Portfolio Analysis You Have Been Given The Expected
Sheet1p8 14 Portfolio Analysis You Have Been Given The Expected Retu
Calculate the expected return, standard deviation, and coefficient of variation for three investment alternatives based on given asset return data, and recommend the most suitable alternative based on these financial metrics.
Paper For Above instruction
Introduction
Portfolio analysis is an essential aspect of investment decision-making, enabling investors to evaluate the risk and return characteristics of different investment options. This analysis involves calculating the expected return, standard deviation, and coefficient of variation for various assets or portfolios to determine which option aligns best with an investor's risk tolerance and return objectives. In this paper, we examine three investment alternatives composed of assets F, G, and H, using specific return data over a four-year period. The primary goal is to compute the expected returns, assess the risk through standard deviation, and determine the most efficient portfolio via the coefficient of variation, ultimately recommending the most suitable investment choice.
Data Description
The data provided includes forecasted returns over a four-year period for three assets, F, G, and H, with the following expected returns:
- Asset F: 17%, 16%, 15%, 14%
- Asset G: 14%, 15%, 16%, 17%
- Asset H: 15%, 16%, 15%, 14%
The data for the three investment alternatives is as follows:
- Alternative 1: 100% of Asset F
- Alternative 2: 50% of Asset F and 50% of Asset G
- Alternative 3: 50% of Asset F and 50% of Asset H
The goal is to calculate the expected return, standard deviation, and coefficient of variation for each alternative to compare their risk-return profiles.
Calculating Expected Returns
The expected return of each alternative is computed as the weighted average of the expected returns of the constituent assets. For Alternative 1, which is solely Asset F, the expected return is simply the average of Asset F’s returns:
Expected return of Asset F (E_F):
E_F = (17% + 16% + 15% + 14%) / 4 = 15.5%
Similarly, for Asset G:
E_G = (14% + 15% + 16% + 17%) / 4 = 15.5%
And for Asset H:
E_H = (15% + 16% + 15% + 14%) / 4 = 15%
Based on the asset allocations:
- Alternative 1 (100% F):
Expected return = E_F = 15.5%
- Alternative 2 (50% F + 50% G):
E_{Alt2} = 0.5 E_F + 0.5 E_G = 0.5 15.5% + 0.5 15.5% = 15.5%
- Alternative 3 (50% F + 50% H):
E_{Alt3} = 0.5 E_F + 0.5 E_H = 0.5 15.5% + 0.5 15% = 15.25%
Calculating Standard Deviations
Standard deviation measures the volatility of returns, indicating the investment risk. It is calculated from the variance, which is the average squared deviation from the mean. For each asset, we compute the variance as follows:
Variance for Asset F:
Var_F = [(17% - 15.5%)² + (16% - 15.5%)² + (15% - 15.5%)² + (14% - 15.5%)²] / 4
= [(1.5%)² + (0.5%)² + (-0.5%)² + (-1.5%)²] / 4
= [(2.25 + 0.25 + 0.25 + 2.25)] / 4 = 5 / 4 = 1.25
Standard deviation for Asset F:
SD_F = √1.25 = approximately 1.12%
Similarly, for Asset G:
Var_G = [(14% - 15.5%)² + (15% - 15.5%)² + (16% - 15.5%)² + (17% - 15.5%)²] / 4
= [(-1.5%)² + (-0.5%)² + (0.5%)² + (1.5%)²] / 4
= [2.25 + 0.25 + 0.25 + 2.25] / 4 = 5 / 4 = 1.25
SD_G = √1.25 ≈ 1.12%
For Asset H:
Var_H = [(15% - 15%)² + (16% - 15%)² + (15% - 15%)² + (14% - 15%)²] / 4
= [0 + (1%)² + 0 + (-1%)²] / 4
= [0 + 1 + 0 + 1] / 4 = 2 / 4 = 0.5
SD_H = √0.5 ≈ 0.71%
Next, for the combined assets in each alternative, the standard deviation involves calculating the variance considering the weights, variances, and covariances. For simplicity, assuming assets are uncorrelated (which is a common assumption for initial estimates), the variance of the portfolio is the sum of the weighted variances:
- For Alternative 2 (50% F, 50% G):
Variance:
Var_{Alt2} = (0.5)² Var_F + (0.5)² Var_G = 0.25 1.25 + 0.25 1.25 = 0.3125 + 0.3125 = 0.625
SD_{Alt2} = √0.625 ≈ 0.79%
- For Alternative 3 (50% F, 50% H):
Variance:
Var_{Alt3} = 0.25 1.25 + 0.25 0.5 = 0.3125 + 0.125 = 0.4375
SD_{Alt3} = √0.4375 ≈ 0.66%
Note: This approximation ignores covariance. For more precise measurements, covariance must be included, but in many preliminary analyses, assuming independence is acceptable.
Calculating Coefficient of Variation
The coefficient of variation (CV) assesses risk per unit of return:
CV = Standard deviation / Expected return
Calculations:
- Alternative 1:
CV_{Alt1} = 1.12% / 15.5% ≈ 0.072
- Alternative 2:
CV_{Alt2} = 0.79% / 15.5% ≈ 0.051
- Alternative 3:
CV_{Alt3} = 0.66% / 15.25% ≈ 0.043
Interpretation: Lower CV indicates a more efficient risk-return tradeoff.
Discussion and Recommendations
Based on the calculations, Alternative 3 offers the lowest coefficient of variation, signaling the best balance of risk and return among the three options. Specifically, it provides a slightly lower expected return than Alternative 1 but with significantly reduced risk, as indicated by the standard deviation and CV. Alternative 2, while offering the same expected return as Alternative 1, carries a marginally lower risk but does not outperform Alternative 3 in terms of risk efficiency.
Investors seeking stability and minimized risk per unit of return should favor Alternative 3, which combines assets F and H for diversification benefits and risk reduction. The findings underscore the importance of analyzing both return and volatility metrics in making informed investment decisions.
Limitations and Further Considerations
The analysis assumes assets are uncorrelated, which might not hold true in real-world markets. Incorporating covariance data could refine the risk estimates. Additionally, historical data, macroeconomic factors, and individual risk appetite should influence final investment choices.
Conclusion
In conclusion, the portfolio combination of 50% Asset F and 50% Asset H (Alternative 3) demonstrates the most favorable risk-adjusted return profile based on the coefficient of variation. This suggests that diversification between these assets can optimize the trade-off between risk and return, making it the recommended investment alternative for investors prioritizing risk efficiency.
References
- Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425-442.
- Litterman, R. (2003). Modern Investment Management: An Equilibrium Approach. Wiley.
- Jorion, P. (2007). Financial Risk Manager Handbook (5th ed.). Wiley.
- Damodaran, A. (2010). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (2nd ed.). Wiley.
- Ross, S. A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, 13(3), 341-360.