Stupid Stats!

[Nutdotnet]

I thought I was done with stats a couple of years ago. My instructor loves to give a very vague example and then on our HW give us something that is much more difficult. I know there are a couple stat, finance, or econ guys/gals that can give me a hand.

Alright-

Single loan. Probability of default is .02. If borrower defaults return to lender is zero. If borrower does not default the return to the lender is .12.

Expected return is- .0976 (9.76%)
Standard Deviation is- .1568 (15.68%)

"Assuming that the probability distribution of possible returns is normally distributed, what is the probability that this single loan will have a negative return?

I know the formula is:

Z= ((x - mean)/std dev). What's the mean? What's x? Maybe I'm way off base.

Here are the four possibilities:
0
0.168
0.268
0.368

Thanks in advance!

 

[Mo0o]

War of 1812

 

[Nutdotnet]

That was a pretty lame effort @ being funny. 😉

 

[nick1985]

yes its the stats that are stupid...

 

[Aquaman]

THe answer is always 47 or C 🙂

Cheers,
Aquaman

 

[Nutdotnet]

Originally posted by: nick1985
yes its the stats that are stupid...

No, I'm the one who can't remember how to do this stuff, but considering the last time I used it was two years ago it's understandable. I'm sure someone here can do this in two seconds...

 

[Nutdotnet]

Come on now, there's no need to crap in my thread asking for help just to pad your post count.

 

[welst10]

Rephrase your question to be more precise. You can't even state a questiion clearly. How can you expected an answer. So when the borrower defaults, the return to leader is how much?

 

[Nutdotnet]

Originally posted by: welst10
Rephrase your question to be more precise. You can't even state a questiion clearly. How can you expected an answer. So when the borrower defaults, the return to leader is how much?

More precise...hmm, when the borrower defaults, the lender gets nothing. I stated, "if the borrower defaults, all is lost". Sorry. It's a fairly straighforward question, I don't know how much more precise I need to be.

I need to find the probability that the return is going to be negative.

Heck, here are the four possibilities:

0
0.168
0.268
0.368

 

[iamme]

just to clarify:

"Now, I need to find the probability that this loan will have a negative return."

do you mean, you need to find the probabilty that the loan will default (i.e. 0 return)?

 

[Nutdotnet]

Originally posted by: iamme
just to clarify:

"Now, I need to find the probability that this loan will have a negative return."

do you mean, you need to find the probabilty that the loan will default (i.e. 0 return)?

Yeah, I think so. The question from my instructor is pretty vague, that's most likely why my question to y'all is vague. But I assume that since this is a single loan, it will either be paid back or it won't. So yeah, the probability that the loan will default.

 

[iamme]

Originally posted by: Nutdotnet

Originally posted by: iamme
just to clarify:

"Now, I need to find the probability that this loan will have a negative return."

do you mean, you need to find the probabilty that the loan will default (i.e. 0 return)?

Yeah, I think so. The question from my instructor is pretty vague, that's most likely why my question to y'all is vague. But I assume that since this is a single loan, it will either be paid back or it won't. So yeah, the probability that the loan will default.

that's why it's confusing.....the problem already states that the probabilty of default is 0.02.

if the default and non-default are the only two options, then:

default = 0.02
non-default = 0.98

(0.02 + 0.98 = 1)

 

[Nutdotnet]

Originally posted by: iamme

Originally posted by: Nutdotnet

Originally posted by: iamme
just to clarify:

"Now, I need to find the probability that this loan will have a negative return."

do you mean, you need to find the probabilty that the loan will default (i.e. 0 return)?

Yeah, I think so. The question from my instructor is pretty vague, that's most likely why my question to y'all is vague. But I assume that since this is a single loan, it will either be paid back or it won't. So yeah, the probability that the loan will default.

that's why it's confusing.....the problem already states that the probabilty of default is 0.02.

if the default and non-default are the only two options, then:

default = 0.02
non-default = 0.98

(0.02 + 0.98 = 1)

Right...I didn't see that. Regardless, I guess that isn't the question. Let me post the question-

"Assuming that the probability distribution of possible returns is normally distributed, what is the probability that this single loan will have a negative return? (There are only 3 decimal places in each possible answer, because the table of normal probabilities that I use only has this many decimal places.)"

 

[welst10]

Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

 

[iamme]

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

 

[welst10]

Originally posted by: iamme

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

I know that. The problem is that he is contradicting. In the first paragraph he said there are only 2 values of return (0 if borrower defaults; 0.12 if he does not), then he said it's normally distributed.

