Sauro Locatelli   |   July 22, 2012

A few weeks ago, I introduced you to the concept of pro-forma portfolios, and explained how we use them to estimate our current portfolios’ position in terms of volatility and beta. There is an Italian saying that could be translated as “to trust is good, not to trust is better.” While the pro-forma portfolios give us the best possible ex-ante estimates of the amount of risk in the portfolios, these are by definition estimates and not reality, and we can only trust them so much. For this reason we have developed two very short-term measures of volatility and beta based on the actual daily portfolio returns, which we routinely compare to the pro-forma estimates to make sure the portfolios are in fact behaving as we expected. The first measure is called one-month time-weighted trailing volatility and starts with the calculation of the equal-weighted average of the portfolio’s daily volatility over trailing 5 days (1 week), 10 days (2 weeks) and 20 days (4 weeks). This number is then divided by the same average volatility calculated for the portfolio’s benchmark. The ratio gives us a measure of how volatile the portfolio is being relative to its benchmark:

Ratio = 1 (neutral): the portfolio is experiencing the same volatility as the benchmark;

Ratio > 1 (above neutral or aggressive): the portfolio is experiencing more volatility than the benchmark;

Ratio < 1 (below neutral or defensive): the portfolio is experiencing less volatility than the benchmark;

The other measure is called one-month time-weighted trailing beta and uses the same approach to calculate the beta of the portfolios versus their respective benchmarks. Both measures are based on 1 month (4 weeks) of data, but since they are the equal-weighted average of three overlapping time frames they give more weight to more recent data. Specifically, the trailing 5 days are accounted for 3 times, the previous 5 days are accounted for twice, and the previous 10 days are accounted for only once. Because of their short-term nature, these measures can be particularly volatile at times, which is why we introduced a one-month moving average to better gauge the direction of the trend. In the chart to the right, you can see that after a brief spike to nearly 1.2, the two measures have come back down to around 0.9, while the one-month moving average has just reached the Mendoza line of 1. This result is perfectly in line with our initial estimates based on pro-forma portfolios, which had indicated that our last trade would take us very close to neutral.