Normal distribution, Expected Values and Variance
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I'm having a hard time with a study question and couldn't find any help in my literature or lectures, so I thought I'd ask here.
The problem is as follows:
At the beginning of the month you have $3000 in an asset A (W0 = 3000). Suppose you have an annual return R on the asset which is given by R ~N(0.1,0.5) [meaning R is normally distributed with a mean of 0.1 and a variance of 0.5]. Your wealth at the end of the year is represented by the random variable W1 = W0(1+R). Find E(W1) and VAR(W1).
Here's what I've tried so far:
E[W1] = E[(W0+W0*R)] = W0 + W0*E[R] = 3000 + 3000*0.1 = 3300
VAR(W1) = W0^2*VAR(R) = 3000^2 * 0.5 = 4'500'000.
However, I am not sure if I've failed to incorporate the fact that it is on a yearly basis (i.e 12 months). In previous problems W0 has been at the beginning of a month, and W1 at the end of said month, and this approach has worked.
In advance, thanks for your help.
math distribution economics
asked Nov 21 at 15:43
4penny
93
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show 1 more comment
up vote
-1
down vote
favorite
I'm having a hard time with a study question and couldn't find any help in my literature or lectures, so I thought I'd ask here.
The problem is as follows:
At the beginning of the month you have $3000 in an asset A (W0 = 3000). Suppose you have an annual return R on the asset which is given by R ~N(0.1,0.5) [meaning R is normally distributed with a mean of 0.1 and a variance of 0.5]. Your wealth at the end of the year is represented by the random variable W1 = W0(1+R). Find E(W1) and VAR(W1).
Here's what I've tried so far:
E[W1] = E[(W0+W0*R)] = W0 + W0*E[R] = 3000 + 3000*0.1 = 3300
VAR(W1) = W0^2*VAR(R) = 3000^2 * 0.5 = 4'500'000.
However, I am not sure if I've failed to incorporate the fact that it is on a yearly basis (i.e 12 months). In previous problems W0 has been at the beginning of a month, and W1 at the end of said month, and this approach has worked.
In advance, thanks for your help.
math distribution economics
asked Nov 21 at 15:43
4penny
93
What is the meaning ofR ~N(0.1,0.5)? You should be careful with your question description about those you are asking. You should provide enough information properly.
– Shudipta Sharma
Nov 21 at 16:18
My bad. It means that R is normally distributed with a mean of 0.1 and a variance of 0.5. Updated the post now.
– 4penny
Nov 21 at 16:37
It's common for the second parameter of the normal to be given as the standard deviation, in which case you'd square the 0.5. If it's variance, your answer is correct. Since R was specified as annual return, you don't need to be adjusting anything to discuss wealth after a year.
– pjs
Nov 21 at 16:37
1
Note that this sort of question would be a better match for stats.stackexchange.com
– pjs
Nov 21 at 16:39
@ShudiptaSharma~is common notation in statistics, to the point that it's reasonable to expect that if somebody doesn't know the notation they probably won't be able to answer the question.
– pjs
Nov 21 at 16:49
|
show 1 more comment
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I'm having a hard time with a study question and couldn't find any help in my literature or lectures, so I thought I'd ask here.
The problem is as follows:
At the beginning of the month you have $3000 in an asset A (W0 = 3000). Suppose you have an annual return R on the asset which is given by R ~N(0.1,0.5) [meaning R is normally distributed with a mean of 0.1 and a variance of 0.5]. Your wealth at the end of the year is represented by the random variable W1 = W0(1+R). Find E(W1) and VAR(W1).
Here's what I've tried so far:
E[W1] = E[(W0+W0*R)] = W0 + W0*E[R] = 3000 + 3000*0.1 = 3300
VAR(W1) = W0^2*VAR(R) = 3000^2 * 0.5 = 4'500'000.
However, I am not sure if I've failed to incorporate the fact that it is on a yearly basis (i.e 12 months). In previous problems W0 has been at the beginning of a month, and W1 at the end of said month, and this approach has worked.
In advance, thanks for your help.
math distribution economics
asked Nov 21 at 15:43
4penny
93
I'm having a hard time with a study question and couldn't find any help in my literature or lectures, so I thought I'd ask here.
The problem is as follows:
At the beginning of the month you have $3000 in an asset A (W0 = 3000). Suppose you have an annual return R on the asset which is given by R ~N(0.1,0.5) [meaning R is normally distributed with a mean of 0.1 and a variance of 0.5]. Your wealth at the end of the year is represented by the random variable W1 = W0(1+R). Find E(W1) and VAR(W1).
Here's what I've tried so far:
E[W1] = E[(W0+W0*R)] = W0 + W0*E[R] = 3000 + 3000*0.1 = 3300
VAR(W1) = W0^2*VAR(R) = 3000^2 * 0.5 = 4'500'000.
However, I am not sure if I've failed to incorporate the fact that it is on a yearly basis (i.e 12 months). In previous problems W0 has been at the beginning of a month, and W1 at the end of said month, and this approach has worked.
