Forecasting Volatility

Variance Covariance (VCV) Matrices

The simplest and most commonly used method for estimating constant variances and covariances is to use variance or covariance–computed from historical return data. These elements are then assembled into a VCV matrix. The following table shows a simple example of a VCV matrix for a group of stocks:

$$ \begin{array}{c|c|c|c} & \textbf{Stock A} & \textbf{Stock B} & \textbf{Stocks C} \\ \hline \text{Stock A} & 1.000 & 1.073 & 1.431 \\ \hline \text{Stock B} & 1.073 & 1.000 & 0.886 \\ \hline \text{Stock C} & 1.431 & 0.886 & 1.000 \end{array} $$

In addition to using variance-covariance matrices, other tools that can be added to an analyst’s processes include:

• VCV Matrices from Multi-factor: These attempt to explain the outcomes of a model (i.e., GDP) using not just one source of influence on the data but many at a time.
• Shrinkage Estimates of VCV Matrices: Broadly speaking, a crude or raw estimate is improved by combining it with other pieces of information. Alternatively, adding more information to a data set is likely to improve its accuracy.
• Estimating Volatility from Smoothed Returns: Smoothed data involves infrequently recorded returns that bias volatility downwards. To compensate, analysts use the general formula:

  $$ \left(\frac { (1 + \lambda) }{ (1 – \lambda) } \right) = \text{true volatility} $$

  Where \(\lambda\) is the true volatility.

• Time-Varying Volatility ARCH Models: They are used to address volatility clustering. 

Question

From which of the following does data used to forecast volatility most commonly come?

1. Observations of past volatility.
2. News and event forecasting.
3. Bayes theorem approach.

Solution

The correct answer is A.

Forecasting volatility in financial markets is essential for investment, option pricing, and financial market regulation. The most common approach to forecasting volatility is to use observations of past volatility, such as historical average, exponentially weighted moving average (EWMA), and GARCH2. These models use past observations of volatility to forecast future volatility.

B and C are incorrect. While news and event forecasting, or the Bayes theorem approach, may also be used, they are not as commonly used as observations of past volatility.

Reading 2: Capital Market Expectations – Part 2 (Forecasting Asset Class Returns)

Los 2 (g) Discuss methods of forecasting volatility