The Market Risk Metrics course covers a number of measures that risk or investment managers may need for evaluating the market risk inherent in their portfolios or when making decisions on asset selection, portfolio allocation and portfolio optimization. We aim to provide a practical step-by-step calculation methodology for each metric considered within the course, together with an interpretation of results and examples.
We begin with an overview of the course and the topics to be addressed for each metric:
We then present detailed posts for each metric. We discuss how holding period returns are calculated and how the measure is scaled to get an annualized figure in the following post:
We then move onto Beta which is calculated for a given instrument in relation to a broad market index. The CAPM adjustment to the metric in terms of the replacement of portfolio returns with market returns is discussed. The measure calculated using EXCEL’s COVAR() and VAR() functions is illustrated. These topics are covered in the following post:
Jensen’s Alpha is discussed next. Using a simple example we show how the alphas are derived using regression analysis, in particular a minimization of least squares estimation approach, and EXCEL’s Solver function. Significance testing of the alpha is also demonstrated. These topics are reviewed in the following post:
For the calculation of the Sharpe Ratio we first consider the calculation of daily and annualized volatility. The calculation process is demonstrated using EXCEL’s STDEV() function. Then we illustrate how the Sharpe ratio is calculated using this derived volatility, the holding period return and the risk free rate of return.
The Treynor Ratio is derived from the holding period return, risk free rate of return and the beta. The procedure for calculating these two ratios is given in the following post:
The next metric that is very useful in assessing market risk is the Value at Risk metric which measures the risk of maximum loss given a specific confidence level and holding period. The following detailed course on VaR covers the calculation of VaR using the simple moving average variance covariance approach, the exponentially weighted average variance covariance approach and the historical simulation approach. The course also covers J-day scaled and portfolio Value at risk calculations:
Following from the discussion of Value at Risk we address the questions: “How much more could you lose, beyond the worst case loss, if the worst case loss occurred? What would you pay to insure yourself against such an instance?” through the calculation of the Put Premium using the Black Scholes formula for the put option of a stock.
The calculation of the put premium, based on the underlying simple moving average variance covariance VaR approach, is reviewed in the following post:
The correlation coefficient is an important tool for quantitatively assessing the linear relationship between two instruments. In the following post we discuss the statistical formula of the metric; how it may be calculated using EXCEL’s CORREL() function; how a correlation matrix may be constructed using EXCEL’s Data Analysis Tool; how the metric may be interpretation with relation to its magnitude and direction; and how the measure may be tested for statistical significance:
[For a more detailed review of the correlation concept you may also like to review the following in-depth course on correlation: Correlation]
While we have discussed the volatility of individual instruments within a portfolio in earlier posts it is also important to know about the portfolio’s risk or volatility as it is not necessarily equal to the sum of the volatilities of the individual instruments within it due to their interdependence with each other. The posts below discuss how portfolio volatility may be calculated by a statistical formula as well as a more practical way of calculating it using the weighted averaged sum of return series:
Finally we wind up the course by a review of volatility trend analysis using volatility trend lines. This graphically representation is used to assess how an instrument’s volatility levels, or alternatively its risk levels, have changed over time:
Our online finance course store, Computational Finance section, contains an EXCEL example file (available for sale) that covers the metrics mentioned above (except for volatility trend analysis):
If you liked this course on risk metrics you may also be interested in the following quantitative courses.
- Calculating Value at Risk (VaR)
- Portfolio Risk Metrics
- Duration Convexity Example
- Valuing Options – Black Scholes Example
- Calculating VaR –EXCEL Example