Asset Allocation in Python

Asset allocation is the most important decision that any investor needs to face, and there is no one-size-fits-all solution that can work for each and every investor. By asset allocation, we mean spreading the investor's total investment amount over certain assets (be it stocks, options, bonds, or any other financial instruments). When considering the allocation, the investor wants to balance the risk and the potential reward. At the same time, the allocation is dependent on factors such as the individual goals (expected return), risk tolerance (how much risk is the investor willing to accept), or the investment horizon (short or long-term investment).

The key framework in asset allocation is the modern portfolio theory (MPT, also known as mean-variance analysis). It was introduced by the Nobel recipient Harry Markowitz and describes how risk-averse...

Evaluating the performance of a basic 1/n portfolio

We begin with inspecting the most basic asset allocation strategy: the 1/n portfolio. The idea is to assign equal weights to all the considered assets, thus diversifying the portfolio. As simple as that might sound, DeMiguel, Garlappi, and Uppal (2007) show that it can be difficult to beat the performance of the 1/n portfolio by using more advanced asset allocation strategies.

The goal of the recipe is to show how to create a 1/n portfolio, calculate its returns, and then use a Python library called pyfolio to quickly obtain all relevant portfolio evaluation metrics in the form of a tear sheet. Historically, a tear sheet is a concise, usually one-page, document, summarizing important information about public companies.

How to do it...

Finding the Efficient Frontier using Monte Carlo simulations

According to the Modern Portfolio Theory, the Efficient Frontier is a set of optimal portfolios in the risk-return spectrum. This means that the portfolios on the frontier:

• Offer the highest expected return for a given level of risk
• Offer the lowest level of risk for a given level of expected returns

All portfolios located under the Efficient Frontier curve are considered sub-optimal, so it is always better to choose the ones on the frontier instead.

In this recipe, we show how to find the Efficient Frontier using Monte Carlo simulations. We build thousands of portfolios, using randomly assigned weights, and visualize the results. To do so, we use the returns of four US tech companies from 2018.

How to do it...

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Finding the Efficient Frontier using optimization with scipy

In the previous recipe, Finding the Efficient Frontier using Monte Carlo simulations, we used a brute-force approach based on Monte Carlo simulations to visualize the Efficient Frontier. In this recipe, we use a more refined method to determine the frontier.

From its definition, the Efficient Frontier is formed by a set of portfolios offering the highest expected portfolio return for a certain volatility, or offering the lowest risk (volatility) for a certain level of expected returns. We can leverage this fact, and use it in numerical optimization. The goal of optimization is to find the best (optimal) value of the objective function by adjusting the target variables and taking into account some boundaries and constraints (which have an impact on the target variables). In this case, the objective function is a function...

Finding the Efficient Frontier using convex optimization with cvxpy

In the previous recipe, Finding the Efficient Frontier using optimization with scipy, we found the Efficient Frontier, using numerical optimization with scipy. We used the portfolio volatility as the metric we wanted to minimize. However, it is also possible to state the same problem a bit differently and use convex optimization to find the Efficient Frontier.

We can reframe the mean-variance optimization problem into a risk-aversion framework, in which the investor wants to maximize the risk-adjusted return:

Here, γ ∈ [0, ∞) is the risk-aversion parameter, and the constraints specify that the weights must sum up to 1, and short-selling is not allowed. The higher...