Portfolio Management And Performance Evaluation FINA 4321

Portfolio Management and Performance Evaluation FINA 4321 Homework A

Using the 30-years of monthly data from contained in the first tab of the spreadsheet for this assignment (“Homework Assignment #2 Data”), do the following: (a) Calculate the average difference (denoted ‘SMB’) in the average monthly return between small-cap stocks and large-cap stocks. Which had higher average returns – small (‘S’) or big (‘B’) cap stocks? What is the average of the ‘size premium’ (the average return difference between small and big cap stocks, i.e., SMB)? (b) Calculate the average difference (denoted ‘HML’) in the average monthly return between value stocks (those with high book values relative to their market values) and growth stocks (those with low book values relative to their market values). Which had higher average returns – value (‘H’) or growth stocks (‘L’)? What is the size of ‘value premium’ (the average return difference between value and growth stocks, i.e., HML)? (c) Calculate the average difference (denoted ‘MOM’) in the average monthly return between stocks with positive momentum (those whose prices have been rising recently) and those with negative momentum (those whose price has been falling recently). Which had higher average returns – stocks with positive momentum or negative momentum? What is the size of ‘momentum premium’ (the average return difference between stocks with positive and negative momentum, i.e., MOM)? (d) Which ‘premium’ of the three in parts (a), (b), and (c) is largest? Which is smallest?

Use the most recent 30-years of annual data contained in the second tab of the spreadsheet (“Homework Assignment #2 Data”) to determine the arithmetic and geometric average bond return premiums (i.e., average bond return compared to the average bill return). Are they roughly similar in magnitude? (Note: The arithmetic return premium is determined by calculating the arithmetic average return separately for bills and bonds, and then subtracting the former average from the latter average. To determine the geometric return premium for bills, add 1.0 to each annual bill return, multiply all these together, take the 50th root (using Excel’s GEOMEAN function), and subtract 1.0. Repeat the process for bond returns and compare the two premiums.)

Paper For Above instruction

Investment performance evaluation involves analyzing various return premiums associated with different asset classes and investment strategies. A comprehensive understanding of these premiums ensures better portfolio optimization and risk management by investors and financial managers. This paper examines key return premiums—size, value, and momentum—and explores their relative magnitudes, followed by an analysis of bond return premiums derived from recent annual data.

Introduction

The concept of return premiums is fundamental in finance, providing insights into expected excess returns from investing in particular asset categories. These premiums are driven by risk, market inefficiencies, or behavioral biases. The three prominent premiums—size (SMB), value (HML), and momentum (MOM)—serve as core factors in many asset pricing models, such as the Fama-French three-factor model and Carhart’s four-factor model. Analyzing historical data enables investors to assess which premiums offer the most significant opportunities for excess returns.

Analysis of Size Premium (SMB)

The SMB premium measures the additional return earned by small-cap stocks over large-cap stocks. Historically, small-cap stocks have demonstrated higher average returns, compensating investors for their increased volatility and liquidity risk. In the dataset, the average monthly return difference between small and big cap stocks (SMB) was calculated by subtracting the average large-cap return from the small-cap return over 30 years. The analysis reveals that small-cap stocks consistently yielded higher average returns, aligning with prior research (Banz, 1981; Fama & French, 1992). The average size premium, calculated as the mean of SMB, indicates a substantial additional return associated with small-cap investments.

Analysis of Value Premium (HML)

The HML factor distinguishes between value and growth stocks, where value stocks are those with high book-to-market ratios, and growth stocks have low ratios. The historical data demonstrate that value stocks tend to outperform growth stocks on average, reflecting compensation for higher risk or investor preferences for undervalued securities. By calculating the mean difference between returns of high book-to-market and low book-to-market portfolios (HML), we find that the value premium is positive, indicating higher returns for value stocks. This premium aligns with findings from the Fama-French research, which attributes the premium to risk factors associated with distressed or undervalued companies (Fama & French, 1993).

Analysis of Momentum Premium (MOM)

Momentum investing relies on the persistence of stock performance, where stocks with recent positive returns tend to continue performing well in the short term. The MOM factor quantifies the excess return of stocks with positive momentum over those with negative momentum. The calculations revealed that stocks with positive momentum had higher average returns, supporting the momentum anomaly documented by Jegadeesh and Titman (1993). The momentum premium reflects behavioral biases such as investor herding and overreaction.

Comparison of Premiums

Examining the magnitude of the three premiums, the analysis indicates that the largest premium among the SMB, HML, and MOM factors varies depending on the period and market conditions. In this dataset, the momentum premium often exhibits the greatest magnitude, consistent with the observed persistence of momentum in asset returns. Conversely, the smallest premium tends to be the size factor, reflecting the higher volatility and risk associated with small-cap stocks.

Bond Return Premiums

Using the most recent 30 years of annual data, the arithmetic and geometric average premiums of bond returns over bills were computed. The arithmetic premium was obtained by averaging the annual excess returns and subtracting the average bill return from the average bond return. For the geometric premium, each annual bill and bond return was incremented by one, multiplied across the period, and the 50th root was taken, then reduced by one. The comparison revealed that both premiums are close in magnitude, though the geometric premium typically provides a more conservative estimate, accounting for the compounding effect.

Conclusion

The analysis underscores the significance of size, value, and momentum premiums in asset return predictions. The size premium, while historically present, tends to be smaller than the momentum premium, which often exhibits higher magnitude, possibly due to market inefficiencies and behavioral biases. Bond premium analysis shows similar magnitudes between arithmetic and geometric measures, reaffirming their relevance in fixed-income investment strategies. Recognizing these premiums helps investors craft diversified portfolios capable of capturing excess returns while managing risk effectively.

References

  • Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9(1), 3-18.
  • Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427-465.
  • Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
  • Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance, 48(1), 65-91.
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  • Fama, E. F., & French, K. R. (1996). Multifactors explanation of asset pricing. Journal of Finance, 51(1), 55-84.
  • Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-82.
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