Handling Derivatives in Attribution
PMAR Web Conference 2020November 10‐11
Claude Giguère
Investment Performance Solutions
Richer Better Easier
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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
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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
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House
Connecting the dots
RocketSame data points
2 different stories
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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
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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%
2 level decision process 1 level decision process
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
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2 level decision process 1 level decision process
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
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Rule # 1
Organize the data the way the portfolio is managed “Connect the dots in the right order”
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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
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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
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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
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FTSE 100 Index Future – London Stock Exchange
Notional Value
65 000 GBP
Price
6 500
Multiplier
10x =
Source: www.theice.com
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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
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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%
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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 =
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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
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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%
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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
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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
=
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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
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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
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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 …
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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%
Portfolio Benchmark Attribution
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%
Portfolio Benchmark Attribution
+ Cost‐of‐carry
Notional exposuresCost‐of‐Carry
Unadjusted exposures
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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
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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
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Weight Mkt Val Cap Inc Total Gain ROR
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”.
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3. With Future – With Notional – No Cost of Carry
Allocation and return “notionally meaningful”.
Return not yet “notionally meaningful”.
Allocation “notionally meaningful”.
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Weight Mkt Val Cap Inc Total Gain ROR
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”.
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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
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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
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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.
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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.
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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
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.
Source: www.spauldinggrp.com/the‐journal
References
Questions or Comments ?
Claude Giguère001.514‐802‐0977
Investment Performance Solutions
Richer Better Easier
www.RobustTechnologies.com