Sharpe ratio

As explained in Build a Robo-Advisor with Python (From Scratch)

The Sharpe ratio is the expected return above the risk-free rate divided by the investment's volatility, measuring expected reward per unit of risk.

The Sharpe ratio evaluates expected reward per unit of risk: SR = (μ − r_f) / σ, where μ is expected return, r_f is the risk-free rate, and σ is volatility. Comparing returns alone can favor leveraged or unusually volatile investments. section 7.2 section 7.2.1

A leveraged investment

A $1 million investment with a 20% expected return, 15% volatility, and a 5% risk-free rate has a Sharpe ratio of (20% − 5%) / 15% = 1.0. Borrowing another $1 million at 5% doubles expected return and volatility, but the ratio remains 1.0: (40% − 5% − 5%) / 30% = 1.0. section 7.2.1

Figure 7.2 Investments above and below CAL

Use the capital allocation line to compare investments by the slope connecting risk-free and risky positions; points above the line offer more expected return for their volatility. section 7.2.1

The denominator includes total portfolio risk, including market and idiosyncratic risk. This makes the Sharpe ratio especially useful when the investment represents the investor’s entire portfolio. section 7.2.4 section 7.3

Choose the measure according to the investment’s role:

• Use the Sharpe ratio when total portfolio risk matters, including risk that cannot be diversified away from the investor’s perspective. section 7.2.4
• Use alpha when evaluating one component of a broader portfolio and non-market, diversifiable risk should be excluded. section 7.2.4

How Build a Robo-Advisor with Python (From Scratch) covers it

How deep it goes

Derives the formula from the capital allocation line, works a leverage example, and distinguishes total from diversifiable risk.

Examples

Uses a leveraged $1 million investment and capital allocation line diagrams to illustrate interpretation and comparison.

What it assumes

Assumes familiarity with expected return, volatility, risk-free rate, leverage, and market versus idiosyncratic risk.

What you can do after

Evaluate investments using expected excess return, volatility, leverage invariance, and portfolio-level risk.

How it connects

Connects expected return, risk-free rate, volatility, leverage, capital allocation line, alpha, and idiosyncratic risk.

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Also explained in

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  liveBookmanning.com
  Investing for ProgrammersThe Sharpe ratio is a portfolio performance measure that compares excess return over the risk-free rate with the portfolio's volatility.

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Related concepts

• risk-adjusted returnmeasures · Risk-adjusted return is investment performance evaluated relative to the amount or type of risk taken to achieve it.
• information ratioequivalent to · The information ratio is the expected return above a benchmark divided by the volatility of the portfolio's return difference from that benchmark.
• alphacontrasts with · Alpha is investment performance beyond a relevant benchmark or the return explained by specified systematic risk factors.
• risk-free returnused by · Risk-free return is the theoretical return on an investment assumed to have no default or other relevant uncertainty risk over a specified horizon.
• tangent planeequivalent to · A tangent plane is the plane that locally best approximates a smooth surface at a specified point.
• slopeproduced by · Slope is the rate at which a dependent quantity changes relative to an independent quantity, often represented by a line’s gradient or a coefficient in a linear relationship.

This explainer was generated by Manning's knowledge graph from the text of Build a Robo-Advisor with Python (From Scratch). The section links point to the parts of the book it draws on.