1215

For assets A and B we know the following: E(R_A) = 0.10, E(R_B) = 0.10, Var(R_A) = 0.18, Var(R_B) = 0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?

A) 0.1500.

B) 0.2114.

C) 0.1102.

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You are not given the covariance in this problem but instead you are given the correlation coefficient and the variances of assets A and B from which you can determine the covariance by Covariance = (correlation of A, B) × Standard Deviation of A) × (Standard Deviation of B).

Since it is an equally weighted portfolio, the solution is:
[( 0.5² ) × 0.18 ] + [(0.5²) × 0.36 ] + [ 2 × 0.5 × 0.5 × 0.6 × ( 0.18^0.5 ) × ( 0.36^0.5 )] 
= 0.045 + 0.09 + 0.0764 = 0.2114

1215

Use the following data to calculate the standard deviation of the return:

• 50% chance of a 12% return
• 30% chance of a 10% return
• 20% chance of a 15% return

A) 3.0%.

B) 1.7%.

C) 2.5%.

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The standard deviation is the positive square root of the variance. The variance is the expected value of the squared deviations around the expected value, weighted by the probability of each observation. The expected value is: (0.5) × (0.12) + (0.3) × (0.1) + (0.2) × (0.15) = 0.12. The variance is: (0.5) × (0.12 ? 0.12)² + (0.3) × (0.1 ? 0.12)² + (0.2) × (0.15 ? 0.12)² = 0.0003. The standard deviation is the square root of 0.0003 = 0.017 or 1.7%.