The “Checklist’ > 9b. Construction: cross-sectional strategies > Backtesting

Backtesting

(9b.67)

Policy

Signal(function of current

information)

Portfolio(vector ofholdings)

h (·) : st ≡

s1,t

·sn,t

∈ it → hsignalt ≡

hsignal1,t

·hsignaln,t

t∈ T

history of market obervations

P&L of

signal portf. Instruments P&L Transaction costs/market impact

πsignalt→t+1 =

∑nn=1 h

signaln,t πn,t→t+1 − c(hsignal

t ,hsignalt−1 )

t∈T

(9b.68)

fractional power/quadratic function

Assumption: signals and instruments P&L are stationary and ergodic (37.9)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > Backtesting

Backtesting

(9b.67)

Policy

Signal(function of current

information)

Portfolio(vector ofholdings)

h (·) : st ≡

s1,t

·sn,t

∈ it → hsignalt ≡

hsignal1,t

·hsignaln,t

t∈ T

history of market obervationsP&L of

signal portf. Instruments P&L Transaction costs/market impact

πsignalt→t+1 =

∑nn=1 h

signaln,t πn,t→t+1 − c(hsignal

t ,hsignalt−1 )

t∈T

(9b.68)

fractional power/quadratic function

Assumption: signals and instruments P&L are stationary and ergodic (37.9)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > Backtesting

Backtesting

(9b.67)

Policy

Signal(function of current

information)

Portfolio(vector ofholdings)

h (·) : st ≡

s1,t

·sn,t

∈ it → hsignalt ≡

hsignal1,t

·hsignaln,t

t∈ T

history of market obervationsP&L of

signal portf. Instruments P&L Transaction costs/market impact

πsignalt→t+1 =

∑nn=1 h

signaln,t πn,t→t+1 − c(hsignal

t ,hsignalt−1 )

t∈T

(9b.68)

fractional power/quadratic function

Assumption: signals and instruments P&L are stationary and ergodic (37.9)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-ante statistical features

Ex-ante statistical features

• Conditional excessSharpe ratio

sr signal(st) ≡Et{Πsignal

t→t+1 − rrft→t+1v

signalt |st}

Sdt{Πsignalt→t+1|st}

(9b.70)

value of constr. charac. portfolio hsignal′t vt

P&L of constr. charac. portfolio hsignal′t Πt→t+1

• Transfer coefficient tct ≡ Crt{Πsignalt→t+1,Π

char−signalt→t+1 } (9b.73)

P&L of free charac. portfolio hsignal′t Πt→t+1

⇓

sr signalt ≈ tct︸︷︷︸transfer coeff.

× ict︸︷︷︸information coefficient

×√d︸︷︷︸

breadth

(9b.72)

tr(Cvt{Πt→t+1,Bsignalt })

tr(Cvt{Bsignalt })

(9b.35)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-ante statistical features

Ex-ante statistical features

• Conditional excessSharpe ratio

sr signal(st) ≡Et{Πsignal

t→t+1 − rrft→t+1v

signalt |st}

Sdt{Πsignalt→t+1|st}

(9b.70)

value of constr. charac. portfolio hsignal′t vt

P&L of constr. charac. portfolio hsignal′t Πt→t+1

• Transfer coefficient tct ≡ Crt{Πsignalt→t+1,Π

char−signalt→t+1 } (9b.73)

P&L of free charac. portfolio hsignal′t Πt→t+1

⇓

sr signalt ≈ tct︸︷︷︸transfer coeff.

× ict︸︷︷︸information coefficient

×√d︸︷︷︸

breadth

(9b.72)

tr(Cvt{Πt→t+1,Bsignalt })

tr(Cvt{Bsignalt })

(9b.35)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-ante statistical features

Ex-ante statistical features

• Conditional excessSharpe ratio

sr signal(st) ≡Et{Πsignal

t→t+1 − rrft→t+1v

signalt |st}

Sdt{Πsignalt→t+1|st}

(9b.70)

value of constr. charac. portfolio hsignal′t vt

P&L of constr. charac. portfolio hsignal′t Πt→t+1

• Transfer coefficient tct ≡ Crt{Πsignalt→t+1,Π

char−signalt→t+1 } (9b.73)

P&L of free charac. portfolio hsignal′t Πt→t+1

⇓

sr signalt ≈ tct︸︷︷︸transfer coeff.

× ict︸︷︷︸information coefficient

×√d︸︷︷︸

breadth

(9b.72)

tr(Cvt{Πt→t+1,Bsignalt })

tr(Cvt{Bsignalt })

(9b.35)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-ante statistical features

Ex-ante statistical features

• Conditional excessSharpe ratio

sr signal(st) ≡Et{Πsignal

t→t+1 − rrft→t+1v

signalt |st}

Sdt{Πsignalt→t+1|st}

(9b.70)

value of constr. charac. portfolio hsignal′t vt

P&L of constr. charac. portfolio hsignal′t Πt→t+1

• Transfer coefficient tct ≡ Crt{Πsignalt→t+1,Π

char−signalt→t+1 } (9b.73)

P&L of free charac. portfolio hsignal′t Πt→t+1

⇓

sr signalt ≈ tct︸︷︷︸transfer coeff.

