Financial risk management

August 2025

1 Questions

Question 5b

Mark Otieno who trades in shares at the Securities Exchange in the spot market follows the rule “When prices are rising - Buy; when prices are falling - Sell”. He ensures that his portfolio is intact at the end of every three months. He has a basic understanding that buy equates to call option and sell equates to put option. For a three-month period, he carried out trade in five listed companies as follows:

Company	Spot price Sh.	Three months expected price	Exercise price Sh.
Safariland	445	Increase by 20%	470
Absaland	415	Increase by 15%	450
CICD	395	Decrease by 10%	370
Jubila	380	Increase by 5%	390
KCIQ	405	Decrease by 15%	395

Additional information:

1. Assume that Mark Otieno only deals with 100 shares at a time.

2. Assume that Mark Otieno exercises his option.

Required:

(i) Compute the price of the shares and indicate the option chosen in each of the five companies.

(ii) Using appropriate computations, determine the gain or loss in each of the tradings in the above companies after three months.

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April 2025

1 Questions

Question 3a

Explain FOUR advantages of over-the-counter agreements in relation to the operations of the derivatives markets.

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December 2024

2 Questions

Question 5b

Kopa Ltd., a United Kingdom (UK) firm sold goods on credit to Belfast Ltd., a firm in the United States of America (USA). This firm expects to receive United States Dollars (USD) 365,000 in six months’ time from now. The firm is considering various choices in order to hedge the transactions exposure and has collected the following data:

The following exchange rates are provided:

Spot rate USD($)/UK(£):	1.5617 – 1.5773
Six months forward rate (USD($)/UK(£):	1.5510 – 1.5625

The money market annual rates are as follows:

	Borrowing (%)	Deposit(%)
United States Dollars ($)	12	9
Sterling pounds (£)	14	11

Foreign currency option prices in cents per sterling pound for a contract size of £12,500 in six months are as follows:

Exercise price	Call option (six months)	Put option (six months)
USD($) 1.70/1 UK(£)	3.7	9.6

Required:

Using appropriate computations, advise Kopa Ltd. on the most suitable hedging strategy to use among the following:

(i) Forward market hedge.

(ii) Money market hedge.

(iii) Currency options.

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Question 4a

Assess THREE differences between “exchange traded options (ETO)” and “over the counter (OTC)” options in relation to derivatives markets.

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August 2024

1 Questions

Question 5b

Ujezi Ltd., a property development company, has gained planning permission for the development of a housing complex at Mua Greens Estate which will be developed over a three-year period.

The resulting property sales less building costs have an expected net present value of Sh.4,000,000 with a cost of capital of 10% per annum. Ujezi Ltd. has an option to acquire land in Mua Greens Estate at an agreed price of Sh.24,000,000 which must be exercised within the next two years.

Immediate building of the housing complex would be risky as the project has a volatility attaching to its net present value of 25%.

One source of risk is the potential for development of Mua Greens Estate as a regional commercial centre for the large number of firms leaving the capital, because of high rents and local business taxes. Within the next two years, an announcement by the government will be made about the development of transport links into Mua Greens Estate from the outlying areas including the area where Ujezi Ltd. hold the land option.

The risk free rate of interest is 5% per annum.

Required:

(i)	Estimate the value of the option to delay the start of the project for two years using the Black Scholes Option Pricing Model (BSOPM) and comment on your findings. Assume that the government will make its announcement about the potential transport link at the end of the two years.
(ii)	On the basis of valuation of the option to delay, estimate the overall value of the project, giving a concise rationale for the valuation method used.
(iii)	Explain TWO other types of real options that may be present relating to the Mua Greens Estate housing development. Hint: Value of call option: $P_s (Nd_1)$ – $P_e (Nd_2). e^{–rfT}$ Where: $\displaystyle d_1 = \frac{ln (P_s/P_e) + (rf + 0.5σ^2)T}{σ \sqrt{T}}$ $d_2 = d_1 – σ \sqrt{T}$ $P_s$$=$Underlying price $P_e$ $=$Strike price σ $=$Volatility rf $=$ Continuity compounded risk-free interest rate T = Time to expiration

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April 2024

3 Questions

Question 3a

Explain the following option trading strategies:

(i) Bull spread.

(ii) Bear spread.

(iii) Covered call.

