CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r28 risk management applications of forward and futures strategies IFT notes

Managing the Risk of an Equity Portfolio LO.a: Demonstrate the use of equity futures contracts to achieve a target beta for a stock portfolio and calculate and interpret the number of fu

Risk Management Applications of Forward and Futures Strategies

1 Introduction 3

2 Strategies and Applications for Managing Interest Rate Risk 3

2.1 Managing the Interest Rate Risk of a Loan Using an FRA 3

2.2 Strategies and Applications for Managing Bond Portfolio Risk 3

3 Strategies and Applications for Managing Equity Market Risk 3

3.1 Measuring and Managing the Risk of Equities 3

3.2 Managing the Risk of an Equity Portfolio 4

3.3 Creating Equity out of Cash 5

3.4 Creating Cash out of Equity 6

4 Asset Allocation with Futures 8

4.1 Adjusting the Allocation among Asset Classes 8

4.2 Pre-Investing in an Asset Class 10

5 Strategies and Applications for Managing Foreign Currency Risk 11

5.1 Managing the Risk of a Foreign Currency Receipt 12

5.2 Managing the Risk of a Foreign Currency Payment 12

5.3 Managing the Risk of a Foreign-Market Asset Portfolio 13

6 Futures or Forwards? 13

7 Final Comments 14

Summary 14

Examples from the curriculum 16

Example 1 16

Example 2 17

Example 3 18

Example 4 19

Example 5 20

Example 6 21

Example 7 22

Example 8 23

Example 9 24

This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA®

Program curriculum Some of the graphs, charts, tables, examples, and figures are copyright

2017, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved

Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the

products or services offered by IFT CFA Institute, CFA®, and Chartered Financial Analyst® are

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1 Introduction

In this reading we will look at how forwards and futures can be used to manage risk

2 Strategies and Applications for Managing Interest Rate Risk

Note: Section 2 is optional, and is a revision of concepts covered earlier

2.1 Managing the Interest Rate Risk of a Loan Using an FRA

Forward rate agreements (FRA) are often used to manage interest rate risk Consider a company

planning to take out a loan at a later date If it fears that the interest rates will rise between now and the

day it takes out the loan, it can enter into a long position in an FRA and lock in the interest rate available

now

Refer to Example 1 from the curriculum

2.2 Strategies and Applications for Managing Bond Portfolio Risk

Duration is a measure of the sensitivity of a bond’s price to change in its yield For example, if the

duration of a bond is 3 then a 1% increase in the yield will lead to a 3% decrease in the bond price

The duration of a bond portfolio can be modified by going long or short on bond futures Going long on

bond futures will increase the portfolio duration Going short on bond futures will decrease the portfolio

duration

Refer to Example 2 from the curriculum

3 Strategies and Applications for Managing Equity Market Risk

3.1 Measuring and Managing the Risk of Equities

We will use beta as our risk measure Beta is a relative risk measure For example, a beta of 1.1 means

that a stock is 10% more volatile than the benchmark A beta of 0.9 means that the stock is 10% less

volatile than the benchmark Beta is calculated as:

𝛽 =𝑐𝑜𝑣𝑠1

𝜎12

Where 𝑐𝑜𝑣𝑠1 is the covariance between the stock portfolio and the index and 𝜎12 is the variance of the

index

We can use futures contract to change the portfolio beta Going long on futures contract increases

portfolio beta Going short on futures contract decreases portfolio beta The number of contracts

required to achieve a target beta is calculated as:

𝑁𝑓 = (𝛽𝑇− 𝛽𝑆

𝛽𝑇 ) (

𝑆

𝑓)

3.2 Managing the Risk of an Equity Portfolio

LO.a: Demonstrate the use of equity futures contracts to achieve a target beta for a stock portfolio

and calculate and interpret the number of futures contracts required

Exhibit 3 demonstrates a scenario where a pension fund wants to increase its equity portfolio beta

because it expects the market to be strong in the near future

Exhibit 3 Using Stock Index Futures to Manage the Risk of a Stock Portfolio

Scenario (2 September)

