Estimate An Appropriate CAPM Model Describing The Return ✓ Solved

Estimate an appropriate CAPM model describing the return

For this assignment, you must complete either Project A or Project B.

Project A: Use the Dataset_#mutual.xls corresponding to your Z#####. To complete this assignment, you will need the returns of the mutual fund # and the factors in the Dataset_#mutual.xls. The variable names and the descriptions of the variables are as follows:

  • MutualFund1_#_ret: Returns of the mutual fund 1
  • MutualFund2_#_ret: Returns of the mutual fund 2
  • CRSP index: Market Index
  • 1-month T-Bill: Risk free rate
  • ExRm: CRSP index minus 1-month T-Bill
  • SMB: Small (market capitalization) minus big factor
  • HML: High (book-to-market ratio) minus low factor
  • MoM: Momentum factor (long prior-month winners and short prior-month losers)
  • TradedLIQ: Traded liquidity factor

Question: (a) Estimate an appropriate CAPM model describing the return of the mutual funds as a function of some or all factors above: CRSP index, 1-month T-Bill, ExRm, SMB, HML, MoM and TradedLIQ. Carry out and report the necessary statistical tests to justify the choice of your specification. Discuss any found issues with respect to omitted variable bias. (b). Compare the performances of the two funds and the exposure of the portfolios to different risk factors by comparing relevant coefficients (such as the intercept and slopes) of the models through appropriate tests.

Overall word limit, 1000 words maximum.

Paper For Above Instructions

Introduction

The financial marketplace is characterized by numerous investment vehicles, among which mutual funds play a pivotal role. This paper aims to apply the Capital Asset Pricing Model (CAPM) using the provided data to estimate the returns of two mutual funds, identify the risk factors that affect their performance, and address any potential omitted variable bias. Additionally, the comparative performance of the two funds will be analyzed in context with applicable financial theories and methodologies.

Dataset Overview

The dataset, as described, includes the returns of two mutual funds along with various financial factors, including the CRSP index, risk-free rate (1-month T-Bill), ExRm, SMB, HML, MoM, and TradedLIQ. Each of these factors represents different dimensions of market behavior and risk that can influence mutual fund returns. These variables provide a robust foundation to conduct an econometric analysis.

CAPM Model Specification

The CAPM, as proposed by Sharpe (1964), outlines a linear relationship between the expected return of an asset and its risk, denoted by the beta coefficient. The general form of the CAPM can be expressed as:

R_it = α + β_1(R_market - R_f) + β_2(SMB) + β_3(HML) + β_4(MoM) + β_5(TradedLIQ) + ε_it

where R_it represents the return of the mutual fund, R_market is the market return, R_f is the risk-free rate, and ε_it is the error term. Each variable's coefficient provides insights into how sensitive the fund's returns are to changes in the corresponding factor.

Estimation and Statistical Testing

Utilizing regression analysis, we will estimate the parameters of the model. It is crucial to perform hypothesis testing on the coefficients to determine their statistical significance. The t-tests can help ascertain whether the coefficients are significantly different from zero, while the F-test can be used to evaluate the overall fit of the model.

In conducting the regression analysis, we will monitor for issues such as multicollinearity using Variance Inflation Factors (VIF) and will plot residuals to check for homoscedasticity and normality. A Durbin-Watson test will help detect autocorrelation in residuals.

Omitted Variable Bias

Omitted variable bias occurs when a relevant variable is left out of the model, potentially skewing the results and giving an inaccurate estimation of the relationship being assessed (Wooldridge, 2016). It is of utmost importance to include all predictive factors to avoid bias. If ignored, the consequences could include misleading implications for investment strategy and risk management.

Comparative Performance Analysis

After the CAPM model is established for both funds, the next step involves comparing their performances. The coefficients of interest are the intercept (α) and the slopes (β's) representing different risk exposures. Tools such as the Wald Test or the Chow Test can be employed to compare these coefficients statistically.

By applying these tests, we can infer which mutual fund exhibits higher sensitivity to market movements and risk factors, thereby determining which fund may be deemed a better investment from different perspectives (Fama & French, 1992).

Conclusion

In summary, this study aims to provide an analytical understanding of mutual fund returns using the CAPM framework, focusing on estimating and comparing the risk-return profiles of two mutual funds. Through rigorous statistical testing, we will ensure the validity of our findings and contribute to informed investment decision-making.

References

  • 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.
  • Pastor, L., & Stambaugh, R. F. (2003). Liquidity Risk and Expected Stock Returns. Journal of Political Economy, 111(3), 642-685.
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3), 425-442.
  • Wooldridge, J. M. (2016). Introductory Econometrics: A Modern Approach. Cengage Learning.
  • Additional Reference 1
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