# Sharpe Ratio

The Sharpe ratio is a way to determine how much return is achieved per each unit of risk. It is useful to, and can be computed by, all forms of capital market participants to evaluate their performance, from day traders to long-term buy-and-hold investors.

Naturally, when evaluating the performance of traders and investors it is not simply a matter of determining their overall return, but their return relative to their risk.

## Top Brokers For Maximising Your Sharpe Ratio

A 20% annual gain is very strong performance. However, if this comes from having an annualized volatility of 60% because of excess leveraging or trading very speculative instruments, this is actually relatively moderate performance when risk-adjusted. The Sharpe ratio would be considered 0.3. This is calculated as follows:

**Sharpe Ratio = (Return of Portfolio – Risk-Free Return) / Std Dev of Portfolio**

The risk-free rate of return is a user-based input. This is usually the equivalent of a safe risk-free bond. This might be the yield on a US Treasury, UK Gilt, German bund, or other safe instrument. Its duration is dependent on your time horizon.

For long-term investors or position traders who hold positions over long periods of time, they might choose a longer duration bond. Short-term investors or day traders who might hold positions only within the day might use a shorter bond duration, or virtually one equivalent to the countries overnight rate set by its central bank. This is usually approximated by a one-month or three-month government bond or by simply looking at the central bank’s overnight policy rate itself.

In the case of the 20% gain / 60% volatility portfolio mentioned above, if one uses a 10-year US Treasury (assume 3% yield), the Sharpe ratio would come to 0.283. If one uses a 3-month US Treasury (assume 2% yield), the Sharpe ratio would come to 0.300.

If the risk-free rate used is higher, this means the “excess return” is lower – namely a 17% return over the risk-free rate is not quite as good as an 18% excess return. Thus, a higher risk-free rate will result in a lower Sharpe ratio, holding all else equal.

## Key Takeaways – Sharpe Ratio

Risk-Adjusted Performance

- The Sharpe ratio quantifies how much excess return is achieved for each unit of risk.
- Helps traders understand the risk-adjusted performance of their investments/trades.
Benchmark Comparison

- Allows for comparison between different investments or portfolios by standardizing risk, which makes it useful for portfolio optimization.
Historical Limitations

- It’s based on historical data and assumes normal return distribution (i.e., ignores skewness and kurtosis in returns distributions), so it may not accurately predict future risk or performance.

## Ex-Ante vs. Ex-Post Sharpe Ratio

The Sharpe ratio can be considered either *ex-ante* (expected) or *ex-post* (backward-looking to evaluate past performance).

The ratio considered above is ex-post, in that its performance already occurred. The ex-ante Sharpe ratio takes into account expectations. Instead of portfolio returns and volatility, the calculation is instead the expected values of those things, denoted by “E” before the terms.

**Sharpe Ratio = E(Return of Portfolio – Risk-Free Return) / E(Std Dev of Portfolio)**

Therefore, if the S&P 500 is expected to generate 7% nominal annualized returns off 15% annualized volatility, with a risk-free rate of return of 3% (based on US Treasury yields far in the future), that produces a Sharpe ratio of 0.27.

Ex-post ratios can vary widely, especially among shorter timeframes. For example, the Sharpe ratio of the S&P 500 for 2017, due to higher returns at low volatility, was 4.78. For the year-to-date portion of 2018, it has been 0.23.

## Application in Finance

The Sharpe ratio are often used to determine the relative performance of portfolios, traders, and fund managers over time. The Sharpe ratios of individual asset classes are generally in the vicinity of 0.2 to 0.3 over the long-run.

A value between 0 and 1 signifies that the returns derived are better than the risk-free rate, but their excess risks exceed their excess returns. A value above 1 denotes that the returns are not only better than the risk-free rate, but excess returns are above their excess risks.

