Download PROBLEM 3

PROBLEM 3
1 the 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.
cumulative
cumulative relative
return interval frequency
relative
frequency frequency
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:
A. Calculate the skewness
B. Explain the finding for skewness in terms of the location of the median and mean
returns
C. Calculate excess kurtosis
D. 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
A. calculate the expected value of ElStop’s annual sales
B. calculate the variance of ElStop’s annual sales
C. calculate the standard deviation of ElStop’s annual sales
2. 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 R F . 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.