PROBLEM 3

1the table below gives the deviations of a hypothetical portfolio’s annual total returns (gross of fees) from its benchmark’s annual returns, for a 12-year period ending in 2003

Portfolio's deviations
from benchmark return
1992 / -7.14%
1993 / 1.62%
1994 / 2.48%
1995 / -2.59%
1996 / 9.37%
1997 / -0.55%
1998 / -0.89%
1999 / -9.19%
2000 / -5.11%
2001 / -0.49%
2002 / 6.84%
2003 / 3.04%

A. Calculate the frequency, cumulative frequency, relative frequency, and cumulative relative frequency for the portfolio’s deviations from benchmark return, given the set of intervals in the table below.

return interval / frequency / cumulative frequency / relative frequency / cumulative
relative
frequency
-9.19<=A<-4.55
-4.55<=B<0.09
0.09<=C<4.73
4.73<=D<9.37

B. Construct a histogram using the data

C. Identify the modal interval of the grouped data

The table below gives the annual total returns on the MSCI Germany Index from 1993 to 2002. The returns are in the local currency. Use the information in this table to answer the following problems.

MSCI Germany Index Total Returns, 1993-2002
year / return
1993 / 46.21%
1994 / -6.18%
1995 / 8.04%
1996 / 22.87%
1997 / 45.90%
1998 / 20.32%
1999 / 41.20%
2000 / -9.53%
2001 / -17.75%
2002 / -43.06%

2. To describe the distribution of observations, perform the following:

A. create a frequency distribution with five equally spaced classes (round up at the second decimal place in computing the width of class interval)

B. Calculate the cumulative frequency of the data

C. Calculate the relative frequency and cumulative relative frequency of the data

D. State whether the frequency distribution is symmetric or asymmetric. If the distribution is asymmetric, characterize the nature of the asymmetry

3. To describe the central tendency of the distribution, perform the following:

A. Calculate the sample mean return

B. Calculate the median return

C. Identify the modal interval (or intervals) of the grouped returns

4. To describe the compound rate of growth of the MSCI Germany Index, calculate the geometric mean return

5. To describe the values at which certain returns fall, calculate the 30th percentile

6. To describe the dispersion of the distribution, perform the following:

A. Calculate the range

B. Calculate the mean absolute deviation (MAD)

C. Calculate the variance

D. Calculate the standard deviation

E. Calculate the semivariance

F. Calculate the semideviation

7. To describe the degree to which the distribution may depart from normality, perform the following:

  1. Calculate the skewness
  2. Explain the finding for skewness in terms of the location of the median and mean returns
  3. Calculate excess kurtosis
  4. Contrast the distribution of annual returns on the MSCI Germany Index to a normal distribution model for returns

PROBLEM 4

  1. You are given the following probability distribution for the annual sales of ElStop Corporation:

Probability Distribution
for ElStop Annual Sales
probability / Sales(millions)
0.20 / $275
0.40 / $250
0.25 / $200
0.10 / $190
0.05 / $180
  1. calculate the expected value of ElStop’s annual sales
  2. calculate the variance of ElStop’s annual sales
  3. calculate the standard deviation of ElStop’s annual sales
  1. As in Example 4-11, you are reviewing the pricing of a speculative-grade, one-year-maturity, zero-coupon bond. Your goal is to estimate an appropriate default risk premium for this bond. The default risk premium is defined as the extra return above the risk-free return that will compensate investors for default risk. If R is the promised return (yield-to-maturity) on the debt instrument and RF is the risk-free rate，the default risk premium is R- RF . You assess that the probability that the bond defaults is 0.06，P(the bond default)=0.06. One-year U.S. T-Bills are offering a return of 5.8 percent, an estimate of RF. In contrast to your approach in Example 4-11，you no longer make the simplifying assumption that the bondholders will recover nothing in the event of a default. Rather, you now assume that recovery will be $0.35 on the dollar, given default.

A.Denote the fraction principal recovered in default as θ. Following the model of Example 4-11, develop a general expression for the promised return R on this bond.

B.Given your expression for R and the estimate of RF , state the minimum default risk premium you should require for this instrument.