AGORA International Journal of Economical Sciences, http://univagora.ro/jour/index.php/aijes 

ISSN 2067-3310, E-ISSN 2067-7669 

Vol. 19, No. 1 (2025), pp. 329-340 

 

329 

 

EXCHANGE-TRADED FUNDS (ETFS) OPTIMIZATION WITH RISK 

PARITY STRATEGIES 

 

D. VELIU 

 

Denis Veliu  

Universiteti Metropolitan Tirana, Albania  

https://orcid.org/0000-0002-6930-7292, E-mail: dveliu@umt.edu.al  

  

Abstract: This paper explores the application of the Risk Parity methodology to 

portfolios constructed using Exchange-Traded Funds (ETFs). In the world where the market 

is becoming more and more global, it is becoming more dynamic in terms of portoflio 

recalibrations, bringing resilience in terms of values. In other words, is it important to 

consider only a short holding period, and adapt the asset allocationn. In opposition to typical 

capital-weighted techniques, risk parity reallocates portfolio weights to ensure that each 

asset contributes an equal amount of risk. The study builds and assesses risk parity portfolios 

using ten assets that comprise the majority of the EA Bridgeway Blue Chip ETF (BBLU). The 

process entails assessing the volatilities and correlations of specific ETFs, adjusting portfolio 

weights to balance risk contributions, and back testing performance under different market 

scenarios. Empirical data shows that risk parity portfolios outperform standard allocation 

approaches in terms of diversification, drawdowns, and the stability of risk-adjusted returns. 

This research illustrates Risk Parity's potential as a strong framework for managing ETF 

portfolios in both institutional and individual investing settings. 

Keywords: Risk Parity, ETF, Portfolio Optimization, Asset allocation, Risk. 

 

Introduction  

Modern finance focuses on risk management and portfolio development. Traditional 

portfolio allocation approaches, such as the 60/40 equity-bond split, prioritize capital 

allocation, which frequently results in an imbalance in risk contributions across asset classes 

(Maillard et al., 2010, pp.2). This strategy can lead to an overreliance on more volatile assets, 

such as stocks, while undervaluing the potential diversification benefits of less volatile asset 

classes, such as bonds or commodities. Risk Parity (RP) provides an alternative paradigm that 

reallocates weights to ensure that each asset contributes equally to overall portfolio risk, 

resulting in a more balanced and diversified portfolio structure (Qian, 2011, pp.2). 

The application of Risk Parity to portfolios built with Exchange-Traded Funds (ETFs) 

is a significant step toward implementing advanced portfolio methods. ETFs are well-known 

for their cost-effectiveness, liquidity, and accessibility, making them an excellent vehicle for 

adopting systematic approaches such as Risk Parity. ETFs also give exposure to a diverse 

variety of asset classes, such as stocks, bonds, commodities, and real estate, which is critical 

for attaining broad diversification (Hill et al., 2015, pp.6).  

This article brings at the practical use of the Risk Parity technique using ETFs.It focus

es on creating portfolios that balance risk contributions across specific ETFs while taking into

https://orcid.org/0000-0002-6930-7292
mailto:dveliu@umt.edu.al


EXCHANGE-TRADED FUNDS (ETFS) OPTIMIZATION WITH RISK PARITY STRATEGIES 

330 

 

 account real world restrictions such as transaction costs and leverage requirements. The 

Conditional Value at Risk (Rockfellar & Uryasev, 2000), or the Expected Shortfall (Artzner 

& Delbaen, 1999) and the traditional mean-variance (Markowitz, 1952), will result in a 

strong concentration on a limited number of assets and poor performance during the out-of-

sample period. These models also rely on predicted returns (Markowitz, 1978, pp.2), which 

are usually calculated using financial models or historical data. These projections are not 

without uncertainty, though, and can be impacted by a number of variables, including shifts 

in investor mood, market circumstances, and economic developments. Suboptimal portfolio 

allocations and performance may result if the predicted returns utilized in the portfolio model 

prove to be incorrect. According to Merton (1980, pp.2), portfolio models that mainly depend 

on expected returns may be extremely vulnerable to shifts in those assumptions. 

