Portfolio Analysis Report

186 Final Report - Jenson Hart.xlsx

Download XLSX • 1.14MB

Executive Summary: 

This report evaluates the client’s existing 30-stock portfolio and discusses whether Fidelity Contrafund (FCNTX) should be added to the client’s investment strategy. Currently, the client has an equally weighted portfolio across 30 stocks, each making up 3.33%. While the original portfolio has performed well historically, generating annual returns of 18.1% with 14.0% volatility, it did not perform as well as the newly optimized portfolio. With the optimized portfolio, returns increased to 21.9%, generating 3.8% alpha while maintaining the same volatility as the original portfolio. Additionally, the tracking error and information ratio were reasonable at 4.9% and 0.78, respectively, showing strong performance relative to the risks taken. 

The wealth projection and Monte Carlo simulation also supported the optimized portfolio compared to the equally weighted one. After 10 years, with a $100,000 starting investment, the optimized portfolio produced a median projected value of roughly $700,000, compared to under $500,000 for the equally weighted portfolio. 

Stress testing showed that the optimized portfolio and the FCNTX fund are exposed to major market shocks. For example, in the beta plus three standard deviations scenario with a 35% market decline, the optimized portfolio fell 38%, while FCNTX declined 35%, showing slightly lower downside sensitivity in this specific stress scenario. FCNTX also performed well historically with a 35.97% 12-month return compared to 25% for the S&P 500 and had stronger Sharpe and Treynor ratios. 

Overall, while the FCNTX fund is fairly strong, the optimized portfolio outperformed it, delivering stronger long-term returns, met the required alpha target, and improved risk-adjusted returns without increasing risk. Through the factor regression, we saw that FCNTX’s strong historical performance can be attributed to its large-cap equity exposure rather than clear manager skill, and because the client already has strong equity exposure in their portfolio, adding FCNTX would create significant overlap. As a result, my final recommendation is not to add FCNTX to the portfolio and instead use the optimized-30 stock portfolio. 

30-Stock Portfolio Analysis: 

The client’s original portfolio consisted of equal weighting across 30 different stocks, with each asset making up 3.33% of the portfolio. This portfolio performed well in the historical backtest, generating an annual return of 18.1% with only 14.0% volatility and a return-to-risk ratio of 1.29. Despite these strong metrics, the portfolio does not distinguish between companies with stronger risk-adjusted returns and those that performed less well due to equal weighting. 

To determine where the portfolio could be improved, I used mean-variance optimization in Excel to reallocate weights among the 30 stocks. I was trying to increase returns while keeping risk at the existing portfolio level. Through doing this, the optimized portfolio produced an annual return of 21.9% compared to the equal-weight return of 18.1%, representing an alpha of 3.8%, while keeping volatility at 14.0%. Additionally, the return-to-risk ratio improved to 1.57, above the target of 1.50, showing that the portfolio became more efficient without taking more risk. Finally, the information ratio was 0.78, indicating that the optimized portfolio generated a strong excess return relative to the amount of tracking error taken.

The historical backtest further supports the optimized portfolio. If the client had invested $100 in their current portfolio, it would have grown to $2,859.06 from April 30th, 2005, to December 31, 2024. The optimized portfolio would have grown to $6,038.05, producing over double the return of the original portfolio. The optimized portfolio also showed better downside performance. The equal-weight portfolio’s largest peak-to-trough was 36.3%, while the optimal portfolio was 29.8%. These are very important metrics to analyze, as they show that the optimized portfolio not only improved returns but also reduced the severity of losses. This is key because losses become exponentially harder to recover from. 

It is also worth noting that the optimization was constrained to make the final allocation more realistic. Each stock had to have a minimum allocation of 1.0%; no stock could exceed a 15.0% allocation; and the risk had to remain consistent with the current portfolio risk. I added other constraints to Excel’s Solver simulation by prohibiting shorting or leverage, meaning negative holdings or total holdings exceeding 100% were not possible. These constraints are important because they add variety to the portfolio and make it more realistic, since it is not excessively concentrated in a couple of stocks, as it would be without them.

Wealth Projections 

The main Monte Carlo analysis focuses on the next 10 years; however, I decided to include both a 10-year and a 30-year wealth projection graph to show the impacts of compounding. This long-term wealth projection is not the main recommendation driver for the 30-stock fund, but it does help show the optimized portfolio’s higher expected return and how it could compound in the future.

