Allocating Risk Between US Sectors as a Portfolio Optimization Strategy, A Study on Risk Parity and Risk Budgeting Portfolio Optimization

Abstract

This thesis aims to study the performance and characteristics of a risk parity and risk budgeting portfolio. The portfolios were constructed by investing in the 11 primary GICS sectors using volatility as the risk measure and market cap weights as budgets for the risk budgeting portfolio. The minimum variance, equally weighted and weight budgeting portfolios were constructed as benchmarks to compare the results. Additionally, the objective portfolios were constructed using the expected shortfall as the risk measure to see if this reduced loss during periods of market stress. Since the covariance matrix is of great importance, two different shrinkage targets were tested, namely a cross-sectional average and a historical target, where the correlation and volatility were shrunk separately. The data used were daily data of US stocks from 1990 to 2022, in addition to testing the same optimization methods on daily sector ETF data from 2017-2022.

The portfolios were constructed as buy-and-hold portfolios with yearly rebalancing where returns and payouts were assumed reinvested. To examine the portfolios, the performance measures investigated included the annualized average return (arithmetic and geometric average in the form of the CAGR), standard deviation, Sharpe ratio, maximum drawdown and the Calmar ratio. In addition, to account for uncertainty in the Sharpe ratio, the probabilisticand deflated Sharpe ratio were examined. To compare the characteristics of the portfolios, relative weight evolutions were plotted, and concentrations were measured in the form of the Herfindahl-Hirschman Index, HHI.

When allocating investments between sectors, both the risk parity and risk budgeting portfolio worked well in avoiding highly concentrated portfolios while the risk of the assets was considered, in opposition to the equally weighted and weight budgeting portfolio. The portfolios did not outperform in terms of achieving higher returns but showed to be robust choices compared to the highly parameter-sensitive minimum variance portfolio.

The study did not find clear evidence of a shrunk covariance matrix obtaining less error than the sample covariance matrix compared to the realized. Neither did the risk parity nor the risk budgeting portfolio show decreased losses when constructed with the expected shortfall as the risk measure.