The ten biggest blue chip stock part of EA Bridgeway Blue Chip ETF (BBLU) are 

selected and optimized in the Risk Parity model using 𝐶𝑉𝑎𝑅𝛼(𝑥) as a risk measure. The 

partial derivatives of the Conditional Value at Risk can be calculated using approximation 

techniques (Tasche, 2000, pp.3). The comparison using Risk Parity methods is made with 

several risk measurements (Conditional Value at Risk and standard deviation) in order to 

obtain a comprehensive pattern. Although the findings are quite similar, it takes a lot less 

time to calculate Risk Parity with Conditional Value at Risk. 

 

Research methodology 

This section outlines the empirical framework for evaluating the six portfolio 

strategies for the ten biggest blue-chip stocks comprising the EA Bridgeway Blue Chip ETF 

(BBLU). The goal is to compare their risk-adjusted performance, diversification benefits, and 

robustness. To provide a complete framework for the portfolio models, the following are 

considered: 

1. 1/N Naïve Portfolio with the same weight for each asset (10% of each asset);  

2. Mean variance without the expected return constrain (MV);  

3. Minimum CVaR (Andersson et al., 2000) without the expected return constrain;  

4. Risk Parity with standard deviation (RP-std); 

5. Risk Parity with Expected shortfall or CVaR (RP-CVaR); 

6. Worst case Risk Parity CVaR (RP-CVaR Naïve);    

The last one is a special case for the worst-case scenario (highest CVaR), useful as an 

upper bound (Colucci, 2013). A similar study was conducted with cryptocurrencies (Veliu & 

Aranitasi, 2024). 

In all these models, the constraint of expected returns is removed, so the minimum 

variance MV and minimum CVaR are at the smallest possible value of the risk measure. 

For a portfolio with n assets, each weight xi and ℛ(𝑥) as a risk measure for the portfolio, the 

vector of the weights is given by:  

x = (x1, x2,.....,xn).  

In the literature (Maillard et al., 2010 p.1), the use of Risk Parity is the case with the 

standard deviation as risk measure. For a portfolio with n assets and weights x = (x1, 

x2,.....,xn), the standard deviation is: 



Denis VELIU 

331 

 

ℛ(𝑥) = 𝜎𝑃(𝑥) = √∑ ∑ 𝑥𝑖𝑥𝑗𝜎𝑖𝑗

𝑛

𝑗=1

𝑛

𝑖=1

= √𝑥′Ω𝑥 

where Ω is the covariance matrix. The marginal risk contribution of the i asset: 

𝑀𝑅𝐶𝑖(𝑥) =
𝜕𝜎𝑃(𝑥)

𝜕𝑥𝑖
=

𝜕𝜎𝑖
2 + ∑ 𝑥𝑖𝜎𝑖𝑗

𝑛
𝑗=1

𝜎𝑃(𝑥)
=

(Ω𝑥)𝑖

√𝑥′Ω𝑥
 

and the total risk contribution: 

𝑇𝑅𝐶𝑖(𝑥) = 𝑥𝑖

𝜕𝜎𝑃(𝑥)

𝜕𝑥𝑖
= 𝑥𝑖

𝜕𝜎𝑖
2 + ∑ 𝑥𝑖𝜎𝑖𝑗

𝑛
𝑗=1

𝜎𝑃(𝑥)
= 𝑥𝑖

(Ω𝑥)𝑖

√𝑥′Ω𝑥
 

The following optimization problem can be used to construct the Risk Parity model: 

𝑥∗ = arg min ∑ ∑ (𝑇𝑅𝐶𝑖(𝑥) − 𝑇𝑅𝐶𝑗(𝑥))
2

𝑛

𝑗=1

𝑛

𝑖=1

 

∑ 𝑥𝑖 = 1

𝑛

𝑖=1

 

𝑥 ≥ 0 

To guarantee the existence of the partial derivatives of 𝐶𝑉𝑎𝑅𝛼(𝑥) some assumptions are 

needed on the distribution of the random vector R = (r1, r2,.....,rn) .  