Assumptions: 

First, for the optimized portfolio, I made sure to use the same 30 stocks rather than adding new securities and placed several constraints on the optimization model: weights had to stay between 0% and 100%, no shorting or leverage allowed, a maximum allocation of 15%, and a minimum of 1%.

Next, for the Monte Carlo simulation and wealth forecasting, I assumed a starting investment of $100,000 with no additional cash flows for all forward-looking simulations. I also used the expected return value of 21.9% and an annual volatility of 14%, forecast over 10 years. The Monte Carlo simulation ran 1,000 different simulations over this time period, and the outcomes were reported at the top of the “Monte Carlo” tab. The average, median, minimum, and maximum values from the simulation are listed, along with the percentile ranks at 5%, 25%, 50%, 75%, and 95%. 

To determine whether FCNTX’s return was driven by true manager alpha or by exposure to common risk factors, I ran single and multi-factor models. I used the Fama-French-Carhart factors for this analysis, which comprise equity risk, momentum risk, small-minus-big risk, and high-minus-low risk. I calculated excess returns by subtracting the risk-free rate from the nominal FCNTX returns. For the single-factor model, I used the equity factor as the only independent variable to measure how much of FCNTX’s performance was explained by broad stock market exposure. For the multi-factor model, I used all four of the Fama-French risk factors to see how the fund was affected by them. 

To see how the portfolio performed across different market conditions, I ran a market regime analysis using monthly S&P 500 returns. I classified the bottom 30% of returns as bear markets, the middle 40% as normal markets, and the top 30% as bull markets. Next, I compared FCNTX’s average return to the S&P 500’s average return within each regime to evaluate whether the fund actually added value in these different market environments. 

For the FCNTX portfolio in the analysis, I used monthly return data for FCNTX and compared its performance against the S&P 500 as the benchmark. The fund’s assets under management were also included on this “Manager – FCNTX” tab to evaluate whether fund size is related to future performance, because as assets grow, it becomes increasingly difficult to deploy that capital into strong investments. 

Additionally, risk-factor data in the workbook were used to conduct Sharpe’s style analysis. I compared FCNTX’s returns to various benchmarks across major asset classes, such as the BCAG and long-term treasuries, as well as specific U.S. sectors like energy. Finally, I looked at the Fama-French-Carhart risk factors used in the factor models. This analysis was constrained to make the weights sum to 100% with no shorting or leverage. The point of this style analysis was to see if FCNTX’s exposure aligned with its stated long-term growth strategy. 

For the stress test analysis, I wanted to analyze how well the optimized 30-stock portfolio and FCNTX portfolio could handle intense market shocks. I used beta estimates from the Global Financial Crisis and the sudden interest rate rise in mid-2013 to simulate a possible bear market drawdown for FCNTX and the optimized portfolio. I chose these two stress scenarios because they represent two distinct risks: a severe equity market downturn and an interest-rate-driven market shock. Next, I applied hypothetical market-shock declines of 25%, 35%, and 50% to estimate how each portfolio would perform under varying levels of downside pressure. 

Monte Carlo Simulation: 

I conducted a historical backtest to highlight the differing outcomes between the original and optimized portfolio and to understand the possible future outcomes of these two portfolios. A Monte Carlo simulation runs 1,000 different scenarios to get a good idea of all possible outcomes. For this simulation, as mentioned above, I used the optimized portfolio’s expected annual return of 21.9%, annual volatility of 14.0%, a 10-year horizon, and a $100,000 starting investment, with no additional contributions, to be conservative. The results were significantly stronger for the optimized portfolio. The median projected value was $700,000 compared to under $500,000 for the equal-weighted portfolio. At the 95th percentile, the expected final value for the optimized portfolio was over $1.2 million compared to $900,000. Even in the lower-end scenarios, at the 5th percentile, the optimized portfolio ended at over $350,000 compared to roughly $250,000 for the equal-weighted portfolio. 

FCNTX Analysis: 

Now that we have completed the analysis of the 30-stock portfolio and provided the assumptions for the paper, we can dive into the second part of the project, the analysis and ultimate recommendation for Fidelity Contrafund, or FCNTX. FCNTX is one of the largest actively managed mutual funds, focusing primarily on large-cap growth companies. Since the client is already invested in an equity-heavy portfolio, the main question is whether FCNTX would add meaningful value or merely increase exposure to similar stocks. To evaluate this, I analyzed FCNTX’s historical performance, risk-adjusted returns, rolling alpha, Sharpe style analysis, and more. 

