Lab · Miễn phí
Sharpe / Treynor / Jensen / Tỷ số thông tin
Tính tất cả các tỷ số lợi nhuận điều chỉnh rủi ro chính song song. Bao gồm so sánh chuẩn mực song song.
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.