Handling Uneven Stock Return Histories in Portfolio Analysis

# Data Issue: Observations in Portfolio Construction


# Data Issue: Observations in Portfolio Construction












## Question

- With 60 data observations, how do I construct a time series analysis properly?

- How to do Certain Calculations such as covariances on data with Gaps and Inconsistencies?

## Background of Question

- I'm currently setting out on doing an assignment for a portfolio theory class

## Dataset Characteristics

- 15 stocks with their price-adjusted monthly returns from 1986-2016 (roughly 400 monthly observations) listed on the ISEQ (Irish Stock Exchange)

## What I think are Data Issues

Allocated stocks do not have like-for-like observations - stocks listed at different times have different numbers of observations for each stock. ( Non-uniform time series)

Only have 60 observations where all stocks have data from the same time period/across the panel.(Do you mean columns? do you mean same dates?)

( Insert screenshot of data points)

- One stock in particular only has 60 observations and is extremely 'blocky' in its returns characteristics. ( ( Insert screenshot of data point)

## Data may cause me problems when I:

Calculate covariances

- should I use the full array (~400 of observations) of my oldest stock (for variance calculations) against the 60 observations of this problematic stock when calculating the variance co-variance matrix?

Compare like with like and cut my observations across my portfolio to 60 observations

- Am I sacrificing descriptive power in my outputs if I do this?

My humblest thanks and best wishes, CM.

## Answer by Ted Taylor of Life (score 2)

https://quant.stackexchange.com/a/34090

Your question shows that you are beginner in time series analysis. Welcome!

## Long Answer to your question

A common approach to analyzing unevenly spaced time series is to transform the data into equally spaced observations using some form of interpolation - most often linear - and then to apply existing methods for equally spaced data. However, transforming data in such a way can introduce a number of significant and hard to quantify biases especially if the spacing of observations is highly irregular.

## Short Answer

It depends

## Where you will find your answers to all of your questions

First start here:

Chapter 10 Introduction to Time Series Analysis Introduction to Time Series Analysis. Lecture 1

Then read these papers as well as what others have shared

- Granger Causality Analysis in Irregular Time Series

- A Framework for the Analysis of Unevenly Spaced Time Series Data

## Please make sure you understand what you are asking otherwise others will not be so nice.

- This means googleing and putting in some effort.Effort is not easy, but part of struggle is important and called 'learning.'

- We are here to help you when you show us your struggles, so that we can help you with little to no effort =)

Do not be discouraged, ask questions, but make sure you google first.

Welcome to QuantFinance Stack Exchange!

## Answer by Alexandre Oliveira (score 1)

https://quant.stackexchange.com/a/33874

For your assignment, use only the returns that you have available, even if they are not complete for entire period. You will be able to run all your analysis.

Notice that This is not a good solution in real world cases, if you want to use your covariance/correlation matrix for optimization or monte carlo simulation as using pairwise correlations may lead to non positive semi-defined matrices.

## Answer by Matthew Gunn (score 0)

https://quant.stackexchange.com/a/34094

Something fairly standard to do is to work with the returns of portfolios constructed on individual firm characteristics rather than the firms themselves. Some basic problems working directly with firms:

- As you discussed, firms come and go from the sample.

- As several have mentioned in the comments, firms can significantly change. Apple in 2005 was a computer hardware company. In 2015, Apple was a mobile phone company, its revenues dominated by iPhone. Shouldn't we expect the covariance properties to be significantly different!?

- If you only use firms where you have data for all years, you are conditioning inclusion in your sample on not delisting, and you may render your estimate of expected returns upwards biased and inconsistent! If someone wrote, "My sample is constructed of all firms which did not go bankrupt or get acquired" or "My sample is constructed of all firms which eventually made it into the S&P500," do you think those firms had above average returns? Of course they did! In general in finance, you can make huge mistakes by using $t+1$ information at time $t$.

If we're willing to do simple, 1980s style finance, a sensible method is to construct yearly rebalanced portfolios based upon firm characteristics known at the time (or several months previously to be safe). The idea is that the portfolio returns will be more stable over time in terms of their statistical properties than individual companies.

As @Alex27629 mentions, you probably can do most of your analysis using only data you have for each company. I'd expect you get defensible results for the purposes of your project.

## Answer by cykor21 (score -1)

https://quant.stackexchange.com/a/33528

- It is unclear what the 'portfolio assignment' is and what kind of results you are expected to deliver.

- 60 points of data points (monthly) when it comes to stock returns is more than enough; whereas conclusions based 20 years of data do not seem reliable as a company in its first 5 years of existence will be completely different than the same company 15 years later - given the company still exists.