software to have an optimize function, at some times based on L. Lasdon’s generalized reduced gradient version 2 (GRG2) math. And no doubt at least for some simple cases that software would also work.Walk before running: So, if really want to do this, then type in some simple cases, e.g., see how difficult it would be to program the relevant tax rules, and see what the spreadsheet software’s built-in optimization can do. If that is doable, then grow from there.For the adult case, accept that interest rates, etc. might be somewhat unpredictable. So cook up a probabilistic model for the uncertainties and continue again. This time the software takes some conditional expectations in the work. Maybe cry out, “More Intel processor cores, Ma!”This adult case is the stochastic case.Not all such problems are impossible computationally: In my Ph.D. dissertation, my software did fine on a slow, single core processor!Really, we shouldn’t be attacking these problems just intuitively or just by hand. I mean, long ago Bellman, Dynkin, Rockafellar, etc. told us what to do! Now it’s just a small matter of some software!Of course, might run the software in the cloud. Then have FPaaS, that is, financial planning as a service! Ah, back to my project: I’m gathering some initial data and proof reading my code for resolving relative URLs! Had to read some BNF (Backus-Naur form, basically a computer science way to define some sets) in an RFC (Internet Engineering Task Force Request for Comments).

      1. Twain Twain

        Determinism: a + b = a + b; ab = ba; a/b = a/bProbability: P(A and B) = P(A) x P(B)Both Determinism and Probability implicitly assume a factor of behavior which is simply false: rationality in human choices.Randomness (stochasticity) has been an incomplete but expedient approach for mathematicians to deal with decision-making, imo.When variables like interest rates go up or down or any type of market metric movement, there are other factors that affect those movements which are not included in the calculations.For example, there’s the testosterone levels of traders which affect risk appetite, the ethical values of Sharia Funds, the socio-political considerations when the FED increases/decreases any of the economic levers they have access to (e.g. whether an election is coming up) and the good old perception biases in our intuitions and personal context when we buy or do something as consumer.This includes Fred’s choice to do “averaging in and averaging out” as well as JLM’s thinking wrt “give it to the kids” which is about his love and consideration for his kids first and the other extraneous factors that affect the price of that real estate on a secondary basis.Why does this matter?Well, the machines aren’t going to be equivalent to our human decision-making and able to truly support decision-making until they can factor in (or at least proxy) those non-deterministic, non-probabilistic factors.It also matters because the AI community is simply not going to have a coherent model for Natural Language understanding and meaning unless we create solutions to measure human subjectivity and not simply the expedient objectivity which we can proxy with deterministic and probabilistic tools.Ah and the Natural Language problem involves Quantum Entanglement (subject-object dynamics between the observed and the observer) which is why Probability is not the panacea tool to solve it because, as Schrödinger’s Cat super-position theory highlights, Probability is about “OR” states whereas we need a tool that enables “AND” states and the integration of those states in a coherent way, over time.

