Calculating Portfolio Beta: A Comprehensive Analysis of Asset Allocation

Introduction

Portfolio management is a critical aspect of investment strategy, involving the allocation of funds across different assets to achieve a desired risk-return profile. Beta, a measure of a stock’s volatility in relation to the market, plays a crucial role in assessing portfolio risk. In this essay, we will analyze the given scenario involving an investment banker recommending a $100,000 portfolio consisting of assets B, D, and F, with varying betas. We will calculate the portfolio’s beta and determine its risk profile.

Asset Allocation and Betas

The investment banker has proposed an asset allocation plan involving three assets: B, D, and F, with respective investments of $20,000, $50,000, and $30,000. Each asset has an associated beta value, representing its sensitivity to market fluctuations. Asset B has a beta of 1.5, asset D has a beta of 2.0, and asset F has a beta of 0.5.

Calculating Portfolio Beta

The formula for calculating the beta of a portfolio is a weighted average of the individual asset betas, considering their investment proportions. Mathematically, the portfolio beta (βp) is given by:

βp = (wB * βB) + (wD * βD) + (wF * βF)

Where:

• wB, wD, and wF are the weights of assets B, D, and F in the portfolio, respectively.
• βB, βD, and βF are the respective beta values of assets B, D, and F.

Given the investment amounts, we can calculate the weights as follows:

• wB = $20,000 / $100,000 = 0.20 (20%)
• wD = $50,000 / $100,000 = 0.50 (50%)
• wF = $30,000 / $100,000 = 0.30 (30%)

Substituting these values along with the beta values of the assets, we get: βp = (0.20 * 1.5) + (0.50 * 2.0) + (0.30 * 0.5) = 0.30 + 1.00 + 0.15 = 1.45

Portfolio Beta Determination

After performing the calculations, we find that the portfolio’s beta is 1.45. This means that the portfolio is expected to be 1.45 times as volatile as the overall market. A portfolio beta greater than 1.0 indicates that the portfolio is riskier than the market, as it has a higher sensitivity to market movements.

Conclusion

In conclusion, the investment banker’s recommended portfolio comprising assets B, D, and F with investments of $20,000, $50,000, and $30,000 respectively, results in a portfolio beta of 1.45. This information is crucial for investors and financial professionals to understand the portfolio’s risk profile and make informed decisions based on their risk tolerance and investment objectives. By considering the beta of each asset and its weight in the portfolio, investors can strategically diversify their holdings to achieve their desired risk-return balance.