0:01

Hello, welcome back.

Â In the last lecture, we talked about preferences, to describe how individuals,

Â households or firms evaluate trade-offs when they are faced with choices.

Â We talked about how a utility function can be used to represent those preferences and

Â measure the decision makers level of satisfaction.

Â Now an important dimension of decision making in finance and

Â economics however is uncertainty.

Â There's probably no decision in economics that does not involve risk,

Â so how do you feel about risk for example?

Â Well, if your like most people, you probably don't like risk that much.

Â In fact, studies of human behavior faced with risk,

Â strongly suggest that human beings are risk averse.

Â We're risk averse, we don't typically like risk that much, so for

Â example, most households will want to ensure their assets.

Â If an actuarial fair insurance is offered to them or

Â most investors will not want to purchase risk assets if they are not

Â delivered an expected return that is larger than the risk re-rate.

Â So when we think about the optimal portfolio choice problem,

Â we assume that investors are risk averse.

Â In this lecture, we're going to talk about what this means,

Â how we describe risk aversion?

Â 1:37

As human beings, we all come with different genes and

Â preferences, and that also goes for attitudes towards risk.

Â Therefore, risk averse is key dimension of how we describe preferences and

Â how we might construct.

Â 1:53

Individuals with a high degree of risk aversions

Â will value safety at a high price while others may not.

Â So somebody with a high risk aversion will be reluctant to

Â face a situation with a risky outcome and

Â she might be willing to pay a high insurance premium to avoid that risk.

Â Or alternatively, a risk adverse individual will require to

Â be compensated If she needs to bear that risk.

Â So let me illustrate this point graphically,

Â we're we are rescuers we don't like risk, right?

Â That means we prefer the sure outcome instead of the uncertain outcome the bird

Â and the hand.

Â Let me illustrate this with the picture for you, okay?

Â So let suppose that we have the following utility function again I have.

Â The Y-axis here, right that gives the level of duty and

Â the X-axis wherever outcomes are, all right?

Â And suppose there are two outcomes, X and Y and

Â let suppose you took the function look something like this, right?

Â Which means that X gives me,

Â this level of utility, you have X, right?

Â And Y gives me, right?

Â 3:14

Your Y, right?

Â And suppose that they each outcome happens with equal probability, right?

Â Health and health, right?

Â So what is your expected utility?

Â Well, clearly, it's one-half times U of X, right?

Â The level of utility you get from X, plus one-half times U of Y, right?

Â Where is that on the graph?

Â Well, it's going to lie on this diagonal line

Â 3:45

I am a terrible drawer, sorry,

Â which is going to be halfway at the midpoint of tis diagonal line.

Â All right, so that is the, let me point this,

Â this is one-half u of x plus one-half u of y.

Â Now, what if you were getting the expected

Â outcome for certain, for sure.

Â What is the expected outcome?

Â Well, it's going to be the midpoint here one-half X plus one-half Y.

Â What if instead of having that app insert an outcome you were given that for

Â sure outcome.

Â What would your utility level be?

Â Well, you would be getting this much more utility,

Â so in fact, you would be getting a higher

Â utility from that certain outcome, right?

Â This is U of one-half x plus one-half Y,

Â which is going to be greater, right?

Â How much more utility you get, defines how risk averse you are, right?

Â Individuals who are risk averse will get a much higher utility

Â out of getting that sure outcome, all right.

Â And what determines that, well graphically you can see that it's that concavity of

Â the line that's the difference between that yellow and blue point.

Â Which tells us how much more you value the sure outcome, so

Â the more risk averse the investor, the more she wants the sure outcome.

Â In other words, the more concave is the acuity function,

Â the more risk averse is the investor.

Â 5:40

So how do we measure an individual's degree of risk aversion?

Â Do you know what your risk aversion coefficient is?

Â Of course, I don't expect you to just rattle a number but we can estimate.

Â Risk aversion indirectly, right?

Â So, suppose I gave you the following lottery, right?

Â So suppose you can win $1,000 with 50% probability,

Â or win $500 with 50% probability.

Â That is, you get $500 for sure but

Â you also have the possibility of winning $1,000.

Â 6:39

Doesn't want to take the lottery at all.

Â On the other hand, if you're willing to pay the fair value of the lottery,

Â 750, right?

Â 50% times 1,000, a 50% times 500 which gives you 750, then you are risk neutral.

Â You have a risk aversion coefficient of 0.

Â Now most people are willing to pay somewhere

Â between 540 to a little over 700,

Â all right, to enter this lottery.

Â So that says that most individuals have risk aversions between 1 and

Â 10, 10 being really really rare.

Â Now, where is this coming from?

Â This comes from a large body of experiments and survey evidence.

Â 7:35

If you're familiar with this show, the stakes on this show are very high and

Â only the winning player gets to return back to the show.

Â So thereâ€™s a lot of pressure and

Â furthermore the participants are very smart so

Â you can't say that they are not that they don't know what they're doing, right?

Â And the study finds that the risk aversion levels that

Â they find are fairly low, near risk neutrality.

Â Now in the financial world, financial advisers often use

Â questionnaires to try to infer risk aversions of their clients.

Â 8:18

Risk aversion is the notion that in face of uncertainty or

Â risk, human beings, we are, generally averse to risk.

Â That is, faced with two alternatives, we will prefer the one with less risk

Â