The devil is in the detail they say. And one detail that has been nagging me extra lately is the issue mentioned in A few simple rows – Restated  that I’m still not sure if my model successfully can ensure positive asset weight only. A feature which I believe is essential for having an investment strategy accessible to anyone, and not only hedge funds. As you will see in this post, this issue is an easy fix. Although, the solution was not what I expected.  I will demonstrate two different models for obtaining dynamic and optimal values of theta, followed by two different methods for translating these thetas into asset weight within my portfolio. In total, this will result in four different model+method combinations for which each combination’s portfolio performance is presented in the end. Are you ready? Model A The first model is the one currently used for obtaining the values of theta within my investment strategy up to date. Since I have already shown you all details behind...

A lot of developments have been made since I first started to open the black box  and shared my investment strategy with you in as in  A few simple rows . Also, as promised, I will today show you the details of my most recent strategy. Namely, the Dolvol + Mom (Dynamic) strategy from Let’s turn the GAS on .  A lot of the things that I show here today are already included in old posts. And for any frequent readers, that may seem a bit repeating. However, since I want everything that I do here to be as open and accessible as possible, I have decided to compile all my most up-to-date work here in one place.  Starting with the method, my investment strategy uses a combination of the parametric portfolio policy  and a generalized autoregressive score  (GAS) model to decide which stocks within the OMX Stockholm 30 Index  to invest in each month.  In essence, I model the asset weights of each stock each month as where 1/N stands for equally weighted benc...

It’s time to present a new alteration of my investment strategy. In doing so, I take use of a model that I have been aiming to include ever since the very start of this project. Namely, the generalized autoregressive sore model, or GAS.  The idea is to use GAS in combination with the parametric portfolio policy  and thereby obtain more dynamic or time-varying values of theta to determine the asset weights. I will soon show you how to do so in practice, and I will also show that this yields good potential for higher returns. But first and foremost, here follows some more theoretical details concerning GAS. I. Generalized Autoregressive Score (GAS) In short, I use GAS for modelling dynamic variables (i.e., dynamic values of theta) via functions of lagged and predetermined variables. This is probably best expressed in the equation below. Omega (ω) stands for the long run or unconditional mean. Hence, this is the value that theta is supposed to converge towards in the long run. B...

The efficient market hypothesis  states that stock prices already reflect all information available on the market, making it sort of impossible for any investor to generate alpha. Some strong believers of this hypothesis, including my favourite finance professor, would even go so far as to state that any abnormal investment gains are only due to pure luck.  Following the somewhat discouraging results since Update #0826 , I plan to dedicate this today's post to comparing my own investment strategy with a set of completely random ones. Compared to those, it might be that I currently just happen to be out of luck.   I want the random strategies to work under similar conditions as my own. That is, the investible stock universe should still be restricted to the OMX Stockholm 30 Index, no short-selling should be allowed, and I require a monthly reallocation scheme.  Keeping this in mind, I start with generating randomized stock weights for, in total, 100 random portf...

As I have shown you already in Let's open the black box and A few simple rows , I currently use the two asset factors past trading volume (dolvol) and market beta (beta) to find the optimal asset allocation in my investment strategy. However, a natural question following this is, of course, “Why am I using these two factors in particular?”.  One of the reasons to start with is that I only turn to asset factors that can be constructed using completely available financial data. My source of such data consists mainly of the sorts that are available via the yfinance python package and the Kenneth R. French data library . The different types of data that I do have access to are, in short, different kinds of stock prices (open, close, adjusted close, high, and low), trading volumes, and some types of factor portfolio returns (market returns, small-minus-big returns, value-minus-growth returns, etc.). And this makes the universe of available asset factors somewhat restricted.  Neve...

This Monday, it is time for a new monthly investment in which I will also use the data available as of 1 August 2022. When doing so, one question worth considering is “how should my previous chosen thetas account for this new market information? The most basic and safe-card-ish way would be to continue with my fixed and previously optimized thetas. But what if it is possible to obtain even better or even more optimal thetas if I optimize over a period containing more and/or more recent information?     Considering this, I look at three different potential strategies for estimating theta. First, I look at a static strategy where I simply keep my previously estimated thetas. I hence continue using these to find my asset weights as described in A few simple rows  Second, I consider an expanding window strategy where I re-estimate the values of theta by including each additional month’s worth of information as it becomes available. Third, I consider a moving window strat...

--- I encourage all of you to see A few simple rows – Restated for the most up-to-date work --- Today, I show you a simple illustration of how the investment strategy works. For brevity, I choose to focus on only five of the most popular OMX 30 constituents. Doing so, I overcome some of the problems associated with irregular pricing dates and missing values and my code will hopefully also become easier to follow.  First, we need data and I use yfinance to download historical prices and volumes.   Second, I take out the adjusted close prices and volumes from the total data frame. These will be used for calculating stock returns and the two asset factors of past trading volume and market beta .  Before we continue any further, it now makes sense to show you some of the math behind the strategy that is largely based on the parametric portfolio policy . If you want to even more about this topic, I recommend you take a look at my master's thesis in finance (a...