Learning outcomes. After watching this video, you will be able to understand the concept of risk aversion. Describe what indifference curves are. Calculate the utility of an investment using the utility function. Utility theory. In this video we will learn about utility theory which later help us answer the question from the last video. Is the 17% additional return appropriate for the 34.29% addition and risk? We start by making two assumptions. One we like more return with less risk. That is we are greedy. Two we are risk averse. But what does it mean to be risk averse? Let me illustrate the idea of risk aversion with an example. Consider the gamble where you flip a coin and are paid 15 if you get a head, and 5 if you get a tail. Assuming that a head and tail are equally likely, each has a probability of 50%. So your expected pay off from this gamble is 0.5 times 15 plus 0.5 times 5 which is equal to 10. The question is, how much would you pay as an entry fee to play this gamble? If you're willing to pay 10, which is the same as the expected pay off. Then you are Risk Neutral. You don't care about the risk of the gamble. If you're willing to pay less than the expected payoff of 10, say 8. Then you are Risk Averse. Here you say, that since the payoff is uncertain, you need some compensation for holding the risk. Hence you're willing to pay less than the expected payoff. The difference in your mind being compensation for bearing the risk of the payoff. If you're willing to pay more than the expected payoff of 10, say 12, then you're a risk lower or Risk Seeker. Here are you're saying that even though the expected payoff is only 10. You like the uncertainty of the risk of the payoff and hence are willing to pay more for it. If you think about it, this kind of behavior is not very common. Going back to our assumptions, we assume that all investors are risk averse. In other words, they demand compensation for bearing risk. Before we answer the question on which of the two investments from the last video is more attractive, you should understand the idea of utility theory. Utility is the happiness a person gets from consuming goods and services. In the case of investments utility is the amount of happiness an investor gets from an investment. What if you have two goods to chose from? How would we measure your happiness? Let's say that the two goods are beer and pizza. The number of beers is on the vertical axis, and the number of pizzas is on the horizontal axis. You feel that you are as happy having ten beers and no pizza. As having five pizzas and no beer. Plug these two points and join them with a straight line. This line is referred to as an Indifference Curve. It shows what different combinations of beer and pizza. Give you the same level of happiness, that is in terms of satisfaction, you are indifferent between all combinations of beer and pizza on the straight line. Returning to the world of investments, we can put expected return of the vertical axis and risk on the horizontal axis. We can then draw multiple indifference curves. As you move towards the top left of the graph, the utility increases. This is referred to as non-satiation. You can always find an indifference curve at the higher utility level by moving towards the top left of the graph. Further note that the indifference curve is not a straight line but a curve. This is because of risk aversion. At low levels of risk, investors are happy with small levels of additional returns. But at higher levels of risk, they demand larger levels of additional risk. We can thus say that more risk of us investors will have steeper indifference curves than less risk of us investors. Investor happiness, or utility may be quantified by using utility functions. We will use what is called a quadratic utility function U is equal to E(r) minus 1/2 times A times sigma squared. Where E(r) is the expected return of the investment. Sigma squared is a variance of its returns, and A is the coefficient of risk aversion. If A is equal to 0 the investor is risk neutral. In other words, there is not one to be compensated for any risk. If A is positive, greater than 0, the investor is risk averse. And if it is negative, less than 0, the investor is a risk lover or a risk seeker. You may verify that this quadratic utility function satisfies our early assumptions on nonsatiation and risk aversion. Next time, we will use the quadratic utility function to help us answer, which of the two investments we saw earlier is better.