Merge pull request #47 from SnowCheetos/dev

less funny readme

README.md

@@ -32,24 +32,31 @@ Fortunately, t̶h̶e̶i̶r̶ ̶p̶a̶r̶e̶n̶t̶s̶ ̶s̶t̶i̶l̶l̶ ̶l̶o̶v
 
 ### Win Small or Lose Big
 
-- For the duration of the fund's existence, their model had an average win rate of $50.75\%$. That's right, they operated on a tiny $0.75\%$ edge over the market, which was enough to turn $\$100$ in 1982 to $\$175,000,000,000$ in 2024. Instead of being very good at Blackjack, they operated a casino. Staying consistent over millions of trades turned out to be much more advantageous than trying to win big on a few trades.
+- For the duration of the fund's existence, their model had an average win rate of $50.75\%$. That's right, they operated on a tiny $0.75\%$ edge over the market, which was enough to turn $\$100$ in 1982 to $\$88,190,084,543$ in 2024. Instead of trying to count cards at Blackjack, they just opened a casino. Staying consistent over millions of trades turned out to be much more advantageous than trying to win big on a few trades.
 
-### Don't Worry About The Wrong Thing
+### Focus on The Right Thing
 
 - Many people are willing to take on exceptional risks in pursue of, at least theoretically, higher possible returns, l̶i̶k̶e̶ ̶t̶h̶a̶t̶ ̶o̶n̶e̶ ̶w̶e̶e̶k̶l̶y̶ ̶F̶D̶ ̶y̶o̶u̶ ̶l̶o̶s̶t̶ ̶y̶o̶u̶r̶ ̶l̶u̶n̶c̶h̶ ̶m̶o̶n̶e̶y̶ ̶o̶n̶ ̶l̶a̶s̶t̶ ̶F̶r̶i̶d̶a̶y̶, and in some cases, risk taking is even being glorified (*not pointing any fingers* 👉🏻 [`_👀_`](https://www.reddit.com/r/wallstreetbets/)). Too often do m̶y̶s̶e̶l̶f̶ traders focus solely on potential (*not even real*) profits while completely ignoring the associated risk. The Medallion Fund, on the other hand, placed a tremendous emphasis on risk reduction. The fund consistently hedged the portfolio near perfectly, which enabled them to use margins that would be otherwise considered risky. 
 
 
 ## Intuitions
-...
+
+It's unlikely that individual could effectively replicate the Medallion Fund, nor would it be the best use of time. The Medallion Fund have billions worth of assets under management, some of the tools and connections available to them are well out of reach for retail investors. 
 
 
 ## Arguments Against Regression Methods
 
-At first glence, it might be tempting to treat this as a *regression* problem and try to predict the price directly using non-linear regression methods such as *Kernel Methods*, *MLP*, or *autoregressive* methods such as *LSTM*. Although there are some merits in their uses, the price actions of any asset, albeit sequential and continuous in nature, can not *strictly*, or even *remotely* be dsecribed as a function of time, but rather a [*Stochastic Process*](https://en.wikipedia.org/wiki/Stochastic_process) (*ot more specifically, a* [*Markov Process*](https://en.wikipedia.org/wiki/Markov_chain)), where each time step, given its current or recent conditions, carries information about the potential future step in the form of a *probability distribution*. 
+At first glence, it might be tempting to treat this as a *regression* problem and try to predict the price directly using non-linear regression methods such as *Kernel Methods*, *MLP*, or *autoregressive* like *LSTM* or t̶h̶e̶ o̶v̶e̶r̶h̶y̶p̶e̶d̶ *Transformers*. 
+
+Although there are some merits justifying their uses, the price actions of any asset, albeit sequential and continuous in nature, can not be dsecribed as simply a function of time. Rather, I would argue that it aligns much better the description of a [*Stochastic Process*](https://en.wikipedia.org/wiki/Stochastic_process), or more specifically, a [*Hidden Markov Model*](https://en.wikipedia.org/wiki/Hidden_Markov_model). 
+
+A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "*What happens next depends only on the state of affairs now*".[[1]](https://en.wikipedia.org/wiki/Markov_chain#:~:text=A%20Markov%20chain%20or%20Markov%20process%20is%20a%20stochastic%20model%20describing%20a%20sequence%20of%20possible%20events%20in%20which%20the%20probability%20of%20each%20event%20depends%20only%20on%20the%20state%20attained%20in%20the%20previous%20event.%20Informally%2C%20this%20may%20be%20thought%20of%20as%2C%20%22What%20happens%20next%20depends%20only%20on%20the%20state%20of%20affairs%20now.%22) A hidden markov model is markov process, where the underlying parameters describing the state transitions is not observable.
+
+Thus, at each time step $t$, rather than trying to predict the future price $p_{t+k}$, it is more ideal to try and predict the *transition probability distribution*. Or in other words, likely conditions of the near future, given observations of the present (*in practice, recent*) conditions. 
 
