04 // Interactive Formula Compendium // FINANCES = (R_p − R_f) / σ_p
Sharpe Ratio, Sortino Ratio & Information Ratio Formula Sheet
The Sharpe Ratio S = (R_p − R_f) / σ_p measures risk-adjusted performance by dividing a portfolio's excess return over the risk-free rate R_f by the standard deviation of its returns σ_p.
Formula Reference
Main Formula
S = (R_p − R_f) / σ_p
Rearranged Forms
S_annualized = √N · (R̄_periodic − R_{f,periodic}) / σ_periodic (Annualization Law)
Sortino = (R_p − MAR) / σ_downside (Downside Deviation Ratio)
IR = (R_p − R_benchmark) / σ_tracking (Information Ratio)
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| S | Annualized Sharpe Ratio (S) | dimensionless |
| Rp | Portfolio Annual Return R_p (%) | % |
| Rf | Risk-Free Rate R_f (%) | % |
| sigma | Portfolio Volatility σ_p (%) | % |
Inputs & Parameters
[%]
[%]
[%]
Calculated Result (Annualized Sharpe Ratio (S))
S =0.8dimensionless
Formula Notes & Background
- Subtract the risk-free return R_f from portfolio return R_p to isolate excess return earned for bearing risk.
- Normalize excess return by total portfolio standard deviation σ_p = √Var(R_p), giving the slope of the Capital Allocation Line (CAL).
- For independent periodic returns (e.g. N = 252 trading days or N = 12 months), mean scales as N and standard deviation scales as √N, so the annualized Sharpe ratio scales by √N.
Step-by-Step Examples
#1: Calculate the Sharpe Ratio of a fund returning 14.0% with 12.5% annualized volatility when T-bills yield 4.0%.
R_p = 14.0%R_f = 4.0%σ_p = 12.5%
S = (14.0 − 4.0) / 12.5 = 10.0 / 12.5
→ S = 0.80
#2: Annualize a daily trading strategy with daily mean excess return 0.05% and daily standard deviation 0.80% across 252 trading days.
Daily Sharpe = 0.05% / 0.80% = 0.0625N = 252 trading days
S_annual = √252 × 0.0625 = 15.8745 × 0.0625
→ S_annual = 0.992
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Frequently Asked Questions
What is considered a good Sharpe Ratio in institutional asset management?+
A long-term Sharpe Ratio of 0.5–0.9 is typical for broad equity indices; ≥ 1.0 is strong; ≥ 2.0 is exceptional (often achieved by market-neutral multi-strategy funds).
Why do some investors prefer the Sortino Ratio over the Sharpe Ratio?+
The Sharpe Ratio penalizes upside volatility and downside volatility equally, whereas the Sortino Ratio divides only by downside semi-deviation below a target return.
Does leverage change a portfolio's Sharpe Ratio?+
If you can borrow at the risk-free rate R_f, leveraging a portfolio scales both excess return (R_p − R_f) and volatility σ_p by the same factor L, leaving the Sharpe Ratio unchanged.