 The conditions for quantile of the portfolio return 𝑋 = 𝑅′𝑥 = ∑ 𝑥𝑖𝑟𝑖
𝑛
𝑖=1  should be 

differentiable respect to the weights 𝑥𝑖.  These i-th asset return 𝑟𝑖 given the others is measured 

as follow: 

𝑟𝑖,𝑡+1 =
𝑃𝑖,𝑡+1 − 𝑃𝑖,𝑡

𝑃𝑖,𝑡
 

From the definition of  𝐶𝑉𝑎𝑅𝛼(𝑥) (Rockfellar & Uryasev, 2000, pp.2) is as follow: 

𝐶𝑉𝑎𝑅𝛼(𝑥) =
1

α
∫ 𝑉𝑎𝑅𝑣(𝑥)d𝑣

α

0

 

Thus, partial derivatives are calculated as follow: 

𝜕𝐶𝑉𝑎𝑅𝛼(𝑥)

𝜕𝑥𝑖
=

1

α
∫

𝜕𝐶𝑉𝑎𝑅𝛼(𝑥)

𝜕𝑥𝑖
d𝑣

α

0

= −
1

α
∫ 𝐸[𝑟𝑖|−𝑅′𝑥 = 𝑉𝑎𝑅𝛼(𝑥)]d𝑣 =

α

0

 

−
1

α
∫ 𝐸[𝑟𝑖|𝑋 = 𝑞𝛼(𝑋)]d𝑣 =

α

0

−  𝐸[𝑟𝑖|𝑋 ≤ −𝑉𝑎𝑅𝛼(𝑥)] 

The Total Risk contribution for each asset i of a portfolio is given from the following 

expression: 

𝑇𝑅𝐶𝑖
𝐶𝑉𝑎𝑅𝛼(𝑥)

(𝑥) = 𝑥𝑖

𝜕𝐶𝑉𝑎𝑅𝛼(𝑥)

𝜕𝑥𝑖
 

The expression in case of continuous returns distribution is the following: 

𝑇𝑅𝐶𝑖
𝐶𝑉𝑎𝑅𝛼(𝑥)

(𝑥) = −𝑥𝑖𝐸[𝑟𝑖|𝑋 ≤ −𝑉𝑎𝑅𝛼(𝑥)] 

 

𝐶𝑉𝑎𝑅𝛼(𝑥) = ∑ 𝑇𝑅𝐶𝑖
𝐶𝑉𝑎𝑅𝛼(𝑥)

(𝑥)

𝑛

𝑖=1

= − ∑ 𝑥𝑖𝐸[𝑟𝑖|𝑋 ≤ −𝑉𝑎𝑅𝛼(𝑥)]

𝑛

𝑖=1

 



EXCHANGE-TRADED FUNDS (ETFS) OPTIMIZATION WITH RISK PARITY STRATEGIES 

332 

 

Numerical approximation for estimating  𝑉𝑎𝑅𝛼(𝑥) and 𝐶𝑉𝑎𝑅𝛼(𝑥) Risk Parity using 

historical data the following assumption are neccessary.   

The calculation of 𝑉𝑎𝑅𝛼(𝑥) and 𝐶𝑉𝑎𝑅𝛼(𝑥) of portfolio returns as follows: 

𝑉𝑎𝑅𝛼(𝑥) ≈ −𝑟p⌊αT⌋
sorted 

𝐶𝑉𝑎𝑅𝛼(𝑥) ≈ −
1

αT
∑ 𝑟p j

sorted

⌊αT⌋

j=1

 

Where the i-th asset return ri consist of T number outcomes  rji with i=1,.....,n and j=1,...,T.  

