SMM729: Derivatives and Risk Management Report - Oct 2017

This report analyzes a company's foreign exchange risk exposure and proposes a hedging strategy using currency futures contracts. It details the rationale for hedging an upcoming transaction, selects an appropriate futures contract, and calculates the required number of contracts. The report then evaluates the performance of the hedge, including margin account dynamics, and calculates losses incurred. Furthermore, the report addresses portfolio risk, including systematic and unsystematic risks, and performs a Value at Risk (VAR) analysis, exploring different VAR estimates and the potential use of derivatives to improve these estimates. The analysis considers the volatility of individual stocks and the portfolio, providing a comprehensive overview of risk management techniques.

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Contents
Question 2..................................................................................................................................1
Report on 20th October 2017...................................................................................................1
Introduction.........................................................................................................................1
Need For hedging the upcoming transaction and details of the appropriate hedging
strategy................................................................................................................................2
Conclusion..........................................................................................................................3
Report on 10th March 2018....................................................................................................3
Introduction.........................................................................................................................3
Performance of the foreign transaction hedge....................................................................4
Margin Account..................................................................................................................4
Conclusion..........................................................................................................................8
Question 3..................................................................................................................................9
Report to the advisory board................................................................................................10
Risks faced by the portfolio and VAR analysis................................................................10
Portfolio Risk:...................................................................................................................10
Portfolio VAR:..................................................................................................................11
Different VAR estimates..................................................................................................12
Back-testing......................................................................................................................14
Use of derivatives to improve the VAR estimates............................................................15
References................................................................................................................................16
Appendix..................................................................................................................................17
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Question 2
Report on 20th October 2017
Introduction
This report discusses the need for hedging the upcoming transaction where the company will
receive £ 9m on the 9th of March 2018. The report also explains the hedging strategy that
should be used to hedge this transaction using the currency futures contracts. After explaining
the need for hedging this transaction, the report chooses the appropriate futures contract on
CME and then it calculates the required number of futures contracts.
Need For hedging the upcoming transaction and details of the appropriate
hedging strategy
The company is expecting to receive a payment of £ 9m on the 9th of March 2018. The
company is based in US, so this transaction will introduce foreign exchange risk from the
depreciation of £. If £ depreciates in future in comparison to today then the company will
receive less dollar amount on 9th March 2018. Therefore, it is advised to hedge such risk from
foreign exchange fluctuation using derivatives (Golden, 2019). Futures and forward contracts
can be used for such type of hedging: Forward contracts are over the counter contract
between two parties that can be customised according to the need of the individual parties but
they involve credit risk; Futures contracts are exchange traded contracts and they have pre-
defined specification but they do not have any credit risk involved as exchange acts as a
counterparty (Hull, 2017). So, futures contracts can be used to reduce the volatility in the
cash-flows arising due to the fluctuations in the foreign exchange rate.
In this future transaction the company will receive £ 9m on the 9th of March 2018. It means
the company is long on £ 9m. In order to hedge this transaction risk the company needs to
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take short position in £ futures contract expiring near the transaction date. This will allow the
company to sell £ 9m for fixed dollars amount on contract expiry date.
Out of the available contracts, CME-STERLING COMP. MAR 2018 - IBC0318 is a suitable
contract. This futures contract has expiry near but later than the transaction date so it will
reduce the basis risk.
To calculate the required number of futures contracts, total transaction value is divided by the
value of single futures contract (Hull, 2017).
This contract is based on £ 62,500.00.
No. of £ futures contracts the company needs to short: 9000000/62500 = 144.
Conclusion
The report discussed the need for hedging the foreign transaction risk due to the fluctuations
in the foreign exchange. The company will receive £ 9m on the 9th of March 2018 so it faces
risk from the devaluation of £ as this will reduce the dollar amount it will receive after
conversion to the home currency. So, the company can short 144 CME-STERLING COMP.
MAR 2018 - IBC0318 contracts to receive a fixed amount on 9th March 2018 by selling £ 9m
at the contract rate.
