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
TotalReturns=(Pend−Pstart)/Pstart∗100%Pend=Account Final AssetsPstart=Account Primary Assets
2. Total Annualized Returns
TotalAnnualizedReturns=Rp=((1+P)250n−1)∗100%P=Total Returnsn=Execution Days
3. Benchmark Returns
Benchmark Returns=(Mend−Mstart)/Mstart∗100%Mend=Benchmark Final AssetsMstart=Benchmark Primary Assets
4. Benchmark Annualized Returns
Benchmark Annualized Returns=Rm=((1+M)250n−1)∗100%M=Benchmark Returnsn=Execution Days
5. Alpha
Alpha=α=Rp−[Rf+βp(Rm−Rf)]Rp=Strategies Annualized ReturnsRm=Benchmark Annualized ReturnsRf=Riskfree Interest Rateβp=Strategies Beta
if α>0, the strategy gains excess returns.
if α=0, the strategy gains general returns.
if α<0, the strategy gains lower than benchmark returns.
6. Beta
Beta=β=Cov(Dp,Dm)Var(Dm)Dp=Strategies Daily ReturnsDm=Benchmark Daily ReturnsCov(Dp,Dm)=The Covariance of Strategies Daily Returns and Benchmark Daily ReturnsVar(Dm)=The Variance of Benchmark Daily Returns
if β>0, the strategy is in opposition direction to the benchmark.
if β=0, the strategy and benchmark are no related.
if 0<β<1, the strategy is in same direction to the benchmark, but smaller range of movement.
if β=1, the strategy is in same direction to the benchmark, and same range of movement.
if β>1, the strategy is in same direction to the benchmark, but bigger range of movement.
7. Sharpe
How much excess returns will be given by per unit of total risk?
Sharpe Ratio=Rp−RfσpRp=Strategies Annualized ReturnsRf=Riskfree Interest Rateσp=The Volatility of Strategies Returns
8. Sortino
How much excess returns will be given by per unit of downside risk?
Sortino Ratio=Rp−RfσpdRp=Strategies Annualized ReturnsRf=Riskfree Interest Rateσpd=Strategies Downside Volatility
9. Information Ratio
Measure the excess returns be given by per unit of excess risk.
Information Ratio=IC=Rp−RmσtRp=Strategies Annualized ReturnsRm=Benchmark Annualized Returnsσt=The Standard Deviation of Difference between Strategies Daily Returns and Benchmark Daily Returns (fetch one year′s data)
10. Benchmark Volatility
Benchmark Volatility=σm=250n∑i=1n(rm−rm¯)2−−−−−−−−−−−−−−−√rm=Benchmark Daily Returnsrm¯=1n∑i=1nrmn=Execution Days
11. Max Drawdown
Max Drawdown=Max(Px−Py)/PxPx,Py=Account Assets on any day, y>x
12. Downside Risk
Downside Risk=σpd=250n∑i=1n(rp−rpi¯)2f(t)−−−−−−−−−−−−−−−−−√rp=Strageties Daily Returnsrpi¯=1i∑j=1irjn=ExecutionDaysf(t)=1, if rp<rpi¯f(t)=0, if rp≥rpi¯
13. The Profit and Loss Ratio
The Profit and Loss Ratio=Total ProfitTotal Loss