The vector of the observed portfolio returns is 𝑅𝑃 = (𝑟𝑝1, … . . , 𝑟𝑝𝑇) where: 

𝑟𝑝𝑗 = 𝑥′𝑟𝑗 with j=1,....,T where 𝑟𝑗 = (𝑟𝑗1, … . . , 𝑟𝑗𝑇). 

where α is level of significance and  rp j
sortedare the sorted portfolio returns such as 

𝑟𝑝 1
𝑠𝑜𝑟𝑡𝑒𝑑 ≤ 𝑟𝑝 2

𝑠𝑜𝑟𝑡𝑒𝑑 ≤ ⋯ 𝑟𝑝 𝑗
𝑠𝑜𝑟𝑡𝑒𝑑 ≤ ⋯ ≤ 𝑟𝑝 𝑗

𝑠𝑜𝑟𝑡𝑒𝑑 

With the time series observation, the approximation of the partial derivatives 𝐶𝑉𝑎𝑅𝛼(𝑥) for 

each asst i becomes: 
𝜕𝐶𝑉𝑎𝑅𝛼(𝑥)

𝜕𝑥𝑖
≈ −

1

αT
∑ 𝑟k i

sorted⌊αT⌋
k=1

 i=1,...,n 

and then the total risk contribution of asset i is 

𝑇𝑅𝐶𝑖
𝐶𝑉𝑎𝑅𝛼(𝑥)

(𝑥) = 𝑥𝑖

𝜕𝐶𝑉𝑎𝑅𝛼(𝑥)

𝜕𝑥𝑖
≈ −

1

⌊αT⌋
𝑥𝑖 ∑ 𝑟k i

sorted

⌊αT⌋

k=1

 

where 𝑟k i
sorted  are the corresponding returns of asset i to the sorted portfolio returns. 

In the rolling windows, in order to the measure the performance the following calculation 

𝜇𝑇
𝑐 (𝑅𝑃) is the compounded return over the whole period (terminal compound return) (Bacon, 

2008, pp.130). 

𝜇𝑘
𝑐 (𝑅𝑃) = ∏(1 + 𝑟𝑝𝑗)

𝑘

𝑗=1

− 1 

To check if the portfolios are well diversified, three diversification measures are considered 

(Caporin et al., 2012). 

If the allocation is as follows,  x = (x1, x2,.....,xn)   with the constraint  ∑ 𝑥𝑖
𝑛
𝑖=1 = 1 in case 

short sales not allowed (𝑥𝑖 ≥ 0) .  The diversification measure is the Herfindal index: 

𝐷𝐻𝑒𝑟 = 1 − 𝑥𝑥′ 

In the same way, the diversification measure is given by (Bera & Park, 2004 p.2). 

𝐷𝐵𝑃 = − ∑ 𝑥𝑖log (𝑥𝑖) 

𝑛

𝑖=1

= ∑ 𝑥𝑖log (
1

𝑥𝑖
) 

𝑛

𝑖=1

 

The 𝐷𝐵𝑃 takes value between 0 (fully concentrated in one asset) and log(n) for the Naïve 

portfolio. 

Another important aspect is the consideration of the transaction costs, and for that, the 

estimation of the turnover of the portfolio: 

𝑇𝑂 = ∑ |𝑥𝑖
𝑡+1 − 𝑥𝑖

𝑡|𝑛
𝑖=1 , 

where 𝑥𝑖
𝑡 denotes the weight of asset i at time t. 

 



Denis VELIU 

333 

 

Results   

         In this study, the dataset covers the period from January 9, 2024 to January 8, 2025 with 

daily frequency.  The data is available at nasdaq.com.  

Table 1. Top EA Bridgeway Blue Chip ETF (BBLU)  

1 Meta Platforms, Inc. Class A Common Stock (META) 

2 NVIDIA Corporation Common Stock (NVDA) 

3 JP Morgan Chase & Co. Common Stock (JPM) 

4 Broadcom Inc. Common Stock (AVGO) 

5 Tesla, Inc. Common Stock (TSLA) 

6 Apple Inc. Common Stock (AAPL) 

7 Visa Inc. (V) 

8 Microsoft Corporation Common Stock (MSFT) 

9 Eli Lilly and Company Common Stock (LLY) 

10 Wells Fargo & Company Common Stock (WFC) 

Source: nasdaq.com 

The reason these stocks are selected is because they comprise the top components of 

the EA Bridgeway Blue Chip ETF (BBLU). In this way, it will be interesting to allocate the 

optimal weights using different strategies and compare their performance among them. 

