handling derivatives in attribution€¦ · higher returns how well investment strategies...

Handling Derivatives in Attribution

PMAR Web Conference 2020November 10‐11

Claude Giguère

Investment Performance Solutions

Richer Better Easier

www.RobustTechnologies.com 2

01

02

03

04

HIRE

Investment management firms

MAKE

Portfolio managers

GOAL

Investment decisions

COMMUNICATE

Higher returns

How well investment strategies Contribute to add value

Demonstrate respect mandate

Evaluate risk to achieve returns

Complex task require Skills

Sophisticated software


The Purpose of Attribution Tell a story

Explains causality of excess returns

In terms that relates to investment strategies employed by manager

The Art of Attribution Art of crafting the right attribution model

Accurately reflects investment management decision process

No matter how complex it may be


House

Connecting the dots

RocketSame data points

2 different stories


Fixed Income

Equity

Cash

U.S. Equity

Allocation

U.K. Equity

Allocation

Story #1

Fixed Income

U.S. Equity

Cash

U.K. Equity

Allocation

Story #2

2 level decision process 1 level decision process


Story #1Story #2

Asset Country

Total ‐1.10% 1.08%

Cash ‐0.65%

Equity ‐0.30% 1.08%

U.S. Equity 0.54%

U.K. Equity 0.54%

Fixed Income ‐0.15%

Allocation Allocation

Asset/Country

Total ‐0.02%

Cash ‐0.65%

Equity 0.78%

U.S. Equity ‐0.08%

U.K. Equity 0.86%

Fixed Income ‐0.15%


RORPF BM BM

Total 100% 100% 6.5%Cash 10% 0% 0.0% RORFixed Income 60% 50% 5.0% PF BM BM Alloc *Equity 30% 50% 8.0% 100% 100% 8.0%U.S. Equity 24% 25% 14.0% 80% 50% 14.0% 0.54%U.K. Equity 6% 25% 2.0% 20% 50% 2.0% 0.54%

Weight

Weight



RORPF BM BM Alloc

Total 100% 100% 6.50%Cash 10% 0% 0.00%Fixed Income 60% 50% 5.00%U.S. Equity 24% 25% 14.00% ‐0.08%U.K. Equity 6% 25% 2.00% 0.86%

Weight

Overweight Underweight

Rescaled forcascading


Rule # 1

Organize the data the way the portfolio is managed “Connect the dots in the right order”


Investment Management Decisions

1

2

3

4

5

10%10%

Country Allocation

Sector / AssetAllocation

Security Selection

CurrencyManagement

Hedging andOverlay

Strategies Futures Forwards Options

Swaps Repos Long / Short


UK Equities

FTSE 100Future

SP TSX60Future

SP 500Future

+ Canada ‐ USA

FTSE 100Future

DAXFuture

+ U.K. ‐ Germany

Investment Strategy

Long/Short Overlay StrategyIncrease exposure to UK Equity


Futures

1 Obligation to purchase or sell a given instrument at a specified date and price (contract).

2 Exchange traded.

3 Daily P&L are marked-to-market into margin account.

4 Long Position is synthetically equivalent to : Borrowing Cash (short) and Buy Asset (Long)

5 Short Position is synthetically equivalent to : Lending Cash (Long) and Sell Asset (Short)

6 Concept of Notional Value. Multiplier (contract size) x Price

Concept of cost-of-carry. Referred as the basis, i.e. difference between cash price and futures’ price7


FTSE 100 Index Future – London Stock Exchange

Notional Value

65 000 GBP

Price

6 500

Multiplier

10x =

Source: www.theice.com


Must exchange cash to get exposure.

vsAssets Futures

Has a real market value.Just notionalP&L

Just initial margin

Marked‐to‐market daily.

Offers equity exposure

Offers currency exposure ~ Except P&L


Assets

Local

iCurrency

Asset

Local iCurrency

70 000

1.2500

77 000

1.3750

Underlying Asset Exposures

Value Return

FX

PriceGBP

21%77 000 1.3750 70 000 1.25

70 000 1.25

10% 10% 1%


Assets

Local

iCurrency

Asset

Local i

7 000

1.2500

7 700

1.3750

Long FTSE 100 Index Future

Value Return???

