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View Full Version : Exam 6 - Question 2 - Covariance = 0.93% ??

Toronto
05-11-2002, 12:29 PM
I think this is an error.

mr.c
05-11-2002, 02:28 PM
I was suspicious as soon as I saw that in the read-through. I was pretty careful throughout the rest of the problem and still got two unlikely answers. Are you going to notify the Society, Toronto?

EdFrog
05-11-2002, 03:11 PM
I think this is an error.
Why do you think this is an error? It seems reasonable to me...

Axsuetarian
05-11-2002, 03:15 PM

exactuary
05-11-2002, 03:55 PM
I think this is an error.
Why do you think this is an error? It seems reasonable to me...

Covariance of .93 or 93% seems a lot more reasonable than 0.93%.

But I wasn't there, what do I know. Can somebody outline the question?

FoxtrotFool
05-11-2002, 04:31 PM
It was two securities, and the cov of the two variance is 93%.

I think it is very reasonable. I would be a bit surprised if the corrolation is 93%. But since cov = s.d.(1)*s.d.(2)*corr, and I think sd1 is 13 and sd2 is 20, cov of 93 is definitely within reason.

Axsuetarian
05-11-2002, 04:38 PM
no, the covariance was listed in the question as 0.93%...it is unreasonable, but that what was given in the question

Fartmanistan
05-11-2002, 04:48 PM
First of all, the covariance was not 93% but like the title of the thread indicates it was .93% or .0093.

I had the same issue and was confused by it in the exam. The interpretations are either that it was an error and that was supposed to be the correlation coefficient or it really was intended to be .93% and the result would imply that due to the lack of covariance, an optimal portfolio would be one in which borrowing was allowed at the risk free rate and thus 100+% and 200+% were the correct answers. This last piece was pointed out to me by a coworker after the exam. I don't believe the exam ever indicated that borrowing was or was not allowed and so an idea answer would include that assuming borrowing is allowed the y* were indeed above 100% and 0% would be invested in risk-free. It was a lot of work just to get to that point though and so I'm thinking it's the difference between a 9 and 10 on the question - no big loss unless I get a 5.

bb
05-11-2002, 05:22 PM
What Utility function did you use?

BigMactuary,
05-11-2002, 06:48 PM
I did not get 100%+ and 200%+.

I made the assumption that U = E(r) - .005A sigma-squared.

Using A = 4, I got a percentage in the 50s I guess. Only with A = 2, my percentage exceeded 100% and I assumed borrowing was allowed.

However, now I am not too sure if by mistake I used .93 and not .93%. But I think my procedure was correct and I jotted down all the assumptions I made and formulas I used. So I am hoping a passing grade on this question.

EdFrog
05-11-2002, 06:56 PM
Just think about the formula for covariance, and plug in some sample numbers. Then compare your answer to what was given in the exam problem, and check for reasonableness.

Retired Bookworm
05-11-2002, 07:29 PM
Fortunately I don't think anyone needs to say a thing... the poor guy who's got to read all our answers is going to see any misprints a few hundred/thousand times.

I recall getting answers in the 10-20% range using the .93%. What I dont recall, is if I correctly used whole numbers for the deviations, by using the util equation with the .005. I can see any small error like that changing the results by factors of ten.

05-12-2002, 12:51 AM
hey, I blew it, too. But it's only a part of the points. I'll bet it's possible to get a 10 on the question after missing that part.

mr.c
05-12-2002, 11:48 AM
Like Fartmanistan, I got y*'s of 100+% and 200+% when I used .93% as the covariance (with whole numbers in the formulas). This was obviously a problem when the problem mentioned nothing about the borrowing rate or if borrowing was allowed at all.

As much as the .93% seems like a mistake, the thing that I dislike more is the fact that the U=E[r]-0.005s^2 utility function is supposed to be the default standard to be used when no other function is present. Is that explicitly mentioned anywhere? Has this been assumed on prior exams?

bb
05-12-2002, 12:05 PM
I decided to use U=E(r)-0.05As2 because with this I got both w1 and w2 below one. Anyone else?