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Question 4c

The following are the financial statements of Bobi Ltd. for the year ended 31 December 2023:

Bobi Limited

Statement of profit or loss for the year ended 31 December 2023:

	Sh.“000”
Revenue	60,000
Cost of sales	(35,000)
Gross profit	25,000
Operating expenses	(10,000)
Operating profit	15,000
Finance cost	(11,000)
Earnings before tax	4,000
Income tax expense	(1,200)
Profit for the year	2,800

Bobi Limited Statement of financial position as at 31 December 2023:

	Sh. “000”	Sh. “000”
Net tangible assets		126,000
Intangible assets		42,000
		168,000
Current assets:
Inventory	48,000
Trade receivables	36,000
Bank balance	4,800	88,800
		256,800
Financed by:
Equities and liabilities:
Equity:
480,000 preference shares (Sh.25 each)		12,000
500,000 ordinary shares (Sh.24 each)		12,000
Share premium		24,000
Retained earnings		16,800
		64,800
Non-current liabilities:
Mortgage (20 years)	48,000
8% debentures	72,000	120,000
		184,800
Current liabilities:
Trade payables	12,000
Notes payable	60,000	72,000
		256,800

Additional information:

1. The Z-score is to be calculated using the following formula:

Z-score = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

Where:

X1 = Working capital/Total assets

X2 = Retained earnings/Total assets

X3 = Earnings before interest and tax/Total assets

X4 = Market value of equity/Book value of debt

X5 = Sales/Total assets 2. The current market price per share is Sh.42.

Required:

(i) The Z-score of Bobi Ltd. for the year ended 31 December 2023.

(ii) Interpret the meaning of Z-score obtained in (c) (i) above.

(iii) Outline THREE limitations of Z-score model.

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Question 5b

In relation to financial risk management, explain FOUR advantages of plain vanilla currency swaps with monthly delivery compared with a strip of forward contracts.

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December 2023

3 Questions

Question 3c

A bond with a five year to maturity has a current value of Sh.92.41, a coupon rate of 8% per annum and a current market yield of 10% per annum.

The bond will be redeemed at a par value of Sh.100.

Required:

Using the Macaulay duration method, compute the bond’s duration.

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Question 5b

One of the most notable qualitative model of predicting corporate failure is Argenti’s A model score. Argenti suggested that the failure process follows a predictable sequence.

Required:

Examine the THREE failure sequence processes as predicted by Argenti’s model score.

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Question 5c

The current share price of Nonop Ltd. is Sh.7.00.

Additional information:

1. The continuously compounded risk free rate of interest is 8% per annum.

2. The variance of the rate of return on the share has been 12% per annum.

Required:

Using the Black-Scholes option pricing model, estimate the value of a European call option on the shares of the company that has an exercise price of Sh.6.60 and has 3 months to run before it expires.

Note: The Black-Scholes formula is given as follows:

$P_c = P_S N(d_1) – Xe^{–rT}N(d_2)$

Where:

N(d) = Cumulative distribution function

$\displaystyle d_1 = \frac{\ln\left[\frac{P_s}{X}\right] + rT}{\delta \sqrt{T}} + 0.5\delta T$

$d_2 = d_1$$- δ√T$

$P_s$ = Share price

$e$ = The exponential constant 2.7183

$X$ = Exercise price of option

$r$ = Annual (continuously compounded) risk free rate of return

$T$ = Time of expiry of option in years

$δ$ = Share price volatility, the standard deviation of the rate of return on shares.

$N(d_x)$ = Delta, the probability that a deviation of loss than dx will occur in a normal distribution with a mean of zero and a standard deviation of one

$\text{l}_{\text{n}}$ = Natural log

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August 2023

2 Questions

Question 3c

You are provided with the following information on put and call options on a stock:

Call price, Co =Sh.6.64

Put price, Po = Sh.2.75

Exercise price, X = Sh.30

Days to option expiration = 219 days

Current stock price, So = Sh.33.19

Number of days in a year = 365 days

Risk free rate is 5%

Required:

Using put-call parity, calculate prices of the following:

(i) Synthetic call option.

(ii) Synthetic put option.

(iii) Synthetic bond.

