# Modeling transaction cost with single-counted turnover ratio

Why do people use "Single-Counted" turnover ratio when modeling for transaction cost. I read a paper (Factor Investing in the Corporate Bond Market) which uses only the purchase side as turnover measure multiplied by a spread assumption.

This seems to assume that the sell side does not cost anything.

## 2 Answers

I couldn't find a definitive reference of this term and it doesn't seem to be widely used.

However, I think I can follow the logic: In their set-up the portfolio is rebalanced monthly. So, at the start positions are taken and costs incurred, since the positions are not liquidated at the end the costs for this month are only one way. After the first month position weights are updated incurring new costs but again one way because liquidation of these positions does not take place, so only one way. This process will continue so there is never a need to liquidate and only one trip will be made per month.

• This reminds me of why it can be difficult to think about multi-period portfolio optimization. The bonds mature in the future. If you're taking into account transaction costs, then there will be costs of investing in new bonds at that point. The only way I've thought of to simplify it (in the multi-period optimization approach) is to abstract away from investing in individual bonds and think more in terms of strategies. – John Dec 13 '16 at 15:32

I would say because when you multiply the total turnover ratio by the full bid ask spread you obtain the double of transaction costs.

The bid ask spread contains the double of transaction costs ( it represents the cost of a round trip - of a consecutive buy and sell order), that is the reason why we often take half of the spread as an indication of the transaction costs. We usually assume that the real transaction costs are : $| \text{price} - \text{mid-quote} |$ which should correspond to $\approx 0.5 * \text{spread}$. If you only take the purchase side (as in the paper you mentioned ) it amounts to compute half of the double spread which is the transaction costs.

Another way would be to compute $[0.5 \times \text{spread} \times \text{purchase turnover} ]+ [0.5 \times \text{spread} \times \text{sell turnover} ]$

which is indeed equal to : $\text{purchase turnover} * \text{spread}$ (assuming symmetry of the bid ask spread and realizing that purchase turnover is equal to sell turnover)