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Report on 10th March 2018
Introduction
The report discusses the performance of the foreign transaction hedge that the company
entered on 20th October 2017. It also discusses about the margin account that is the initial
margin, maintenance margin and variance margin.
Performance of the foreign transaction hedge
The company entered into the foreign transaction hedge on 20th October 2017. The company
shorted 144 CME-STERLING COMP. MAR 2018 - IBC0318 futures contracts.
On 20th October 2017, the settlement price of this contract was F0 = $1.3253.
On 9th March 2018, the settlement price of this contract was F1 = $1.3852.
These prices tells for how much dollar amount a company will getting for every pound it will
sold. As F1 is greater than F0, that means the pound appreciated against dollar during this
period. That is a negative scenario for the company as it shorted 144 futures contract on 20th
October 2017. In other words the company entered into futures contracts to sell a £ for
$1.3253 but the settlement price has now increased to $1.3852 per £. According to this
futures contract the company will be selling pounds at lower dollar amount.
Loss per £ on one futures contract = (F1 - F0) = (1.3852 - 1.3253) = $0.0599.
Total dollar Loss on 144 futures contract = (Loss per £) * (£ per contract) * (No. of
Contracts) = 0.0599 * 62500 * 144 = $539100.
Spot Exchange Rate on 9th March 2018 (USD per £) = 1.3867
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If the company had not entered into these futures contract, the un-hedged outcome at the spot
exchange rate = £9000000 * 1.3867 =$12480300.
Therefore, Hedged outcome = Un-hedged outcome - Loss in futures contracts = $12480300 -
$539100 = $11941200.
The company faced loss of $539100 in futures contracts.
Margin Account
Initial Margin per contract = $2000.
Total Initial Margin = 2000 * 144 = $288000.
Maintenance Margin per contract = $1600.
Total Maintenance Margin = $230400.
Following table shows the daily changes in the margin account:
CME-STERLING
COMP. MAR
2018 - SETT.
PRICE (IBC0318)
USD per £ Opening
Margin
Account
Profit/Loss Ending Margin
Account
Variation
Margin
20-10-2017 $1.3253 $2,88,000.00 $0.00 $2,88,000.00 $0.00
23-10-2017 $1.3261 $2,88,000.00 -$7,200.00 $2,80,800.00 $0.00
24-10-2017 $1.3197 $2,80,800.00 $57,600.00 $3,38,400.00 $0.00
25-10-2017 $1.3314 $3,38,400.00 -$1,05,300.00 $2,33,100.00 $0.00
26-10-2017 $1.3215 $2,33,100.00 $89,100.00 $3,22,200.00 $0.00
27-10-2017 $1.3181 $3,22,200.00 $30,600.00 $3,52,800.00 $0.00
30-10-2017 $1.3258 $3,52,800.00 -$69,300.00 $2,83,500.00 $0.00
31-10-2017 $1.3340 $2,83,500.00 -$73,800.00 $2,09,700.00 $78,300.00
01-11-2017 $1.3305 $2,88,000.00 $31,500.00 $3,19,500.00 $0.00
02-11-2017 $1.3117 $3,19,500.00 $1,69,200.00 $4,88,700.00 $0.00
03-11-2017 $1.3123 $4,88,700.00 -$5,400.00 $4,83,300.00 $0.00