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Question 4a

Kobe Ltd. is about to replace its existing delivery vehicle with a new design of a vehicle that offers greater fuel economy. The company estimates that replacing the existing vehicle will save running costs of Sh.200,000 per year. There are two financing options available:

Option 1: Borrowing funds and purchasing the vehicle

The vehicle could be purchased for Sh.3,400,000 using a bank loan with an after tax cost of borrowing of 4% per year. The vehicle would have a useful life of four years and would have a residual value of Sh.1,400,000 at the end of that period. Straight line tax allowable depreciation is available on the vehicle. The vehicle would be subject to a special tax of Sh.60,000 at the end of each year of operation. The tax expenses are corporation tax deductible.

Option 2: Leasing the vehicle

The vehicle could be leased for a period of four years for a payment of Sh.600,000 per year, payable at the start of each year. The lessor will pay the special tax. Lease payments are a corporation tax deductible expense.

The firm after tax weighted average cost of capital is 8%. The company pays corporation tax at a rate of 30% one year in arrears.

Required:

(i) Advise Kobe Ltd. on whether it should lease or borrow to finance the new vehicle.

(ii) Examine THREE reasons other than possible after tax cost advantages why Kobe Ltd. may choose to lease rather than buy the new delivery vehicle.

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April 2023

3 Questions

Question 4b

Pine Ltd. is considering an investment in one of two corporate bonds namely A and B. Both bonds have a par value of Sh.1,000 and pay coupon interest on an annual basis.

The market price of bond A is Sh.1,079.60 with a coupon rate of 6% and is due to be redeemed at par in five years. Bond B is about to be issued with a coupon rate of 4% and will also be redeemable at par in five years.

Additional information:

1. Both bonds are expected to have the same gross redemption yield (yield to maturity).

2. The yield to maturity of a company bond is determined by its credit rating.

Pine Ltd. considers duration of the bond to be a key factor when making decisions on which bond to invest in.

Required:

(i) The Macaulay duration for bond A and bond B.

(ii) Discuss TWO limitations of duration as a measure of a bond price to changes in interest rates.

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Question 4a

Explain THREE differences between “futures contracts” and “forward contracts”.

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Question 2b

Consider a two-period binomial model in which a share currently trades at a price of Sh.65. The share price can go up 20% or down 17% each period. The risk free rate is 5%.

Required:

The price of a put option expiring in two periods with an exercise price of Sh.60.

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December 2022

2 Questions

Question 3c

Advise on the cheapest method based on your results in (b) (i) – (b) (iii) above.

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Question 5a

Explain FIVE limitations of financial derivatives used in financial risk management.

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August 2022

1 Questions

Question 3b

A United States (US) company buys goods worth 1,440,000 Euros (€) from a German company payable in 30 days. The US company wants to hedge against the Euro (€) strengthening against the United States dollar ($).

The following exchange rates are provided:

Current spot rate: $/€ 0.9215 – 0.9221

Futures exchange rate: $/€ 0.9245.

The standard size of a 3 month € futures contract is €125,000. In 30 days time, the spot rate is 0.9345 – 0.9351 $$$/€ and closing futures price will be 0.9367 $$$/€.

Required:

Determine the net outcome of the futures currency hedge.

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April 2022

2 Questions

Question 3d

The current market price per ordinary share of Kanga Ltd. is Sh.58. A call option exists on the company’s shares with an exercise price of Sh.52 and with six months to maturity.

The option can only be exercised on maturity, that is, it is a European option.

The risk free rate of return is 6% and the variance of the rate of return on the shares is 15%.

Required:

Using the Black-Scholes option pricing model, estimate the value of the call option.

Black - Scholes Option Pricing Formula:

Value of call = $S N (d_i) -K e^{rt} N(d_2)$

Where:

$\displaystyle d_i = \frac{ln[\frac{S}{K}] + (r + \frac{\sigma^2}{2})t}{\sigma \sqrt{t}}$

$d_2 = d_1- \sigma \sqrt{t}$

S = Current value of the underlying asset

K = Strike price of the option

t = Life to expiration of the option

r = Riskless interest rate corresponding to the life of the option.

$\delta$ = Standard deviation of the underlying asset’s return

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Question 3c

Summarise four disadvantages of using futures contracts as financial instruments.

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Pilot December 2021

2 Questions

Question 5a

Alpha will receive US dollars 400,000 in 3 month’s time. The company treasurer has determined the following:

Spot rate	Dollars1.8250-Dollars 1.8361
3 months forward	Dollars1.8338-Dollars 1.8452

Money market rates	Borrowing	Deposit
US Dollars	5.1%	4.2%
Sterling	5.75%	4.5%

The money market rates are annual rates.

