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

Level III

Risk Management Applications of Forward
and Futures Strategies
Summary
Graphs, charts, tables, examples, and figures are copyright 2016, CFA Institute.
Reproduced and republished with permission from CFA Institute. All rights reserved.


Uses of Equity Futures Contracts
Futures contracts can be used to change a portfolio’s beta.
Going long on futures contracts increases portfolio beta.
Going short on futures contracts decreases portfolio beta.

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:

𝑁𝑓 =

𝛽𝑇 − 𝛽𝑆
𝛽𝑓

𝑉 1+𝑟
𝑁𝑓 =
𝑞𝑓

𝑆
𝑓

𝑇

This method saves transaction costs and preserves liquidity.
Investing V* in bonds and buying Nf* futures contracts at a price of f is equivalent to buying Nf*q/(1 + δ)T units of stock.
We can construct a synthetic position is cash by selling futures
against a long stock position.

𝑉 1+𝑟
𝑁𝑓 = −
𝑞𝑓

𝑇

2


Using Equity and Bond Futures to Adjust Asset Allocation
A $300 million fund is 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. We would like to temporarily adjust the asset allocation to 50
percent stock and 50 percent bonds.

Sell $90 million of stock by converting it to cash using stock index futures

𝑁𝑠𝑓

𝛽𝑇 − 𝛽𝑆 𝑆
0.00 − 1.10 $90,000,000
=(
)
=

= −515.63
𝛽𝑓
𝑓𝑆
0.96
$200,000

Buy $90 million of bonds by using bond futures
𝑀𝐷𝑈𝑅𝑇 − 𝑀𝐷𝑈𝑅𝐵 𝐵
𝑁𝑏𝑓 = (
)
𝑀𝐷𝑈𝑅𝑓
𝑓𝑏

6.5 − 0.0 $90,000,000
=(
)(
) = 771.97
7.2
$105,250

3


Pre-investing
We can ‘pre-invest’ by taking long positions in futures contracts.
Will receive $10 million in three months. We want to pre-invest $6 million in stocks at an
average beta of 1.08 and $4 million in bonds at a modified duration of 5.25. 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.

𝑁𝑠𝑓 =

𝛽𝑇 − 𝛽𝑆
𝛽𝑓

𝑆
1.08 − 0.0
=
𝑓
0.97

𝑁𝑏𝑓 =

𝑀𝐷𝑈𝑅𝑇 − 𝑀𝐷𝑈𝑅𝐵
𝑀𝐷𝑈𝑅𝑓

$6,000,000
= 31.74
$210,500

𝐵
5.25 − 0.0
=
𝑓
6.05

$4,000,000
= 29.99
$115,750

A long position in a futures contract is equivalent to being long the underlying plus a loan.
This is essentially a fully leveraged position on the underlying asset.

4


Currency Risk
Risk associated with foreign currency receipt can be managed by selling forward (or futures)
contracts on the foreign currency.
Example: An American company will receive €50 million in three months.
What is the risk and how can this be managed using forward contracts?
Risk associated with foreign currency payments can be managed by
buying forward (or futures) contracts on the foreign currency.
With respect to a foreign currency portfolio, the possible currency hedging strategies are:
1. Hedge market risk and not currency risk. Here we will earn the foreign risk free rate.
2. Hedge both. Here we will earn the domestic risk free rate.
3. Hedge currency risk but not market risk.
4. Hedge neither.
The effectiveness of the hedge depends on:
1. how well hedging instrument is correlated with investment portfolio.
2. how well the final investment value is predicted.

5