Final answer:
The question pertains to calculating the portfolio variance for a combination of two stocks with known variance, standard deviation, and correlation. By using the formula for portfolio variance and the given values, including the weights of the investments, it's possible to determine the overall risk of the combined investment.
Step-by-step explanation:
To calculate the portfolio variance for a portfolio consisting of two stocks, FIN and ACCT, with respective variances and standard deviation, and a high correlation of 0.98, we would use the portfolio variance formula. This calculation involves the variances of individual stocks, the amount invested in each stock, and the covariance between the two stocks. Given the data: FIN variance = 0.142, ACCT standard deviation = 0.41 (Variance = Standard deviation squared, so ACCT variance = 0.412), investment in FIN = $177, and investment in ACCT = $175, the portfolio variance can be found through the following expression:
Portfolio Variance = w12×σ12 + w22×σ22 + 2× w1× w2×σ1×σ2×ρ
Where w1 and w2 are the weights (proportion of total investment) in FIN and ACCT respectively, σ1 and σ2 are the standard deviations of FIN and ACCT, and ρ is the correlation coefficient between FIN and ACCT.
To perform this calculation:
- Calculate the weights of each stock in the portfolio: w1 = $177 / ($177 + $175) and w2 = $175 / ($177 + $175)
- Calculate the variance of ACCT (since we are given the standard deviation): σ22 = 0.412
- Substitute the values into the portfolio variance formula and solve for the portfolio variance.
This calculation will give you the total risk of the portfolio, considering the individual risks of the stocks and their correlation. High correlation indicates that the stocks move together in a similar direction, which affects the overall portfolio variance.