Standard Performance: 

First, it is important to highlight the overall performance of the FCNTX portfolio. The standard performance statistics show that the fund has outperformed the S&P 500 over several key time periods. Over the past 12 months, FCNTX returned 35.97%, compared to 25.02% for the S&P 500, generating an alpha of nearly 11%. If we extrapolate this over five years, the fund returned 124.09% compared to 97.02% for the benchmark. The fund’s average annual return was 13.08%, above the S&P 500’s 11.27%, while also having a standard deviation only 0.20% higher. Finally, regarding other key statistics, FCNTX had a beta of 0.95, meaning it was less market-sensitive than the S&P 500, which has a beta of 1. The fund’s Sharpe ratio of 0.86 exceeded the benchmark’s 0.75, and its Treynor ratio of 0.14 was also higher than the S&P 500’s 0.11. The downside risk statistics also support this conclusion, as FCNTX had a 95% Value at Risk percentage of -12.01% compared to -13.51% for the S&P 500, meaning that in a severe downside scenario, FCNTX is expected to lose less than the S&P 500. Finally, the historical 5% VaR was -7.05% compared to -7.34% for the benchmark. These results show that the fund has produced slightly better returns than the S&P 500, while not taking on substantially more risk. 

Factor Models: 

To better understand the reasons for this level of performance by FCNTX, I conducted single and multi-factor analysis to determine if the fund’s returns were from manager skill or driven by factor exposure. First, in the single-factor model, FCNTX had an equity beta of 0.923, with an incredibly high t-stat of 43.18, showing that the fund’s market exposure is highly statistically significant. In the single-factor model, the fund produced an annualized risk-adjusted alpha of 2.43%, which was statistically significant with a t-stat of 2.08. Based on this, it seems like the manager has skill, and we could reject the null hypothesis. However, once I conducted the multi-factor model and included size, value, and momentum exposure, the annualized risk-adjusted alpha fell to 1.10%. It was also no longer statistically significant, with a t-stat of just 1.28. The multi-factor betas indicate that FCNTX had significant exposure to equities, suggesting that the fund is tilted toward large-cap, growth, and momentum stocks. Overall, this weakens the argument that FCNTX’s outperformance is due to manager skill, as much of the fund’s outperformance can be explained by its exposures.

Rolling Alpha and AUM/Forward Alpha: 

The rolling alpha and AUM analyses show that FCNTX has historically added value, although the evidence is weaker when evaluating the future performance. The rolling results show that FCNTX produced a positive 3-year alpha in 67.8% of observations. While this is not bad, it is less consistent than the longer time frames. The 5-year success ratio was 72.5%, and the 10-year was 95.8%, showing that FCNTX’s alpha is much more reliable over longer periods. The rolling Sharpe ratio yielded similar results. FCNTX beat the S&P 500’s Sharpe ratio in 74.7% of 5-year periods and 87.3% over 10 years, suggesting that the fund often added value on a risk-adjusted basis, too. That being said, the AUM and forward alpha analysis were not as strong for FCNTX. As time increased from one to ten years, the alpha decreased, showing that as the fund’s AUM grows, its ability to produce excess returns compared to the benchmark generally decreases, especially in the 1 to 3-year period, as they now have more than $150 billion in AUM. The AUM/Forward alpha had correlations of -0.16 and -0.15 over the 1 and 3-year period, as you can see with the negative trend-line below. Overall, while the fund has performed well in the past, its size raises concerns about its future alpha generation.  

Stress Testing: 

To see how the optimized 30-stock portfolio and the FCNTX portfolio did during extremely bearish market conditions, I conducted multiple stress tests using beta estimates from historical market downturns. I used betas from the Global Financial Crisis of 2007-2009 and the sudden interest rate rise from April 2013 to July 2013. The reason for selecting a sudden interest rate rise as a stress test scenario is that I believe that, with current rising costs and inflation, interest rates will continue to rise over the next several months. I also used betas from a beta + three standard deviations scenario and a beta correlation of 1, to see how other bearish scenarios would impact the two portfolios. These scenarios modeled 25%, 35%, and even a 50% market drop. While I will not go through each beta estimate scenario and the resulting portfolio impact, the optimized portfolio declined by 38.06% in the beta + three standard deviations scenario under a 35% market shock. This reduced the $100,000 portfolio to $61,935.75. FCNTX declined by 35.69%, losing $35,687.94 and reducing the portfolio value to $64,312.06. These results show that both portfolios remain exposed to severe equity market shocks, although FCNTX showed slightly less downside sensitivity in the beta plus three standard deviations scenario. 