-As an example, if d̶a̶d̶d̶y̶ Jerome Powell said "AI" four times during a news conference at 3PM, it becomes 1̶0̶0̶%̶ a bit more likely for *NVDA* to close higher that day, but it's not guaranteed. As an counter example, if Jimmy estimates that J̶i̶m̶m̶y̶'̶s̶ ̶0̶-̶D̶T̶E̶ ̶F̶D̶ ̶p̶u̶t̶ *NVDA* will close i̶n̶ ̶t̶h̶e̶ ̶m̶o̶n̶e̶y̶ at $\$150$ simply based on the fact that J̶i̶m̶m̶y̶ ̶h̶a̶s̶ ̶a̶ ̶s̶m̶o̶o̶t̶h̶ ̶b̶r̶a̶i̶n̶ it was $\$140$ at 3PM, we wouldn't consider Jimmy's argument to be very valid, which essentially is what many regression models tries to do, no offense to all the innocent r̶e̶g̶r̶e̶s̶s̶i̶o̶n̶ ̶m̶o̶d̶e̶l̶s̶ Jimmys in the world. The point being, at each time step $t$, rather than trying to predict the future price $p_{t+k}$, it is more ideal to try and predict the *transition probability distribution*. Or in other words, likely conditions of the near future, given observations of recent conditions. 
+And hey, don't just take my word for it, according to [wikipedia](https://en.wikipedia.org/wiki/Renaissance_Technologies#:~:text=In%201988%2C%20the%20firm%20established%20its%20most%20profitable%20portfolio%2C%20the%20Medallion%20Fund%2C%20which%20used%20an%20improved%20and%20expanded%20form%20of%20Leonard%20Baum%27s%20mathematical%20models%2C), the Medallion Fund's algorithm in 1988 used an improved and expanded form of [*Baum–Welch Algorithm*](https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm), a type of EM algorithm for computing parameters from *Hidden Markov Models*, it's can be assumed that the Medallion Fund also assumes, to some degree, that the market represents a hidden markov process.
 
-And hey, don't just take my word for it, [*Louis Bachelier*](https://en.wikipedia.org/wiki/Louis_Bachelier), credited to be the first person to model market price actions as stochastic processes (*and also the accidental discovery of Brownian Motion*), presented his now (*somewhat*) famous [*Bachelier Model*](https://en.wikipedia.org/wiki/Bachelier_model) on his PhD thesis (*Théorie de la spéculation, published 1900*) at the age of 30 s̶o̶ ̶m̶a̶y̶b̶e̶ ̶i̶t̶'̶s̶ ̶t̶i̶m̶e̶ ̶f̶o̶r̶ ̶y̶o̶u̶ ̶t̶o̶ ̶g̶e̶t̶ ̶a̶ ̶r̶e̶a̶l̶ ̶j̶o̶b̶, it was one of the first models that can be used to effectively determine the fair price of options, and it went on to inspire the creation of the infamous [*Black-Scholes Model*](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model), which for better or worse, was essential to this trillion dollar n̶a̶t̶i̶o̶n̶a̶l̶ ̶d̶e̶b̶t̶ financial derivatives industry we have today.
+As a side note, [*Louis Bachelier*](https://en.wikipedia.org/wiki/Louis_Bachelier), credited to be the first person to model market price actions as stochastic processes (*and also the accidental discovery of Brownian Motion*), presented his now (*somewhat*) famous [*Bachelier Model*](https://en.wikipedia.org/wiki/Bachelier_model) on his PhD thesis (*Théorie de la spéculation, published 1900*) at the age of 30 s̶o̶ ̶m̶a̶y̶b̶e̶ ̶i̶t̶'̶s̶ ̶t̶i̶m̶e̶ ̶f̶o̶r̶ ̶y̶o̶u̶ ̶t̶o̶ ̶g̶e̶t̶ ̶a̶ ̶r̶e̶a̶l̶ ̶j̶o̶b̶, it was one of the first models that can be used to effectively determine the fair price of options, and it went on to inspire the creation of the infamous [*Black-Scholes Model*](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model), which for better or worse, was essential to this trillion dollar n̶a̶t̶i̶o̶n̶a̶l̶ ̶d̶e̶b̶t̶ financial derivatives industry we have today.
 
 # Usage
 

legacy/README.MD

@@ -0,0 +1,5 @@
+
+
+- As an example illustrating the market as a markov process, let's imagine the prices for NVDA is a markov process, where each time step $t$, holds a transition probability distribution. For simplicity, say $30\%$ going up, $30\%$ going down, $40\%$ staying flat. If d̶a̶d̶d̶y̶ Jerome Powell said "AI" four times during a news conference at 3PM, this event may cause the probability of going up to increase, say to $50\%$, while decreasing the probability for the other two.
+
+- To provide a counter example, if Jimmy estimates that J̶i̶m̶m̶y̶'̶s̶ ̶0̶-̶D̶T̶E̶ ̶F̶D̶ ̶p̶u̶t̶ NVDA will close i̶n̶ ̶t̶h̶e̶ ̶m̶o̶n̶e̶y̶ at $\$150$ simply based on the fact that J̶i̶m̶m̶y̶ ̶h̶a̶s̶ ̶a̶ ̶s̶m̶o̶o̶t̶h̶ ̶b̶r̶a̶i̶n̶ it was $\$140$ at 3PM, we wouldn't consider Jimmy's argument to be very valid, no offense to all the innocent r̶e̶g̶r̶e̶s̶s̶i̶o̶n̶ ̶m̶o̶d̶e̶l̶s̶ Jimmys in the world.