BB Holdings (BBH) is a US conglomerate Its pension fund generates market forecasts internally and

receives forecasts from an independent consultant As a result of these forecasts, BBH expects the

market for large-cap stocks to be stronger than it believes everyone else is expecting over the next two

months

Action

BBH decides to adjust the beta on $38,500,000 of large-cap stocks from its current level of 0.90 to 1.10

for the period of the next two months It has selected a futures contract deemed to have sufficient

liquidity; the futures price is currently $275,000 and the contract has a beta of 0.95 The appropriate

number of futures contracts to adjust the beta would be:

$38,500,000

$275,000 ) = 29.47

So it buys 29 contracts

Scenario (3 December)

The market as a whole increases by 4.4 percent The stock portfolio increases to $40,103,000 The stock

index futures contract rises to $286,687.50, an increase of 4.25 percent

Outcome and Analysis

The profit on the futures contract is 29($286,687.50 – $275,000.00) = $338,937.50 The rate of return

for the stock portfolio is:

$40,103,000

$38,500,000− 1 = 0.0416 or 4.16%

Adding the profit from the futures gives a total market value of $40,103,000.00 + $338,937.50 =

$40,441,937.50 The rate of return for the stock portfolio is:

$40,441,937.50

$38,500,000.00− 1 = 0.0504 = 5.04%Because the market went up by 4.4 percent and the overall gain

was 5.04 percent, the effective beta of the portfolio was:

0.0504

0.044 = 1.15

Thus, the effective beta is quite close to the target beta of 1.10

However, a point to note is that increasing the beta increases the risk If the beta is increased and the

market falls, the loss on the portfolio will be greater than if the beta had not been increased

Refer to Example 3 from the curriculum

3.3 Creating Equity out of Cash

LO.b: Construct a synthetic stock index fund using cash and stock index futures (equitizing cash)

Stock index futures are often used to create synthetic positions in equity The advantage of this method

is that it saves transaction costs and preserves liquidity

A stock can be combined with a short position in a futures contract to create a risk-free payoff This can

be expressed as follows:

Long stock + Short futures = Long risk-free bond

This equation can be rearranged as:

Long stock = Long risk-free bond + Long futures

This shows that a synthetic equity position can be created by combining a risk free bond with futures

contracts

If the amount of money to be invested is V The number of futures contracts required to create a

synthetic equity position is calculated using the equation:

T = time to expiration of futures

δ = dividend yield on the index

r = risk-free rate

q = futures contract multiplier

Exhibit 4 demonstrates a scenario where a synthetic position in equity is created

Exhibit 4 Constructing a Synthetic Index Fund

Scenario (15 December)

On 15 December, a US money manager for a firm called Strategic Money Management (SMM) wants to

construct a synthetic index fund consisting of a position of £100 million invested in UK stock The index

will be the FTSE 100, which has a dividend yield of 2.5 percent A futures contract on the FTSE 100 is

priced at £4,000 and has a multiplier of £10 The position will be held until the futures expires in three

months, at which time it will be renewed with a new three-month futures The UK risk-free rate is 5

percent Both the risk-free rate and the dividend yield are stated as annually compounded figures

we are actually synthetically investing:

2,531(£10)£4,000

(1.05)0.25 = £100,012,622

in stock So we put this much money in risk-free bonds, which will grow to £100,012,622(1.05)0.25 =

£101,240,000 The number of units of stock that we have effectively purchased at the start is:

𝑁𝑓∗ 𝑞

(1 + 𝛿)𝑇 = 2,531(10)

(1.025)0.25= 25,154.24

If the stock had actually been purchased, dividends would be received and reinvested into additional

shares Thus, the number of shares would grow to 25,154.24(1.025)0.25 = 25,310

Scenario (15 March)

The index is at ST when the futures expires

Outcome and Analysis

The futures contracts will pay off the amount:

Futures payoff = 2,531(£10)(ST – £4,000) = £25,310ST – £101,240,000

This means that the fund will pay £101,240,000 to settle the futures contract and obtain the market

value of 25,310 units of the FTSE 100, each worth ST Therefore, the fund will need to come up with

