How much turnover is required to get portfolios back to their constraints?

## Previously

“Low (and high) volatility strategy effects” created 6 sets of random portfolios as of 2007 and showed their performance up to about a month ago. This post explores how much turnover it takes to get the portfolios to obey their constraints at the ending point.

## Turnover

Figures 1 through 6 show the distribution of turnover (buys plus sells) required to move the portfolios back to obeying their constraints in 2012 February.

Figure 1: Distribution of rebalancing turnover for the “vanilla” portfolios. The only constraint that can be broken in the vanilla portfolios is the maximum weight of 4%. So the turnover in Figure 1 is only from selling off the stocks with too much weight (and buying back other stocks).

Figure 2: Distribution of rebalancing turnover for the “low variance” portfolios.

Figure 3: Distribution of rebalancing turnover for the “low volatility” portfolios.

Figure 4: Distribution of rebalancing turnover for the “low beta” portfolios.

Figure 5: Distribution of rebalancing turnover for the “high volatility” portfolios.

Figure 6: Distribution of rebalancing turnover for the “high beta” portfolios.

## Summary

- All three of the low volatility style cohorts have about the same turnover.
- However, it is possible that “minimum variance” turnover could be sensitive to the 120% allowance we make for the variance constraint.
- The two high volatility style cohorts have turnover similar to each other, and — unsurprisingly — higher than that for low vol.

## Portfolio Probe Appendix

#### utility

When we are rebalancing the random portfolios, we are not aiming at any particular utility. But we do want to minimize the amount of turnover when finding a portfolio that obeys all the constraints.

The mechanism that was used was:

- set all expected returns to zero
- set the trading cost to be the stock price
- set the utility to “maximum return”
- avoid the annoying warning about optimization without a variance with
`do.warn=c(novar=FALSE)`

This optimization is minimizing the turnover because it is minimizing the cost which is proportional to the turnover. As a bonus the cost of the trade is the fraction of turnover (buys plus sells), so there is no need to make a call to `valuation`

or `summary`

.

#### universe

Four of the six cohorts involve selecting from a subset of the overall universe. The trick to get the portfolios to obey that type of constraint was:

- set the universe to the union of the names in the portfolio and the names in the new subset that is required
- force closing trades on the assets in the portfolio that are not in the new subset