## Market Risk Metrics – Introduction

*in*Finance

Market risk is the risk that movements in market prices will adversely impact the value of an investment. There are four principal categories of market risk or risk factors: equity risk, interest rate risk, currency risk and commodity risk. Exposure to market risk for a particular entity is based on:

- Volatility of the underlying risk factors
- The entity’s portfolio’s sensitivity to this volatility

We may assess volatility or alternatively the riskiness of an entity’s portfolio in a number of ways. We can calculate Value at Risk, or VaR for short, to determine the worst case loss that an entity could suffer over a given holding period and with a given probability. We could calculate the Put premium to assess the amount that could be lost in excess of the VaR amount. We may calculate various risk-to-reward performance measures, such as the Sharpe and Treynor ratios, to look at return in conjunction with risk rather than or a standalone basis. We can use the correlation coefficient to determine a particular instrument’s relationship with that of another within a given risk category or even across risk categories.

In this case we have looked at a number of ways in which the market risk in each of the categories or factors are assessed. These methods include:

- Holding period return
- Beta with respect to market indices
- Jensen’s Alpha
- Sharpe Ratio
- Treynor Ratio
- Value at Risk
- Put Premium
- Correlation Coefficient
- Portfolio volatility
- Volatility Trend Analysis

Volatility Trend Analysis, Portfolio volatility, Value at Risk and Put Premium are useful in assessing the levels of risk in the factors (equity, interest rate, commodity, currency) impacting market risk. The remaining measures are means by which decisions on asset selection, portfolio allocation and portfolio optimization may be made.

In the posts that follow we will demonstrate a step-by-step methodology for calculating each of the measures mentioned above with detailed numerical examples for each measure. We also show how the results from the calculation may be interpreted. In particular for the given measures we will cover the following areas:

*Holding Period Return*

- The calculation of the holding period return
- The calculation of the scaled holding period return

*Beta with respect to market indices*

- The calculation of beta using EXCEL functions for covariance and variance

*Jensen’s Alpha*

- The calculation of Jensen’s Alpha using regression analysis, in particular, a least squares estimation approach
- Testing the significance of the results obtained

*Sharpe Ratio*

- The calculation of daily volatility, annualized volatility and the Sharpe Ratio

*Treynor Ratio*

- The calculation of the Treynor Ratio

*Value at Risk (VaR)*

- The calculation of VaR using the Variance Covariance approach.
- The calculation of VaR using the Historical Simulation approach.
- The calculation of scaled VaR

*Put Premium*

- The calculation of the put premium, i.e. the extent of the worst case loss, using the simple moving average (SMA) Variance Covariance approach as the underlying VaR methodology.

*Correlation Coefficient*

- The calculation of the correlation coefficient by statistical formula
- The calculation of the correlation coefficient by EXCEL’s CORREL() function
- The calculation of a correlation matrix using EXCEL’s DATA ANALYSIS tool
- The interpretation of the magnitude of the resulting value(s) using Rules of Thumb
- Testing the significance of the results obtained

*Portfolio volatility*

- The calculation of portfolio volatility using statistical formula
- The calculation of portfolio volatility using a weighted average return series.

*Volatility Trend Analysis*

- The construction of a volatility trend line graph