£101,240,000, but as noted above, the money invested in risk-free bonds grows to a value of

£101,240,000

SMM, therefore, pays this amount to settle the futures contracts and effectively ends up with 25,310

units of the index, the position it wanted in the market

Refer to Example 4 from the curriculum

3.4 Creating Cash out of Equity

LO.c: Explain the use of stock index futures to convert a long stock position into synthetic cash

The relationship between a futures contract and the underlying stock is:

Long stock + Short futures = Long risk-free bond

Hence we can construct a synthetic position is cash by selling futures against a long stock position

The number of futures contract required is calculated as:

𝑁𝑓 = −𝑉(1 + 𝑟)

𝑇

𝑞𝑓

The negative sign means that we are selling futures

Exhibit 5 illustrates a scenario where pension fund wants to convert its stock position to cash

Exhibit 5 Creating Synthetic Cash

Scenario (2 June)

The pension fund of Interactive Industrial Systems (IIS) holds a $50 million portion of its portfolio in an

indexed position of the NASDAQ 100, which has a dividend yield of 0.75 percent It would like to convert

that position to cash for a two-month period It can do this using a futures contract on the NASDAQ 100,

which is priced at 1484.72, has a multiplier of $100, and expires in two months The risk-free rate is 4.65

stock synthetically converted to cash is really:

−𝑁𝑓∗ 𝑞𝑓

(1 + 𝑟)𝑇 =339($100)(1484.72)

(1.0465)2/12 = $49,952,173 This amount should grow to $49,952,173(1.0465)2/12 = $50,332,008 The number of units of stock is:

The stock index is at ST when the futures expires

Outcome and Analysis

The payoff of the futures contract is

–339($100)*(ST – 1484.72) = –$33,900ST + $50,332,008

As noted, dividends are reinvested and the number of units of the index grows to 33,900 shares The

overall position of the fund is:

Stock worth 33,900 ST

Futures payoff of –33,900 ST + $50,332,008

or an overall total of $50,332,008 This is exactly the amount we said the fund would have if it invested

$49,952,173 at the risk-free rate of 4.65 percent for two months Thus, the fund has effectively

converted a stock position to cash

Refer to Example 5 from the curriculum

4 Asset Allocation with Futures

We can allocate a portfolio among asset classes using futures

4.1 Adjusting the Allocation among Asset Classes

LO.d: Demonstrate the use of equity and bond futures to adjust the allocation of a portfolio

between equity and debt

Exhibit 6 presents an example where a portfolio manager wants to reduce his allocation to stocks and

increase the allocation to bonds

Exhibit 6 Adjusting the Allocation between Stocks and Bonds

Scenario (15 November)

Global Asset Advisory Group (GAAG) is a pension fund management firm One of its funds consists of

$300 million allocated 80 percent to stock and 20 percent to bonds The stock portion has a beta of 1.10

and the bond portion has a duration of 6.5 GAAG would like to temporarily adjust the asset allocation

to 50 percent stock and 50 percent bonds It will use stock index futures and bond futures to achieve

this objective The stock index futures contract has a price of $200,000 (after accounting for the

multiplier) and a beta of 0.96 The bond futures contract has an implied modified duration of 7.2 and a

price of $105,250 The yield beta is 1 The transaction will be put in place on 15 November, and the

horizon date for termination is 10 January

Action

The market value of the stock is 0.80($300,000,000) = $240,000,000 The market value of the bonds is

0.20($300,000,000) = $60,000,000 Because it wants the portfolio to be temporarily reallocated to half

stock and half bonds, GAAG needs to change the allocation to $150 million of each

Thus, GAAG effectively needs to sell $90 million of stock by converting it to cash using stock index

futures and buy $90 million of bonds by using bond futures This would effectively convert the stock into

cash and then convert that cash into bonds Of course, this entire series of transactions will be synthetic;

the actual stock and bonds in the portfolio will stay in place

Using Equation 5, the number of stock index futures, denoted as Nsf, will be:

𝑁𝑠𝑓= (𝛽𝑇− 𝛽𝑆

𝛽𝑓 )