06-11-2017 $1.3227 $4,83,300.00 -$93,600.00 $3,89,700.00 $0.00
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07-11-2017 $1.3222 $3,89,700.00 $4,500.00 $3,94,200.00 $0.00
08-11-2017 $1.3167 $3,94,200.00 $49,500.00 $4,43,700.00 $0.00
09-11-2017 $1.3212 $4,43,700.00 -$40,500.00 $4,03,200.00 $0.00
10-11-2017 $1.3251 $4,03,200.00 -$35,100.00 $3,68,100.00 $0.00
13-11-2017 $1.3169 $3,68,100.00 $73,800.00 $4,41,900.00 $0.00
14-11-2017 $1.3218 $4,41,900.00 -$44,100.00 $3,97,800.00 $0.00
15-11-2017 $1.3218 $3,97,800.00 $0.00 $3,97,800.00 $0.00
16-11-2017 $1.3237 $3,97,800.00 -$17,100.00 $3,80,700.00 $0.00
17-11-2017 $1.3271 $3,80,700.00 -$30,600.00 $3,50,100.00 $0.00
20-11-2017 $1.3290 $3,50,100.00 -$17,100.00 $3,33,000.00 $0.00
21-11-2017 $1.3289 $3,33,000.00 $900.00 $3,33,900.00 $0.00
22-11-2017 $1.3373 $3,33,900.00 -$75,600.00 $2,58,300.00 $0.00
23-11-2017 $1.3373 $2,58,300.00 $0.00 $2,58,300.00 $0.00
24-11-2017 $1.3382 $2,58,300.00 -$8,100.00 $2,50,200.00 $0.00
27-11-2017 $1.3369 $2,50,200.00 $11,700.00 $2,61,900.00 $0.00
28-11-2017 $1.3423 $2,61,900.00 -$48,600.00 $2,13,300.00 $74,700.00
29-11-2017 $1.3474 $2,88,000.00 -$45,900.00 $2,42,100.00 $0.00
30-11-2017 $1.3573 $2,42,100.00 -$89,100.00 $1,53,000.00 $1,35,000.0
0
01-12-2017 $1.3516 $2,88,000.00 $51,300.00 $3,39,300.00 $0.00
04-12-2017 $1.3519 $3,39,300.00 -$2,700.00 $3,36,600.00 $0.00
05-12-2017 $1.3491 $3,36,600.00 $25,200.00 $3,61,800.00 $0.00
06-12-2017 $1.3424 $3,61,800.00 $60,300.00 $4,22,100.00 $0.00
07-12-2017 $1.3518 $4,22,100.00 -$84,600.00 $3,37,500.00 $0.00
08-12-2017 $1.3448 $3,37,500.00 $63,000.00 $4,00,500.00 $0.00
11-12-2017 $1.3389 $4,00,500.00 $53,100.00 $4,53,600.00 $0.00
12-12-2017 $1.3367 $4,53,600.00 $19,800.00 $4,73,400.00 $0.00
13-12-2017 $1.3471 $4,73,400.00 -$93,600.00 $3,79,800.00 $0.00
14-12-2017 $1.3501 $3,79,800.00 -$27,000.00 $3,52,800.00 $0.00
15-12-2017 $1.3383 $3,52,800.00 $1,06,200.00 $4,59,000.00 $0.00
18-12-2017 $1.3441 $4,59,000.00 -$52,200.00 $4,06,800.00 $0.00
19-12-2017 $1.3435 $4,06,800.00 $5,400.00 $4,12,200.00 $0.00
20-12-2017 $1.3441 $4,12,200.00 -$5,400.00 $4,06,800.00 $0.00
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21-12-2017 $1.3435 $4,06,800.00 $5,400.00 $4,12,200.00 $0.00
22-12-2017 $1.3432 $4,12,200.00 $2,700.00 $4,14,900.00 $0.00
25-12-2017 $1.3432 $4,14,900.00 $0.00 $4,14,900.00 $0.00
26-12-2017 $1.3431 $4,14,900.00 $900.00 $4,15,800.00 $0.00
27-12-2017 $1.3440 $4,15,800.00 -$8,100.00 $4,07,700.00 $0.00
28-12-2017 $1.3479 $4,07,700.00 -$35,100.00 $3,72,600.00 $0.00
29-12-2017 $1.3557 $3,72,600.00 -$70,200.00 $3,02,400.00 $0.00
01-01-2018 $1.3557 $3,02,400.00 $0.00 $3,02,400.00 $0.00
02-01-2018 $1.3628 $3,02,400.00 -$63,900.00 $2,38,500.00 $0.00
03-01-2018 $1.3547 $2,38,500.00 $72,900.00 $3,11,400.00 $0.00
04-01-2018 $1.3586 $3,11,400.00 -$35,100.00 $2,76,300.00 $0.00
05-01-2018 $1.3597 $2,76,300.00 -$9,900.00 $2,66,400.00 $0.00