Required:

Determine whether a forward contract hedge or a money market hedge should be undertaken.

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Question 4c

In relation to financial risk management, briefly explain four advantages of financial derivatives.

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December 2021

2 Questions

Question 4c

Jaram Ltd., a United Kingdom (UK) based firm bought goods on credit worth 365.000 United States Dollars (USD) from a firm in the United States of America (USA) payable in six months time from now. The company is considering various choices in order to hedge the transactions exposure and has collected the following data:

Exchange rate (USS/1£):
Spot rate	1.3648-1.3722
Six months forward rate	1.3515-1.3655

The annual money market rates are given as follows:

	Borrowing rate (%)	Deposit rate (%)
US Dollars ($)	12	9
Sterling Pounds (£)	14	11

The foreign currency option prices (cents per Sterling Pound) for a contract size of £15,000 are as follows:

Exercise price	6-month call option	6-month put option
$1.40	4.7	9.5

Required:

Determine the amount payable using:

(i) Forward market cover.

(ii) Money market cover.

(iii) Currency options.

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Question 1c

XYZ Limited's share is currently selling at Sh.10. The share price will increase by 5% or reduce by 5% six months from now. The risk free rate of return is 6% and the strike price is Sh.10. The option will be exercised after six months.

Required:

Using the risk neutral approach, determine the value of a put option at the initial node of the binomial tree.

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September 2021

1 Questions

Question 1c

Explain four reasons why derivative instruments have continued to become more popular in financial markets.

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May 2021

1 Questions

Question 1c

Dafina Limited is an export - import firm based in Kenya.

On 1 August 2020, the company exported tea to the United States of America (USA) on a 3-month credit amounting to US$10.000.000.

Additional information:

1.	The rates in the forex and money market were as follows:

		Ksh/1USS
	1 August 2020	105
	1 December 2020	101
		Interest rates (per annum)
	Kenya	18%
	USA	12%
2.	The customer will settle the amount on I December 2020.

Required:

(i) Using the interest rate parity, determine the expected 3-months forward exchange rate as at 1 December 2020.

(ii) Using suitable computations, advise Dafina Limited on the better hedging strategy between a forward market and money market hedge.

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November 2020

2 Questions

Question 2c

You have recently been hired as a financial manager at Panblock Limited, a locally incorporated company that deals in imported building materials from the United States of America (USA). As the person in charge of negotiating the exchange rates, you have noted the following indicative exchange rates and interest rates:

3-months forward exchange rates	105 KES/USD
Spot exchange rate	100 KES/USD
3-months interest rate in Kenya	8% per annum
3-months interest rate in USA	5.8% per annum

Assume that Panblock Limited can borrow as much as KES 1,000,000.

Required:

(i) Determine whether the interest rate parity (IRP) is currently holding.

(ii) Demonstrate how you could undertake a covered interest arbitrage assuming that IRP is not holding.

(iii) Determine the arbitrage profit.

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Question 4b

An investor has acquired a call option whose exercise price is Sh. 100. The option's premium is Sh.5 per option.

The following are the possible market prices (in shillings) of the option:

114 112 110 108 106 105 104 102 100 98 96 94

Required:

(i). Determine the options value based on each of the above market prices.

(ii). Determine the profit or loss associated with the option on the basis of each of the possible market prices

(iii).Represent the information in (b) (ii) above in a diagram where the x- axis represents market price and y - axis represents profit or loss for the option buyer.

(iv).Interpret the graph in (b) (iii) above.

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November 2019

1 Questions

Question 4a

Distinguish between the following terms as used in the context of derivatives market:

(i) "Currency option" and "currency swap".

(ii)"Interest rate swap" and "interest rate collar".

(iii) "Hedgers" and speculators".

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May 2019

1 Questions

Question 4a

Kadzenga Limited is a Kenyan company with a substantial proportion of its trade with companies in the United States (US). Kadzenga Ltd. invoiced a US firm 60,000 United States Dollars (USD) receivable 3 months from now. Additional information:

1	The borrowing rate is 3% above the bank base rate while the investing rate is 2% below the bank base rate. These rates apply both in Kenya and the United States.
2	The bank base rates in Kenya and the US are 15% and 10% per annum respectively.
3	The exchange rates in the forex market between the Kenya Shilling (Ksh) and the United States Dollar (USD) are as follows:

		Ksh/1 US (S)
	Spot exchange rate:	103-105
	One month forward rate:	102-103
	3-months forward rate:	101-102

Required:

Calculate the amount to be received by Kadzenga Limited using:

(i) Forward contract hedge.

