Trading Terms

最新推荐文章于 2024-09-22 09:00:00 发布

kangzuoning

最新推荐文章于 2024-09-22 09:00:00 发布

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分类专栏： Quant&Trading

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本文详细介绍了量化投资中常用的绩效评估指标，包括总收益率、年化收益率、基准收益率等，并解释了如何通过这些指标衡量投资策略的有效性。

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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

$Total Returns = (P_{end}-P_{start} ) / P_{start} * 100\% \\ P_{end} = Account\space Final\space Assets \\ P_{start}=Account\space Primary\space Assets$

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

$Total Annualized Returns=R_p=((1+P)^\frac{250}{n}-1) * 100\% \\ P = Total\space Returns \\ n=Execution\space Days$

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

$Benchmark\space Returns=(M_{end}-M_{start})/M_{start}*100\% \\ M_{end}= Benchmark\space Final\space Assets \\ M_{start}=Benchmark\space Primary\space Assets$

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

$Benchmark\space Annualized\space Returns=R_m=((1+M)^\frac{250}{n}-1)*100\% \\ M = Benchmark\space Returns \\ n=Execution\space Days$

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

$Alpha=\alpha=R_p- [R_f+\beta_p(R_m-R_f)] \\ R_p=Strategies\space Annualized\space Returns \\ R_m=Benchmark\space Annualized\space Returns \\ R_f=Riskfree\space Interest\space Rate \\ \beta_p=Strategies\space Beta$

if $\alpha>0,$ the strategy gains excess returns.
if $\alpha=0,$ the strategy gains general returns.
if $\alpha<0,$ the strategy gains lower than benchmark returns.

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

$Beta=\beta=\frac{Cov(D_p,D_m)}{Var(D_m)} \\ D_p=Strategies\space Daily\space Returns \\ D_m=Benchmark\space Daily\space Returns \\ Cov(D_p,D_m)=The\space Covariance\space of\space Strategies\space Daily\space Returns\space and\space Benchmark\space Daily\space Returns \\ Var(D_m)=The\space Variance \space of \space Benchmark \space Daily\space Returns$

if $\beta>0$ , the strategy is in opposition direction to the benchmark.
if $\beta=0$ , the strategy and benchmark are no related.
if $0<\beta<1$ , the strategy is in same direction to the benchmark, but smaller range of movement.
if $\beta=1$ , the strategy is in same direction to the benchmark, and same range of movement.
if $\beta>1$ , the strategy is in same direction to the benchmark, but bigger range of movement.

7. Sharpe
$\space$ $\space$ $\space$ How much excess returns will be given by per unit of total risk?

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

$Sharpe\space Ratio=\frac{R_p - R_f}{\sigma_p}\\ R_p=Strategies\space Annualized\space Returns \\ R_f=Riskfree\space Interest\space Rate \\ \sigma_p=The\space Volatility\space of\space Strategies\space Returns$

8. Sortino
$\space$ $\space$ $\space$ How much excess returns will be given by per unit of downside risk?

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

$Sortino\space Ratio=\frac{R_p - R_f}{\sigma_{pd}}\\ R_p=Strategies\space Annualized\space Returns \\ R_f=Riskfree\space Interest\space Rate \\ \sigma_{pd}=Strategies\space Downside\space Volatility$

9. Information Ratio
$\space$ $\space$ $\space$ Measure the excess returns be given by per unit of excess risk.

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)

$Information\space Ratio=IC=\frac{R_p - R_m}{\sigma_t}\\ R_p=Strategies\space Annualized\space Returns \\ R_m=Benchmark\space Annualized\space Returns \\ \sigma_t=\\ The\space Standard\space Deviation\space of\space Difference\space between\space Strategies\space Daily\space Returns\space and\space Benchmark\space Daily\space Returns\space (fetch\space one\space year's\space data)$

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 \sum i = 1 n (r m - r m ¯) 2 - - - - - - - - - - - - - - - \sqrt 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 \sum i = 1 n r m n = E x e c u t i o n D a y s

$Benchmark\space Volatility=\sigma_m=\sqrt{\frac{250}{n} \sum_{i=1}^{n}(r_m-\bar{r_m})^2}\\ r_m=Benchmark\space Daily\space Returns \\ \bar{r_m}=\frac{1}{n} \sum_{i=1}^{n}r_m\\ n=Execution\space Days$

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

$Max\space Drawdown=Max(P_x-P_y)/P_x\\ P_x, P_y=Account\space Assets\space on\space any\space day,\space \space y>x\\$

12. Downside Risk

D o w n s i d e R i s k = σ p d = 250 n \sum i = 1 n (r p - r p i ¯) 2 f (t) - - - - - - - - - - - - - - - - - \sqrt 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 \sum 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 \geq r p i ¯

$Downside\space Risk=\sigma_{pd}=\sqrt{\frac{250}{n} \sum_{i=1}^{n}(r_p - \bar{r_{pi}})^2 f(t)}\\ r_p=Strageties\space Daily\space Returns \\ \bar{r_{pi}}=\frac{1}{i} \sum_{j=1}^{i}r_j\\ n=Execution Days\\ f(t)=1,\space if\space\space\space r_p< \bar{r_{pi}}\\ f(t)=0,\space if\space\space\space r_p\geq \bar{r_{pi}}$

13. The Profit and Loss Ratio