Toronto
05-12-2002, 04:36 PM
I used the covariance as 0.93%. Using the Utility function:

U = E(r) - .005Ao^2

A) y=1.02, A=4

B) y=2.05, A=2

I assumed some round off error and rounded the answers to y=1 and y=2.

Here is why I think covariance of 0.93% is incorrect. When A&gt;0 the investor is risk adverse. If an investor is risk adverse they will not borrow at the risk-free rate because they are net lenders (ie. will only lend at risk-free rate). When I have a value of A=2 and I find that the investors is selling short 100% of the risk-free asset, I was positive an error was made.

I'm pretty upset with this error too. It either means:

i) They didn't proof read the exam.

ii) They don't know what they're doing.

What I also found weird was that I looked at the Jam and found three questions in there almost identical to Exam 6 (ie.
the question above, the option question (10 marks) and the RBC question in the morning session (6 marks)). Not to mention that 4 questions were the same or very similar to former exam questions.

Is the Soa making a deal with Carmody?

:horse:

Snow White
05-12-2002, 04:57 PM
For risk aversion A = 2, I did 2 solutions: The first one was assuming borrowing was allowed. Then I also assumed that borrowing was not allowed and found the optimal portfolio that maximizes the utility function. Do you think this is what they were looking for?

Fartmanistan
05-12-2002, 07:21 PM
I think that is a fantastic way to answer the question since I do recall a Carmody sample problem where Jim's mom will not let him borrow and solving for the optimal portfolio gives &gt;100% in risky assets. Carmody then goes on to solve for the maximum utility with no borrowing. Wish I would have thought of it but then I had already used up my allotted time for that question anyway. I would bet my life that the 100+% and 200+% answers were right. Also, I suppose you could use a different utility function than the E(r) - .005Asigma^2 if you stated it clearly. I do think that you would lose some points though since the above utility function is jammed down our throats for several chapters and it would be reasonable to expect us to have that memorized just like the umpteen million other things.

Davo
05-13-2002, 10:11 PM
The problem specified three things....cov = 0.93%, sd1=13% and sd2=20%...you get different result depending on how you intererpreted this information. cov=sd1*sd2*rho (rho = correlation) thus rho = cov/(sd1*sd2). If you treat these numbers as whole numbers you get rho = (0.93)/(13*20) = 0.003577. If you treat them as decimals you get rho = (.0093)/(0.13*0.20) = 0.3577. The later is what I belive they intended for the exam. Either way I think you should get full credit since both interpretations should be common enough.

EconWiz
05-14-2002, 01:05 AM
Do you need to calculate the correlation in this question? Isn't it possible to compute w1, w2, and y using covariances?

I made a careless algebraic error on this one, but I think a big source of confusion in answering this question had to do with when to use percentages (with a multiplier of 0.005 in the utility function) or decimals (with 0.05) in the formulas. :roll:

bigfatbaby
05-14-2002, 09:28 AM
Since they did not give you a utility function and everybody has a different utility function why should we have had to assume one from the book or make one up. I just decided to explain the process step by step with out actually going through the math twice.

Of course I've never passed one of these tests so what do I know.

Indep
05-14-2002, 01:03 PM
For risk aversion A = 2, I did 2 solutions: The first one was assuming borrowing was allowed. Then I also assumed that borrowing was not allowed and found the optimal portfolio that maximizes the utility function. Do you think this is what they were looking for?

I thought you only did it twice when there was a seperate borrowing rate. Was there? I can't remember now.

The Bomb
05-14-2002, 01:15 PM
I don't recall there being a risk-free borrowing rate, only a T-bill rate. Therefore, I assumed that one could borrow at that T-bill "risk-free" rate.

Regarding which utility function to use, I agree that since they didn't specify which one to use, we are somewhat given (some) carte-blanche.

For example, I see a lot of people used .005*(something).

If I recall correctly, I used U = r_f - y*( E(r_p) - r_f) - (.01A)*(y^2)*(Sigma_p)^2.

I thought I remembered doing a few problems like this in the Investments text. I haven't taken the time to go back and look at my notes...sometimes I feel like I'm just beating a dead horse when I discuss these questions ad nauseam after the exam.

Wag, the Dog
05-14-2002, 06:22 PM
You can lead a dead horse to water, but you can't make him post.