Solutions Manual for Risk
Management and Financial
Institutions 6th Edition By John Hull
(All Chapters 1-28, 100% Original
Verified, A+ Grade)
This is The Only Original and
Complete Solutions Manual for 6th
Edition, All Other Files in the
Market are Fake/Old/Wrong
Edition.
Supplement/Excel Files Download
Link is Added at The End of PDF
File.
,Solutions to Further Problems
Risk Management and Financial
Institutions
Sixth Edition
John C. Hull
1
,Chapter 1: Introduction: Risk-Return Trade-offs
1.15.
Suppose that one investment has a mean return of 8% and a standard deviation of return of 14%.
Another investment has a mean return of 12% and a standard deviation of return of 20%. The
correlation between the returns is 0.3. Produce a chart similar to Figure 1.2 showing alternative
risk-return combinations from the two investments.
The impact of investing w1 in the first investment and w2 = 1 – w1 in the second investment is
shown in the table below. The range of possible risk-return trade-offs is shown in figure below.
w1 w2 µP σP
0.0 1.0 12% 20%
0.2 0.8 11.2% 17.05%
0.4 0.6 10.4% 14.69%
0.6 0.4 9.6% 13.22%
0.8 0.2 8.8% 12.97%
1.0 0.0 8.0% 14.00%
1.16.
The expected return on the market is 12% and the risk-free rate is 7%. The standard deviation of
the return on the market is 15%. One investor creates a portfolio on the efficient frontier with an
expected return of 10%. Another creates a portfolio on the efficient frontier with an expected
return of 20%. What is the standard deviation of the return on each of the two portfolios?
3
, In this case the efficient frontier is as shown in the figure below. The standard deviation of
returns corresponding to an expected return of 10% is 9%. The standard deviation of returns
corresponding to an expected return of 20% is 39%.
1.17.
A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets
and the standard deviation of 2% of assets. How much equity (as a percentage of assets) does the
company need to be (a) 99% sure that it will have a positive equity at the end of the year and (b)
99.9% sure that it will have positive equity at the end of the year? Ignore taxes.
(a) The bank can be 99% certain that profit will better than 0.8−2.33×2 or –3.85% of assets. It
therefore needs equity equal to 3.85% of assets to be 99% certain that it will have a positive
equity at the year end.
(b) The bank can be 99.9% certain that profit will be greater than 0.8 − 3.09 × 2 or –5.38% of
assets. It therefore needs equity equal to 5.38% of assets to be 99.9% certain that it will have a
positive equity at the year end.
1.18.
A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the
last year, the risk-free rate was 5% and major equity indices performed very badly, providing
returns of about −30%. The portfolio manager produced a return of −10% and claims that in the
circumstances it was good. Discuss this claim.
When the expected return on the market is −30% the expected return on a portfolio with a beta of
0.2 is
0.05 + 0.2 × (−0.30 − 0.05) = −0.02
or –2%. The actual return of –10% is worse than the expected return. The portfolio manager has
achieved an alpha of –8%!
4
Management and Financial
Institutions 6th Edition By John Hull
(All Chapters 1-28, 100% Original
Verified, A+ Grade)
This is The Only Original and
Complete Solutions Manual for 6th
Edition, All Other Files in the
Market are Fake/Old/Wrong
Edition.
Supplement/Excel Files Download
Link is Added at The End of PDF
File.
,Solutions to Further Problems
Risk Management and Financial
Institutions
Sixth Edition
John C. Hull
1
,Chapter 1: Introduction: Risk-Return Trade-offs
1.15.
Suppose that one investment has a mean return of 8% and a standard deviation of return of 14%.
Another investment has a mean return of 12% and a standard deviation of return of 20%. The
correlation between the returns is 0.3. Produce a chart similar to Figure 1.2 showing alternative
risk-return combinations from the two investments.
The impact of investing w1 in the first investment and w2 = 1 – w1 in the second investment is
shown in the table below. The range of possible risk-return trade-offs is shown in figure below.
w1 w2 µP σP
0.0 1.0 12% 20%
0.2 0.8 11.2% 17.05%
0.4 0.6 10.4% 14.69%
0.6 0.4 9.6% 13.22%
0.8 0.2 8.8% 12.97%
1.0 0.0 8.0% 14.00%
1.16.
The expected return on the market is 12% and the risk-free rate is 7%. The standard deviation of
the return on the market is 15%. One investor creates a portfolio on the efficient frontier with an
expected return of 10%. Another creates a portfolio on the efficient frontier with an expected
return of 20%. What is the standard deviation of the return on each of the two portfolios?
3
, In this case the efficient frontier is as shown in the figure below. The standard deviation of
returns corresponding to an expected return of 10% is 9%. The standard deviation of returns
corresponding to an expected return of 20% is 39%.
1.17.
A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets
and the standard deviation of 2% of assets. How much equity (as a percentage of assets) does the
company need to be (a) 99% sure that it will have a positive equity at the end of the year and (b)
99.9% sure that it will have positive equity at the end of the year? Ignore taxes.
(a) The bank can be 99% certain that profit will better than 0.8−2.33×2 or –3.85% of assets. It
therefore needs equity equal to 3.85% of assets to be 99% certain that it will have a positive
equity at the year end.
(b) The bank can be 99.9% certain that profit will be greater than 0.8 − 3.09 × 2 or –5.38% of
assets. It therefore needs equity equal to 5.38% of assets to be 99.9% certain that it will have a
positive equity at the year end.
1.18.
A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the
last year, the risk-free rate was 5% and major equity indices performed very badly, providing
returns of about −30%. The portfolio manager produced a return of −10% and claims that in the
circumstances it was good. Discuss this claim.
When the expected return on the market is −30% the expected return on a portfolio with a beta of
0.2 is
0.05 + 0.2 × (−0.30 − 0.05) = −0.02
or –2%. The actual return of –10% is worse than the expected return. The portfolio manager has
achieved an alpha of –8%!
4