        1. sigmaalgebra

          I got up to check on some long running software. Yup, it was not going well. There was a bug. I put in few statements to capture some intermediate values, ran the software on a small case, quickly, saw where the bug was, fixed the bug, and restarted the software. The software will now run for about an hour and I will check it again.For your Determinism: a + b = a + b; ab = ba; a/b = a/b that’s a long way from a characterization or even a description of determinism. Those algebraic expressions just have next to nothing to do with determinism.For your Probability: P(A and B) = P(A) x P(B) that’s a long way from a description of the subject of probability. In probability. your statement is the definition of independence of the events in the set {A, B}.For your Both Determinism and Probability implicitly assume a factor of behavior which is simply false: rationality in human choices. at least in what I wrote, there was no assumption that in behavior there is rationality in human choices. For Randomness (stochasticity) has been an incomplete but expedient approach for mathematicians to deal with decision-making, imo. We can go into a lab, measure a number, and call that number the value of a random variable, say, X. If for some set T, and for each time t in set T, we get such a random variable, then we can index the random variables by time t and get, borrowing subscript notation from D. Knuth’s TeX, X_t. Then {X_t | t in T} is a stochastic process. Or, more simply, a stochastic process is a set of random variables indexed by time.Sometimes a stochastic process is indexed by space instead of time or, as in ocean waves, both space and time.The real world is just awash in stochastic processes — the 3 degree K background radiation, other cases of radio noise, air temperature on my back porch, the path of a home run baseball, the value of Google’s stock, the price of WTI crude oil, the price of BitCoin, the readings of some seismometer in California, the arrival times of visitors at a Web site, each time USV makes an investment, each time Fred buys BitCoin, each time I post at AVC, @JLM:disqus ‘s EKG, and as many more examples, as you might wish.My definition above of a stochastic process is, for a short treatment, fairly careful and essentially the same as the definitions in the treatments of stochastic processes by authors such as J. Doob, E. Dynkin, A. Shiryaev, J. Neveu, K. Ito, J. Tukey, J. von Neumann, E. Cinlar, etc.The definition and subject applies also to human decision making whether that is rational or not. When variables like interest rates go up or down or any type of market metric movement, there are other factors that affect those movements which are not included in the calculations. Yes, interest rates are examples of stochastic processes, and this fact need assume or say nothing about “other factors that affect those movements”. Or such a stochastic process is yet another collection of random variables indexed by time, and maybe we do or maybe we don’t have more related information or some explanations. For example, there’s the testosterone levels of traders which affect risk appetite, the ethical values of Sharia Funds, the socio-political considerations when the FED increases/decreases any of the economic levers they have access to (e.g. whether an election is coming up) and the good old perception biases in our intuitions and personal context when we buy something as consumer. We do not need to notice such things to have a stochastic process. Well, the machines aren’t going to be equivalent to our human decision-making and able to truly support decision-making until they can factor in (or at least proxy) those non-deterministic, non-probabilistic factors. That machines be equivalent in any very meaningful sense to “human decision-making” is not promising, claimed, or even always necessary.In some cases, it is possible to make some progress predicting “human decision making”, e.g., some of the good ad targeting on the Web. But such effort get their predictions by means a very long way from what really goes on between the ears of a human. I doubt that anyone has yet had an Intel processor between their ears and lived to tell about it!The SAT tests claim that they have useful predictions of college academic performance — maybe they do, but their means are a long way from what is between the ears of a human.Long ago psychologists observed that just using the dimensionality reduction of principal components (starting with the polar decomposition) it is possible to do fairly well predicting what humans will do from just 14 or so numbers. Roughly, humans are, to a reasonably