Week 2: Cost drag

The only loss on this syllabus that is guaranteed — what you paid to open a position, before the market had an opinion about it.

1 March 2027committableyours to commit, and assessableOpen the slides

Nothing happened last week. Whatever you bought is roughly where you left it, and you are already down. This lecture is the arithmetic of that, and it is the one lecture in the course whose conclusion applies to every single person in the room.

The quote has two prices#

When you looked up the thing you bought, you probably saw one number. There were two. Someone will buy from you at the bid and someone will sell to you at the ask, and the ask is higher. The gap is the spread, and it is the fee you pay for the existence of somebody willing to trade with you.

Take a quote of $39.96 bid and $40.00 ask. You paid the ask. If you changed your mind one second later, you would receive the bid. So the instant you bought, the position was worth

$40.00 − $39.96  =  $0.04 per unit
        $0.04 / $40.00  =  0.10%

less than you paid. Nobody was wrong about anything. There was no news.

Then the platform charges you#

Add whatever your platform charges per transaction. At $5 to open and $5 to close, on a $10,000 position, that is

$10 / $10,000  =  0.10%

So a complete round trip — in and out, one decision, no opinion about the market — costs

0.10%  +  0.10%  =  0.20%
                 =  $20.00 on $10,000

We just did this in class: the whole room opened a position and closed it inside fifty minutes. Check your account. The market did not move enough to matter and about $20 is missing per $10,000. Write it in your position log with the side of the quote recorded, because that column is what this week is for.

Now leave it alone for forty years#

Twenty dollars is not interesting. What makes it the second lecture rather than a footnote is that this kind of cost recurs, and recurring costs compound against you exactly the way returns compound for you.

Suppose the total drag on a position is 1% per year — platform fees, spreads on the trades you do make, the small percentage a fund takes. After forty years you are holding

0.99^40  =  0.669

that is, 66.9% of what you would otherwise have had. A third of it is gone. Not to a crash, not to a bad decision, not to anything that appeared in a newspaper. To a number so small that it is usually quoted as a reassurance.

Do it with your own number instead of 1%. If you make four round trips a year at the 0.20% we measured today, your drag is

4 × 0.20%  =  0.80% per year
0.992^40   =  0.725

You keep 72.5%, and 27.5% of the outcome went to the act of transacting. Four trades a year is not active. Most people in this room will do four trades in March.

The part that matters for week 12#

Cost drag is the only failure mode in this course you are certain to realise, which is why it comes second and why it is always available as an answer in Assignment 1. It needs no bad luck, no bad judgement and no market event. It needs you to have opened a position, and you did that last week.

It is also the thinnest answer available, because the diagnosis is a subtraction. The interesting losses need you to have chosen something, and you have not chosen anything yet. Next week you will find out that you did.