The Costs of Search

Imagine you are selling an old bike on craigslist. You list it for $100. A few days go by, and nobody responds. Finally, somebody sends you a message saying they'll buy it for $90. You'd rather get more, but at the same time you can't count on them waiting, so you have to decide whether or not accept or reject their bid.

In another scenario, you might be trying to buy a bike. If you buy it new at the store this month, you can use a coupon before it expires and/or the store runs out of inventory. But you might be able to get it used on craigslist or Ebay.

In both scenarios, you are presented with a certain trade that may not be optimal. You have to balance several requirements. It's more likely you should accept if you really need the cash/good urgently. You should also accept quickly if it takes a lot of effort to stay in the market or evaluate each deal. On the other hand, you want to wait when you think that you're likely to find a much better deal later. You're also more willing to wait if you don't have to worry about the possibility that you'll never be able to trade at all.

In the Lending Club market, several of these factors come into play. New loans come in and out. The loans stay on the platform for at most 2 weeks, less if they are fully funded before then. You might want to wait to see if other people show interest in the loan, since that could be a sign that it's a good loan. But then you're a step behind them. If you're analyzing loans manually, it takes effort to look at each loan. Doing automated modeling and investing solves these problems.

However, with an automated model you still have the issue of money sitting around un-invested. That is, you have to somehow balance the lost interest against the expected gain of investing in a better loan tomorrow (or next week) versus an ok one today.

Now, while effort and lost interest are both factors causing you to prefer investing sooner than later, they are actually quite different from the perspective of returns of scale.

That is, say in one situation you have $10000 to invest and the other you have $100. If it takes a lot of effort to analyze loans, then you will search more when you have to invest $10000 than when you have to invest $100. A 1% improvement is $100 instead of $1. But if it's no effort, then there's no difference in how you act between the two.

What about lost interest? Since interest is just expressed as a fraction of principal, it doesn't matter whether it's $10000 or $100, right? However, the problem is again the finite nature of the market.

Another example: Let's say you are planning a small outing for 10 people at Las Vegas. You would just have everyone take a bus there and think nothing more of it. If you had to plan for 10000 people, you start to question whether or not there are enough buses going from where you are to Las Vegas in a timely manner.

Now, let's say you expect there to be one good-enough loan per week, with principal around $1000. In this case, the larger investor is at a disadvantage, because the majority of his money is sure to be lying around, whereas the smaller investor can easily make his purchase fully. In stock market terms, we would say that larger traders have a larger market impact. This is a disadvantage for them. There isn't enough supply for their demand (or demand for their supply), so they either have to wait or accept a worse deal.

From an effort perspective, there isn't really a increasing or diminishing returns to scale. That is to say, you'll probably have to look at  roughly 100 times more loans to invest 100 times the money. However, with the perspective of interest lost, size becomes much more annoying due to scale. Taking the above example, if you can only purchase $1000 of loans a week, and you have $10000, the last $1000 will have to wait 10 weeks before it is invested. If you have $100000, you'll have to wait 100 weeks to be fully invested (by that time you'll be almost 2/3 done with your first few loans). The problem basically gets worse at a roughly quadratic rate, whereas the effort problem only gets worse at a linear rate.

The upshot of this is that you should probably have slightly lower standards when initially investing your money if you're putting in a lot at once. Otherwise you'll have a huge backlog. Once you've done that, you can raise your standards when reinvesting; since money is constantly trickling in and out, you won't have to worry about market impact.