What is a Rate of Return?

Hi, we were talking about terminology. I'm going to spend a few minutes on the concept of rate of return. Because remember, and let me draw a timeline for you. So if you draw a timeline We'll have fun together. So we'll draw a timeline 0, 1. Remember, they're points in time, 0 and 1, but there is also a period of time, so that one period has elapsed between 0 and 1. Again, the nature of the problem will define the This is a year, a month, a day, right? There are people called daily traders, right? They trade on every day trying to make money.

So it depends on the nature of the beast and the nature of the problem or the eye of the beholder. So let's define what the rate of return is. Unlike PV and FV, which are at points in time, rate of return is over time. So suppose I have $100.

At time one. And I put it in the bank and after one period the money becomes $102. Okay?

So what has happened? I put in money in the bank at 100 and then your bank says you have 102 after one year has passed. The important thing is it can't be 102 today because somebody's making money for nothing. It's called a free lunch. If you give 100 and get 102 right back, somebody's being silly and believe me a bank won't be silly like that. So time has passed, and you get 102 back. What is the return? A return is a very intuitive concept. In fact when I say it in class, almost everybody nods and says, of course it's that. Turns out, return is 102, which is what?

The value in the future minus 100, which is the value of what you've invested, divided by the initial amount. And it turns out to be 2%. So that's the notion of a return. I want to emphasize it because we are a beginners class. So I don't want to presume anything. I hope this has helped you. Right now we've kept it only to one period, and we'll stick with that simply because I want things to build on themselves, rather than frustrate you with too much complexity, okay? Whenever complexity comes, it will be due to the real world, not because I'm trying to make it complex for you. So let me share an insight with you, and then we'll talk about it.

The main insight is a dollar today is worth more than a dollar tomorrow. And this will be seen everywhere. What's the point I'm making here? It's that if I were to give you, say one dollar today, and then I said wait a second, actually I won't give you a dollar today, I'll give you a dollar one year from now, which one would you prefer? And let's go though this very simple exercise together. But think about it for a minute and then we come and do it together.