# Buisness Finance

**Topics:**Capital asset pricing model, Investment, Probability theory

**Pages:**11 (2341 words)

**Published:**September 12, 2012

QUESTION # 01

Jerome J. Jerome is considering investing in a security that has the following distribution of possible one-year returns: Probability of Occurrence|0.10|0.20|0.30|0.30|0.10|

Possible return|-0.10|0.00|0.10|0.20|0.30|

a.What is the expected return and standard deviation associated with the investment? b.Is there much “downside” risk? How can you tell?

SOLUTION:-

(a) Data

Pi = 0.10, 0.20, 0.30, 0.30, 0.10

Ri = -0.10, 0.00, 0.10, 0.20, 0.30

= ??

= ??

R2

Formula

= RiPi

=

POSSIBLE RETURN, Ri|PROBABILITY OF OCCURRENCE, Pi|(Ri) (Pi)|(Ri - )2 (Pi)| -0.10|0.10|-.01|(-.1 -.11)2(.10)|

0.00|0.20|.00|( .00 - .11)2(.20)|

0.10|0.30|.03|( .10 - .11)2(.30)|

0.20|0.30|.06|( .20 - .11)2(.30)|

0.30|0.10|.03|( .30 - .11)2(.10)|

|Σ = 1.00|Σ = .11 =|Σ = .0129 = σ2|

|(.0129).5 = 11.36% = σ|

(b) There is a 30 percent probability that the actual return will be zero (prob. E(R) = 0 is 20%) or less (prob. E(R) < is 10%). Also, by inspection we see that the distribution is skewed to the left. QUESTION # 02

Summer Storme is analyzing an investment. The expected one-year return on the investment is 20 percent. The probability distribution of possible returns is approximately normal with a standard deviation of 15 percent. a.What are the chances that the investment will result in a negative return? b.What is the probability that the return will be greater than 10 percent? 20 percent? 30 percent? 40 percent? 50 percent? SOLUTION:-

(a) Data

R = 0%

= 20%

= 15%

Z =??

Formula

Z = (R -) /

For a return that will be zero or less, standardizing the deviation from the expected value of return we obtain: Z = (0% - 20%)/15%

= -1.333 standard deviations.

Turning to Table V at the back of the book, 1.333 falls between standard deviations of 1.30 and 1.35. These standard deviations correspond to areas under the curve of .0968 and .0885 respectively. This means that there is approximately a 9% probability that actual return will be zero or less. (Interpolating for 1.333, we find the probability to be 9.13 %.)

(b) Data

R = i)- 10%ii)- 20%iii)- 30%iv)- 40%v)- 50%

= 20%

= 15%

Z = ??

Formula

Z = (R -) /

i-10 percent:

Standardized deviation = (10% - 20%)/15%

= -0.667.

Probability of 10 percent or less return = (approx.) 25 percent. Probability of 10 percent or more return = 100% - 25% = 75 percent. ii-20 percent:

Standardized deviation = (20% - 20%)/15%

= 00.

50 percent probability of return being above 20 percent.

iii-30 percent:

Standardized deviation= (30% - 20%)/15%

= +0.667.

Probability of 30 percent or more return = (approx.) 25 percent. iv-40 percent:

Standardized deviation = (40% - 20%)/15%

= +1.333.

Probability of 40 percent or more return = (approx.) 9 percent -- (i.e., the same percent as in part (a)). v-50 percent:

Standardized deviation = (50% - 20%)/15%

= +2.00.

Probability of 50 percent or more return = 2.28 percent.

QUESTION # 03

Suppose that you were given the following data for past excess quarterly returns for Markese Imports, Inc., and for the market portfolio: QUATER|EXCESS RETURNS MARKESE|EXCESS RETURNS MARKET PORTFOLIO| 1|0.04|0.05|

2|0.05|0.10|

3|-0.04|-0.06|

4|-0.05|-0.10|

5|0.02|0.02|

6|0.00|-0.03|

7|0.02|0.07|

8|-0.01|-0.01|

9|-0.02|-0.08|

10|0.04|0.00|

11|0.07|0.13|

12|-0.01|0.04|

13|0.01|-0.01|

14|-0.06|-0.09|

15|-0.06|-0.14|

16|-0.02|-0.04|

17|0.07|0.15|

18|0.02|0.06|

19|0.04|0.11|

20|0.03|0.05|

21|0.01|0.03|

22|-0.01|0.01|

23|-0.01|-0.03|

24|0.02|0.04|

On the basis of this information, graph the relationship between the two sets of excess returns and draw a characteristic line. What is the approximate beta? What can you say about the systematic risk of the stock, based on past experience?

SOLUTION:-

First of all the graph will be plotted with a characteristic line...

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