In advance, thanks for your help.
math distribution economics
math distribution economics
asked Nov 21 at 15:43
4penny
93
asked Nov 21 at 15:43
4penny
93
edited Nov 21 at 16:29
asked Nov 21 at 15:43
4penny
93
asked Nov 21 at 15:43
4penny
93
asked Nov 21 at 15:43
4penny
93
93
What is the meaning ofR ~N(0.1,0.5)? You should be careful with your question description about those you are asking. You should provide enough information properly.
– Shudipta Sharma
Nov 21 at 16:18
My bad. It means that R is normally distributed with a mean of 0.1 and a variance of 0.5. Updated the post now.
– 4penny
Nov 21 at 16:37
It's common for the second parameter of the normal to be given as the standard deviation, in which case you'd square the 0.5. If it's variance, your answer is correct. Since R was specified as annual return, you don't need to be adjusting anything to discuss wealth after a year.
– pjs
Nov 21 at 16:37
1
Note that this sort of question would be a better match for stats.stackexchange.com
– pjs
Nov 21 at 16:39
@ShudiptaSharma~is common notation in statistics, to the point that it's reasonable to expect that if somebody doesn't know the notation they probably won't be able to answer the question.
– pjs
Nov 21 at 16:49
|
show 1 more comment
What is the meaning ofR ~N(0.1,0.5)? You should be careful with your question description about those you are asking. You should provide enough information properly.
– Shudipta Sharma
Nov 21 at 16:18
My bad. It means that R is normally distributed with a mean of 0.1 and a variance of 0.5. Updated the post now.
– 4penny
Nov 21 at 16:37
It's common for the second parameter of the normal to be given as the standard deviation, in which case you'd square the 0.5. If it's variance, your answer is correct. Since R was specified as annual return, you don't need to be adjusting anything to discuss wealth after a year.
– pjs
Nov 21 at 16:37
1
Note that this sort of question would be a better match for stats.stackexchange.com
– pjs
Nov 21 at 16:39
@ShudiptaSharma~is common notation in statistics, to the point that it's reasonable to expect that if somebody doesn't know the notation they probably won't be able to answer the question.
– pjs
Nov 21 at 16:49
What is the meaning of
R ~N(0.1,0.5)? You should be careful with your question description about those you are asking. You should provide enough information properly.– Shudipta Sharma
Nov 21 at 16:18
What is the meaning of
R ~N(0.1,0.5)? You should be careful with your question description about those you are asking. You should provide enough information properly.– Shudipta Sharma
Nov 21 at 16:18
My bad. It means that R is normally distributed with a mean of 0.1 and a variance of 0.5. Updated the post now.
– 4penny
Nov 21 at 16:37
My bad. It means that R is normally distributed with a mean of 0.1 and a variance of 0.5. Updated the post now.
– 4penny
Nov 21 at 16:37
It's common for the second parameter of the normal to be given as the standard deviation, in which case you'd square the 0.5. If it's variance, your answer is correct. Since R was specified as annual return, you don't need to be adjusting anything to discuss wealth after a year.
– pjs
Nov 21 at 16:37
It's common for the second parameter of the normal to be given as the standard deviation, in which case you'd square the 0.5. If it's variance, your answer is correct. Since R was specified as annual return, you don't need to be adjusting anything to discuss wealth after a year.
– pjs
Nov 21 at 16:37
1
1
Note that this sort of question would be a better match for stats.stackexchange.com
– pjs
Nov 21 at 16:39
Note that this sort of question would be a better match for stats.stackexchange.com
– pjs
Nov 21 at 16:39
@ShudiptaSharma
~ is common notation in statistics, to the point that it's reasonable to expect that if somebody doesn't know the notation they probably won't be able to answer the question.– pjs
Nov 21 at 16:49
@ShudiptaSharma
~ is common notation in statistics, to the point that it's reasonable to expect that if somebody doesn't know the notation they probably won't be able to answer the question.– pjs
Nov 21 at 16:49
|
show 1 more comment
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What is the meaning of
R ~N(0.1,0.5)? You should be careful with your question description about those you are asking. You should provide enough information properly.– Shudipta Sharma
Nov 21 at 16:18
My bad. It means that R is normally distributed with a mean of 0.1 and a variance of 0.5. Updated the post now.
– 4penny
Nov 21 at 16:37
It's common for the second parameter of the normal to be given as the standard deviation, in which case you'd square the 0.5. If it's variance, your answer is correct. Since R was specified as annual return, you don't need to be adjusting anything to discuss wealth after a year.
– pjs
Nov 21 at 16:37
1
Note that this sort of question would be a better match for stats.stackexchange.com
– pjs
Nov 21 at 16:39
@ShudiptaSharma
~is common notation in statistics, to the point that it's reasonable to expect that if somebody doesn't know the notation they probably won't be able to answer the question.– pjs
Nov 21 at 16:49