good approximation, just 14 dimensional creatures. This does not mean that there is a real, symmetric, non-negative, semi-definite matrix as in the polar decomposition, between the ears. Or principal components work, but that’s not because that’s just how humans really work between their ears.E.g., for day t let X_t be the change in the closing S&P average from day t – 1. For a simple, first-cut treatment, assume that the probability distribution of X_t is the same for all t, that is, the set of random variables {X_t} is identically distributed. Of course, as stock market analysts have long had to conclude, for some t, knowing X_s for times s < t does essentially nothing to help us predict X_t. So, it follows that the set of random variables {X_t} is independent.Then the price change over, say, 20 days is the sum of the price changes for each of the 20 individual days. So, we have a sum of 20 random variables, independent and identically distributed. With one more assumption, a tricky one with the Lindeberg-Feller treatment I will omit but easy enough to believe in practice, by the central limit theorem the change over the 20 days is fairly accurately Gaussian. Then, tap lightly and conclude that in the case E[X_t] = 0 the stochastic process {X_t} is the famous stochastic process Brownian motion.Point: We have concluded Brownian motion making no assumptions about human behavior. It also matters because the AI community is simply not going to have a coherent model for Natural Language understanding and meaning unless we create solutions to measure market subjectivity and not simply the expedient objectivity which we can proxy with deterministic and probabilistic tools. First, the prospects for natural language understanding at all comparable to that of humans is visible on the horizon only to people subject to delusions.Second, natural language understanding has next to nothing to do with the stock markets.Maybe you are saying that you envision a computer program that could listen to people talking, maybe traders or market analysts, and have the program predict market movements. While I’d say that next to none of such a project is at all promising, perhaps surprisingly or curiously, the first approaches that work well may have nothing to do with how to measure market subjectivity. Third there may be some ways to measure market subjectivity. without getting into natural language understanding.Yes, maybe in some relatively strong sense, if we could write software that had good natural language understanding and could think like humans, be they rational or not, then maybe we would have a way to predict the market.Alas, also we may not: E.g., we know in fine detail the basics of all the physics and chemistry in the atmosphere that determines the weather, but, still, detailed weather predictions get to be essentially meaningless more than two weeks or so in advance. So, we have to suspect that if we had all the human details you have suggested, we might still be left with just Brownian motion.Yet, J. Simons showed that it is possible to make money in the markets. For just how the heck he did that, have to ask him. Ah and the Natural Language problem involves Quantum Entanglement (subject-object dynamics between the observed and the observer) which is why Probability is not the panacea tool to solve it because, as Schrödinger’s Cat super-position theory highlights, Probability is about “OR” states whereas we need a tool that enables “AND” states and the integration of those states in a coherent way, over time. To me, any connection between the natural language problem and quantum entanglement is about as weak as anything we can envision.Instead of discussing Schrödinger’s Cat, it’s easier just to stay with the microscopic concept of collapse of the wave function. Even there I have to beg off — my physics profs didn’t much understand such things, and I have not yet gotten back to some high quality work in physics to get a good understanding for myself. Once I did take a fairly careful pass through the first half of von Neumann’s book on quantum mechanics (before my career pulled me into a different direction), but that first half is just some nicely done mathematics a bit far from the details of the physics. Actually, some months ago I got a highly recommended text on quantum mechanics, found the thing awash in egregious, elementary mathematical mistakes, and gave up on that book — a waste of time, money, and effort.When my current project is done, I intend to return to mathematical physics, and then I should be able to comment on the Einstein-Podolsky-Rosen paradox, spooky action at a distance, quantum entanglement, etc.

