When choosing an investment strategy, it's important to have a solid understanding of past performance metrics to determine potential risks and returns. In this article, we'll discuss some of the common metrics used to evaluate investment performance.

## General Performance Metrics

#### Time-Weighted Returns

When measuring the performance of a portfolio, returns are simply the money gained or lost. Time-weighted returns represent the ratio of the gain (or loss) to the total portfolio value, and they are expressed as a percentage. It's important to evaluate the performance of an investment over different time periods, as returns can vary greatly.

Let's consider two hypothetical portfolios with the following simulated performance:

Over the last 30 days and 365 days, both portfolios had similar returns. But at the 90 day mark, Portfolio One had an 11.5% return while Portfolio Two had a 6.4% return. Therefore, evaluating performance over different time periods can help investors make informed decisions about their investment strategies.

## Risk Metrics

Also risk metrics are important for evaluating the potential risks associated with an investment strategy. Two commonly used metrics are volatility and the Sharpe ratio.

#### Volatility

As we have seen here, volatility, or standard deviation, measures the fluctuations in time-specific returns and is used often as a proxy for the riskiness of the portfolio. The lower the volatility, the less risky the portfolio is considered to be.

Here, we have also seen how volatility of the components of a portfolio influence the volatility of the portfolio itself.

Let's return to our hypothetical portfolios. Over the last 365 days, both portfolios had similar returns. But Portfolio One had a volatility of 13.14% while Portfolio Two had a volatility of 14.31%. Naturally this suggests that Portfolio Two is riskier than Portfolio One.

### Sharpe Ratio

The Sharpe ratio is a measure of risk-adjusted return that combines time-weighted returns and volatility. Therefore, it's used to compare different portfolios and strategies, with a higher Sharpe ratio indicating better returns relative to the risk taken on. Sharpe Ratio is calculated by time-weighted returns divided by volatility.

In our hypothetical portfolios, Portfolio One had a Sharpe ratio of 2.3, while Portfolio Two had a Sharpe ratio of 2.12. This suggests that Portfolio One had better returns relative to the risks taken on compared to Portfolio Two.

## More complex Performance Metrics

In addition to the performance metrics already discussed, there are several other important measures to consider when evaluating investment strategies: Treynor value, Jensen measure, Value at Risk (VaR), and maximum drawdown.

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**Treynor value**is a risk-adjusted measure of portfolio performance that takes into account the portfolio's beta, or sensitivity to market movements. It is calculated as the excess return of the portfolio over the risk-free rate divided by the portfolio's beta. In practice a higher Treynor value indicates better risk-adjusted performance. Moreover, if we suppose a risk-free rate equal to 2% and the Beta of the first portfolio equal to 1.2 the Treynor value is 23.58%.The

**Jensen measure**, also known as Jensen's alpha, measures a portfolio's risk-adjusted performance relative to its expected return, based on its level of systematic risk. It is calculated as the portfolio's excess return over its expected return, adjusted for its beta. A positive Jensen measure indicates that the portfolio has performed better than expected, while a negative value suggests underperformance.**Value at Risk (VaR)**is a measure of the potential losses that an investment portfolio may incur over a certain time period, with a specified level of confidence. Thus, VaR is typically expressed as a dollar amount or percentage of the portfolio's total value, and represents the maximum potential loss that the portfolio could suffer over the specified time period, given the level of confidence.**Maximum drawdown**is a measure of the largest percentage decline in value that a portfolio has experienced over a specified time period. It represents the peak-to-trough decline in the portfolio's value, and is often used as a measure of downside risk.

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