Finance Homework Solutions

This content provides comprehensive solutions to various finance homework questions, including topics such as model acceptance, volatility estimation, Basel regulations, and operational risk. Each question is addressed with detailed calculations and explanations, making it a valuable resource for students seeking to understand complex finance concepts and improve their academic performance.

FINANCE
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TABLE OF CONTENTS
Que. 9.14 Should accept or reject the model...............................................................................3
Que. 10.21....................................................................................................................................3
Que. 10.22 Estimating parameters for EWMA as well as GARCH (1,1) model:.......................5
Que. 12.19....................................................................................................................................5
Que. 12.21....................................................................................................................................6
Que. 13.13....................................................................................................................................6
Que. 13.14....................................................................................................................................7
Que. 14.12....................................................................................................................................7
Que. 14.13....................................................................................................................................8
Que. 14.14 Investigating impact on results by applying extreme value theory...........................9
Que. 20.12 Estimation of operational risk in different situations or parameters.........................9
Que. 20.13 Explanation about which loss is more concerned...................................................10
Que. 20.15..................................................................................................................................10
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Que. 9.14 Should accept or reject the model
Formula of Kupiec’s two-tailed test:
-2ln[(1-p)^n-m p^m] + 2In[(1-m/n)^n-m (m/n)^m] (4)
At the 5% confidence interval or probability degree of freedom is such as 3.84 which is
determined using chi-square distribution. On the basis of value 3.84 it has been assessed that
whether the model needs to accept or reject.
p = 0.01
m = 15 observations
n = 1000 days
−2 ln[0.999^985 × 0.01^15] + 2 ln[(1 − 15/1000)^985 × (15/1000)^15]
= 2.19
= 2.19 < 3.84
At this scenario value to model that is 2.19 is lesser than 3.84. Hence, it can be
ascertained that we should not reject the model and accept it.
Que. 10.21
(a) Long run average volatility:
= 0.000002 / 0.02
= 0.0001
= 0.0001 * 100
= 0.01
= 1% per day
Hence, long run average volatility in this case is 1% per day.
(b) When there are current existing volatility is at the rate of 0.5% then estimated variance in
different number of days is calculated as below:
Estimated volatility in 20 days:
√0.000183 = 0.0135
= 1.35%
Estimated volatility in 40 days:
√0.000156 = 0.0125
= 1.25%
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Estimated volatility in 60 days:
√0.000137 = 0.0117
= 1.17%
(c) Volatility needs to use at price for 20-, 40- and 60- day options:
Volatility for 20- day options:
As per the equation: α = ln (1/0.98) = 0.0202
252 | 0.0001 + [(1-e^-0.0202*2)/(0.0202*20)] [0.015^2 – 0.0001] |
= 0.051
= 22.61%
Volatility for 40- day options:
22.63%
Volatility for 60- day options:
20.85%
(d) If the volatility enhance from 1.5% to 2% per day the impact on the volatility of different
days is given as below:
For 20 days:
0.0001 – 0.98 (0.02^2 - 0 0001)
= √0.0003 = 0.0173
Expected volatility = 1.73%
For 40 days:
√0.000234 = 0.0153
Expected volatility = 1.53%
For 60 days:
√0.00019 = 0.0138
Expected volatility = 1.38%
(e) In case of increase the event from 1.5% to 2% per day then estimated volatility for different
days as below:
For 20- days:
1-e^-0.0202*20 | 23.81/22.61 | (31.75 – 23.81)
= 6.88%
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Estimated volatility = 22.61+6.88
= 29.49%
For 40- days:
Estimated volatility = 22.63 + 4.74%
= 27.37%
For 60- days:
Estimated volatility = 20.85 + 4.85%
= 25.70%
Que. 10.22 Estimating parameters for EWMA as well as GARCH (1,1) model:
On the basis of data determined indicate that optimal value of λ in the EWMA model is
like as 0.958 as well as at the same condition the log likelihood objective function is such as
11,806.4767. Apart from this according to the GARCH (1,1) model, the optimal datas and values
of (t), α (alfa) as well as β (beta) are like as 0.0000001330, 0.04447 as well as 0.95343
respectively. Hence, on the basis of all such calculations the long run average daily volatility of
the stock and shares prices determined between the period of July 27, 2005 as well as July 27,
2010 is such as 0.7954% or 0.80%. Apart from this, value of the log likelihood objective
function is such as 11,811.1955.