Market Regime: 

Market regime analysis evaluates how FCNTX performed across different market environments compared to the S&P 500, rather than just the optimized portfolio. Through this analysis, we can see the fund did well. FCNTX outperformed the S&P 500 in all but one of the three market environments. In the bull market, it achieved a 99.85% capture ratio, falling 0.15% short with a 5.43% return compared to the S&P 500’s 5.44%. In normal and bear market conditions, FCNTX outperformed the benchmark. It achieved an average return of 1.58% in normal market conditions, compared to 1.44% for the S&P 500, and in bear market conditions, the fund lost 3.82% compared to 4.15% for the S&P 500. Overall, the market regime analysis shows that while FCNTX performed relatively well across different market environments compared to the benchmark, the outperformance was not very strong. 

Style Analysis and Risk Factors: 

Sharpe’s Style Analysis was used to assess whether FCNTX’s actual return pattern aligns with its stated large-cap growth strategy. With the two constraints placed on the solver model mentioned above, the strongest result came from the major asset class model, where FCNTX had an 81.90% exposure to the Russell 1000 Growth. The major asset class model had an R-squared of 94.60%, indicating that the model explained a significant portion of the fund’s return variation. While the other sectors did not have as high an R-squared or information ratio, looking at these areas was key, as it reinforced that FCNTX behaves like a growth-oriented equity fund with meaningful technology and momentum exposure. 

The beta coefficients also help explain FCNTX’s factor exposure and whether those exposures are statistically significant. The fund has strong, significant exposure to the equity market, with 91% allocated to the equity factor and 8.96% to momentum, with no meaningful exposure to SMB or HML. This is to be expected as the fund is a U.S. large-cap fund. The positive momentum beta suggests that the fund also has exposure to stocks with stronger recent performances, making their returns look stronger in the short term. These factor exposures are key because they show that some of FCNTX’s historical performance may come from its growth and momentum characteristics, rather than pure manager skill. 

It is also important to highlight how FCNTX would fit within the rest of the client’s portfolio. Because the fund behaves mainly like a large-cap growth equity fund, it would likely overlap with some of the growth-oriented exposure already in the optimized 30-stock portfolio.

This weakens the case for adding FCNTX (discussed more in-depth in the final investment decision section) because the fund does not provide a unique source of returns. So while the fund has performed historically well against the benchmark, the client already has a strong equity exposure through its optimized portfolio, so adding FCNTX seems like an unnecessary redundancy that would reduce diversification and increase risk. 

Before my final investment recommendation and decision for the client, it is important to mention some limitations/drawbacks of the assumptions made. One limitation of this analysis is that the results rely heavily on historical data. While this is typical for making fund recommendations, it is possible that future returns differ from what these models predict. The optimization is also sensitive to the inputs used, so any changes to returns or risk would impact the optimized weights. For the FCNTX fund, past alpha may not necessarily be a good indicator of future performance, especially as the fund’s AUM continues to increase. Finally, the factor models and style analysis explain historical exposures, but the fund manager can and likely will change allocations over time, thus changing the risk profile and the reliability of this analysis. 

Final Investment Decision: 

Overall, based on the analysis conducted and as alluded to throughout, I would not recommend adding FCNTX to the client’s portfolio at this time. FCNTX is a strong fund and has performed quite well historically with a near 36% 12-month return compared to 25% for the S&P 500, as well as a higher Sharpe ratio of 0.86 compared to 0.75 and slightly better risk statistics based on VaR analysis. The main concern, however, comes from the style analysis, as the fund’s performance appears heavily tied to broad equity, large-cap growth, and momentum exposure. In the multi-factor model, annualized alpha fell to 1.10% and was no longer statistically significant after controlling for the Fama-French factors. Since the client already has a strong equity exposure in their existing holdings, adding more equity would reduce diversification. The optimized portfolio is a strong option because it achieved one of the client’s main objectives of alpha above 3% while keeping volatility at 14% and producing stronger long-term wealth creation, and is not exposed to the AUM risk that FCNTX is. Therefore, while FCNTX is a solid standalone option, it does not add enough diversification or generate statistically significant risk-adjusted alpha to justify including it in the client’s portfolio. I recommend using the optimized 30-stock portfolio as the client’s main strategy, as it better aligns with their return, risk, and diversification goals.