08-01-2018 $1.3595 $2,66,400.00 $1,800.00 $2,68,200.00 $0.00
09-01-2018 $1.3562 $2,68,200.00 $29,700.00 $2,97,900.00 $0.00
10-01-2018 $1.3539 $2,97,900.00 $20,700.00 $3,18,600.00 $0.00
11-01-2018 $1.3566 $3,18,600.00 -$24,300.00 $2,94,300.00 $0.00
12-01-2018 $1.3764 $2,94,300.00 -$1,78,200.00 $1,16,100.00 $1,71,900.0
0
15-01-2018 $1.3764 $2,88,000.00 $0.00 $2,88,000.00 $0.00
16-01-2018 $1.3821 $2,88,000.00 -$51,300.00 $2,36,700.00 $0.00
17-01-2018 $1.3907 $2,36,700.00 -$77,400.00 $1,59,300.00 $1,28,700.0
0
18-01-2018 $1.3920 $2,88,000.00 -$11,700.00 $2,76,300.00 $0.00
19-01-2018 $1.3900 $2,76,300.00 $18,000.00 $2,94,300.00 $0.00
22-01-2018 $1.4007 $2,94,300.00 -$96,300.00 $1,98,000.00 $90,000.00
23-01-2018 $1.4026 $2,88,000.00 -$17,100.00 $2,70,900.00 $0.00
24-01-2018 $1.4242 $2,70,900.00 -$1,94,400.00 $76,500.00 $2,11,500.0
0
25-01-2018 $1.4145 $2,88,000.00 $87,300.00 $3,75,300.00 $0.00
26-01-2018 $1.4184 $3,75,300.00 -$35,100.00 $3,40,200.00 $0.00
29-01-2018 $1.4104 $3,40,200.00 $72,000.00 $4,12,200.00 $0.00
30-01-2018 $1.4177 $4,12,200.00 -$65,700.00 $3,46,500.00 $0.00
31-01-2018 $1.4200 $3,46,500.00 -$20,700.00 $3,25,800.00 $0.00
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01-02-2018 $1.4287 $3,25,800.00 -$78,300.00 $2,47,500.00 $0.00
02-02-2018 $1.4152 $2,47,500.00 $1,21,500.00 $3,69,000.00 $0.00
05-02-2018 $1.4023 $3,69,000.00 $1,16,100.00 $4,85,100.00 $0.00
06-02-2018 $1.3979 $4,85,100.00 $39,600.00 $5,24,700.00 $0.00
07-02-2018 $1.3899 $5,24,700.00 $72,000.00 $5,96,700.00 $0.00
08-02-2018 $1.3940 $5,96,700.00 -$36,900.00 $5,59,800.00 $0.00
09-02-2018 $1.3825 $5,59,800.00 $1,03,500.00 $6,63,300.00 $0.00
12-02-2018 $1.3843 $6,63,300.00 -$16,200.00 $6,47,100.00 $0.00
13-02-2018 $1.3893 $6,47,100.00 -$45,000.00 $6,02,100.00 $0.00
14-02-2018 $1.4003 $6,02,100.00 -$99,000.00 $5,03,100.00 $0.00
15-02-2018 $1.4106 $5,03,100.00 -$92,700.00 $4,10,400.00 $0.00
16-02-2018 $1.4037 $4,10,400.00 $62,100.00 $4,72,500.00 $0.00
19-02-2018 $1.4037 $4,72,500.00 $0.00 $4,72,500.00 $0.00
20-02-2018 $1.4000 $4,72,500.00 $33,300.00 $5,05,800.00 $0.00
21-02-2018 $1.3948 $5,05,800.00 $46,800.00 $5,52,600.00 $0.00
22-02-2018 $1.3969 $5,52,600.00 -$18,900.00 $5,33,700.00 $0.00
23-02-2018 $1.3982 $5,33,700.00 -$11,700.00 $5,22,000.00 $0.00
26-02-2018 $1.3974 $5,22,000.00 $7,200.00 $5,29,200.00 $0.00
27-02-2018 $1.3926 $5,29,200.00 $43,200.00 $5,72,400.00 $0.00
28-02-2018 $1.3778 $5,72,400.00 $1,33,200.00 $7,05,600.00 $0.00
01-03-2018 $1.3776 $7,05,600.00 $1,800.00 $7,07,400.00 $0.00
02-03-2018 $1.3795 $7,07,400.00 -$17,100.00 $6,90,300.00 $0.00
05-03-2018 $1.3836 $6,90,300.00 -$36,900.00 $6,53,400.00 $0.00
06-03-2018 $1.3893 $6,53,400.00 -$51,300.00 $6,02,100.00 $0.00
07-03-2018 $1.3902 $6,02,100.00 -$8,100.00 $5,94,000.00 $0.00
08-03-2018 $1.3801 $5,94,000.00 $90,900.00 $6,84,900.00 $0.00
09-03-2018 $1.3852 $6,84,900.00 -$45,900.00 $6,39,000.00 $0.00
Initial Margin = $288000.
