I mentioned a moment ago that I'm a professor here at the Wharton School and it's interesting to be a professor of finance because a lot of the founding fathers and mothers of the field are still with us. In fact, the original founding father of the field is still with us. His name is Harry Markowitz. He's in his 90s now and he essentially invented this whole field of finance and portfolio theory as a graduate student in Chicago back in the early fifties. Then he won the Nobel Prize for this work in 1990 and he still added. I say if you go Google Harry Markowitz you'll see he's still working this area, he's working in this area of Robo-Advising. So I want to talk about what it is that Dr. Markowitz did and how it is essentially what you will find now under the hood of a robo-advising app and his insights from the 50s are exactly the insights we're using today and you see they're all about how if you want to invest for an expected return you're going to have to bear some risk. You're going to have to bear some risk. You'd like to do it without risk but that's magical thinking. We are not doing magical thinking. Now, Harry Potter doesn't have to worry about his retirement plan. But we do know magical thinking for us and when you, so you're vesting for return, you have to worry about how much risk you're taking and what Dr. Markowitz showed was how to take the least risk for the expected return that you are targeting. That is the sort of special sauce of what robo advising is bringing to the client. Now that you're going to get somewhere with no risk or even necessarily going to get right where you want. Because that's the essence of risk that things can happen and you're taking a risk except that. But at least you can take the least risk necessary for your expected return goals. So to understand what Dr. Markowitz did back in the 50s, I need start with the fundamental precepts or axioms of economics especially, as they relate to investing. There's basically two precepts. I don't think you're going to find two controversial. One of them is simply that people always prefer more to less. I don't think I'm going out on a limb there, that people prefer more to less. So you've got that people prefer more to less and then the other one which is going to give us more of the excitement is that, yes people prefer more to less but they get decreasing amount of utility out of the next dollar, the more wealthy they get. So if you have a million bucks, the enjoyment you get out of another dollar, the million first dollar isn't as much as if you only had 1000 bucks. You have 1000 bucks give another dollar, you get more enjoyment out of that. So you always enjoy another dollar but you enjoy that extra dollar at decreasing amount as you have more and more. So if you were to draw a picture where on this axis is how much money you have and then on this axis is how much utility, how much enjoyment you get out of that money, the line is going to go up but it's going to go up at this decreasing rate and mathematician would say it's a concave function. Those of you who took economics in college will certainly remember that. This just picture of utility curve which has this curve to it. It's curving down but it's never going downwards. You've never have so much money of giving more actually less happy. It's going up at a decreasing rate. So just with those two, I think not controversial precepts, let's see what you can get out of it. Well, the main thing you get out of it for our purposes here, is that people are going to be risk averse. By which I mean that for generally speaking are not going to want to take a risk everything else equal. So as a thought experiment, imagine someone offered you, "Hey, I'm given you a choice. You can just- I can give you 1000 bucks, for sure 1000 bucks or we can make it a gamble. So a gamble so that I flip the coin and if it comes up heads I'm going to give you 2,000 bucks. But if it comes up tails you get nothing." So it's the same expected value. Either way the expected amount I'm giving you is a 1000 bucks. But with that gamble, it's either zero or 2,000. So if you're risk averse you'd say, "Well, just give me the 1000 bucks. I don't want to take the gamble with the same expectation just give me the 1000 bucks." You can see that's going to come straight out of that utility curve, with that bend to it. You're going to want just a 1000 bucks and not the bet. Because for the simple reason that you get more out of the first thousand than out of the second thousand. because here is a decreasing utility, more out of the first thousand than the second thousand. So you're really not going to want to take that bet to risk losing the first thousand for the chance of getting the second thousand. You're not going to want to do that. So we would call that risk averse. By the way, we can be even a little more precise about this and maybe we'll get back to this when we talk later about how robo-advisors customize. If I want to know how risk averse you are, I can learn about that by asking you questions like this. I could say, "So you don't- if between 1,000 bucks and this gamble of zero, 2,000 you want the 1,000. Well, what if it's not a thousand What if it's 990? Do you want 990 more than the zero or 2,000? You do have a 980. How about 970?" So I could just sort of go down to the point we say way, stop. You'd rather, you're happy. You're ambivalent between getting 970 bucks or zero and 2,000. So there's essentially, there's this difference there. This 970 what we would call your certainty equivalent. That's an economist would call it. So there's a three percent discount from the 1,000 that it's actually worth and the 970 it's worth to you because of your risk aversion. That three percent difference is an important number. It tells me how risk averse you are. If you'd said, Not 970 but 940. Then, that's more risk averse and that's information that I can use to customize my portfolio suggestion for you. [inaudible] I will give you something that's a little less risky for your money if you said 940 versus 970. So we can get back to that. So the key point for now, is that people are generally going to be risk averse. So just following up on that thought, when you think about choosing a portfolio for risk averse people, then one thing you could say right away is that, Well, everyone likes more expected return but they want less risk. One way you can sort of be more formal than say, "For a given expected return you would want to have the lowest risk. " Or putting another way, "For a given risk you want to have the highest expected return." That's going to be the challenge for a robo-advising app. How do you think about that? How do you think about for a given expected return what would be the lowest risk for which you could achieve that and for a given risk what's the highest expected return you can get?. So in our next lecture, we will look at how Dr. Markowitz looked at this problem of minimizing risk for expected return and how it is that robo advisors are going to bring this to bear for their clients.