Que. 12.19
Basel I is a rule and regulation which framed and implemented by the international
banking where minimum amount of the derivatives in the account is to be kept. Apart from this
in the add-on amount the Basel I helpful and supportive for investors in order to manage the
minimum capital requirements of the derivatives. By considering the provided statement it can
be said that when the value of transactions in the banking will improve and raises then amount of
derivative transactions also enhance. Higher the amount of total derivative transactions are more
helpful to the individual as well as investors for managing requirements and needs of the fund
and capital. As discussed Basel I supportive for the individuals to make the transactions so due to
this add-on amount also improve by which total derivative transactions fund and capital also
improves. Further, the investor will able to recover higher amount in case he will become
defaulter or unable to provide appropriate and adequate fund. Hence, it can be argued from the
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current statement that Basel I will be definitely increase because as the add-on amount raises
then total fund under the Basel I also ehance.
Que. 12.21
On the basis of credit equivalent amount which derived under the Basel I for all the three
transactions which are done by the bank are such as follows:
(a) 3 + 0.005*100
= 3.5
(b) 0.01*150
= 1.5
(c) 7 + 0.01*50
= 7.5
Total credit equivalent amount which required for the bank under the Basel I is worth 3.5
+ 1.5 + 7.5 = 12.5. The reason is that corporations and companies has highly risk weight which
such as 50% for the off-balance sheet items and accordance to that weighted amount is worth of
6.25. Hence, capital or amount of fund needed is such as 0.08 * 6.25 or 0.5 million.
By considering and applying netting amount is 3-5+7 = 5. Therefore value of NRR is like
as 5/10 = 0.5. Apart from this, amount of the credit equivalent in millions of dollars is like as:
5 + (0.4+0.6*0.5) * (0.005*100+0.01 * 150+0.01*50) = 6.75.
Risk weighted amount is like as 3.375 and in this case amount of fund needed is like as
0.08 * 3.375 = 0.27. At this position and scenario the netting amendment declines ca[ital by rate
of 46%.
Under the Basel II when the approach like as standardized is to be implemented the
company has a weighted risk of rate 20% and under the same required amount of capital is worth
of $0.108 million.
Que. 13.13
The Basel international regulations make extensive use of external ratings for example:
from Moody's, Standard and poor index (S&P) as well as Fitch indices. Furthermore, the Dodd-
Frank Act does not give permission as well as allow external ratings to be used and adopt in rules
and regulations.
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Moreover, the Volcker provision restricting proprietary trading by the non commercial as
well as non commercial banks which operating in the country have not been adopted and
implemented by the most jurisdictions outside the respective country.
Que. 13.14
(A) Net stable funding ratio:
Amount of stable funding which is available with the bank on the basis of given balance
sheet is calculated as below:
25*0.9 + 15*0.8 + 44*0.5 + 16*1.0
= 22.5 + 12 + 22 + 16
= 72.5
Amount of stable funding which is required as below:
3*0 + 5*0.05 + 4*0.5 + 18*0.65 + 60*0.85 + 10*1.0
= 0 + 0.25 + 2 + 11.7 + 51 + 10
= 74.95
The net stable funding ratio is as follows:
72.5 / 74.95
= 0.967
(B) Extra amount needs to deposits:
By considering the above values if X is the amount of retail deposits require is such as:
72.5+0.9X = 74.95+0.05X
After making solution of the above equation value is:
0.85X = 2.45
X = 2.45 / 0.85
X = 2.88
Que. 14.12
In this case at the confidence interval 97.5%, quantile of a normal distribution with the
mean or average value zero as well as standard deviation 6 million is worth of 11,760 million.
Furthermore, at this condition value equal to 11,760 million is such as 0.0097 which is very
lower and negligible.