          1. Twain Twain

            Determinism: a + b = a + b; ab = ba; a/b = a/b is perfectly valid.In Determinism the outcome is contingent upon and directly mappable to some function that acts on the input, in this case the variables a and b.So deterministic logic says that when we add a and b we don’t create ab. Probability: P(A and B) = P(A) x P(B) is also perfectly valid. It’s the probability of the independent event of A and B occurring.Now, remember, we are not questioning whether Probability is the tool to measure stochasticity but whether it’s sufficient for measuring SUBJECTIVITY.How Brownian motion works is not the same as how our brains work.Let’s anchor this in a real-life situation. Suppose that two people randomly say these sentences:Person A: I’m investing in Bitcoins because it’s innovative.Person B: Bitcoin’s unproven. I’m sticking with real estate ‘cos I know what I’m investing in and I can touch it.Now, we can certainly increase the number of variables by surveying more people and we can create a stochastic model for who’s likely to be pro-Bitcoin and who’s likely to be pro-real estate.However, that’s still about Probability solving for stochasticity in the sample population but not the subjectivity spread.

          2. sigmaalgebra

            For your Determinism: a + b = a + b; ab = ba; a/b = a/b is perfectly valid. “Valid” Yes. Having something significant or meaningful to do with determinism? No.For your In Determinism the outcome is contingent upon and directly mappable to some function that acts on the input, in this case the variables a and b. That actually begins to get to what determinism means and, thus, is a lot better.But there are still some really serious problems. If I was reading a book trying to learn from a statement like that, then the book would become airborne, crash against a wall, and soon be starting a fire in my fireplace for winter.Sorry ’bout that. All I can do is to try, again, to help.First objection: “the outcome”. What “outcome” from what whatever; whatever the heck are we talking about; what is the context; what’s going on? Something’s going on that has something to do with an “outcome”, but what is that?Maybe: Let’s say that a process is something, say, an activity, that continues over time. So, since we are interested in mathematical descriptions, at each time t the process is doing some activity. Such a process might be an instance of a disease, say, cancer, that is active over some interval of time. The process might be an asteroid detected near Mars, in a mostly elliptical orbit around the sun, and maybe coming within a million miles of earth. The process might be the prices of GE stock on the NYSE. The process might be what my wrist watch does until its battery runs down the next time.Typically in a process, the activity changes or evolves over time.Typically a process has a state which commonly is, for some positive integer n, some n numbers. It would be standard to arrange these n numbers in an n-tuple or a vector. Call this n -tuple x. Typically we want to define the state as a function of time, t. So, we write for the state of the process x_t, that is, with the t as a subscript.Then, typically for this process there is a function f returns a description of the activity of the process as a function of time t and the state of that process x_t at time t. So the function is, say, f(t, x_t). Again, the value of this function is a description of the process at time t, in whatever form we have decided to use to describe the process. For many problems in classic physics, that description might be just position and velocity.Say we get interested in the process at time t = 0. Then, for a definition, the process is deterministic provided there are functions g, h so that x_t = g(t, x_0) and, for the function f we have mentioned, f(t, x_t) = h(t, x_0) So, we leave out contingent upon and directly mappable Why? Because for such a general concept as a process, “contingent upon” is too vague.We also leave out “directly mappable” because what is meant my “mappable” is far too vague; that is, it appears that a function is involved, but when a function is involved we need to be explicit to the level of something clear as glass and much harder, need to make clear both the range and domain of the function and for each element of the domain something about how the function returns a corresponding element of the range. Just saying map, mapping, mappable, is far too vague.Computer science makes this mistake a lot as if being vague is a point of pride; really, the cause is just bad writing and poor understanding from lack of good education from solid material. Learn about functions from, say, a good course in abstract algebra and just will never write such nonsense.Some of the Microsoft documentation throws around map, mapping, mappable, etc. in totally sloppy ways, and each time I must peel myself off the walls where I’ve deposited myself one Angstrom thick in outrage. The writers have seen some words they want to use, don’t really understand what the words mean or how to describe what they mean, and just throw the words in like some salt in some soup.People that talk about map, mapping, mappable, in really vague terms are a poor crowd to be associated with — certainly never want to work with them. To be nice to them, send them back to college for a good undergraduate pure math major.Next, saying “mappable to some function”, whether also say “directly” or not, is, to be kind, in a word, taken literally, just nonsense.So, again, we leave out contingent upon and directly mappable and, instead, do use some mathematical concepts and otherwise use the least technical and most simple language we can. We illustrate with examples. We are explicit beyond any chance of ambiguity.Whew. Maybe there is a better definition in, say,Michael Athans and Peter L. Falb, Optimal Control: An Introduction to the Theory and Its