FX

Price

Notional Value

70 000 GBP

Price

7 000

Multiplier

10x =


Notional

Local

iCurrency

Notional

Local i

70 000

1.2500

77 000

1.3750

Long FTSE 100 Index Future

Value Return

‐Notional(contra)

‐Notional(contra)

Borrow cash

Buy assets


Notional

Local

iCurrency

Notional

Local i

70 000

1.2500

77 000

1.3750

Value Return

Future Gain

Multip.Price T0

Price T1

PriceROR

Gain(GBP)

FX RateT0

FX RateT1

FXROR

Gain(USD)

10 7,000 7,700 10% 7,000 1.2500 1.3750 10% 9,625.00

GBPT0

GBPT1

Gain(GBP)

USDT0

USDT1

Diff(USD)

70,000 77,000 7,000 87,500 105,875 18,375

Notional Value

Local Return

9,625 87,500

11.00% USD=

Base Return

875 87,500

= 1.00% USD

Currency Return

8,750 87,500

= 10.00% USD

7,000

70,000 10.00% GBP=

10% 1%


Rule # 3

Differentiate between Currency vs Market exposures

Rule # 2

Use Notional Exposure (with Cash Offset)

Rule # 1

Organize the data the way the portfolio is managed


Arbitrage Free Theory

Investor should indifferentbetween

Buy Underlying Assets

Receive Dividend

Capital Gain on stocks

Keep Cash

Receive P&LReceive Interest

Long Future

𝐹𝑢𝑡𝑢𝑟𝑒𝑃𝑟𝑖𝑐𝑒 𝑆𝑝𝑜𝑡𝑃𝑟𝑖𝑐𝑒 1 𝑟𝑓 𝑑𝑖𝑣Cost‐of‐carryCost‐of‐carry

=


Source: A re‐examination of the relationship between FTSE100 index and futures prices

Juan Tao, 2008 https://dspace.lboro.ac.uk/2134/8071

Cornell, Bradford and French, Kenneth R., (1983), The pricing of stock index futures, Journal of Futures Markets, 3, issue 1, p. 1‐14.Cornell, Bradford and French, Kenneth R., (1983), The pricing of stock index futures, Journal of Futures Markets, 3, issue 1, p. 1‐14.

Reference


Arbitrage Free Theory

Long Future Invest Cash

70,000

700

‐2% 3%

‐1,400 2,100

Buy Assets Receive Dividends

70,000

700

0% 1%

0 700


Long Future Invest Cash

70,000

7 000

7% 3%

4 900 2,100

Buy Assets Receive Dividends

70,000

7 000

9% 1%

6 300 700

Let’s use this as an example …


MV Wgt Gain ROR Wgt ROR Allocation Selection TotalTotal 170,000 100% 10,000 5.88% 100% 8.60% ‐2.72% 0.00% ‐2.72%Cash 100,000 59% 3,000 3.00% 20% 3.00% ‐2.17% 0.00% ‐2.17%Equities 70,000 41% 7,000 10.00% 80% 10.00% ‐0.54% 0.00% ‐0.54%

Portfolio Benchmark Attribution

Long position $ 70 000 Equities Gain $ 4 900

MV Wgt Gain ROR Wgt ROR Allocation Selection TotalTotal 170,000 100% 14,900 8.76% 100% 8.60% ‐2.72% 2.88% 0.16%Cash 100,000 59% 3,000 3.00% 20% 3.00% ‐2.17% 0.00% ‐2.17%Equities 70,000 41% 11,900 17.00% 80% 10.00% ‐0.54% 2.88% 2.34%


MV Wgt Gain ROR Wgt ROR Allocation Selection TotalTotal 170,000 100% 14,900 8.76% 100% 8.60% 0.16% 0.00% 0.16%Cash 30,000 18% 900 3.00% 20% 3.00% 0.13% 0.00% 0.13%Equities 140,000 82% 14,000 10.00% 80% 10.00% 0.03% 0.00% 0.03%


+ Cost‐of‐carry

Notional exposuresCost‐of‐Carry

Unadjusted exposures


Rule # 4

Account for the Cost‐of‐carry

Rule # 3

Differentiate between Currency vs Market exposures

Rule # 2

Use Notional Exposure (with Cash Offset)