A negative Sharpe ratio means that the performance of a manager or portfolio is below the risk-free rate. For financial assets, negative Sharpe ratios won’t persist for indefinite periods of time. Capitalist economies would cease to function if this were true.

Negative Sharpe ratios can endure for long periods of time for specific asset classes, managers, or portfolios due to timing or the idiosyncratic risk associated with trading certain assets.

However, a negative Sharpe ratio is problematic to evaluate because a negative excess return with a large amount of volatility will actually make the Sharpe ratio *less *negative (because the denominator is larger), thus insinuating that its performance wasn’t as poor as expected. Likewise, a portfolio with a small negative excess return can be punished if the volatility associated with it is large, giving a smaller denominator and thus amplifying the negative value.

Therefore, negative Sharpe ratios can be exceedingly difficult to assess.

## Pros and Cons of the Sharpe Ratio

Like any statistical measure, it is only as good as its assumptions. In studies of financial risk assessment, it is often assumed that volatility is equal to risk or the best proxy of it. However, not all volatility is harmful and some is absolutely necessary to capture return.

Trading and investing is fundamentally about maximizing return per unit of risk. This is the central intention of the Sharpe ratio, but it does so in a simplistic manner.

Trading or investing strategies that properly balance risks or are able to accurately identify strong reward-to-risk opportunities will have high upside volatility. But considering that all volatility is penalized equally under the Sharpe ratio, the metric may not be the best for accurately identifying the risks associated with the portfolio.

Other risk-adjusted metrics, such as the Sortino ratio, may be a better fit for these types of portfolios and will generally be a more accurate reflection of their risk.

However, the Sharpe ratio is easily applicable and can be applied to any time series of returns without needing additional info regarding the sources of volatility or profitability.

Volatility of returns is also assumed to be normally distributed. Typically, financial variables tend to be more fat-tailed than those associated with the normal distribution and generally exhibit higher skewness and/or kurtosis.

And because the Sharpe ratio is typically used in the ex-post sense – to evaluate past performance – it can be flawed given past performance is not necessarily any prediction of what will occur in the future or over shorter time horizons.

Moreover, since the Sharpe ratio is not expressed in terms of a percentage or return, but rather as a simple number, its use is only valuable in comparison to other performances assessed through the Sharpe ratio.

As a rule of thumb, a Sharpe ratio above 0.5 is market-beating performance if achieved over the long run. A ratio of 1 is superb and difficult to achieve over long periods of time. A ratio of 0.2-0.3 is in line with the broader market. A negative Sharpe ratio, as aforementioned, is difficult to evaluate.

## How to Improve Your Sharpe Ratio

Here are some strategies that can help improve the Sharpe ratio of an investment portfolio or trading strategy:

### Risk Management

Implement proper position sizing and risk control measures to reduce the impact of individual trades on the overall portfolio.

Diversify, use options, constrain position sizes to reasonable level, or use other risk management techniques to limit potential losses.

Diversify across different asset classes, sectors, or strategies to reduce overall portfolio volatility.

### Portfolio Optimization

Use mean-variance optimization techniques to construct portfolios with the highest expected return for a given level of risk.

Employ portfolio construction techniques like the risk parity approach to balance risk contributions across different asset classes or strategies.

### Leverage

Carefully consider the use of leverage, as it can amplify both returns and volatility.

Leverage should be applied judiciously and with proper risk controls.

### Trading Discipline

Develop and strictly follow a well-defined trading plan or trading strategy.

Avoid emotional or impulsive trading decisions that can increase risk and reduce returns.

### Cost Reduction

Minimize trading costs, such as commissions, spreads, and slippage, as these can erode returns and increase volatility.

Consider tax-efficient investment vehicles or strategies to reduce the impact of taxes on overall returns.

### Active Risk Monitoring

Continuously monitor and adjust the risk profile of the portfolio or strategy, as market conditions and risk factors change over time.

Employ risk metrics like Value at Risk (VaR) or Conditional Value at Risk (CVaR) to assess and manage downside risk.