Figure 1. The Heatmap of the correlation matrix 

 
Figure 1 presents a heatmap-style correlation matrix where each cell contains a 

numerical value representing the correlation between two variables. All diagonal values are 

100% (in red), which reflects perfect correlation of each variable with itself. Red: Represents 

the highest positive correlation (close to 100%). Green: Represents weaker or negative 

correlations. Yellow/Orange: Represents moderate positive correlations. The heatmap 

suggests a symmetric matrix (correlation matrices are symmetric by definition). The variables 

are represented both horizontally and vertically, indicating the relationship between the same 

set of items. Many variables exhibit strong positive correlations (>80%) as indicated by the 

red and orange cells. Clusters of high correlation suggest that certain variables behave 

similarly or share strong linear relationships. Yellow cells indicate moderate correlations 

(40%–70%). These relationships are still positive but weaker than the stronger clusters. 

Moderate correlations could imply indirect relationships or shared dependence on other 

factors. The -12.8% correlation stands out as a clear example of an inverse relationship 

between two variables. This suggests that as one variable increases, the other tends to 

decrease. Negative correlations, though rare in this matrix, might signal opposing behavior or 

complementary roles like in the case of ELI with VISA. 

META NVIDIA JPM AVGO TESLA APPLE VISA Micro ELI WFC

META 100.0%

NVIDIA 83.9% 100.0%

JPM 84.7% 88.8% 100.0%

AVGO 81.8% 82.1% 80.0% 100.0%

TESLA 68.7% 62.3% 79.3% 81.5% 100.0%

APPLE 71.7% 83.5% 81.6% 85.7% 78.7% 100.0%

VISA 67.6% 48.8% 71.0% 60.9% 80.0% 47.5% 100.0%

Micro 50.1% 61.3% 43.7% 56.2% 36.8% 50.2% 22.0% 100.0%

ELI 50.3% 66.1% 41.7% 44.1% 4.1% 53.3% -12.8% 53.2% 100.0%

WFC 71.9% 73.7% 87.9% 65.7% 73.3% 56.2% 78.8% 39.8% 11.1% 100.0%



EXCHANGE-TRADED FUNDS (ETFS) OPTIMIZATION WITH RISK PARITY STRATEGIES 

334 

 

 

Figure 2. The graph of the returns of the ten assets 

 
The Figure 2 represents the daily returns of 10 assets plotted over a time period of 

approximately 251 days. The daily returns fluctuate around zero, with the majority of returns 

falling within the range of -0.15 to 0.25. The spikes indicate days with significant movements 

in returns, likely driven by market events. From a visual inspection, there are some similar 

patterns across the lines, suggesting potential correlation between certain assets. 

Before creating a rolling window, in Table 2 are showed the first iteration using 125 

observations:  

 

Table 2. The allocation in % in of each of assets 

Optimization Model META NVIDIA JPM AVGO TESLA APPLE VISA Micro ELI WFC TOTAL 

R.P. with std 6.17% 5.17% 13.93% 5.27% 5.83% 12.19% 13.36% 11.39% 12.45% 14.24% 1 

Minimum Variance 0.00% 0.06% 14.35% 0.02% 0.07% 14.41% 31.43% 10.41% 15.48% 13.78% 1 

R.P. with CVaR 7.62% 5.65% 12.04% 6.60% 4.92% 11.63% 16.18% 11.68% 10.69% 12.98% 1 

Minimum CVaR 0.65% 4.44% 3.41% 0.00% 0.00% 15.25% 27.27% 9.06% 14.71% 25.20% 1 

Naïve 10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 1 

R.P. CVaR naïve 7.94% 4.19% 13.70% 4.29% 6.06% 13.29% 13.75% 10.49% 13.49% 12.81% 1 

