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In this short video. Were going to pick up with the concept of risk risk aversion and then look at an application. So when i talk about what it to be risk averse and were going to look at an application that guides us into what a risk.

Averse investor would do what kind of choices would a risk. Averse investor. Make so recall with risk aversion.

We assume that people are risk. Averse. This is a basic assumption you see in economics and finance.

Thats used to guide and predict human behavior. What this means is that people do not like risk all else equal. So if you hold every other factor.

Equal an investment people would always choose the one with lower risk of course not everything else is equal. Which can make things more complicated. But this all else equal is important because if the reward is there people will take a risk so risk.

Averse investors will take risk for a higher expected return if they think the higher expected return is sufficient to compensate them for what they dont like. Which is risk. So risk aversion is also alternatively described as risk requires compensation investors take on additional risk in other words additional uncertainty over their actual returns.

If theyre compensated by a higher expected return if they expect in the long run. They might be better off by taking the risk then theyll take the risk again. I want to emphasize that risk aversion doesnt mean people do not take risk people take risks.

All the time people dont just use safe investments. They use risky. Investments.

That doesnt mean theyre not risk. Averse. Risk.

Aversion. Means. That people dont take uncompensated risks.

Right risk aversion means. That theres a risk return trade off that riskier assets have to carry a higher expected return if they dont people wont take on that risk so it means. Theres a trade off between risk and return.

It does not mean that people avoid risk. Alternatively. Risk.

Aversion is also going to mean that people pay to avoid risk. That the whole idea of insurance. So for example property or renters insurance.

Means that people pay a premium to avoid the financial risk of losing their possessions suddenly in a fire or theft or some other type of incident. Like that people pay to avoid certain risks because were risk averse and so were better off. If we can get someone else to bear that risk depending on the price.

So. Call. The risk.

A premium is a higher expected return that compensates the buyer for taking the risk risk requires compensation. We call that compensation. A risk premium.

So for example if a risk premium is the yield on us treasury bonds. They tend to be lower than the yield on corporate bonds. Why because the corporate bonds have a higher risk of default and they compensate investors for that higher risk by offering a higher yield.

So they can be attractive related to the concept of risk. Aversion. Is risk neutrality.

A risk neutral investor. Would only care about expected return and not the risk. That surrounds the return so the fundamental uncertainty of the return doesnt bother a risk neutral investor.

Theyre just concerned about the expected return risk. Neutrality. Is a concept investors just arent risk neutral.

We see nothing in investor behavior. That would suggest that investors are risk neutral. So heres a simple example and then well do one thats a bit more complicated so consider the coin flip game.

And so consider a plane flip game where heads you get zero dollars tails. You get two im sorry tails. You get 100.

So the expected value of this coin flip game 50 on 0 50. Probability of 100. The expected value of this point flipped game is 50.

So suppose i give you the choice of playing this game. Or i say forget the game. And ill just give you 50 well youre not indifferent between that a risk.

Averse investor. Would always take the 50 50. Certain is better than a risk of not getting anything a risk neutral investor.

Really wouldnt care between the claimed flip game. And the 50 upfront so this kind of a difference between risk averse and risk neutral. So.

Now. Lets take a look at a more complicated.

Example so here. Im going to have three investments and each investment. Im giving the return structure the possible returns and the probability of each of these returns.

I also gone ahead and calculated the standard deviation of each of these investments below so notice investment. Three is actually certain its a risk free investment 2. Return absolutely certain.

Which means. It has a standard deviation of zero. Theres no variability in return investment to two possible returns each with equal probability.

Which implies a certain standard deviation investment three theres investment. One there are three possible returns probability structure standard deviation. So i have three questions here and well take each one in turn.

Well try and answer each one in turn. Here. So we want to look at this investment structure.

And say. Which investment would be preferred by a risk. Averse.

Investor or can we even say. Which one they would choose can we eliminate any of these three investments that would be chosen by a risk. Averse investor.

In other words. Given this choice. Do we know what they will not choose.

And then finally lets think about what a risk neutral investor might prefer so the first step to answer any of those three questions is to calculate the expected return on each of the three investments. So lets do that now so investment. One had three possible returns minus 2.

6. And 10. And theres the associated probability within each of those returns.

We get an expected return of four percent investment. Two has two possible returns minus 5. 12.

Equal probability that gives us an expected return of three and a half percent and then finally investment. Three is certain there was a certain return of 2. So the expected return is 2.

So we have the expected returns and now im going to go back to that table. And so well compare the expected return and the standard deviation for each of the three investments. So heres my revised table.

I have three investments with this expected returns and the associated standard deviation. So lets go back to the first of the three questions. I asked can we say for certain which investment would be preferred by a risk.

Averse investor. Yes or no and why well this is the highest expected return. But it also has a higher standard deviation than investment three.

So if we just look at investment one in three for a moment while investment one promises a higher expected return that return is uncertain investment three has a lower return. But its giving you no risk so the answer here is really no we cant actually look at these three investments and pick out the one that all risk averse investors would definitely want while investment. One has the highest expected return it has more risk than investment.

Three is this enough compensation for the risk. If we dont know for some risk. Averse investors theyll take investment one theyll say the risk is compensated and ill go this way.

Other cautious investors might say you know what that extra expected return isnt worth it to take that kind of risk. I dont want to and theyll stick with investment three. Well what about investment two well that brings us to the second bulleted question.

We talked about can we say for certain. Which investment would not be chosen by a risk. Averse investor.

The answer here is yes. And its going to be investment. Two and lets think about why well investment.

Two here has a lower expected return than investment one three and a half percent lower than four percent. But at the same time here in this example. Ive set up investment two has a significant gently higher standard deviation so less reward more risk well who would want that well no one so investment to with a lower expected return and higher risk is clearly inferior to investment one a risk.

Averse investor. Would never choose investment to over investment wine. Given.

The choice between these two rescue. A risk. Averse investor will never choose investment to finally last.

Question is can we say for certain what a risk neutral investor. Would do well recall a risk. Neutral.

Investor. Isnt really concerned about the risk of the return. Theyre just concerned about the overall return.

So here a risk neutral investor would actually choose investment one. Because it has the highest expected return in reality. Investors are risk.

Averse and they would be looking more carefully at the risk return trade off. .

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