 

[Nutdotnet]

Originally posted by: iamme

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

I wish there were, unfortunately no.

I have-

Probability of Loan Default- 2%
Lender loses funds if borrower defaults
Return to lender if borrower does not default- 12%

Expected return- 9.76% = (0.98*0.12)+0.02*(-100%)
Standard Deviation- 15.68% = Sq Rt. of - (0.98)*(0.12-0.0976)^2+(0.02)*(-1-0.0976)^2

 

[Nutdotnet]

Originally posted by: welst10

Originally posted by: iamme

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

I know that. The problem is that he is contradicting. In the first paragraph he said there are only 2 values of return (0 if borrower defaults; 0.12 if he does not), then he said it's normally distributed.

I'm repeating what is in the assignment.


Assume that the probability of a borrower defaulting on a loan is 0.02. If the borrower defaults, the lender loses the entire amount of funds loaned. If the borrower does not default, the return to the lender will be 0.12.

 

[welst10]

Originally posted by: Nutdotnet

Originally posted by: iamme

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

I wish there were, unfortunately no.

I have-

Probability of Loan Default- 2%
Lender loses funds if borrower defaults
Return to lender if borrower does not default- 12%

Expected return- 9.76% = (0.98*0.12)+0.02*(-100%)
Standard Deviation- 15.68% = Sq Rt. of - (0.98)*(0.12-0.0976)^2+(0.02)*(-1-0.0976)^2

So when borrower defaults, the return is NOT zero (like you said), it's -1.00. In that case, the probably of negative return is 0.02.

 

[iamme]

Originally posted by: welst10

Originally posted by: iamme

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

I know that. The problem is that he is contradicting. In the first paragraph he said there are only 2 values of return (0 if borrower defaults; 0.12 if he does not), then he said it's normally distributed.

i agree, that this is worded funny.....the expected return is 0.0976, could that be the mean?

 

[iamme]

Originally posted by: welst10

Originally posted by: Nutdotnet

I wish there were, unfortunately no.

I have-

Probability of Loan Default- 2%
Lender loses funds if borrower defaults
Return to lender if borrower does not default- 12%

Expected return- 9.76% = (0.98*0.12)+0.02*(-100%)
Standard Deviation- 15.68% = Sq Rt. of - (0.98)*(0.12-0.0976)^2+(0.02)*(-1-0.0976)^2

So when borrower defaults, the return is NOT zero (like you said), it's -1.00. In that case, the probably of negative return is 0.02.

yeah, that's incosistent. Nutdotnet, i think you need to scan the actual page 😛

 

[maziwanka]

you want the p(x<0). so the z statistic you seek has x=0, mean=expectation, and you have the SD. go from there.

 

[Nutdotnet]

Originally posted by: welst10

Originally posted by: Nutdotnet

Originally posted by: iamme

Originally posted by: welst10
Your question is strange as stated right now.

So if the return is a discrete variable that can take 2 values (0 or 0.12). The probably of negative return is of course 0.

well it was stated that it's a normal distribution, which implies that it's continuous, not discrete.

are there anymore numbers available?

I wish there were, unfortunately no.

I have-

Probability of Loan Default- 2%
Lender loses funds if borrower defaults
Return to lender if borrower does not default- 12%

Expected return- 9.76% = (0.98*0.12)+0.02*(-100%)
Standard Deviation- 15.68% = Sq Rt. of - (0.98)*(0.12-0.0976)^2+(0.02)*(-1-0.0976)^2

So when borrower defaults, the return is NOT zero (like you said), it's -1.00. In that case, the probably of negative return is 0.02.

Well, yes and no. The lender does not receive his money back, so the return IS zero (the return from the borrower). The lender loses all funds lent.

And no, the probability is not .02. The probability of default is .02.

It's either-

0
0.168
0.268
0.368

These are the choices.

 

[iamme]

ok, i got the answer.....it's 0.268

i'll post the work in a sec.

Originally posted by: maziwanka
you want the p(x<0). so the z statistic you seek has x=0, mean=expectation, and you have the SD. go from there.

that's correct. try drawing the distribution.

it's a function of return, with mean = 0.0976 (the peak of the curve)

0 is a value (X) to the left of the mean.

 

[Nutdotnet]

Originally posted by: maziwanka
you want the p(x<0). so the z statistic you seek has x=0, mean=expectation, and you have the SD. go from there.

Ahh..

So would it be this?-

z = ((0-.976)/.1568)

which would give me- -0.62244898 for Z

Probability would be- 0.266823281