Portfolio management: an experience during COVID-19

The purpose of this article is to analyze Brazilian indexes using Modern Portfolio Theory and check if it works in a challenging scenario.

Introduction

During black swan events is hard to discuss portfolio management and how to invest during such uncertain times. Especially if you are outside Brazil and must worry about the value of your currency. Systematic risk cannot be eliminated, such as economic pitfalls where the government can deceive their citizens creating artificial inflation rates, which is possible in developing economies. In terms of stocks, systemic risks are a set of scenarios in which a certain business can no longer exist, and they are difficult to predict. Examples of these unpredictable scenarios are happening with the stocks of airline companies and businesses that are focused on tourism, it is difficult to predict their future.

One well-known strategy to select a portfolio is MPT (Modern Portfolio Theory) by Harry Markowitz in 1952. The idea is to look at diversification using covariance between options to select a portfolio with minimum risk or, for a given return, provides the minimum risk (efficient frontier). All individual assets will determine the curve and a subset of all assets with a certain weight has the best solution on the curve.

Figure 1 — Concept of the efficient frontier. It is possible to determine a curve that captures the return with less risk. (font: analystnotes.com @2020–04–05)

The experiment

To avoid the potential for unreliable results due to biased information stemming from knowledge of the past, this study will adopt a systematic approach to portfolio creation. Specifically, a portfolio procedure will be established over a span of more than ten years, with periodic re-evaluation. This method will ensure the use of a standardized index, without any predetermined selection of a particular option.

Portfolio options

In Brazil, several widely recognized indexes are utilized by investors to assess the performance of the market. This analysis utilized the following indexes:

1. IPCA — An index that tracks the inflation rate in the country, with some government stocks benchmarked to this index and an additional value, such as IPCA+4% in a given year.
2. Poupança — A long-standing index that offers high liquidity for remunerated investment funds.
3. CDI — A financial system index offered by institutions for investment purposes.
4. Ouro — The gold index.
5. Boi — The cattle index, included in this analysis due to personal interest.
6. IBOVESPA — The Brazilian stock market index.
7. Dólar — The exchange rate between the Brazilian Real and the US Dollar.

To comprehend the interactions between these options, covariance and correlation are useful starting points, as depicted in Figure 2.

Figure 2 — Example of investment covariance for the period of 2009–01 to 2020–03.

A good and healthy portfolio to protect from risks should have these negative values of covariance (and correlation) between the options. (Ex: IBOVESPA and dollar usually dance in different directions).

Procedure to create the portfolio

As previously noted, this study establishes a portfolio over a ten-year period, with annual evaluations. At the start of each year, an analysis of the preceding twelve months will be conducted, and a portfolio for the entire year will be established.

Rather than aiming for the minimum risk on the efficient frontier, a fixed target return was established as the objective for the portfolio and the recommendation was followed accordingly.

Results and discussions

The portfolio uses only the standard index as mentioned and was able to beat the CDI index, which is one of the purposes. IBOVESPA are [RAM1] not behaving as a growth economy. The Dollar slightly beat the index on March/2020, although it was presented on the portfolio in times of uncertainty.

Figure 3 — Time series created by the portfolio showing above-average results thought the analyzed period. The series ends in 2020-March.

Figure 4 — Percentage of Dollars on the portfolio. In 2019 and 2020 there were recommendations to allocate around 10%

The selection for 2020 provided by the simulation was able to protect the portfolio from a huge drop that (we know now) happened in the market. Note that the IBOVESPA in 2019 provided a great return (but with high risk) and the dollar was added to the portfolio as an edge from this risk.

Table 1 — Recommend portfolio for 2020. Expected return every month with the volatility expected. The volatility was the biggest if compared with the other simulated years. The expected return is a fixed value for all the years during the simulation. (0.86% per month)

Figure 5 — Efficient frontier for the proposed Portfolio. Analyzed at the end of 2019 as described in the procedure session.

Conclusion and improvements

The portfolio, thus far, has shown promise even during catastrophic events. There are valuable insights to be gleaned from the allocation strategies. For example, in the most recent portfolio, allocating funds to the gold (Ouro) index may not have been an intuitive choice, as it showed a decline in value in 2019. However, its ability to retain value compared to other options proved to be a wise decision.

One potential improvement is to incorporate a forward-looking approach by utilizing predictive models for index selection. While this may not fully mitigate the impact of unpredictable black swan events, it could provide a more informed basis for decision-making.

Another improvement would be to incorporate real stock and market offerings into the portfolio options. This would entail including all Brazilian stock options in the analysis and evaluating not just the recommended options, but also other conservative investment opportunities.

See my repository for the source code: https://github.com/robertoamansur/finance_analysis