Tania Collins Has A 2 Stock Portfolio With A Total Value

Tania Collins Has A 2 Stock Portfolio With a Total Value Of 10000

Tania Collins possesses a two-stock investment portfolio valued at $10,000. Within this portfolio, $3,000 is allocated to Stock A, which has a beta of 0.80, and the remaining amount is invested in Stock B, carrying a beta of 1.40. The goal is to calculate the overall beta of her portfolio.

Portfolio beta is a weighted average of the individual stocks' betas, based on their proportion of the total investment. The formula is:

Portfolio Beta = (Weight of Stock A × Beta of Stock A) + (Weight of Stock B × Beta of Stock B)

Calculating the weights:

  • Weight of Stock A = Value of Stock A / Total Portfolio Value = $3,000 / $10,000 = 0.3
  • Weight of Stock B = Remaining value / Total portfolio = ($10,000 - $3,000) / $10,000 = $7,000 / $10,000 = 0.7

Substituting these into the portfolio beta formula:

Portfolio Beta = (0.3 × 0.80) + (0.7 × 1.40) = 0.24 + 0.98 = 1.22

Thus, Tania Collins's portfolio beta is 1.22.

Paper For Above instruction

The calculation of the overall beta of a stock portfolio is fundamental in understanding the portfolio's sensitivity to market movements. Beta measures the extent to which the value of a stock or portfolio fluctuates in relation to the overall market. A beta of 1 indicates that the stock or portfolio moves in line with the market, while a beta less than 1 suggests lower volatility, and greater than 1 indicates higher volatility. In Tania Collins's case, her portfolio comprises two stocks, and calculating the combined beta involves weighting each stock's beta based on its proportion of the total investment.

To determine the portfolio's beta, we first identify the value invested in each stock and their respective weights in the total portfolio. With $3,000 invested in Stock A with a beta of 0.80, and the remaining $7,000 invested in Stock B with a beta of 1.40, the weights are simple to compute. Stock A's weight is 0.3, while Stock B's weight is 0.7. These weights are crucial because they account for the relative size of each position in the overall portfolio, influencing the combined beta.

The principal formula for portfolio beta combines these weights with the individual stock betas, emphasizing that the overall risk profile is a blend of the risks inherent in each stock, scaled appropriately. The weighted sum reflects the overall sensitivity of the portfolio to market returns. A portfolio beta greater than 1, such as 1.22 in this instance, implies that the portfolio is slightly more volatile than the market, indicating higher risk but potentially higher returns during bullish periods. Conversely, if the beta were less than 1, the portfolio would be considered less risky and more stable.

Understanding the portfolio beta allows investors like Tania Collins to align their investments with their risk tolerance and investment goals. A higher beta often correlates with higher risk and potential returns, while a lower beta suggests stability with moderate gains. The calculation of these metrics is integral to portfolio management and strategic asset allocation, offering insights into the potential response of an investment to market changes.

In conclusion, the methodical calculation of a portfolio's beta, as demonstrated by Tania Collins's example, involves applying the weighted average model. The resulting beta of 1.22 indicates the combined sensitivity of her two-stock portfolio to market movements. Such analysis is vital for investors seeking to optimize their portfolios according to their risk appetite and market expectations, illustrating the practical application of financial theories in real-world investing.

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