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# Interview question

Discussion in 'Risk Management' started by Soon2Bgreat, Jan 29, 2012.

1. ### Soon2Bgreat

Came across this question a few years back at a sufficiently douchey invmnt mgmt company and wanted to see the reaction here.

The question is this:

You are managing a portfolio - would you rather A) gain 20% for 4yrs and then lose 50% in the fifth or B) lose 50% in the first year and gain 20% for the remaining four years.

...there was no further instruction given. Wanted to see how ET would respond. IMO, it's pretty straightforward, but apparently that's not the case, lol.

2. ### hkrahra

I`d rather gain 50% in a month,then gain 200% in a month,then gain 350% in a month...etc...

3. ### Soon2Bgreat

Lol, ok, well I'd certainly rather gain 350% in a month than 50%.

4. ### cyoungmark

Well from a standpoint of money you would want to lose 50% first then earn 20%. This is because if you gained 20% then lost 50% you would be losing 50% of the portfolio value after you already gained 20% for however many years.

But if you were managing your own fund, you would want to gain a good track record and gather investors, So you would take the 20% first.

5. ### S2007S

Take a \$1000

A.
1000 X 20% = 1200
1200 X 20% = 1440
1440 X 20% = 1728
1728 X 20% = 2073.60

2073.60 X 50% = \$1036.80

B.
1000X 50% = 500
500 X 20% = 600
600 X 20% = 720
720 X 20% = 864

864 X 20% = \$1036.60

Thats apparently the case....its extremely straight forward.

6. ### Mo06

There's the possibility that after losing 50% in the first year, your services would no longer be required.

So not a difficult choice that one...

7. ### bwolinsky

It's really a terrible question, but if they let you use a calculator you would have a 1.2^4/1.5=1.3824-1=38.24% return with 4 20% years and a 50% drop in the fifth than if you had a 50% drop in the first year, and 20% every year thereafter.

The calculation of 0.5*(1.2)^4-1=1.0368-1=3.68%.

The difference would require a calculator to know with certainty, but the question is more about whether you understand compounding in the context of financial math than it is an opinion. It's basic quant math in the CFA Curriculum, but you would generally expect the applicant to be able to solve this without any problems or silly explanation to rationalize the two. It is a quantitative question.

8. ### bwolinsky

You are wrong, Cy young.

No, I think you're wrong.

A: P X 1/2 X (1.2^4) = P X [ (1.2 ^ 4) / 2]
B: P X 1.2^4 X 1/2 = P X [ (1.2 ^ 4) / 2]

A = B.

However, many investors would leave after seeing half their portfolio disappear in the first year. So, company and manager would lose their MER.

10. ### bwolinsky

Once again Bhardy, the effect is compounding. You've divided by the wrong value.

It is not (1.2^4)/2, it is (1.2^4)/1.5, that would imply a 100% greater loss than 50%. Dividing by 3/2's is the 50% loss over the gain. Dividing by 2 is incorrect.

They aren't the same, Bhardy. One compounded earlier then lost, whereas the one that compounded later would be compounded with less.

This is where CFA Curriculums would trump the clueless.

#10     Jan 30, 2012
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