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I wanted to start this thread to talk about friction, by which I mean commission, spreads and slippage. The following is from a draft of my book-in-progress called The Beta Theory. I have included the section on commissions. If there is interest, I will follow up with the sections on spreads and slippage.

**Friction: Commissions, spreads and slippage. How to determine realizable gains for quantitative trading models.**

Active traders who use quantitative trading models typically use back-testing software to validate and fine-tune their models. Backtesting software typically shows excellent results with high-turnover models that trade small-cap thinly-traded stocks. However, there is often a large difference between back-testing results and achievable returns. This difference is particularly great for actively traded models that incorporate thinly-traded small cap stocks. This difference comes primarily from two factors. First are the costs of trading, which I refer to as “friction.” The second is the problem of “data mining,” where a model is over-fit to a certain dataset, but not predictive of future events. In this discussion I will focus on the costs of ** friction**.

Let’s assume we have developed a quantitative investment model “ValueGrowth 1.0” and we back-test it. Our back-testing shows an Average Annual Compound Return (AACR) of 60%! In twenty years a $10,000 stake will compound to over $12 million dollars! We are going to be rich! Or are we?

Unfortunately, our back-testing software does not account for ** friction** from things such as commissions, spreads, and slippage. These are significant for frequent traders when trading in thinly-traded small-cap stocks. Let’s take a detailed look at the costs of these different sources of “friction.”

**Commissions.**

Whenever we trade stocks we must pay a commission to our broker. A typical discount commission is about $10 for each trade. To realize a gain in every stock we must buy it, then sell it, for a total of two transactions. If we typically have an 8 stock portfolio which we rebalance weekly with a 75% turnover, we end up with about 12 trades (6-in and 6-out) each week. With a $10/trade commission, this works out to about $120 in commission costs every week. $120 is 1.2% of our $10,000 portfolio. But our 60% AACR has only a 0.91% return each week. Oh oh! If we subtract 1.2% from our 0.91% return, we lose 0.29% each week! And we have more “** friction**” to account for. Acheiving 60% returns is gong to be harder than we thought! What do we do?

If we had a ** bigger portfolio** we would be less affected by commission costs. For example, let’s assume a portfolio of $100,000 Now our costs are only 0.12%/week. This gives us a weekly return of 0.79%, or an annual average compound return of about 50%. The friction of commissions makes a serious dent in our returns, but we can absorb the cost of commissions and still make a handsome profit.

** Another solution is to trade less often.** If we only have $10,000, we can reduce the cost of commissions by trading less often. If we trade every two-weeks, assuming a similar turnover, we reduce the impact of commissions considerably. Unfortunately, the back-testing results of our model only shows a 50% return for two-week rebalancing. Still, doing the math, a 50% AACR calculates out to a 1.57% return every two weeks. Subtracting the 1.2% commission cost leaves us with 0.37% return every two weeks. This gives us a 21% AACR, which is considerably better than the money-losing one-week model. Trading every four weeks gives even better results. Our model only shows a 45% AACR for 4-week rebalancing, which is 2.9%/period. Subtracting 1.2% leaves us with 1.7%, a 24.5% ACCR.

*One problem with actively traded models is that periodic returns are quite small. Commissions can quickly eat up the returns in small portfolios. Solutions include:*

*1. **Trading a larger portfolio so that commissions are a smaller percentage*

*2. **Reducing the number of stocks in the portfolio so that there are fewer trades*

*3. **Trading less frequently to reduce commission costs. *

*4. **Getting a discount on commissions.*

One-week rebalancing of small portfolios creates only the illusion of profits. We have already seen that our small-portfolio model works better with a 4-week rebalancing when we take into account commission costs.

It is important to consider the size of your portfolio and the number of trades, so that commissions do note significantly affect the ** periodic return**. With $100,000 and an 8-stock portfolio we can still make excellent profits with our 1-week trading model. Aha! Rich again! Or are we?

Next, we will talk about spreads.

michael

The Beta Theory

TWQS1