(ii) Money market hedge.

(iii) Using the results obtained in (a) (i) and (a) (ii) above, advise the management of Kadzenga Limited on the best hedging strategy.

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November 2018

2 Questions

Question 3b

Chigiri Investment Limited is a company based in Kenya. The company exported goods on credit to a firm in the United States of America (USA). The company expects to receive US$ 800,000 in one year's time.

The current spot exchange rate is IUS$ = KES.60.

However, Chigiri Investment Limited created a probability distribution for the forward spot rate in one year as follows:

Probability	Forward spot rate KES/1 US $
20 50 30	61 63 67

Additional information:

1	One year put options on the USS are available with an exercise price of KES.63 and a premium of KES. 4 per US$.
2	One year call options are available on the USwithanexercisepriceofKES.60apremiumofKES3perUS.
3	The future spot rate is estimated in a year's time to be KES. 62 per 1US$.
4	The following are the money market annual rates:

		Kenya Annual rates (%)	USA Annual rates (%)
	Borrowing Deposit	18 9	12 6

Required:

(i) Determine whether a forward market hedge, money market hedge or currency option hedge would be the most appropriate hedging strategy for the company.

(ii) Advise a prospective investor, the most appropriate hedging strategy if no hedging takes place.

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Question 4a

A financial analyst is interested in using the Black-Scholes Model (BSM) to value call options on the stock.

The following information is available:

1. The price of the stock is Sh.35.

2. The strike price is Sh.30.

3. The option matures in 9 months.

4 The volatility of returns of the stock is 0.30.

5. The risk-free rate is 10%.

Required:

The value of a call option using the Black-Scholes Model.

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May 2018

2 Questions

Question 5c

Kikumi Ltd. expects to receive 750.000 Euros from a credit customer in the European Union in 6 months' time. The spot exchange rate is 2.349 Euros (EUR) per United States Dollar (USD) and the 6-month forward rate is 2.412 Euros per USD.

The following commercial interest rates are available to Kikumi Ltd.

	Deposit rate per annum (%)	Borrowing rate per annum (%)
EUR USD	4.0 2.0	8.0 3.5

Kikumi Ltd. does not have any surplus cash to use in hedging the future Euro receipt.

Required:

Evaluate whether the money market hedge or a forward hedge would be preferred.

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Question 4a

In relation to derivatives markets and contracts:

(i) Highlight four characteristics that are common to both forward contracts and futures contracts.

(ii) Differentiate between a "straddle" and a "strangle".

(iii) Outline three methods of terminating a swap contract.

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November 2017

1 Questions

Question 5b

Jacques Ltd. is a company based in France where the Euro (€) is widely used. The company has recently imported raw materials from the USA and has been invoiced for US Dollars ($) 240,000 payable in 3 months' time.

In addition, the company has exported finished goods to the USA and Australia. The customer in the USA has been invoiced for US Dollars ($) 69,000 payable in 3 months' time and the Australian customer has been invoiced for Australian dollars (ASD) 395,000 payable in 4 months' time.

The current spot and forward exchange rates are given as follows:

US Dollars ($) / 1 Euro (€)

Spot rate 0.9830 - 0.9850

3 months' forward 0.9520 - 0.9525

Euro (€)/1 ASD

Spot rate 1.8890 - 1.8920

4 months' forward 1.9510 - 1.9540

The current money market interest rates per annum are given as follows:

Lending Borrowing

USA 10% 12%

Australia 14% 16%

France 11% 13%

Required:

Show how the company can hedge its foreign exchange exposure using:

(i) Forward market cover.

(ii) Money market cover.

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May 2017

1 Questions

Question 4b

Biashara Ltd. is an import-export company based in Kenya. On 1 January 2017, the company exported coffee worth LUS $140,000 to the United States (US) of America on a five-month credit.