 

Table 2 represents the portfolio weights for 10 assets under different optimization 

models. The Risk Parity (R.P. with std) with Standard Deviation, which aims to balance risk 

contribution across assets using standard deviation as the risk metric, is Heavily weighted on 

JPM (13.93%), Apple (13.36%), and ELI (12.45%). Minimum Variance focuses heavily on 

Apple (31.43%) and JPM (14.35%), with near-zero weights for META and others. Risk 

Parity with CVaR (Conditional Value-at-Risk) is similar to R.P. but uses CVaR to account 

for tail risk. JPM (12.04%) and VISA (16.18%) have higher weights, reflecting their 

perceived stability under extreme conditions. 

Minimum CVaR minimizes portfolio tail risk. VISA (27.27%) and WFC (25.20%) 

dominate the allocation, likely reflecting their low downside risk. Naïve (Equal Allocation) 

assigns an equal 10% weight to all assets, disregarding risk or return considerations. 

R.P. CVaR Naïve is a special case in which has the worst-case scenario (highest 

CVaR, useful as an upper bound (Colucci, 2013). JPM (13.7%) and VISA (13.75%) maintain 

higher weights but are more evenly distributed compared to other R.P. models. 



Denis VELIU 

335 

 

Naïve allocation provides the most diversified portfolio, while others heavily 

concentrate on specific assets. Minimum Variance and Minimum CVaR models allocate 

significant weights to assets with perceived lower risk. The JPM & VISA Dominance 

consistently receives higher weights in most models, indicating their importance in 

minimizing risk or balancing contributions. Tesla and AVGO tend to receive lower weights, 

likely due to higher volatility or correlation with other assets. 

In order to keep the portfolio updated, the calculation is made each week, based on the 

past 25 weeks, the asset allocation. The rolling window is made with L=125 days (6 months) 

and H=5 days, where L are the daily observations used to estimate the weights and H is the 

holding period for the performance of the portfolio using the compound return. The 

performance is given by the following graph 1. 

 

Graph 1. The performance of the portfolios in ETF fund using the compound return. 

 
Source: Computed with Matlab 

Graph 2. The performance of EA Bridgeway Blue Chip ETF (BBLU)  

 
Source: Nasdaq.com  



EXCHANGE-TRADED FUNDS (ETFS) OPTIMIZATION WITH RISK PARITY STRATEGIES 

336 

 

Graph 1 aims to evaluate how different portfolio optimization strategies perform over 

a rolling half-year period, with a five-day investment horizon, highlighting the trade-offs 

between return and risk for each strategy. Graph 1 presents a detailed comparison of the 

performance of different portfolio optimization strategies over time. Most strategies show 

similar patterns with noticeable ups and downs, reflecting market dynamics, for which are 

represented using the graph 2. By the end of the time period, some strategies (e.g., "Risk 

Parity CVaR" and "M-V") outperform others, reaching higher compound returns. The 

"Uniform" strategy (black) generally underperforms compared to other approaches. The first 

graph uses compound returns as the performance metric, whereas the second graph uses the 

ETF price. 

Graph 3. The riskiness of the portfolios measured by the standard deviation (Volatility) 

 
Source: Computed with Matlab 

Graph 4. The riskiness of the portfolios measured by the CVaR 

 
Source: Computed with Matlab 



Denis VELIU 

337 

 

The CVaR graph focuses on extreme downside risks, while the volatility graph 

examines total risk. If a strategy shows lower volatility (graph 3), it may also show lower 

CVaR (graph 4), but this is not always guaranteed. For instance, strategies designed to reduce 

overall risk (e.g., Risk Parity) might perform differently in tail-risk scenarios. The CVaR 

values are higher than volatility values, consistent with CVaR capturing extreme losses 

beyond a certain threshold, whereas volatility reflects average dispersion. Comparing the two 

graphs can reveal how a strategy balances overall risk (volatility) with tail risk (CVaR). A 

strategy with low CVaR but higher volatility may be suitable for risk-averse investors, while 

others might prefere strategies with low volatility for consistent returns. The patterns in the 

two graphs are likely similar in overall behavior, as both measure aspects of risk across time 

and are influenced by the same portfolio strategies. However, there may be some nuanced 

differences depending on how each metric reacts to market changes. 

