Personal portfolio optimization notes based on ‘Portfolio Optimization: Theory and Application’ by Daniel Palomar. I have no claim on the original material; these are simply concepts documented from my perspective.
In the previous sections we were looking at single stock and time and asking “Can yesterday predict today?”. Which is realm of Machine #1, which we try to get μ\mu and ∑\sum, asset structure is about optimisation, Machine #2. In asset structure, we basically stop considering the assets one by one independently and model them jointly. This is … Read more
The other question is: is the stock market a completely random casino, or are there hidden patterns we can predict?, in math jargon terms: If the market is i.i.d., then we would have no Machine #1 to predict future μ\mu and σ\sigma. Academics in the 1970s studied the market and created a rule called the Efficient-Market Hypothesis (EMH). EMH … Read more
Vanilla Markowitz assumes that the stock market behaves like a perfect bell curve, which also known as Gaussian (Normal) Distribution: Gaussian Distribution is very useful for explaining physical concepts like human height or thermal noise, because physical world have limitations. Whereas finance world involved with human emotions, that’s where everything mixes up. If we use … Read more
The price of an asset is the most obvious quantity in financial markets. Denoted by pt.p_t. For future references: So why do we take logarithm of raw price? Because raw prices doesn’t show the percentage, where we care about percentage For example, We have two stocks with A=10$ and B=100$. If both stocks go up by … Read more
In academic finance, “stylised facts” simply means “Universal Rules of Thumb”. These are the behaviours that happen so consistently across all markets and all decades so that we accept them as facts. Let’s start to explain harsh realities of stock market: How do we choose our data then? There are 3 ways to look at … Read more
The two main components for portfolio design are data modeling and portfolio optimisation. In above figure, the μ\mu and ∑\sum are bold, meaning that they represent vectors and matrices. Because we are dealing with all stocks at once, we have lists and grids. Flowchart is simple: Resources Portfolio Optimisation: Theory and Application by Daniel P. Palomar, Page 4.
Modern portfolio theory started with Harry Markowitz. His idea is that risk-averse investors should optimize their portfolio based on a combination of two objectives: In Pre-Markowitz era, investors also looked at expected return and risk, but instead of considering overall portfolio, they considered every single stock in isolation, Markowitz changed this by looking at the … Read more