Additional information:

1	The exchange rates in the forex markets were (are expected to be) as follows: KSh/1 USS 1 January 2017 100 31 May 2017 102
2	The lending and borrowing rates in the two countries are as follows:

		Annual lending rate	Annual borrowing rate
	Kenya USA	18% 14%	19% 15%

3	The importer will settle the outstanding amount on 31 May 2017.

Required:

(i). Cin Using the interest rate parity relationship, compute the expected 5-month forward exchange rate as at 31 May 2017.

(ii). Advise Biashara Ltd, on which is the better hedging strategy berween a forward contract and a money market hedge.

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November 2016

2 Questions

Question 5a

Explain how currency swaps could be used to hedge against the foreign exchange operating exposure of a firm.

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Question 5d

Highlight two shortcomings of the Black-Scholes option pricing model.

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May 2016

2 Questions

Question 5b

Jasper Ltd. is a company based in Nairobi, Kenya which does business with companies based in Tanzania. From such trade, Jasper Ltd. expects the following cash flows in the next six months, in the currencies specified:

Payments due in 3 months	: Ksh.116,000
Receipts due in 3 mont	: Tsh.1,970,000
Payments due in 6 months	: Tsh.4,470,000
Receípts due in 6 months	: Tsh.1,540,000

The exchange rates in the Nairobi market are as follows:


Spot	17.106 - 17.140
Three months forward	0.82 - 0.77 cents premium
Six months forward	1.39 - 1.34 cents premium

	Interest rates
Ksh. Tsh.	Borrowing 12.5% 9%	Lending 9.5% 6%

Required:

The net Kenya shilling receipts/payments that Jasper Ltd. might expect for both its three month and six month transactions if the company hedges foreign exchange risk on the: (i) Forward foreign exchange market.

(ii) Money market.

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Question 5a

Discuss four techniques that a company might use to hedge against the foreign exchange risk involved in foreign trade.

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November 2015

2 Questions

Question 5a

The main driver of option valuation is the volatility of returns of the associated asset.

Support the above statement.

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Question 5c

Granada Ltd., a UK-based company, imports computer components from the Far East. The trading currency is the Singapore dollar (SS) and the value of the deal is $S$28$ million. Three month's credit is given. The current spot exchange rate is $S$2.8$ to one sterling pound (£). Because of recent volatility in the foreign exchange markets, Granada Ltd.'s directors are worried that a rise in the value of the $S$$ could wipe out the profits on the deal. Three alternative hedging methods have been suggested as follows:

A forward market hedge.
A money market hedge.
An option hedge.

Granada Ltd.'s treasurer has provided the following information:

1. The three-month forward rate is $S$2.79:£1.$

2. Granada Ltd. can borrow Singapore dollars at 2% interest rate per annum and sterling pounds at 5% per annum.

3. Deposit rates are 1% per annum in Singapore and 3% per annum in the UK.

4. A three-month American call option to buy $S$28$ million at an exercise rate of $S$2.785:£1$ could be purchased at a premium of $£200,000$ on the London OTC option market.

Required:

(i) Indicate which would be a better hedge between the forward market hedge and the money market hedge.

(ii) Evaluate the option hedge if the following spot rates were applicable in three months' time: $S$2.78:£1. S$2.82:£1.$

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Pilot September 2015

2 Questions

Question 3a

Briefly discuss the meaning and importance of the following terms as used in option pricing:

(i) Delta.

(ii) Theta.

(iii) Vega.

(iv) Rho.

(v) Gamma.

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Question 3b

Assume that your company has invested in 100,000 shares of Usaidizi Ltd., a manufacturer of light bulbs. You are concerned about the recent volatility in Usaidizi Ltd.'s share price due to the unpredictable weather in Uganda. You wish to protect your company's investments froma possible fall in Usaidizi Ltd. share price until winter in three months

time, but do not wish to sell the shares at present.

No dividends are due to be paid by Usaidizi Ltd. during the next three months.

Market data:

Usaidizi Ltd. current share price: Sh.20
Call option exercise price: Sh.22
Time to expiry: 3 months
Volatility of Usaidizi Ltd. shares 50% (standard deviation per year)

Assume that option contracts are for the purchase or sale of units of 1,000 shares.

Required:

(i) Devise a delta hedger that is expected to protect investment against changes in the share price until the weather changes. Delta may be estimated using $N(d_1)$.

(ii) Comment on whether such a hedge is likely to be totally successful.

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Financial risk management

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