Graph 5. The turnover of the portolios  

 
Source: Computed with Matlab 

Turnover measures the amount of trading required to rebalance a portfolio to align 

with a given strategy. Higher turnover generally implies higher transaction costs and more 

frequent portfolio adjustments. Mean Variance and CVaR are focused in a smaller number of 

stocks, thus the portfolio turnover will be higher. 

Graph 6. The number of assets focused 

 
Source: Computed with Matlab 



EXCHANGE-TRADED FUNDS (ETFS) OPTIMIZATION WITH RISK PARITY STRATEGIES 

338 

 

Risk Parity, being less sensitive to extreme market events or return estimates, 

generally has the lowest turnover. Another way to check the diversification is using the 

Herfindal and Bera Park indexes. 

Graph 7. The Herfindal Index 

 
Source: Computed with Matlab 

Graph 8. The Bera Park Index 

 
Source: Computed with Matlab 

The Herfindal (graph 7) and the Bera Park (graph 8) have the same traits with the 

highest value in the Uniform Portfolio and closer values with Risk Parity strategies. This 

means that these portfolios are well diversified. The CVaR and mean variance focus on less 

assets that have the same traits. 

All the algorithms are made coding in Matlab without using AI. Today there are 

several articles that compare the AI role (Tirana & Bejleri, 2024, p.2). 



Denis VELIU 

339 

 

CONCLUSIONS 

This study demonstrates the effectiveness of applying the Risk Parity methodology to 

optimize ETF portfolios, offering a compelling alternative to traditional portfolio allocation 

techniques. By focusing on balancing risk contributions rather than capital weights, Risk 

Parity provides a more diversified and stable investment framework. Using ten assets that 

comprise the EA Bridgeway Blue Chip ETF (BBLU), the research compared various 

optimization strategies, including Risk Parity with standard deviation, Risk Parity with 

CVaR, Minimum Variance, Minimum CVaR, and Naïve allocation. 

The results highlight the advantages of Risk Parity strategies in achieving superior 

diversification and risk-adjusted returns. Specifically, Risk Parity with CVaR proved 

particularly effective in managing tail risks, showcasing robust performance under different 

market scenarios. Unlike traditional methods such as Minimum Variance, which tend to 

concentrate heavily on a few low-risk assets, Risk Parity models distribute risk more evenly 

across the portfolio, mitigating the impact of extreme market events and ensuring a more 

stable return profile. 

The rolling window analysis confirmed that dynamic reallocation based on recent data 

enhances the responsiveness of portfolios to changing market conditions. While the Naïve 

strategy provides the highest diversification, it lacks risk considerations, leading to 

suboptimal outcomes in volatile markets. In contrast, Risk Parity strategies consistently 

achieved a balance between risk management and return optimization. 

This research underscores the utility of ETFs as cost-effective and accessible 

instruments for implementing sophisticated portfolio optimization techniques like Risk 

Parity. By addressing practical constraints such as transaction costs and turnover, the study 

bridges the gap between theoretical portfolio models and their real-world application. This 

emphasizes also the dynamic of the markets.  

It is important to note that in these strategies, the resilience of risk management is 

also evident in terms of cost-effectiveness, particularly when faced with transaction costs 

during portfolio calibration. 

Also, the financial resilience in these models applied to ETF funds is important in 

terms of downturns of the markets to mitigate the number of losses of values. 

Future research could explore extending this framework to broader datasets, including 

alternative asset classes and global markets. Additionally, integrating machine learning 

techniques to forecast risk and enhance allocation models could further improve portfolio 

performance. Overall, Risk Parity offers a strong foundation for managing ETF portfolios in 

both institutional and individual investing contexts, providing a pathway for more resilient 

and diversified investments. 

 

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