Annales finance 2009 2010 esc

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Sample exam solutions
Sample exam #1: 20 questions Sample exam #2: 20 questions Sample exam #3: 20 questions

Sample exam #1

Answer: A

QUESTION 1
A stock’s price on December 1 was $50, and on December 31 of the same year it was $40. The stock also paid a $2 dividend in December. What was this stock’s rate of return in December?

(40+2-50)/50= -16%.

A. B. C. D. E. F.

-16% -20%-21% -24% -25% -30%

Sample exam #1

Answer: C

QUESTION 2
The graph below shows the market price of assets A, B, and C recorded at monthly intervals over the course of one year. None of these assets paid dividends during this year. Based on this graph, rank these three assets from the lowest standard deviation of returns to the highest.

Monthly prices of assets A, B, and C
70 60 50We do not have the exact returns so we cannot calculate the standard deviations exactly. It is nonetheless easy to see that returns on Asset B are the least volatile of the three assets. Choosing between A and C, clearly A has the higher volatility of returns. So B is the least risky, followed by A, and followed by C. NB: if you are curious, the actual standard deviations of monthly returns(which, again, you cannot calculate directly from the graph – you need to know the exact returns!) are as follows: asset A: 9.1%;

Price

40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 12

Asset A Asset B Asset C

asset B: 2.9%; asset C: 16.4%.

Month

A. B. C. D. E. F.

A, B, C A, C, B B, A, C B, C, A C, A, B C, B, A

Sample exam #1

Answer: A

QUESTION 3
Refer again to the conditions ofthe previous question. What is the ranking, from lowest to highest, of these assets’ geometric average monthly returns?

We know from lecture that the geometric average return summarizes the investment’s past performance. It is easy to see that during these 12 months, A performed the worst, B performed better, and C performed the best.

A. B. C. D. E. F.

A, B, C A, C, B B, A, C B, C, A C,A, B C, B, A

Sample exam #1

Answer: F

QUESTION 4
An economist needs to make an assumption about the distribution of stock market returns in the following year. She decides to use the following numbers: +30% return with 0.3 probability +10% return with 0.6 probability - 30% return with 0.1 probability According to the economist’s assumptions, what is the expected return on the stockmarket?

This is just like the coin-tossing example from lecture. E[r]=30*0.3+10*0.6+(-30)*0.1=12%

A. B. C. D. E. F.

0% 3% 6% 9% 10% 12%

Sample exam #1

Answer: D

QUESTION 5
Refer again to the conditions of the previous question. According to the economist’s assumptions, what is the standard deviation of the stock market return?

This is just like the coin-tossing example inlecture:
Deviation from mean Return +30 +10 -30 Probability 0.30 0.60 0.10 return 18 -2 -42 Squared deviation 324 4 1764 Probability x squared deviation 97.2 2.4 176.4

Variance = 97.2+2.4+176.4=276 Standard deviation = 2761/2 = 16.6

A. B. C. D. E. F.

0.0% 6.5% 12.0% 16.6% 30.0% 45.7%

Sample exam #1

Answer: D

QUESTION 6
Refer again to the conditions of Question 4. After longdeliberation, the economist decides to change the lowest possible return in her assumptions from -30% to -20%. All other assumptions remain the same. By what amount does this change the market risk premium assumed by the economist?

The risk-free rate stays as before, but the expected market return changes by 0.1*(-20-(-30))=1%. So the market risk premium increases by 1%.

A. B. C. D. E. F.

-10%-6% -1% 1% 6% 10%

Sample exam #1

QUESTION 7
Look at the graph below. Portfolios A, B and C contain only two assets: stock X and stock Y. What is the ordering of A, B and C, from the portfolio with the smallest proportion of stock X, to the portfolio with the largest proportion of stock X?

Answer: C Can see the answer by analogy with the Carrefour-Michelin example, i.e. from the geometry...
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