Total Variation Margin Posted = $890100.
Total loss = $539100
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Ending Margin Balance = Initial Margin - loss + Variation Margin = $639000.
Conclusion
By entering into the futures contracts the company received $11941200, which is $539100
less than the amount it would have received in no-hedge scenario. This is because the pound
appreciated against dollar during this hedging period and the company was long pounds in
this foreign transaction but to hedge it the company shorted futures contracts. The main aim
of this hedging strategy using futures was to reduce the volatility of the company’s cash-
flows by fixing the future dollar amounts it will receive. So, the hedging has achieved this
purpose although company received less net dollar amount as compared to un-hedged
scenario due to the loss in futures contract. In these futures contracts the company posted
initial Margin of $288000 and it had posted the total variation margin of $890100 due to the
losses on futures contracts that reduced the balance in its margin account below the
maintenance margin of $230400.
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Question 3
(For this analysis it is considered that today’s date is 25th Jan 2018.)
Report to the advisory board
Risks faced by the portfolio and VAR analysis
Portfolio Risk:
The company is holding an equity portfolio that consists of:
UK Equity Portfolio Company Number of Shares
Tesco 1,200,000
Rolls Royce 750,500
BP 835,575
Centrica 1,825,500
Easy Jet 915,385
HSBC 250,785
The following table tells the weight of the each of the six companies according to the current
share price as on 25th Jan 2018.
Portfolio No. of shares Share price on 25th
Jan 2018
In money terms Weight
TSCO 1200000 209.7 251640000 7.71%
RR. 750500 836.89 628085945 19.26%
BP. 835575 516.7 431741603 13.24%
CNA 1825500 134.9 246259950 7.55%
EZJ 915385 1651 1511300635 46.33%
HSBA 250785 768.4 192703194 5.91%
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Total 3261731327 100.00
%
This equity portfolio faces two types of risks systematic risk and unsystematic risk. The
unsystematic risk is due to the company specific factors and it can be eliminated by the
process of diversification. As this is a diversified portfolio consisting of the stocks from
different industries so the idiosyncratic risk is low for this portfolio. The systematic risk tells
about the riskiness of company relative to the broad market. It is the risk related to the
general equity market. So, the portfolio faces risk from the decline in the value of these
stocks.
The following table represents the return and volatility (standard deviation) of these
individual stocks and the whole portfolio:
TESC
O
ROLLS-
ROYCE
HOLDING
S
BP CENTRIC
A
EASYJE
T
HSBC
HOLDING
S
Daily Std. dev. 1.61% 1.76% 1.55
%
1.38% 2.09% 1.34%
Daily Std. dev. Of the
portfolio
1.28%
The volatility of this portfolio given by the daily standard deviation of 1.28% tells how
spreads out the daily returns are around the mean value. So, the value of the portfolio is
volatile and it can result in the decreased value of the portfolio due to the negative market
movement. Such kind of risk is known as the market risk (Science Direct, n.d.).