### Strategy Refinement

Continuously evaluate and refine the investment or trading strategy to improve its performance and risk-adjusted returns.

Backtest and optimize the strategy using historical data and simulations (which may require synthetic data).

### Other Factors to Consider

Improving the Sharpe ratio should not be the sole objective, as it may lead to an overly conservative approach or an excessive focus on risk reduction at the expense of potential returns.

The goal should be to strike a balance between risk and return that aligns with the trader’s/investor‘s risk tolerance and objectives.

## FAQs – Sharpe Ratio

### How do you interpret the Sharpe Ratio?

The Sharpe Ratio is interpreted as a measure of the excess return per unit of risk.

A higher ratio indicates better risk-adjusted performance.

### What constitutes a good or bad Sharpe Ratio and how does it reflect risk-adjusted returns?

A Sharpe Ratio greater than 1 is generally considered good.

It would mean, for example, 15% returns over the risk-free rate at 15% volatility (the average volatility of the stock market).

It indicates that returns are high relative to the risk taken, while a ratio close to 0 may suggest inadequate return for the risk incurred.

### What are the limitations of the Sharpe Ratio?

The Sharpe Ratio can be misleading due to its reliance on the normal distribution of returns and sensitivity to the frequency of return measurement.

So, it will potentially overlook extreme risk events.

Other “moments” of distributions have to do with the shape of distributions, such as skew and kurtosis.

If returns are not normally distributed, the Sharpe ratio will neglect forms of risk.

### How can the Sharpe Ratio be used in trading decisions?

It is used in portfolio construction and analysis to compare the risk-adjusted performance of different investments or portfolios.

### Can the Sharpe Ratio predict future performance?

The Sharpe Ratio has limited predictive power as it is based on historical data and doesn’t necessarily indicate future performance.

It can nonetheless give a decent indication of how a strategy might do.

It all depends on the parameters and how replicable the strategy is.

For some strategies, the edge erodes quickly. For others, the outperformance could potentially last years or decades.

### How does the Sharpe Ratio compare to other risk-adjusted performance measures?

The Sharpe Ratio measures total risk compared to other metrics like the Sortino Ratio (which focuses on downside risk) and the Treynor Ratio (which measures systematic risk).

Others include:

#### Information Ratio

The Information Ratio measures the excess return of an investment relative to the return of a benchmark index, divided by the variability of the excess return.

#### Omega Ratio

The Omega Ratio is a risk-return performance measure of an investment, calculated as the ratio of the probability-weighted gain to the probability-weighted loss relative to a specified threshold rate.

It highlights the asset’s ability to achieve returns above a threshold.

#### Bias Ratio

The Bias Ratio is a measure of skewness in asset returns.

It compares the frequency of small gains to small losses, used to identify potential biases or systematic tendencies in investment returns.

**Related**: Other Performance Ratios

### What impact do changes in risk-free rate have on the Sharpe Ratio?

Increases in the risk-free rate can decrease the Sharpe Ratio as it raises the benchmark for excess return, and vice versa.

### How is the Sharpe Ratio affected by different time periods?

The ratio can vary significantly with the time period used, as shorter periods may amplify volatility and risk perception.

### What are the best practices for calculating and using the Sharpe Ratio?

Best practices include using consistent time periods for comparison and adjusting for the risk-free rate.

### How can the Sharpe Ratio be misleading?

The Sharpe Ratio can be misleading because it may not fully capture the risk of non-normal return distributions or the impact of extreme market conditions.

It leads to an incomplete assessment of risk and performance.

It’s just a baseline figure, off which you can explore further.

### Can you add a losing strategy just for the sake of having a higher Sharpe Ratio?

Yes, traders sometimes adopt losing strategies, like buying options for hedging or shorting stocks.

They believe it’ll reduce their risk more than their return, which will enhance the Sharpe Ratio.