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# Portfolio Management【Reading 44】Sample

An asset manager’s portfolio had the following annual rates of return:
 Year Return 20X7 +6% 20X8 -37% 20X9 +27%

The manager states that the return for the period is −5.34%. The manager has reported the:
 A) geometric mean return.
 B) arithmetic mean return
 C) holding period return.

Geometric Mean Return = = −5.34%
Holding period return = (1 + 0.06)(1 − 0.37)(1 + 0.27) − 1 = −15.2%
Arithmetic mean return = (6% − 37% + 27%) / 3 = −1.33%.

Over the long term, the annual returns and standard deviations of returns for major asset classes have shown:
 A) a positive relationship.
 B) a negative relationship.
 C) no clear relationship.

In most markets and for most asset classes, higher average returns have historically been associated with higher risk (standard deviation of returns).
A bond analyst is looking at historical returns for two bonds, Bond 1 and Bond 2. Bond 2’s returns are much more volatile than Bond 1. The variance of returns for Bond 1 is 0.012 and the variance of returns of Bond 2 is 0.308. The correlation between the returns of the two bonds is 0.79, and the covariance is 0.048. If the variance of Bond 1 increases to 0.026 while the variance of Bond B decreases to 0.188 and the covariance remains the same, the correlation between the two bonds will:
 A) remain the same.
 B) increase.
 C) decrease.

P1,2 = 0.048/(0.0260.5 × 0.1880.5) = 0.69 which is lower than the original 0.79.
If the standard deviation of returns for stock A is 0.40 and for stock B is 0.30 and the covariance between the returns of the two stocks is 0.007 what is the correlation between stocks A and B?
 A) 17.14300.
 B) 0.00084.
 C) 0.05830.

CovA,B = (rA,B)(SDA)(SDB), where r = correlation coefficient and SDx = standard deviation of stock x
Then,  (rA,B) = CovA,B / (SDA × SDB) = 0.007 / (0.400 × 0.300) = 0.0583
If the standard deviation of asset A is 12.2%, the standard deviation of asset B is 8.9%, and the correlation coefficient is 0.20, what is the covariance between A and B?
 A) 0.0001.
 B) 0.0022.
 C) 0.0031.

The formula is: (correlation)(standard deviation of A)(standard deviation of B) = (0.20)(0.122)(0.089) = 0.0022.
Stock A has a standard deviation of 10.00. Stock B also has a standard deviation of 10.00. If the correlation coefficient between these stocks is - 1.00, what is the covariance between these two stocks?
 A) -100.00.
 B) 1.00.
 C) 0.00.

Covariance = correlation coefficient × standard deviationStock 1 × standard deviationStock 2 = (- 1.00)(10.00)(10.00) = - 100.00.
The correlation coefficient between stocks A and B is 0.75. The standard deviation of stock A’s returns is 16% and the standard deviation of stock B’s returns is 22%. What is the covariance between stock A and B?
 A) 0.3750.
 B) 0.0264.
 C) 0.0352.

cov1,2 = 0.75 × 0.16 × 0.22 = 0.0264 = covariance between A and B.
If two stocks have positive covariance, which of the following statements is CORRECT?
 A) The rates of return tend to move in the same direction relative to their individual means.
 B) The two stocks must be in the same industry.
 C) If one stock doubles in price, the other will also double in price.

This is a correct description of positive covariance.
If one stock doubles in price, the other will also double in price is true if the correlation coefficient = 1. The two stocks need not be in the same industry.
A measure of how well the returns of two risky assets move together is the:
 A) standard deviation.
 B) covariance.
 C) range.

This is a correct description of covariance. A positive covariance means the returns of the two securities move in the same direction.
A negative covariance means that the returns of two securities move in opposite directions.
A zero covariance means there is no relationship between the behaviors of two stocks.  The magnitude of the covariance depends on the magnitude of the individual stock’s standard deviations and the relationship between their co-movements.
The covariance is an absolute measure of movement and is measured in return units squared.

The covariance of the market's returns with the stock's returns is 0.008. The standard deviation of the market's returns is 0.1 and the standard deviation of the stock's returns is 0.2. What is the correlation coefficient between the stock and market returns?
 A) 0.40.
 B) 0.91.
 C) 0.00016.

CovA,B = (rA,B)(SDA)(SDB), where r = correlation coefficient and SDx = standard deviation of stock x
Then,  (rA,B) = CovA,B / (SDA × SDB) = 0.008 / (0.100 × 0.200) = 0.40
Remember: The correlation coefficient must be between -1 and 1.
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