Portfolio VAR:
Value at Risk (VAR) is a statistical measure of the risk of an investment. It gives the
probability of the portfolio loss being less than a particular value in a particular time-period
(Hull, 2012). For example, a daily 95% portfolio VAR of £ 2 million means that there is 95%
chance that daily loss on the portfolio will be less than £ 2 million. In other words, there is
5% chance that the loss in the portfolio value will be more than £ 2 million.
Such kind of VAR calculations assume that portfolio returns are normally distributed. The
VAR gives the probability in lower tail. So, a 5% significance level i.e 5% probability in
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lower tail occurs at 1.65 standard deviations away from the mean. The VAR is first calculated
for a short period and then extended using square root rule. So, daily returns are used for this
purpose and it is assumed that mean daily return is Zero. So, 95% daily VAR of the portfolio
is given as 1.65 * daily standard deviation of the portfolio * portfolio value.
The advantage of using VAR as a risk measure is that it quantifies the risk into a single
number which is easy to understand. Another advantage is its universal acceptability and
wide applicability to a single asset or whole portfolio or at a firm level. The limitations of the
VAR is that to find the portfolio VAR a lot of estimations and calculations are required
regarding not only the return and risk of each asset but their pairwise correlations also (Hull,
2012). This makes the whole process too lengthy and difficult for a diversified portfolio.
Another issue is that it makes lot of assumptions regarding the return distribution and so
VAR number will be inaccurate if these assumptions are not valid. There are also various
approaches to the VAR calculation and different approaches can result in different VAR
values for the same portfolio.
Different VAR estimates
Variance Covariance method using simple moving average volatility or exponential
weighted moving average volatility:
The variance covariance method is a parametric approach which assumes that the return data
based on daily prices have a normal distribution. The volatility is estimated using simple
moving average or exponential weighted moving average. This VAR measure is calculated
using this standard deviation or volatility and the normal distribution factor at a particular
confidence level.
This approach makes an assumption that daily returns follow normal distribution. This makes
this approach easy to understand but to find portfolio VAR using this method a lot of
calculations is required regarding pairwise correlation calculation. Also, this assumption of
normality is not true in reality as distribution of stock returns exhibit non-normality due to
fat-tails and this may lead to unreliable VAR estimates.
The simple moving average approach gives equal weight to all the returns in the given data
series but exponential weighted moving average gives more weight recent returns data. The
simple moving average gives equal emphasis on all the return data and it does not consider
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that old data may be less relevant today. The EWMA method overcomes this issue by having
a parameter, Lambda (with value between 0 and 1) and by using exponentially declining
weights on the returns data. The value of lambda decides the emphasis given to the data and
the length of data actually considered. If lambda value is smaller the weight will decay
quickly that is giving higher weight to recent data and considering small data as weight will
decay to zero quickly and vice-versa in case of higher lambda. The convention is to use a
larger dataset and value of 0.94 for lambda.
For the given portfolio,
Simple Moving Average Method:
10-day Standard deviation of portfolio 4.05%
95% 10-day VAR of portfolio = 1.65*Std. dev.
Of portfolio 0.066754018
95% 10-day VAR of portfolio in % terms 6.68%
95% 10-day VAR of portfolio in money terms=
VAR * portfolio value(£3261731327) £217733671.41
EWMA Method:
10-day EWMA Volatility 3.2291%
Portfolio EWMA 10-day 95% VAR = 1.65 *
10-day EWMA Volatility
0.05327955
Portfolio EWMA 10-day 95% VAR in % terms 5.33%
Portfolio EWMA 10-day 95% VAR in money
terms = VAR * Portfolio Value(£3261731327)
£173783576.17
Historical Simulation Method
This is a non-parametric approach which does not require much statistical assumptions
regarding the price return data. To calculate the portfolio VAR using historical simulation,
the daily price data is used to calculate daily returns for each stock. Then the current portfolio
allocation (weights) is used to calculate portfolio historical return. Afterwards, this return
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data is ordered on the basis of the daily returns. Then a return at a particular percentile gives
us the VAR depending upon the specified level of significance (Gurrola-Perez and Murphy,
2015). The advantage of this method is that it does not assume any distribution of the data
set but uses actual return data. But it is based on the belief that past pattern of price returns is
an indicative of the future returns.
