In portfolio management, risk management and derivative pricing, volatility plays an important role. So important in fact that you can find more volatility models than you can handle (Wikipedia link). What follows is to check how well each model performs, in and out of sample. Here are three simple things you can do:

# Tag: Econometric

## A shrinkage estimator for beta

In the post pairs trading issues one of the problems raised was the unstable estimates of the stock’s beta with respect to the market. Here is a suggestion for a possible solution, which is not really a solution but more stuff to do to make you feel less stupid when trading based on your fragile estimates.

## Information Criteria for Autoregression

Some knowledge about the bootstrapping procedure is assumed.

In time series analysis, Information Criteria can be found under every green tree. These are function to help you determine when to stop adding explanatory variables to your model.

## Bootstrapping time series – R code

Bootstrapping in its general form (“ordinary” bootstrap) relies on IID observations which staples the theory backing it. However, time series are a different animal and bootstrapping time series requires somewhat different procedure to preserve dependency structure.

## OLS beta VS. Robust beta

In financial context, $\beta$ is suppose to reflect the relation between a stock and the general market. A broad based index such as the S&P 500 is often taken as proxy for the general market. The $\beta$, without getting into too much detail, is estimated using the regression: **$$stock_i = \beta_0+\beta_1market_i+e_i$$ ** A $\widehat{\beta_1}$ of say, 1.5 means that when the market goes up 1% the specific stock goes up 1.5%. (Ignoring all the biases at the moment!)

## Reducing Portfolio Fluctuation

**THIS IS NOT INVESTMENT ADVICE. ACTING BASED ON THIS POST MAY, AND IN ALL PROBABILITY WILL, CAUSE MONETARY LOSS.**

Most of us are risk averse, so in our portfolio, we prefer to have stocks that will protect us to some extent from market deterioration. Simply put, when things go sour we want to own solid companies. This will reduce return fluctuation and will help our ulcer index against large downwards market swings. Large caps are such stocks. But which large caps should we chose? The squared returns are often taken as a proxy for the volatility so, keeping simplicity in mind, I use those.