𝑆

𝑓𝑆where βT is the target beta of zero, βS is the stock beta of 1.10, βf is the futures beta of 0.96, S is the

market value of the stock involved in the transaction of $90 million, and fs is the price of the stock index

Using Equation 4, the number of bond futures, denoted as Nbf, will be:

𝑁𝑏𝑓 = (𝑀𝐷𝑈𝑅𝑇− 𝑀𝐷𝑈𝑅𝐵

𝐵

𝑓𝑏where MDURT is the target modified duration of 6.5, MDURB is the modified duration of the existing

bonds, MDURf is the implied modified duration of the futures (here 7.2), B is the market value of the

bonds of $90 million, and fb is the bond futures price of $105,250 The modified duration of the existing

bonds is the modified duration of a cash position The sale of stock index futures provides $90 million of

synthetic cash that is now converted into bonds using bond futures Because no movement of actual

cash is involved in these futures market transactions, the modified duration of cash is effectively equal

During this period, the stock portion of the portfolio returns –3 percent and the bond portion returns

1.25 percent The stock index futures price goes from $200,000 to $193,600, and the bond futures price

increases from $105,250 to $106,691

Outcome and Analysis

The profit on the stock index futures transaction is –516($193,600 – $200,000) = $3,302,400 The profit

on the bond futures transaction is 772($106,691 – $105,250) = $1,112,452 The total profit from the

futures transaction is, therefore, $3,302,400 + $1,112,452 = $4,414,852 The market value of the stocks

and bonds will now be:

Stocks: $240,000,000(1−0.03) =$232,800,000

Bonds: $60,000,000(1.0125) =$60,750,000

Total $293,550,000

Thus, the total portfolio value, including the futures gains, is $293,550,000 + $4,414,852 = $297,964,852

Had GAAG sold stocks and then converted the proceeds to bonds, the value would have been:

Exhibit 7 provides a scenario where a manager wants to convert a portion of his long-term bond

portfolio to cash to improve liquidity The key point to note is that reducing duration to replicate a short

term instrument does not remove the problem that long term instruments, which are still held, may

have to be liquidated

Exhibit 8 provides a scenario where a manager wants to adjust allocation between one equity class

(large-cap) and another (mid-cap)

Refer to Example 6 from the curriculum

4.2 Pre-Investing in an Asset Class

LO.e: Demonstrate the use of futures to adjust the allocation of a portfolio across equity sectors and

to gain exposure to an asset class in advance of actually committing funds to the asset class

Say we expect the equity markets to rise over the next six months and want to benefit from the bull run

without making an up-front investment We can ‘pre-invest’ in equity by taking a long position in a

six-month equity futures contract The key is to create a position with the appropriate beta A similar

approach can be used to ‘pre-invest’ in bonds but here the key is to create a position with the

appropriate duration

Exhibit 9 presents an example where an entity wants to pre-invest in stocks and bonds

Exhibit 9 Pre-Investing in Asset Classes

Scenario (28 February)

Quantitative Mutual Funds Advisors (QMFA) uses modern analytical techniques to manage money for a

number of mutual funds QMFA is not necessarily an aggressive investor, but it does not like to be out of

the market QMFA has learned that it will receive an additional $10 million to invest Although QMFA

would like to receive the money now, the money is not available for three months If it had the money

now, QMFA would invest $6 million in stocks at an average beta of 1.08 and $4 million in bonds at a

modified duration of 5.25 It believes the market outlook over the next three months is highly attractive

Therefore, QMFA would like to invest now, which it can do by trading stock and bond futures An

appropriate stock index futures contract is selling at $210,500 and has a beta of 0.97 An appropriate

bond futures contract is selling for $115,750 and has an implied modified duration of 6.05 The current

date is 28 February, and the money will be available on 31 May The number of stock index futures

contracts will be denoted as Nsf, and the number of bond futures contracts will be denoted as Nbf

Action

QMFA wants to take a position in $6 million of stock index futures at a beta of 1.08 It currently has no

position; hence, its beta is zero The required number of stock index futures contracts to obtain this

