Question

1. If the variance of ONLY one asset in a two-asset portfolio changes, what other metric changes?
   1. Weight of the asset whose variance changes
   2. Covariance between the two assets in the portfolio
   3. Variance of the other asset
   4. All of the above
   5. None of the above

2. Given the following calculate the geometric mean yield for the entire holding period:

Year	BV	EV
1	100	120
2	120	137
3	137	122
4	122	98
5	98	100

1. 7.2%
2. 7.3%
3. 7.4%
4. 7.5%
5. 0%

3. Using the information below, calculate the expected return:

Economy	Probability	Return
Strong	0.2	20.0%
Weak	0.7	-10.0%
Mild	0.1	5.0%

1. 17.2%
2. -2.2%
3. 17.4%
4. -2.5%
5. 17.6%

4. Which of the following would cause the Security Market Line to pivot upward:

1. A pharmaceutical company receives FDA approval for a new drug
2. Real growth rate of the economy declines
3. The expected rate of inflation increases
4. All of the above
5. None of the above

5. Given the following, calculate the covariance of returns for these two assets:

2006	2007		2008	2009
A)    0.1	0.12		0.07	0.15
B) 0.08	0.04		0.11	0.13

1. 0.01%
2. 0%
3. -0.01%
4. 0.05%
5. -0.05%

6. Calculate the standard deviation of a portfolio comprised of the following two assets that have a correlation coefficient of 0.5:

E(r )	Std Dev	Weight
0.08	0.02	0.7
0.04	0.06	0.3

1. 2.8%
2. 2.9%
3. 3.0%
4. 3.1%
5. -2.2%

7. Suppose the standard deviations of each asset increases by 30% of their original values but the correlation coefficient does not change. What happens to the portfolio standard deviation?
   1. It also increases by 30%
   2. It increases by more than 30%
   3. It increases by less than 30%
   4. It decreases by 30%
   5. I don’t know, but this class is awesome!

8. What is the efficient frontier?
   1. The set of portfolios the represent the best combination of risk and return
   2. The set of portfolios that dominate all other portfolios
   3. The set of portfolios from the MVP to the maximum-risk portfolio
   4. All of the above
   5. None of the above

9. Which is not included in the efficient frontier?
   1. Stocks
   2. Bonds
   3. Real Estate
   4. The risk-free asset
   5. Artwork

Answer 1

1) The answer is B. If the variance of ONLY one asset in a two-asset portfolio changes, Covariance between the two assets in the portfolio will change. While calculating covariance using correlation and standard deviation,

Covariance(X,Y) = Correlation(X,Y) * Standard deviation of X * Standard deviation of Y

Variance of X = (Standard deviation of X)²

Variance of Y = (Standard deviation of Y)²

If variance of one asset changes, its standard deviation will change and hence Covariance between the two assets in the portfolio will change.

Weight of the asset whose variance changes will have no changes since calculating weight doesn't require variance.

Variance of the other asset won't change because the assets are not dependent.

2) Answer is Option D.

Calculating Returns:

Year	BV	EV	Formula	Returns
1	100	120	(EV / BV) - 1 = (120/100) -1	0.20 or 20%
2	120	137	(EV / BV) - 1 = (137/120) -1	0.1417 or 14.17%
3	137	122	(EV / BV) - 1 = (122/137) -1	-0.1095 or -10.95%
4	122	98	(EV / BV) - 1 = (98/122) -1	-0.1967 or -19.67%
5	98	100	(EV / BV) - 1 = (100/98) -1	0.0204 or 2.04%

Geometric mean = [(1+R1)*(1+R2)*(1+R3)*(1+R4)*(1+R5)]^1/5 - 1 = [(1+0.20)*(1+0.1417)*(1-0.1095)*(1-0.1967)*(1+0.0204)]^1/5 - 1 = 0%

3) Answer is option D.

Expected Return = Sum of Probability*Return

Expected Return = (0.2 * 20%) + (0.7 * -10%) + (0.1 * 5%) = -2.5%