Applications. For your Now, remember, we are not questioning whether Probability is the tool to measure stochasticity but whether it’s sufficient for measuring SUBJECTIVITY. stochastic, no matter what some popular screeds write, means, from people who know what the heck they are talking about, a collection of random variables indexed by, usually, time.For stochasticity we try not to use words like that! I don’t, never have, and never will. But, then I made an A in a course from Cinlar’s book from a star student of Cinlar, worked throughR. B. Blackman and J. W. Tukey, The Measurement of Power Spectra: From the Point of View of Communications Engineering did a lot with the fast Fourier transform, etc., got a high end Camaro out of it, helped the company I was in win a contract having to do with a control system for a system driven by the stochastic process, ocean waves, helped another company use stochastic processes, a Markov process subordinated to a Poisson process, to get a rush answer for the US Navy, etc.And my Ph.D. dissertation, on stochastic optimal control, was for how to control in the best way possible a system driven by a stochastic process. I worked out the detailed applied math, paid careful attention to the tricky issue of measurable selection, found a fast way to do the calculations, and wrote and successfully ran software for the calculations.Still, I don’t use words like stochasticity or work with people who do!For Probability is the tool to measure stochasticity but whether it’s sufficient for measuring SUBJECTIVITY. probability theory should not be said to measure any such things or anything.Instead, maybe someone wants a mathematical model of some kind that can analyze and/or predict some actions, behaviors, etc. from people being subjective. Okay. Ad targeting has been doing just that for over 100 years with newspapers, magazines, radio, TV, and now the Internet and the Web. Especially with third party cookies, there is a lot of computation and TCP/IP communications for each ad on each Web page as viewed by each user.E.g., magazines Vogue, Teen Vogue, Seventeen, the few times I glanced at them, seemed to have a lot of pictures of pretty girls and/or young women, but they didn’t have a lot of ads for NAPA auto parts, Hoosier Tires drag slicks, Champion stark plugs, drill plates, taps and dies, micrometers, calipers, masonry drills, etc.It’s too bad about Sears: Their line of Craftsman tools has been terrific, and I’ve had my hands around them off and on since I was five or so. Currently in the back of my SUV I have a really nice Craftsman 1/2″, or maybe it’s 3/4″, drive socket breaker bar, about two feet long, with a deep socket the right size for the lug nuts on the wheels. It’s terrific: No pain, strain, or damage to me or the lug nuts, and right away, effortlessly, can remove the lug nuts, in rain, ice, snow, mud, whatever — piece of cake. Don’t look for ads for such things in magazines for young women! Yup, ad targeting, including for highly subjective decisions, is very old stuff!Do the ad targeting calculations describe, emulate, model, etc. what really goes on between the ears of a person? Or, Newton argued that the motions of the planets were caused by the masses of the bodies in the solar system, their current positions and velocities, his law of gravity, and his second law of motion. The result was an initial value problem for a system of ordinary differential equations. Later work in ordinary differential equations showed that such a system had a unique solution. Thus the equations described a deterministic process. Do we have something similar for actions, behaviors, etc. of people being subjective. Nope, and I’m not holding my breath waiting for such.What Newton did, that is, reducing the problem of planetary motion to his laws and differential equations, is sometimes called reductionism. Can we do similar reductionism for subjective human behavior? Nope, not yet. Still, can we do effective ad targeting for the highly subjective, even emotional, behavior of young women reading their favorite magazines or Web sites? Yup.In such targeting, is some probability theory involved? Can be, yup.Does such use of probability theory mean that an approach of reductionism to explaining human behavior will be probabilistic, i.e., have as the first cause some random number generator that is independent of everything else in the universe? Maybe, maybe not — tough to say.If we were to take our approach of reductionism all the way down to quantum mechanics, then, sure, we could conclude, first-cut, intuitively, that essentially subjective human behavior, maybe all of human behavior, was driven by some stochastic processes independent of everything else in the universe. Would this role for stochastic processes mean that human behavior could not be predicted? Not necessarily and likely not: The work I did for the US Navy was in the end a Monte-Carlo simulation and, thus, had the calculations driven by a random number generator, and the results were, still, nicely predictable in a fairly narrow band.Note: Even to define what it means for a collection of stochastic processes to be independent is something of a challenge. J. Neveu does a good job here!Of course in that Navy work the random number generator I used was from one of Knuth’s books, and of course he got it from Coveyou and McPherson, who, yes, worked at Oak Ridge, naturally enough, where there was a lot of interest in some really high quality random numbers for some really precise Monte Carlo simulations of certain specific nuclear reactions of high interest to US national security.Lesson: That a system is driven by a stochastic process does not mean that nothing about that system can be predicted with useful accuracy.It’s too early in the day for more such background in pure and applied math. Besides, I was up nearly all night getting some of my software to run and need a nap.

