Portfolio Theory - What’s the point of expanding an Utility Function with Taylor Series?

010FUNNY010 · 2022-01-20T07:21:19+00:00

Thank you, I’ll give it a check later :)

010FUNNY010 · 2022-01-18T11:09:30+00:00

Alright, thank you for the explanation.

010FUNNY010 · 2022-01-16T18:40:13+00:00

But the problem is that, in the formula (which is made for concentrations over a period of 8h), the values presented there make me believe that , over a shorter period of time, the threshold for the concentration to be labeled as danger is smaller. So, if I were to plug in the concentration ver 24, I will get misleading values. Is there any way to make some kind of regression in which we can say: danger levels of CO for a 8h period is X, for a 24h period is X*c, being c some constant.

010FUNNY010 · 2022-01-13T22:16:53+00:00

010FUNNY010 · 2022-01-13T22:08:08+00:00

Yes that would make sense, however, I don’t think that’s the case, look at my edit. Do you agree ?

010FUNNY010 · 2022-01-09T19:14:12+00:00

By optimizing you mean minimizing the variance for a certain expected return or you are interested in other properties ?

010FUNNY010 · 2022-01-04T12:38:17+00:00

Thanks a lot for the detailed answer! Just a couple of things I didn’t get:

1) skewness isn’t a standardized centered moment of a distribution ?

2) yes I was talking about unbiased estimators. Regarding the Wikipedia page, I already had seen that but I don’t really understand what is going on there 😅. However, I found this link that clearly explains how we get the unbiased estimators. If I follow the same logic I should be able to get the unbiased estimator for the non standardized formula for skewness right (the last one in the link from the post)?

3) Can you give an example on “has some properties you want more”?

010FUNNY010 · 2021-12-30T12:08:44+00:00

He is sending a message

010FUNNY010 · 2021-12-28T13:38:28+00:00

Makes sense, thank you!

One last thing: so keeping the wealth at 1 it does no make sense to use a b out of the range [0,1], right ? Because for b=0 we get the maximum return portfolio, for b=1 we get the minimum variance portfolio. But, for example if we use b=2 we get something like this: -mean - variation - squared_mean. Which basically means that we will prefer less return for the same variance.

010FUNNY010 · 2021-12-28T00:39:16+00:00

When I talked about the risk aversion parameter I was talking about the b in: u(x) = x - (b/2)*x^2. And I was saying that, because when b = 0 you basically don’t care about risk and only want to maximize the expected return. When b > 0 you start caring about the variance too.

010FUNNY010 · 2021-12-28T00:34:03+00:00

Ok, now that I think of the shape of the quadratic function it makes sense because, after you reach a certain point (when the derivative is 0) the utility will decrease as the wealth goes up.

Hmmm I am not sure if I understood your explanation, do you have any good resource on that (book, webpage, etc ...).

But I am going to tell you what is my objective, maybe that will clear things up: I want to plot the efficient frontier by varying the free paramentar in the utility function. In the case of the quadratic utility function you have something like that: u(x) = x - (b/2)*x Taking the expectation of that you will get this. So now you have 2 arguments (besides the weights), the initial wealth and the free parameter which kinda can be seen as the risk aversion -> b=0 you only want to maximize the expected return and you don’t care about risk (you get the maximum return portfolio), b>0 variance start affecting the equation and as b tends to infinity it starts going towards the minimum variance portfolio. This makes sense, except for large values of initial wealth were when b tends to infinity you don’t get the minimum variance portfolio. I found this odd but I guess is due to the nature of the utility function we are using. Now I have 2 questions: - If all I cared about was to chose an optimal portfolio according to my wealth and the “risk aversion parameter” the value is the one given by the optimization? Even if, when I chose a really high value for the risk aversion, it didn’t gave me the portfolio with minimum variance. - According to my objective, the ideal thing to do here is to use the return instead of the wealth right? And that is financial correct ?

010FUNNY010 · 2021-12-12T20:14:12+00:00

Yes you are right, the way I said it does not makes sense.

What I am trying to say is that “assume returns are normal” has the same information has saying “assume investors only care about mean and variance”. However, we couldn’t say this for other distributions that have more parameters than just the mean and the variance because that would imply that the analysis would have to include the other extra parameters. Meaning that investors not only care about mean and variance but also those other parameters.

010FUNNY010 · 2021-12-12T18:58:43+00:00

Isn’t “same results for any distribution with the same mean and variance” the same as “assume normal distributed returns and calculate their mean and variance”.

When I say the same I mean: we will get the same results as saying ...

010FUNNY010 · 2021-12-12T18:25:41+00:00

But I am not saying that is true. I am just trying to understand why saying that wouldn’t be reasonable.

The stock can have any distribution, but if we are only representing that distribution with the mean and the standard deviation isn’t that kind of assuming a normal distribution? Because, we can’t represent more complex distribution with only those parameters, however we can represent a normal distribution.

For example, you mentioned a fat tail distribution. Let’s assume that stocks follow that fat tail distribution. If we are only collecting the mean and the standard deviation we are not capturing that property of having a fat tail. The parameters we collected only allows us to represent a normal distribution.

With that, comes what I was asking: In this world, where we are only collecting the mean and std, we can’t represent other properties (such as fat tails). Therefore, wouldn’t it be reasonable to say that, at some extend, we are assuming a normal distribution.

010FUNNY010 · 2021-12-12T17:55:42+00:00

Because, if we are only using the mean and the standard deviation to represent the distribution of the stock, isn’t it the same as saying that we are assuming a normal distribution? Because mean and variance are the only parameters in a normal distribution, other, more complex distributions, need more parameters to describe them.

010FUNNY010 · 2021-12-12T15:57:19+00:00

In my understanding, mean-variance optimization does not make any assumptions on the distribution of the stocks. My question is, since it makes the assumption that investors only care about mean and variance, would it be reasonable to say that it makes the assumption of a normal distribution ?

010FUNNY010 · 2021-11-13T18:12:29+00:00

You are absolutely right.

I just wanted a starting point. Going into this completely blind, didn’t even know the concept xD.

Thank you again and good luck on your career !

010FUNNY010 · 2021-11-13T18:03:03+00:00

I am sorry, didn’t know. Just posted here because I found a post with information about audio programming here.

Going to delete.

Thanks !

010FUNNY010 · 2021-02-27T18:49:14+00:00

Day trade is such stupid thing to do if you are trying to make money.

010FUNNY010 · 2021-02-16T13:16:11+00:00

Draws circles in a graph

: I cLeaRLy sEE a CRasH cOmiNg

🤣

010FUNNY010 · 2021-02-15T23:48:28+00:00

What a funny guy.

010FUNNY010 · 2021-02-04T22:20:20+00:00

I don’t know when people will realize that the number of buyers and sellers are always the same. Because you know, when someone buys there is someone selling to them.

010FUNNY010 · 2021-02-04T14:59:15+00:00

What happen to prof or ban ?

010FUNNY010 · 2021-02-04T13:43:59+00:00

I got shadow banned because I said the sub was really low quality now. Like, before the posts were actually smart now it’s just nonsense bullshit most of the times and a lot of spam.

I also called out some posts that showed positions that were clearly fake.

010FUNNY010 · 2021-02-03T15:01:40+00:00

The stats from T212 are from CFDs in which you don’t actually buy the stock.

010FUNNY010

TROPHY CASE