## Measure Portfolio Performance

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There are countless ways to quantify stock portfolio performance and risk characteristics. It is important to be able to compare your portfolio relative to a benchmark or against other portfolios. While it is impractical (and unnecessary) to understand every portfolio metric available, there are a few which are prolific throughout the professional investment industry and should be understood when analyzing portfolio performance.

### Overview:

It is important not to be overly obsessed with any single metric but to rather look at your portfolio from different angles and through different lenses to get the full picture.

### Sharpe Ratio:

The sharpe ratio calculates the risk-adjusted return of a portfolio. It is the average return earned in excess of the risk-free rate per unit of volatility or total risk.

Over time it has become the most widely used method for calculating risk-adjusted return. It provides a way to compare performance from different portfolios while adjusting for risk.

Formula: (mean portfolio return - risk-free rate) / standard deviation of portfolio return

The sharpe ratio quantifies the excess return achieved by holding a risky asset (eg: your portfolio) instead of simply holding a risk-free asset (eg: treasury bills).

Because the sharpe ratio strips out the risk-free rate as well as accounting for volatility, it helps to determine if a portfolios return has been due to smart portfolio construction or simply due to a higher level of risk.

A risk-free asset can be thought of as having a sharpe ratio of 0. The aim of your portfolio is therefore to have a higher sharpe ratio. A value of 1 is generally considered to be reasonably good, however higher values are common. In general the higher the sharpe, the better.

#### Drawbacks:

While this ratio is popular and commonly used, it has several drawbacks which have been improved upon in other metrics.

One such drawback is that this ratio uses standard deviation of returns which assumes that all returns are normally distributed. However returns on financial assets are generally not normally distributed. For example the return distributions of an option selling strategy will typically be vastly different to a trend following strategy.

Comparing portfolios using the sharpe ratio without understanding the characteristics of the underlying strategy of those portfolios can be very misleading.

Another drawback is that the sharpe ratio penalizes upside as well as downside volatility. This means that large positive jumps in return are viewed just as badly as large negative jumps in return. Investors are typically happy to accept upside volatility because that relates to a jump in profits. However, viewed through the lens of the sharpe ratio, this kind of upside volatility is penalized and viewed negatively.

### Sortino Ratio:

The Sortino ratio is similar to the sharpe ratio however it does not penalize upside volatility. In essence this ratio retains the benefits of the sharpe ratio but allows for the fact that investors do not see upside return volatility as being negative.

Formula: (mean portfolio return - risk-free rate) / standard deviation of negative returns

The sortino ratio is considered by many to be a better measure of risk-adjusted return than the sharpe ratio.

### Calmar Ratio:

The calmar ratio is often used to assess hedge fund performance and is a measure of performance relative to risk.

It is calculated by taking the average annual rate of return (often over a three-year period) and dividing it by the maximum drawdown over that period.

Formula: (mean portfolio return - risk-free rate) / max drawdown

### Omega Ratio:

The omega is a ratio of probability weighted returns above a threshold level to probability weighted returns below the threshold. It is a measure of performance that does not assume normally distributed returns.

The sharpe ratio only takes into account the mean and variance which can be misleading as already discussed. The omega ratio on the other hand contains more information about the return distribution including the mean, variance, skew and kurtosis.

As a result, the omega ratio more accurately reflects the historical behavior of a portfolio.

### Beta:

Beta measures the volatility or systematic risk of a portfolio relative to the market. Thought of in another way, Beta is the tendency of a portfolios returns to respond to swings in the market.

Formula: the calculation consists of dividing the covariance of the portfolio and benchmark returns by the variance of the benchmark returns.

Interpretation:

• 0: the portfolio does not change in line with the market but instead acts independently.
• 0 to 1: the portfolio is theoretically less volatile than the market. If the market goes up the portfolio will typically go up but to a lesser degree.
• >1: the portfolio is theoretically more volatile than the market. If the market goes up the portfolio will typically go up but to a larger degree.

Beta can also be negative which indicates that there is an inverse relationship between the movement of the portfolio and the market. As is the case with the positive beta values explained above, increasingly negative values result in increasingly pronounced moves.

### Alpha:

The excess returns of a portfolio over and above that of the market (or a benchmark). A high alpha is desired because it indicates the value generated by the portfolio over and above what can be achieved by simply following the market.

Conceptually, alpha can also be thought of as the portion of a portfolios return that is uncorrelated to the market.

### Up / Down Capture Ratio:

The up capture ratio measures the percentage of market gains captured by the portfolio while the markets were rising. The down capture ratio measures the percentage of market losses captured by the portfolio while the markets were falling.

An up capture ratio of greater than 100 indicates that while the market was up, the portfolio was up even more. An up capture ratio of less than 100 indicates that while the market was up, the portfolio was up to a lesser extent.

The goal is therefore to have an up capture ratio of greater than 100, with higher values being better.

A down capture ratio of less than 100 indicates that while the market was losing, the portfolio lost less. A down capture ratio greater than 100 indicates that while the market was down, the portfolio lost more.

The goal is therefore to have a down capture ratio of less than 100, with lower values being better.

### Diversification Ratio:

The diversification ratio quantifies the risk reduction benefited by a portfolio in terms of volatility as a result of diversification.

The risk of a portfolio is lower than the combined risks of the assets within the portfolio provided those assets are not fully correlated. Achieving a high diversification ratio is therefore not simply a case of combining many assets into a portfolio, but is rather about combining the right assets in terms of correlation.

Formula: Ratio of the weighted average volatility of the individual assets in the portfolio divided by the volatility of the portfolio

A diversification ratio of 1 indicates that no volatility benefit has been achieved. The higher the value (above 1), the better.

### Intra-Portfolio Correlation:

This metric quantifies diversification in terms of the correlation of the portfolios assets.

Formula: A weighted average for all unique pairwise correlations within a portfolio.

The intra-portfolio correlation ranges between 0% and 100% with higher values indicating a higher level of diversification.

As is the case with the diversification ratio, the intra-portfolio correlation is not just about combining many stocks into a portfolio, but rather about how the positions correlate to each other and their relative sizes (allocations).

If maximum diversification is the goal of your portfolio, then an ideal target for the intra-portfolio correlation would be 50% (however this will typically be difficult to achieve in practice).

### Summary:

It is important to understand your portfolios performance and risk characteristics. Simply focusing on your portfolios returns masks an incredible amount of information (and potential risk). As with most things, when it comes to success in the markets, the devil is in the detail.

To analyze your portfolios diversification characteristics, tools like the Portfolio Analyzer can be used.

To backtest your portfolio to determine its performance and risk characteristics, tools like the Portfolio Backtester can be used.

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