# FAQ

- Check correlations between securities of interest;
- Quantify the risk in a portfolio;
- Analyze whether the existing portfolio risk is balanced;
- Measure the impact of any new positions;
- Compare portfolio statistics with those of a broad market index;
- Test risk metrics across different time frames;
- Supplement market analysis with a quantitative perspective.
- Identify substitutes and complements for existing portfolio holdings.

1. Select security tickers for your portfolio. You can now combine instruments listed on different stock exchanges worldwide.

2. Specify percentage portfolio weights for each holding. The system accepts negative values as well, but the sum of the weights has to be 100% in any case.

3. Using the drop-down menu, choose your preferred look-back period for the price data. If there are insufficient data for the selected period, the dates will be truncated to the earliest date that is available for all selected tickers. We strongly recommend running calculations in different time frames to check for consistency of estimates.

4. Hit the "Calculate" button and let the system do the number crunching. For large portfolios, this process may take some time, thus please be patient while historical data is downloaded and analyzed.

Below is a brief description of the risk metrics that are available to the users in the Risk section of this website:

*Total Return* - return over the selected time frame. It is adjusted for all applicable splits and dividend distributions, adhering to CRSP standards. The number is not annualized. Portfolio return is calculated assuming daily rebalancing.

*Risk contribution* – a proportion of total portfolio risk, measured by the standard deviation, which is attributable to a particular holding in a portfolio. Different securities carry varying levels of risk, thus their individual contributions to the aggregate portfolio risk are typically not equal to their allocation weights. Risk contributions are computed from the covariance matrix. This presentation provides a more detailed explanation with related algebra.

*Volatility *– a measure of variation in financial instrument’s price. Volatility is calculated as the standard deviation of security’s returns realized over a period of time. The higher the volatility, the riskier the security.

*Beta* – a measure of security’s sensitivity to the market, which is calculated using linear regression analysis. For example, a beta of 1.3 implies that a security, on average, moves 1.3% for each 1% movement in the market. The lower the beta, the less sensitive the security is to the market. InvestSpy uses SPY ETF as a proxy for the market.

*Value at Risk (VaR)* – a measure to quantify the level of financial risk within an investment portfolio over a specific time frame. For instance, a daily VaR of 3% at a 99% confidence level implies that the portfolio is expected to lose no more than 3% of its total value on 99 days out of 100. VaR on InvestSpy is calculated using parametric (variance-covariance) approach, meaning that it is derived directly from the estimated portfolio volatility under the assumption of normal distribution returns.

*Maximum drawdown* *(MaxDD)* – a percentage expression of the largest drop from a peak to a bottom in the selected period of time. It shows the magnitude of the worst loss an investor would have incurred before a new peak was achieved.

*Correlation* – a measure of the co-movement between two financial variables over time. Correlation coefficient can range from -1 to +1, where values close to +1 imply that securities typically move in the same direction, whilst negative correlations suggest that instruments tend to move in opposite directions. The correlation coefficient of 0 would mean that securities are linearly independent of each other and their co-movement is predominantly random.

*Intra-portfolio correlation (IPC)* – a measure of diversification, calculated as a weighted average of intra-portfolio correlations. It measures the propensity for portfolio components to move together and ranges from -1 to +1, with values approaching +1 indicating the lowest level of diversification. A high IPC typically implies that systematic rather than idiosyncratic risk is predominant in a portfolio. Its mathematical expression is as follows:

where w(i) - the fraction invested in asset i; w(j) - the fraction invested in asset j; p(ij) - the correlation between assets i and j. The expression may only be computed when i≠j. A more detailed break-down of the IPC can be found in this paper.

*R-squared* - a statistic that measures how well the model fits the actual data. It is simply a square of the correlation coefficient between the actual values of the independent variable and those predicted by the factor model. As the correlation coefficient can only range between -1 and +1, the R-squared values always lie between 0 and +1. As an alternative explanation, this metric can be thought of as representing the percent of variance which is explained by the specified factor model. R-squared never decreases when additional variables are added.

Factor analysis is a statistical technique that identifies what combination of pre-selected ETFs would have most closely replicated the actual performance of the chosen security over a specified time period. It is based on returns-based style analysis that was developed by Noble Prize winner William Sharpe.

1. Select a list or lists of ETFs to be used for the analysis.

2. Specify a look-back period for the price data. If there are insufficient data for the selected period, the dates will be truncated to the earliest date that is available for all tickers.

This functionality has been deliberately left out to keep users analyzing their portfolios rather than rely on blindfold optimization. There are a few good reasons for this:

- If expected returns model is included in the optimization engine, this leads to unstable weights and excessive portfolio turnover;
- Optimization towards minimum risk tends to excessively overweight assets with low volatility or negative correlations;
- The precision of historical estimates is limited, thus such statistics should preferably be used for guidance rather than prescriptive action.