$6,000,000

$210,500 ) = 31.74

So QMFA buys 32 stock index futures contracts

To gain exposure at a duration of 5.25 on $4 million of bonds, the number of bond futures contracts is

𝑁𝑏𝑓 = (𝑀𝐷𝑈𝑅𝑇− 𝑀𝐷𝑈𝑅𝐵

𝑀𝐷𝑈𝑅𝑓 ) (𝐵

𝑓) = (

5.25 − 0.06.05 ) (

$4,000,000

$115,750 ) = 29.99 Thus, QMFA buys 30 bond futures contracts

Scenario (31 May)

During this period, the stock increased by 2.2 percent and the bonds increased by 0.75 percent The

stock index futures price increased to $214,500, and the bond futures price increased to $116,734

Outcome and Analysis

The profit on the stock index futures contracts is 32($214,500 – $210,500) = $128,000 The profit on the

bond futures contracts is 30($116,734 – $115,750) = $29,520 The total profit is, therefore, $128,000 +

$29,520 = $157,520

Had QMFA actually invested the money, the stock would have increased in value by $6,000,000(0.022) =

$132,000, and the bonds would have increased in value by $4,000,000(0.0075) = $30,000, for a total

increase in value of $132,000 + $30,000 = $162,000, which is relatively close to the futures gain of

$157,520 The difference of $4,480 between this approach and the synthetic one is about 0.04 percent

of the $10 million invested This difference is due to the fact that stocks and bonds do not always

respond in the manner predicted by their betas and durations and also that the number of futures

contracts is rounded off

Refer to Example 7 from the curriculum

5 Strategies and Applications for Managing Foreign Currency Risk

A company that engages in business in other countries has the following foreign currency risks:

 Transaction exposure: Risk associated with changes in exchange rate during the period in which

a transaction was initiated and was later completed

 Translation exposure: Risk associated with translating the value of assets back into domestic

currency

 Economic exposure: Risk associated with the relationship between exchange rate changes and

changes in the asset values in the foreign market

LO.f: Explain exchange rate risk and demonstrate the use of forward contracts to reduce the risk

associated with a future receipt or payment in a foreign currency

This LO is covered in Section 5.1 and 5.2

5.1 Managing the Risk of a Foreign Currency Receipt

Exhibit 10 provides a scenario where a company wants to manage the risk of a foreign currency receipt

Exhibit 10 Managing the Risk of a Foreign Currency Receipt

Scenario (15 August)

H-Tech Hardware, a US company, sells its products in many countries It recently received an order for

some computer hardware from a major European government The sale is denominated in euros and is

in the amount of €50 million H-Tech will be paid in euros; hence, it bears exchange rate risk The

current date is 15 August, and the euros will be received on 3 December

Action

On 15 August, H-Tech decides to lock in the 3 December exchange rate by entering into a forward

contract that obligates it to deliver €50 million and receive a rate of $0.877 H-Tech is effectively long

the euro in its computer hardware sale, so a short position in the forward market is appropriate

Scenario (3 December)

The exchange rate on this day is ST, but as we shall see, this value is irrelevant for H-Tech because it is

hedged

Outcome and Analysis

The company receives its €50 million, delivers it to the dealer, and is paid $0.877 per euro for a total

payment of €50,000,000($0.877) = $43,850,000 H-Tech thus pays the €50 million and receives $43.85

million, based on the rate locked in on 15 August

5.2 Managing the Risk of a Foreign Currency Payment

Exhibit 11 provides a scenario where a company wants to manage the risk of a foreign currency

payment

Exhibit 11 Managing the Risk of a Foreign Currency Payment

Scenario (2 March)

American Manufacturing Catalyst (AMC) is a US company that occasionally makes steel and copper

purchases from non-US companies to meet unexpected demand that cannot be filled through its

domestic suppliers On 2 March, AMC determines that it will need to buy a large quantity of steel from a

Japanese company on 1 April It has entered into a contract with the Japanese company to pay ¥900

million for the steel At a current exchange rate of $0.0083 per yen, the purchase will currently cost