Reference: JoinQuant
Total Returns
Total Annualized Returns
Benchmark Returns
Benchmark Annualized Returns
Alpha
Beta
Sharpe
Sortino
Information Ratio
Algorithm Volatility
Benchmark Volatility
Max Drawdown
Downside Risk
Winning Ratio
Daily Winning Ratio
The Profit and Loss Ratio
1. Total Returns
T o t a l R e t u r n s = ( P e n d − P s t a r t ) / P s t a r t ∗ 100 % P e n d = A c c o u n t F i n a l A s s e t s P s t a r t = A c c o u n t P r i m a r y A s s e t s
2. Total Annualized Returns
T o t a l A n n u a l i z e d R e t u r n s = R p = ( ( 1 + P ) 250 n − 1 ) ∗ 100 % P = T o t a l R e t u r n s n = E x e c u t i o n D a y s
3. Benchmark Returns
B e n c h m a r k R e t u r n s = ( M e n d − M s t a r t ) / M s t a r t ∗ 100 % M e n d = B e n c h m a r k F i n a l A s s e t s M s t a r t = B e n c h m a r k P r i m a r y A s s e t s
4. Benchmark Annualized Returns
B e n c h m a r k A n n u a l i z e d R e t u r n s = R m = ( ( 1 + M ) 250 n − 1 ) ∗ 100 % M = B e n c h m a r k R e t u r n s n = E x e c u t i o n D a y s
5. Alpha
A l p h a = α = R p − [ R f + β p ( R m − R f ) ] R p = S t r a t e g i e s A n n u a l i z e d R e t u r n s R m = B e n c h m a r k A n n u a l i z e d R e t u r n s R f = R i s k f r e e I n t e r e s t R a t e β p = S t r a t e g i e s B e t a
if α > 0 , α = 0 , α < 0 ,
6. Beta
B e t a = β = C o v ( D p , D m ) V a r ( D m ) D p = S t r a t e g i e s D a i l y R e t u r n s D m = B e n c h m a r k D a i l y R e t u r n s C o v ( D p , D m ) = T h e C o v a r i a n c e o f S t r a t e g i e s D a i l y R e t u r n s a n d B e n c h m a r k D a i l y R e t u r n s V a r ( D m ) = T h e V a r i a n c e o f B e n c h m a r k D a i l y R e t u r n s
if β > 0 β = 0 0 < β < 1 β = 1 β > 1
7. Sharpe
S h a r p e R a t i o = R p − R f σ p R p = S t r a t e g i e s A n n u a l i z e d R e t u r n s R f = R i s k f r e e I n t e r e s t R a t e σ p = T h e V o l a t i l i t y o f S t r a t e g i e s R e t u r n s
8. Sortino
S o r t i n o R a t i o = R p − R f σ p d R p = S t r a t e g i e s A n n u a l i z e d R e t u r n s R f = R i s k f r e e I n t e r e s t R a t e σ p d = S t r a t e g i e s D o w n s i d e V o l a t i l i t y
9. Information Ratio
I n f o r m a t i o n R a t i o = I C = R p − R m σ t R p = S t r a t e g i e s A n n u a l i z e d R e t u r n s R m = B e n c h m a r k A n n u a l i z e d R e t u r n s σ t = T h e S t a n d a r d D e v i a t i o n o f D i f f e r e n c e b e t w e e n S t r a t e g i e s D a i l y R e t u r n s a n d B e n c h m a r k D a i l y R e t u r n s ( f e t c h o n e y e a r ′ s d a t a )
10. Benchmark Volatility
B e n c h m a r k V o l a t i l i t y = σ m = 250 n ∑ i = 1 n ( r m − r m ¯ ) 2 − − − − − − − − − − − − − − − √ r m = B e n c h m a r k D a i l y R e t u r n s r m ¯ = 1 n ∑ i = 1 n r m n = E x e c u t i o n D a y s
11. Max Drawdown
M a x D r a w d o w n = M a x ( P x − P y ) / P x P x , P y = A c c o u n t A s s e t s o n a n y d a y , y > x
12. Downside Risk
D o w n s i d e R i s k = σ p d = 250 n ∑ i = 1 n ( r p − r p i ¯ ) 2 f ( t ) − − − − − − − − − − − − − − − − − √ r p = S t r a g e t i e s D a i l y R e t u r n s r p i ¯ = 1 i ∑ j = 1 i r j n = E x e c u t i o n D a y s f ( t ) = 1 , i f r p < r p i ¯ f ( t ) = 0 , i f r p ≥ r p i ¯
13. The Profit and Loss Ratio
T h e P r o f i t a n d L o s s R a t i o = T o t a l P r o f i t T o t a l L o s s