          3. Twain Twain

            Ha! Our little exchanges are such fun!Yes, Newton’s laws of motion are an obvious example of determinism. Yes, again, we are not challenging the principles nor the proofs involving whichever sets, series, tuples of random variables (over time) you want that Probability models stochasticity neatly.What we’re trying to discover is what are the mathematical tools to deal with this bit: “Do we have something similar for actions, behaviors, etc. of people being subjective.”Now, by way of background, Max Tegmark of MIT proposed the existence of “Perceptronium, the most general substance that can feels SUBJECTIVELY SELF-AWARE.”* http://www.pbs.org/wgbh/nov…Previously, in Brownian motion theory, the particles were proven to behave stochastically but assumed to have no subjectivity.Tegmark’s theory is (as yet) unproven. Its stumbling block seems to be related to the limitations of Probability for measuring subjectivity.Ad targeting is predicated on Probability and OR, by the way.

          4. sigmaalgebra

            I’ve outlined how probability and stochastic processes work. What we’re trying to get to is discover whether there are mathematical tools to deal with this bit: “Do we have something similar for actions, behaviors, etc. of people being subjective.” The limits of what can be done with existing pure and applied math are not at all clear.If one wants to make progress on mathematical and scientific descriptions, solid and fundamental, with reductionism, of “people being subjective”, then no doubt there’s a lot of math on the shelves of the research libraries that will be needed. Necessary? Definitely. Sufficient? Not clear.For “people being subjective” can do, say, ad targeting, which can be powerful and valuable, but this is not many steps above just empirical curve fitting, that is, we have nothing as fundamental and powerful as Newton’s second law.For really understanding what is going on, really how the human brain works, say, as well as we know how a car works or the planets move, with “people being subjective”, we do not know or have even a clue.Basically we just do not know how the brain works, the human brain or any but, say, a few neurons of some worm or some such.By analogy, we are like a person who knows nothing about anything about a car or anything mechanical, e.g., maybe is just fresh from some tribe in the upper Amazon that has never seen anything or anyone from current civilization, looking at a car at a distance, and trying to know what’s under the hood and how it works. That person couldn’t even figure out that the car had pistons, assuming it did.So, broadly, we don’t know how to understand “people being subjective” in any way that is reductionism, as is often said in physics, “from first principles” (we are missing the principles), or is deterministic or mechanistic (like a machine).For Perceptronium, that sounds a lot like the frictionless inclined plane one physics prof I had talked about (saying that they came only from Holy Mother Russia) or the famous, miracle metal Unobtainium.Actually, it’s easy to think of problems where so far we can’t make even a dent or a scratch. Part of the trick of making progress is to work on problems where we can make progress.Gee, my long running software just ended, about on time. Time to check the results!

          5. Twain Twain

            Super, so we’ve resolved the knotty problem of identifying the problem set of interest: whether we can mathematically measure subjectivity.There is indeed no “first principles” model for people’s subjectivity nor for how the brain functions nor for Natural Language understanding.The latter was discussed recently in this Google video with Geoff Hinton and Ray Kurzweil:* https://www.youtube.com/wat…And Geoff Hinton has been referring to “Dark Knowledge” and “an obscure 2006 paper Caruana and his collaborators showed that the knowledge in the ensemble could be transferred to a single, efficient model by training the single model to mimic the log probabilities of the ensemble average. This technique works because most of the knowledge in the learned ensemble is in the relative probabilities of extremely improbable wrong answers.”* http://www.ttic.edu/dls.phpSo……for all stochastic complexities the answer seems to be…log probabilities of the ensemble average.

          6. Twain Twain

            The Natural Language problem may be more related to Quantum Waves and Fields than initially apparent.What if words are both waves and particles?Rather than the current syntactic structures with Hidden Markov applied to them?

  20. William Gadea

    You could see it as satisficing, but I think dollar-cost averaging might be done by an optimizer who knows what they don’t know. It might be about cognitive humility.

