Lab · 免费
夏普 / 特雷诺 / 詹森 / 信息比率
并排计算所有主要风险调整后回报比率。包含基准并排比较。
Funds
Country focus sets the risk-free rate (4.45%) and the market index (S&P 500, expected return 10.0%, σ_m 15.0%).
Portfolio inputs
Benchmark / Information ratio
R_f = 4.45% (country = United States)
R_m = 10.0% (long-run mean of S&P 500)
σ_m = 15.0%
R_m = 10.0% (long-run mean of S&P 500)
σ_m = 15.0%
Sharpe ratio
0.419
(R_p − R_f) / σ_p
Treynor ratio
6.86%
(R_p − R_f) / β_p
Jensen's α
1.44%
vs CAPM E[r]
Information ratio
0.500
(R_p − R_b) / TE
M² (Modigliani²)
10.74%
R_f + Sharpe × σ_m
Side-by-side comparison
Portfolio Sharpe0.42
Benchmark Sharpe0.37
Jensen's α1.44%
Info ratio0.50
Reading the results: Sharpe is the canonical reward-per-σ. Treynor uses β instead of σ — useful when the portfolio is already a piece of a diversified allocation. Jensen's α is the CAPM intercept — positive means the manager beat the line. The Information Ratio is active management's quality score: excess return per unit of tracking error vs the benchmark.