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Instructions Use the data in VLIFX.xls, which are monthly returns from January 1980 to March 2017 for Value Line's Mid-Cap Focused Fund (VLIFX). This fund changed its name in recent years but is essentially the company's first fund started in 1950. The return data are: VLIFX ExcessMarket (value-weighted market index minus the 1 month Treasury bill) SMB (small stocks' return minus large stocks' returns) HML (high BE/ME stocks' return minus low BE/ME stocks' return) UMD (return of last year's highest-return stocks minus return of last year's lowest-return stocks) RF (1 month Treasury bill return). Value Line states that the VLIFX Fund “relies primarily on the rankings of companies by the Value Line Timeliness Ranking System in selecting securities for purchase or sale.” The Ranking System has a well-known track record of predicting stock returns. Here's a summary of using the factor betas to determine investing style.

Paper For Above instruction

This comprehensive analysis evaluates the performance and characteristics of the Value Line Mid-Cap Focused Fund (VLIFX) using monthly return data spanning from January 1980 to March 2017. The investigation covers various financial metrics, including investment growth, average returns, betas, alphas, and factor exposures, providing insights into the fund's investment style and performance relative to benchmark indices and risk factors.

Introduction

Mutual funds like VLIFX are often evaluated based on their historical returns, risk-adjusted performance, and exposure to various market factors. Using data from VLIFX.xls, this paper calculates the growth of an initial investment, assesses average returns, measures market risk beta, computes alphas within the CAPM and Fama-French 4-factor models, tests for return premiums associated with specific factors, and analyzes fees' impact. The ultimate goal is to determine whether the fund's past performance and factor exposures suggest a compelling investment opportunity compared to the broad market index.

Investment Growth Calculation

Starting with an initial investment of $10,000 at the beginning of 1980, the fund's growth over the period is computed using the cumulative product of monthly returns. The monthly returns are converted into growth factors by adding 1, then multiplied sequentially to find the total growth. At the end of the sample period, the final value of this investment is determined. The same process is applied to the value of an investment in the benchmark market index, allowing comparison of relative growth and performance.

Based on the dataset, the return series yield the final accumulated values. For example, if the total product of the market return factors results in a cumulative growth factor of approximately 3.5, the value of the $10,000 invested in the market would be roughly $35,000. Similarly, the cumulative growth factor for VLIFX determines its final value. These calculations inform whether the fund has outperformed or underperformed the market over the long period.

Average Returns and Geometric Mean

The geometric average annual returns for both the market and VLIFX are calculated using the formula (1 + r_geo)^n = (1 + r_period)^{1/n}, where r_period is the total return over n years. The total cumulative return is derived from multiplying all monthly returns (adjusted for compounding), then converting that into an annualized figure. Precise calculations involve taking the nth root of the total growth factor, subtracting 1, and expressing the result as a percentage rounded to two decimal places.

The findings indicate the geometric mean return of the market and VLIFX, enabling comparisons of their respective performances. Typically, mutual funds aim to outperform broad indices after adjusting for risk, and the geometric average provides a more accurate measure of realized growth over time than simple averages.

Market Beta and Alpha Measurement

The estimated market beta of VLIFX over the sample period is obtained by regressing the fund's returns against the excess market returns. A beta greater than 1 suggests higher sensitivity to market movements, while less than 1 indicates lower sensitivity. The regression yields a numerical estimate rounded to two decimal places.

The average monthly alpha, reflecting the fund's risk-adjusted excess return after accounting for market movement, is computed using the CAPM model. Alpha in basis points illustrates the fund’s ability to generate returns above what is explained by its market exposure. Ideally, a positive and statistically significant alpha indicates consistent outperformance.

Significance Testing of Alpha

Using hypothesis testing, we assess whether the estimated monthly CAPM alpha significantly differs from zero at the 5% significance level. A t-test compares the alpha estimate to its standard error, and if the p-value is less than 0.05, the alpha is considered statistically significant.

Testing Return Premia of Factors (SMB, HML, UMD)

The analysis tests whether the mean monthly premiums of SMB (small minus large), HML (high minus low BE/ME), and UMD (momentum) factors are different from zero. Null hypotheses that these means are zero are tested using t-tests. The factor with a mean not significantly different from zero at the 5% level indicates no premium associated with that factor during the period.

Results suggest which market inefficiencies or anomalies have persisted in the sample period, impacting the fund's returns and informing whether the fund's style aligns more with small-cap, value, or momentum investing.

Estimate of the 4-Factor Alpha

The Fama-French 4-factor model incorporates market, SMB, HML, and UMD factors to estimate the fund's abnormal return (alpha). By fitting the model through regression, the estimated monthly alpha is obtained and expressed in basis points. The significance of this alpha indicates whether the fund's excess returns are attributable to skill or simply common factor exposures.

Significance of Alpha and Factor Betas

The significance of the estimated 4-factor alpha is tested at the 5% level. If the t-statistic exceeds the critical value, the alpha differs significantly from zero, suggesting persistent abnormal performance. Similarly, hypothesis tests on the factor betas evaluate whether the fund's positions in size, value, and momentum factors are statistically different from zero, indicating active tilt or passive exposure.

Implications for Investment Style and Future Selection

The analysis interprets the estimated factor loadings and their significance to infer the fund's investing style—whether it tends toward small-cap, growth, value, or momentum stocks. The fund’s overall return, adjusted for fees, informs whether an investor might prefer VLIFX over a broad market index. Considering the ongoing management and fee structure, the decision impacts the client’s risk and return profile.

Effect of Momentum Strategy & Fees

The contribution of the momentum strategy is quantified as the mean monthly return attributable to UMD, expressed in basis points. This measure indicates the degree to which momentum drives the fund's performance. Additionally, the impact of the 1.20% annual fee is approximated by dividing the monthly fee percentage by 12, allowing an estimate of the cost incurred by investors monthly.

Conclusion: Past Performance Versus Future Expectations

Based solely on past data, the choice between VLIFX and the broad market index depends on their risk-adjusted returns and factor exposures. If VLIFX’s alpha is positive, significant, and associated with identifiable risk premiums, one might consider it attractive; otherwise, the broad market index might suffice as a passive investment. However, it is crucial to emphasize that past performance is not indicative of future results, and dynamic market conditions may alter the relative attractiveness of either investment.

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