  21. Jim Peterson

    When I see a great deal on a fabulous, profitable company I go in 100% immediately of what I want to invest. The good deal won’t last long. Averaging in from early 2009 wouldn’t have worked out as well as being committed and just buying.If it’s a speculative unknown like Bitcoin your way seems like a great one.

  22. panterosa,

    While making bets is fun, and competitive, there is always the temptation to want to have one’s wins make one look clever.

  23. Madhu Kodali

    Averaging does help maintain some sanity. I have not been able to put my arms around Bitcoin concept until now. I just read this piece from a central banker…. http://www.stlouisfed.org/p… David Andolfatto explained it in simple terms. Bitcoin chart does look like it passed a classic bubble scenario and it might be a good time to buy. Time to signup Coinbase and buy a few bitcoins. I am sure this is not going to be an easy ride even now with regulatory and other hurdles. But, thanks to people like Fred Wilson and Marc Andreessen et al to identify, support, educate and promote these promising technologies.

  24. Dan Epstein

    Fred, you may have touched on this before. Do you view bitcoin as more of an asset or a currency?

    1. fredwilson


  25. Douglas Craver

    Just want to say thanks for this post. As I’m studying up to start investing this is a simple yet important approach I hadn’t come across anywhere.

  26. Matt Hardy

    Is this the same strategy USV takes when portfolio companies IPO? Or do you distribute stock to LPs and let them manage it from there?

    1. fredwilson

      we almost always distribute

  27. dgay07

    We take this approach when we invest in new hedge fund managers. Given markets are volatile and cyclical it just makes sense to us to approach it this way. We also do the same with our portfolio investments as you state, but will add that secondary purchases can be a nice way to average down cost and increase position.

  28. showmyhomework

    What a great blog post Fred. I’ve been a spectator on the AVC blog for years. Never contributed but moving forward, I’m going to be contributing in the comments. MBA Mondays were awesome. The Archive button is a source of goodness for any entrepreneur.

  29. LE

    I’m buying 1.5 bitcoin every weekI think there has to be a way to reword this to another “base” to make it a large number. The press and people like large numbers.People don’t care about or pay attention to small numbers. Big numbers impress. Right?For example 10oz of gold doesn’t sound as big as $12,000 USD.So there has to be a way of conveying this, a new additional nomenclature, such as “bitcoin equivalents”.$500 sounds better than 1.5 bitcoins. (See attached converter now comes up in google btw..) Not to mention that $500 is less than 1.5 bitcoins by a slight amount, today at least.I just did a deal buying and selling something in Canada. During the entire deal I stated all the numbers in USD to my buyer so they would sound smaller. To the seller in Canada though they were stated in CAD because that was a larger number. (Not just because they were Canadian I could have used USD with them..)So in this case the seller got 100,000 CAD but the buyer only paid 89,791 USD (was actually higher than that btw was into 6 figures in the end..)This was a deliberate manipulation to achieve the above concept.[graphic attached]

  30. LE

    The point of averaging in and averaging out is you never get the top or the bottom, but you get the average. And the average is just fine with me.Dollar cost averaging is just a mind trick put out by the financial military industrial complex in order to ease the minds of grandma to keep her in the market. Stock drops? Great buy more! At the end of the year you’ve paid an average cost of $x so the fact that you bought some at $100 and at the end of the year it’s $70 doesn’t matter! Don’t loose sleep over that everything’s cool. Go get ready for Thanksgiving dinner with the family.The good news is there are enough people that buy into it that that it works to keep people in the market.The same “trick” of course doesn’t work with other things have you ever noticed that?If you were deciding to make an investment in a company and found that their sales were declining for a 5 year period but on average were higher than the preceding 5 year period how would you feel about that? Sure it’s not the same thing but your brain has been trained to recognize that revenue trends, for lack of a good explanation, don’t decrease they increase. Internet eyeballs were a mind trick around companies that never made any money.Years ago I found a great mind trick to get by the fact that my ex wife used to get all these parking tickets in the city. I was really pissed off. Then one day she told me what she would have spent more $$ to pay for parking and avoid the tickets (since you don’t always get a ticket but you always would pay for parking). Low and behold it was cheaper to get tickets (in Philly as long as they don’t tow that is). It saved money (iirc). All the sudden all the anger of “tickets” vanished just like that. Perspective and rationality can many times relieve boatloads of anxiety and negativity.