Rule # 1

Organize the data the way the portfolio is managed


Weight Mkt Val Cap Inc Total Gain ROR

Portfolio 100% 170,000.00 6,300.00 3,700.00 10,000.00 5.88%

Cash 59% 100,000.00 ‐ 3,000.00 3,000.00 3.00%Cash USD 29% 50,000.00 ‐ 1,500.00 1,500.00 3.00%Margin USD 29% 50,000.00 ‐ 1,500.00 1,500.00 3.00%Equities 41% 70,000.00 6,300.00 700.00 7,000.00 10.00%Stocks 41% 70,000.00 6,300.00 700.00 7,000.00 10.00%Future 0% ‐ ‐ ‐

1. Starting Portfolio

Manager wants toincrease equity exposure

70 000

Risk Free 3% T0 T1 Gain# Contract 1 Market Price 7,000 7,490 Trade Units 10 Notional Value 70,000 74,900 4,900



Portfolio 100% 170,000.00 11,200.00 3,700.00 14,900.00 8.76%

Cash 59% 100,000.00 ‐ 3,000.00 3,000.00 3.00%Cash USD 29% 50,000.00 ‐ 1,500.00 1,500.00 3.00%Margin USD 29% 50,000.00 ‐ 1,500.00 1,500.00 3.00%Equities 41% 70,000.00 11,200.00 700.00 11,900.00 17.00%Stocks 41% 70,000.00 6,300.00 700.00 7,000.00 10.00%Future 0% 4,900.00 4,900.00 #DIV/0!

2. With Futures – No Notional Value

Gain

Allocation and return not “notionally meaningful”.


3. With Future – With Notional – No Cost of Carry

Allocation and return “notionally meaningful”.

Return not yet “notionally meaningful”.

Allocation “notionally meaningful”.



Portfolio 100% 170,000.00 11,200.00 3,700.00 14,900.00 8.76%

Cash 18% 30,000.00 ‐ 900.00 900.00 3.00%Cash USD 29% 50,000.00 ‐ 1,500.00 1,500.00 3.00%Margin USD 29% 50,000.00 ‐ 1,500.00 1,500.00 3.00%Contra ‐41% (70,000.00) (2,100.00) (2,100.00) Equities 82% 140,000.00 11,200.00 2,800.00 14,000.00 10.00%Stocks 41% 70,000.00 6,300.00 700.00 7,000.00 10.00%Future 41% 70,000.00 4,900.00 2,100.00 7,000.00 10.00%

4. With Future – With Notional – With Cost of Carry

Allocation and return “notionally meaningful”.


6 125 USD4 900 GBP

7 490Local

Currency1.3750

i 612.50 USD

6 737.50 USD

Base

Risk Free3%

2 100 GBP2 625 USD1.2500

Price 7 000

Notional70 000 GBP


Other derivatives…Futures on Bonds

US 10 YR NOTE W3 SEP Notional Duration Maturity

Delta = 1

Option of Futures Notional x Delta Duration Maturity

Delta = [0,1]

Underlying

Underlying

Swaps

Pay Leg

Receiving Leg

Duration Maturity

Duration Maturity

Repos Notional Duration Maturity


In summary• Must reflect notional exposure.

• Offset cash exposure• Long position : Borrow cash (short) – Buy assets (long)• Short position : Lend cash (long) – Sell assets (short)

• Settled variation margin remains as asset exposure (and not cash) until the future position is liquidated. Exposure measured using current price.


In summary• Must properly recognize the type of exposures. Assets vs Currencies.• Future on FTSE 100 does not offer currency exposure (GBP).

• Only asset exposure.• The only impact on currency return is FX Rates on variation margins settling in GBP.

32


In summary• Must adjust for risk free rate.

• Represent opportunity cost of purchasing the assets rather than engaging in a future contract.

• To reflect the cost of carry. Referred as the basis, i.e. difference between cash price and futures’ price (generally risk free rate minus expected dividends)

• Makes return comparable to underlying assets in the benchmark


.

Source: www.spauldinggrp.com/the‐journal

References

Questions or Comments ?

Claude Giguère001.514‐802‐0977

[email protected]

Investment Performance Solutions

Richer Better Easier

www.RobustTechnologies.com

handling derivatives in attribution€¦ · higher returns how well investment strategies...

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