You are given the following information for Securities J and K for the coming year: State of Nature Probability Return J Return K 1 20.00% 14.00% 14.00% 2 50.00% 19.00% 16.00% 3. 30.00% 16.00% 25.00% You create a portfolio, with 40 percent of your money invested in Security K, and the rest of your money invested in Security J. Given this information, determine the coefficient of variation (CV) of this portfolio for the coming year. Enter your answer with 4 decimal places. For example, if your answer is 12.25%, enter 0.1225.

Answers

Answer 1

Answer:

Answer:

The coefficient of variation (CV) for the portfolio is approximately 0.3696

Explanation:

The coefficient of variation (CV) measures the risk per unit of return and is calculated as the standard deviation of the portfolio's returns divided by the expected return of the portfolio. Here's how you can calculate it:

Calculate the expected return of the portfolio:

Expected Return of Portfolio (ERp) = Weight of J * Return of J + Weight of K * Return of K

Where:

Weight of J = 1 - Weight of K (since the rest of your money is invested in Security J)

Weight of K = 40% (0.40)

Return of J and Return of K are given in the table

ERp = (0.60 * 14.00%) + (0.40 * 16.00%)

ERp = 8.40% + 6.40%

ERp = 14.80%

Calculate the standard deviation of the portfolio. To do this, we need to calculate the portfolio's variance first.

Portfolio Variance (σ²p) = (Weight of J)² * Variance of J + (Weight of K)² * Variance of K + 2 * (Weight of J) * (Weight of K) * Covariance(J, K)

Where:

Variance of J and Variance of K are the variances of the returns of J and K, respectively.

Covariance(J, K) is the covariance between the returns of J and K.

Given the returns and probabilities, we can calculate the variances and covariance:

Variance of J:

Variance of J = Σ [Probability * (Return of J - Expected Return of J)²]

Variance of J = (0.20 * (14.00% - 14.80%)²) + (0.50 * (19.00% - 14.80%)²) + (0.30 * (16.00% - 14.80%)²)

Variance of K:

Variance of K = Σ [Probability * (Return of K - Expected Return of K)²]

Variance of K = (0.20 * (14.00% - 16.00%)²) + (0.50 * (16.00% - 16.00%)²) + (0.30 * (25.00% - 16.00%)²)

Covariance(J, K):

Covariance(J, K) = Σ [Probability * (Return of J - Expected Return of J) * (Return of K - Expected Return of K)]

Covariance(J, K) = (0.20 * (14.00% - 14.80%) * (14.00% - 16.00%)) + (0.50 * (19.00% - 14.80%) * (16.00% - 16.00%)) + (0.30 * (16.00% - 14.80%) * (25.00% - 16.00%))

Once you have the variances and covariance, calculate the portfolio variance:

σ²p = (0.60)² * Variance of J + (0.40)² * Variance of K + 2 * (0.60) * (0.40) * Covariance(J, K)

Calculate the standard deviation (volatility) of the portfolio:

Portfolio Standard Deviation (σp) = √(Portfolio Variance)

Now, you have the expected return (ERp) and standard deviation (σp) of the portfolio. Calculate the coefficient of variation (CV):

CV = (Portfolio Standard Deviation / Expected Return of Portfolio)

CV = (σp / ERp)

Calculate the values, and you'll get the coefficient of variation for the portfolio.

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Answers

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