  31. sigmaalgebra

    What you are doing is not necessarily just satisficing. Instead, you are getting,first-cut, a good combination of expectationand variance.The first-cut, simple way to analyzing the benefits of averaging is just the lawof large numbers, but this needs an assumptionthat what is being averaged is identicallydistributed and at least uncorrelated or,for the strong law, independent, and theseassumptions do not hold in this practicalcase.So maybe a way to support such averagingwould be to assume that the prices were froma Brownian motion process with drift and use theassumptions available for the increments inBrownian motion. From such a consideration,first-cut, intuitively, a guess would be that youare getting a good combination of expectationand variance. Then do something with someassumptions about a utility functionand argue that keeping variance down this wayis a good thing, better than just satisficing.But, keeping down variance is easy — everyonewho is broke does this easily! The main difficulty,challenge, goal, etc. is just to make the darnedmoney!Sure, Zuck did that. Now I wonder, how accuratewere Sorkin’s characterizations? Ah, we’ll neverknow!

  32. Sam

    So we can now peg Fred as a conservative high-risk investor.

  33. Bernard Desarnauts

    Case in point also with the related funding by Wealthfront. Not only great service but awesome vision statement I quote from https://blog.wealthfront.co… “…More importantly, they were looking for a service that was automated. Investing for the long term requires reliability, rationality and consistency — exactly the features that a software-based service can offer.”

  34. Tim Dierks

    Normally, wouldn’t averaging in imply buying a constant number of dollars in Bitcoin every period, so you get more when it’s cheap, less when it’s expensive?Similarly, when you say you average your way out of a stock, do you sell a certain $ amount or a certain number of shares in each regular period? Ideally, it seems like you’d like the inverse of averaging in (sell more shares when it’s high, less when it’s low), but I don’t see how to do that without a more complex model.100% agree on satisficing vs. optimizing (which may include having a “good enough” model here). Stress of optimizing isn’t worth it when you’re doing OK and you have low certainty about the perfect solution anyway.

  35. Amar

    <quote>”I have a reminder in my calendar and I buy some every week at the same time (I bought some this morning)”</quote>I am curious why you are not using coinbase’s feature to buy a preconfigured amount on a defined frequency. Is there a reason you prefer alarm + manual buy instead?

  36. arustgi

    This is a great post.I got introduced this concept of accumulating and dispensing assets through ‘sharebuilder’ which used to have a ‘automatic buying’ program where you could buy stocks for $1 a trade, as long as those trades happen periodically and at a predetermined time. Unfortunately, when CapitalOne bought it, they changed that program to make it quite unattractive.The basket of stocks that i have bought and sold using this approach, have over time drastically outperformed the basket of stocks that i have bought and sold using an single market – timing transaction.I wonder, if over a long time, and across several transaction, ‘satisfying’ indeed leads to optimization.

  37. Vasia Pupkin

    Averaging in doesn’t make mathematical sense for assets that have positive expected returns. If you average into an asset like that, then, in expectation, you will pay a worse price.

  38. sigmaalgebra

    Ever thought about empirically back testingusing old market data?Is there an easy way to do that?

  39. Azreen

    Awesome post, Fred. There’s tonnes of wisdom to be learnt here. Biggest takeaway for me here is to be able to trust the process and remain disciplined to execute, and not get greedy or distracted. Always harder to do, no matter how many times we learn it.

  40. Bogdan Iordache

    How does this apply to financing a startup (if the case)?

  41. joeydee740

    Transaction costs can ruin this strategy for little leaguers like me.