Volatility Clustering

Discussion in 'Options' started by Panurgo, Nov 13, 2007.

  1. Panurgo



    we know that prices follow a brownian motion so the returns are considered to be independent random variables. However there is a clearly evidence that the squared returns are not indipendent, but they are autocorrelated.
    This is the well-known phenomenon of volatility clustering: large price variations are more likely to be followed by large price variations (and vice versa). This holds true for most asset classes, where we know from historical data that the magnitudo of the movements will increase (or decrease), but of course we don't know the sign.

    My question is:
    Can we produce best risk adjusted returns knowing this?

    For example: assume we have two portfolios with the same share (we call it STK), A and B. We know in advance that STK has the same positive autocorrelation in squared returns for year Jan 1 to Dec 31 that it has in his history.

    Portfolio A: on Jan 1 we buy 1000 STK at 100, actual volatility is 15%. On Dec 31 we have a net return of +10% with a standard dev. of 20%.

    Portfolio B: on Jan 1 we buy 1000 STK at 100, actual volatility is 15% , but we adjust our exposition as volatility move. E.g. on Jan 2 vol rises to 17% (since STK goes down), so at the close we sell some shares since we know that tomorrow will be probably riskier, and so on. We do this until Dec 31, when we have to compare results with our A portfolio.

    Excluding the transactional costs, can in your opinion on average portfolio B beats A in terms of RISK ADJUSTED returns? E.g, if the risk free return is 4% and on Dec 31 B has a return of 8% with a St. dev. of 8% it has a Sharpe ratio of 0.5, compared to the 0.3 of A.