Value of standard error is such as follows:
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1/f(x) √q(1-q)/n
n = 2000
f(x) = 0.0097
q = 0.975
= 1/0.0097 √[0.975(1-0.975)] / 2000
= 0.358
At the confidence interval or 0.995 quantile of the normal distribution are such as +2.576
as well as -2.576 which provides value given as below:
[13 - (2.576 * 0.358) ; 13 + (2.576 * 0.358)]
= [12.08 ; 13.92]
Que. 14.13
(A) The one day 99% VaR
DJIA 3000
FTSE 3000
CAC 1000
NIKKEI 3000
Total portfolio 10000
Portfolio value 10000
Average return 0.012
Standard deviation 0.05
Confidence interval 0.99
Minimum return -0.1043
Value of portfolio -11043
VaR (value at risk) 21043.2
(B)
Value of standard error as per section 14.3
n 1000
f(x) 0.01
q 0.95
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Standard error = 1/f(x) √q(1-q)/n
= 1/0.01 √[0.99(1-0.99] / 1000
Standard value = 0.314
The Weighting-of-observations procedure in Section 14.3 gives the one day 99% VaR
(Value at Risk) equal to the amount worth of 282,204 as considered the above mentioned
example and calculation. Furthermore, the one day 99% Value at Risk when the λ parameter in
this current and existing procedure is changed and varied from the value 0.995 to 0.99
confidence interval.
(C) Using volatility updating procedure
By considering as well as using the volatility updating procedure on the basis of Section
14.3 which provides the one day 99% Value at Risk equal to the value and amount worth of
602,968 as considered the example. Moreover, value of the existing parameter λ is varied from
the 0.94 to 0.96.
Que. 14.14 Investigating impact on results by applying extreme value theory
u = 350
ln (350) = 5.86
In this case with the help of extreme value theory the value of overall portfolio on the
basis of section 14.3 will be affects and changes by 5.86.
Que. 20.12 Estimation of operational risk in different situations or parameters
Probability = 1%
Confidence interval = 99.97%
Value of portfolio = 10 million
(A) When α parameter equal to 0.25
K * (10,000,000)^-0.25 = 0.01 So that K = 0.56234.
The 99.97% worst case loss is x where 0.56234 * X^-0.25 = 0.0003.
In this case x = 12,345,679,010,000
(B) When α parameter equal to 0.5
K * (10,000,000)^-0.5 = 0.01 So that K = 31.62.
The 99.97% worst case loss is x where 31.62 * X^-0.5 = 0.0003.
In this case x = 11,111,113,500
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(C) When α parameter equal to 0.9
K * (10,000,000)^-0.9 = 0.01 So that K = 19,952.62
The 99.97% worst case loss is x where 19,952.62 * X^-0.9.
In this case x = 492,138,674.
Que. 20.13 Explanation about which loss is more concerned
In this current case there are bank and insurance company both providing loss to the
investor in different ways. The loss given by the bank is unsystematic and not occur due to
market conditions and other external factors. Furthermore, it can be recover as well; as control
by the banks using different methods and strategies. Apart from this, loss of the bank can be
diversified by putting strict and effectual control on internal systems as well as transactions by
which transactions with the counter party not able to take place of loss. Hence, the bank loss ids
the more concerned because of not having appropriate and effectual strategies to control over the
internal process and transactions. In this condition or unsystematic kind of risk the value of risk
is not been already included in the profit or return which will be provided by the bank to the
investors.
On the other side the loss which comes under the insurance company is because of the
systematic risks which cannot be control by an individual or company both. In addition to this, it
is not diversifiable as well as inherent to the nature and kind of business entity. Hence, in this the
investors cannot done anything because the level of risk is already been adjusted and inherent in
the rate of return which is calculated to determine level of profit and margin which will be
earned from the insurance company.
Que. 20.15
In this case using the bid-offer spread, optimal trading strategy for trading in the stock
market on different successive days is are such as 33.4, 31.1, 28.7, 26.2, 23.5, 20.9, 18.7 as well
as 17.4. In this on an average time until selling is such as 4.00 days. There are different
confidence levels and on that levels selling also differs which is such as given below:
Confidence interval (CI) Average times until selling (in days)
90% 4.20 days
95% 4.13 days
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99% 4.00 days
99.9% 3.87 days
99.99% 3.78 days
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