95% daily VAR of the portfolio by historical
simulation method is the return at lowest 5th
percentile
-£65782780.04
10-day 95% VAR = daily VAR * square root
of 10
£208023415.7
Back-testing
Back-testing process is used to compare the losses estimated by VAR method with the actual
losses or values in a testing period (Finance Train, n.d.). It tells if the real losses are as per the
VAR estimates. In other words, back-testing is used to evaluate the accuracy of the VAR
estimates. VAR predictions need to be recalculated in case it differs a lot from the back-
testing values in order to reduce the risk of unexpected losses. The test period for back-testing
must be an adequately long to make sure that enough actual return observations are available
to generate actual return distribution.
Back-testing is very important because the VAR methods use a lot of assumptions and which
can lead to under or over estimating of the risk. So, back-testing is used to check the
performance of the VAR methods. But there is also an issue with such kind of simple
forecasting as this test is dependent upon the particular sample of the actual returns used and
depending upon this back-testing can produce different results for the same model as
exceptions from the VAR estimate will vary with the sample. So, statistical tests can be used
depending upon different conditions to decide whether to accept or reject a VAR model. If a
VAR method passes these tests it is accepted and if VAR method fails the underlying reasons
like wrong assumptions or model misspecifications are examined. The back-testing definitely
helps in this regard but even these results are not fully certain so VAR measures are
supplemented with other techniques and measures like stress testing to reduce risk of
unexpected losses in future.
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The back-testing is done practically by choosing a test-period and then observing the number
of times the losses exceed the VAR estimates. The number of times the actual losses is
greater than the VAR number is then compared with the frequency number given by the VAR
confidence level. For the given portfolio, 95% 10-day portfolio VAR is £217733671.41,
£173783576.2 and £208023415.7 according to simple moving average variance covariance,
EWMA and historical-simulation method respectively. At this 95% confidence level the
actual losses are expected to exceed 2.6 times out of the test-period of 52 10-days period. It is
seen on comparing this value with the actual breaches that the numbers of periods where
losses exceed VAR number were 0, 3 and 1 for simple variance covariance, EWMA and
Historical Simulation method. So, there seems no issue in VAR estimates according to
variance covariance method and historical simulation method but the EWMA VAR method
estimates need to be re-evaluated and reason for it can be the choice of lambda value.
Use of derivatives to improve the VAR estimates
Derivatives like futures or options could be used to improve the VAR estimates over the
period of next six months by taking opposite position (short position because the company
holding the portfolio is already having a long position) in the derivatives so as to hedge the
market risk of the portfolio. This can be done by using the minimum variance hedge ratio that
gives the optimal hedge ratio that is the ratio of derivatives position to the spot position which
minimizes the overall variance of the portfolio. Such variance reduction is used to increase
the accuracy and precision of the VAR estimates.
15

References
Finance Train. (n.d.). Backtesting Value at Risk (VaR). [Online]. Available at:
https://financetrain.com/backtesting-value-at-risk-var/. [Accessed 4 August 2019]
Golden, P. (2019). FX: Corporate hedging goes forwards – and backwards. [Online].
Available at: https://www.euromoney.com/article/b1fftmc1s6fx0l/fx-corporate-hedging-goes-
forwards-and-backwards. [Accessed 4 August 2019]
Gurrola-Perez, P. and Murphy, D. (2015). Filtered historical simulation Value-at-Risk
models and their competitors. [Online]. Available at:
https://www.bankofengland.co.uk/working-paper/2015/filtered-historical-simulation-value-
at-risk-models-and-their-competitors. [Accessed 4 August 2019]
Hull, J. C. (2017). Options, Futures, and Other Derivatives. 10th ed. New york, USA: Pearson
Education.
Hull, J. C. (2012). Risk Management and Financial Institutions. 3rd ed. New york, USA: John
Wiley & Sons Inc.
Science Direct. (n.d.). Market Risk. [Online]. Available at:
https://www.sciencedirect.com/topics/economics-econometrics-and-finance/market-risk.
[Accessed 4 August 2019]
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Appendix
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