× ict︸︷︷︸information coefficient

×√d︸︷︷︸

breadth

(9b.72)

tr(Cvt{Πt→t+1,Bsignalt })

tr(Cvt{Bsignalt })

(9b.35)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-ante statistical features

Ex-ante statistical features

• Conditional excessSharpe ratio

sr signal(st) ≡Et{Πsignal

t→t+1 − rrft→t+1v

signalt |st}

Sdt{Πsignalt→t+1|st}

(9b.70)

value of constr. charac. portfolio hsignal′t vt

P&L of constr. charac. portfolio hsignal′t Πt→t+1

• Transfer coefficient tct ≡ Crt{Πsignalt→t+1,Π

char−signalt→t+1 } (9b.73)

P&L of free charac. portfolio hsignal′t Πt→t+1

⇓

sr signalt ≈ tct︸︷︷︸transfer coeff.

× ict︸︷︷︸information coefficient

×√d︸︷︷︸

breadth

(9b.72)

tr(Cvt{Πt→t+1,Bsignalt })

tr(Cvt{Bsignalt })

(9b.35)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-post statistical features

Ex-post statistical features

• Realized excessSharpe ratio

sr t ≡ewmaτHL

w (t, πsignal· − rrf· vsignal·−1 )

ewm_sdτHLw (t, πsignal

· )(9b.75)

moving average operator (3a.185)

moving standard deviation operator (3a.188)

• Realized transfercoefficient tct ≡ ewm_crτHL

w (t, πsignal· , πfree−signal

· ) (9b.79)

moving correlation operator (3a.190) hfree−signal′t︸ ︷︷ ︸

(9b.47)

πt→t+1

⇓ (9b.72)

sr t ≈ tct × ict ×√d (9b.80)

realized information coefficienttr(ewm_cv

τHLw (t,π·,β

signal·−1 ))

tr(ewm_cvτHLw (t,β

signal·−1 ))

(9b.78)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-post statistical features

Ex-post statistical features

• Realized excessSharpe ratio

sr t ≡ewmaτHL

w (t, πsignal· − rrf· vsignal·−1 )

ewm_sdτHLw (t, πsignal

· )(9b.75)

moving average operator (3a.185)

moving standard deviation operator (3a.188)

• Realized transfercoefficient tct ≡ ewm_crτHL

w (t, πsignal· , πfree−signal

· ) (9b.79)

moving correlation operator (3a.190) hfree−signal′t︸ ︷︷ ︸

(9b.47)

πt→t+1

⇓ (9b.72)

sr t ≈ tct × ict ×√d (9b.80)

realized information coefficienttr(ewm_cv

τHLw (t,π·,β

signal·−1 ))

tr(ewm_cvτHLw (t,β

signal·−1 ))

(9b.78)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-post statistical features

Ex-post statistical features

• Realized excessSharpe ratio

sr t ≡ewmaτHL

w (t, πsignal· − rrf· vsignal·−1 )

ewm_sdτHLw (t, πsignal

· )(9b.75)

moving average operator (3a.185)

moving standard deviation operator (3a.188)

• Realized transfercoefficient tct ≡ ewm_crτHL

w (t, πsignal· , πfree−signal

· ) (9b.79)

moving correlation operator (3a.190) hfree−signal′t︸ ︷︷ ︸

(9b.47)

πt→t+1

⇓ (9b.72)

sr t ≈ tct × ict ×√d (9b.80)

realized information coefficienttr(ewm_cv

τHLw (t,π·,β

signal·−1 ))

tr(ewm_cvτHLw (t,β

signal·−1 ))

(9b.78)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-post statistical features

Ex-post statistical features

• Realized excessSharpe ratio

sr t ≡ewmaτHL

w (t, πsignal· − rrf· vsignal·−1 )

ewm_sdτHLw (t, πsignal

· )(9b.75)

moving average operator (3a.185)

moving standard deviation operator (3a.188)

• Realized transfercoefficient tct ≡ ewm_crτHL

w (t, πsignal· , πfree−signal

· ) (9b.79)

moving correlation operator (3a.190) hfree−signal′t︸ ︷︷ ︸

(9b.47)

πt→t+1

⇓ (9b.72)

sr t ≈ tct × ict ×√d (9b.80)

realized information coefficienttr(ewm_cv

τHLw (t,π·,β

signal·−1 ))

tr(ewm_cvτHLw (t,β

signal·−1 ))

(9b.78)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update

The “Checklist’ > 9b. Construction: cross-sectional strategies > BacktestingEx-post statistical features

Ex-post statistical features

• Realized excessSharpe ratio

sr t ≡ewmaτHL

w (t, πsignal· − rrf· vsignal·−1 )

ewm_sdτHLw (t, πsignal

· )(9b.75)

moving average operator (3a.185)

moving standard deviation operator (3a.188)

• Realized transfercoefficient tct ≡ ewm_crτHL

w (t, πsignal· , πfree−signal

· ) (9b.79)

moving correlation operator (3a.190) hfree−signal′t︸ ︷︷ ︸

(9b.47)

πt→t+1

⇓ (9b.72)

sr t ≈ tct × ict ×√d (9b.80)

realized information coefficienttr(ewm_cv

τHLw (t,π·,β

signal·−1 ))

tr(ewm_cvτHLw (t,β

signal·−1 ))

(9b.78)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-28-2017 - Last update