HELP! i want to believe that this question is wrong

CFA Level I
#1

If the correlation between Pluto and Neptune is 0.25, determine the expected return and standard deviation of a portfolio that consists of 65% Pluto Corporation stock and 35% Neptune Corporation stock.

A)

10.3% expected return and 2.58% standard deviation.

B)

10.3% expected return and 16.05% standard deviation.

C)

10.0% expected return and 16.05% standard deviation.

Your answer: B was correct!

ERPort

= (WPluto)(ERPluto) + (WNeptune)(ERNeptune)

= (0.65)(0.11) + (0.35)(0.09) = 10.3%

σp

= [(w1)2(σ1)2 + (w2)2(σ2)2 + 2w1w2σ1σ2 r1,2]1/2

= [(0.65)2(22)2 + (0.35)2(13)2 + 2(0.65)(0.35)(22)(13)(0.25)]1/2

= [(0.4225)(484) + (0.1225)(169) + 2(0.65)(0.35)(22)(13)(0.25)]1/2

= (257.725)1/2 = 16.0538%

Why use 13 and 22 instead of .13 and .22??

ALSO

Current spot rates are as follows:

1-Year: 6.5% 2-Year: 7.0% 3-Year: 9.2%

Which of the following is CORRECT

A)

For a 3-year annual pay coupon bond, all cash flows can be discounted at 9.2% to find the bond’s arbitrage-free value.

B)

For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond’s arbitrage-free value.

C)

The yield to maturity for 3-year annual pay coupon bond can be found by taking the geometric average of the 3 spot rates.

Your answer: C was incorrect. The correct answer was B) For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond’s arbitrage-free value.

Spot interest rates can be used to price coupon bonds by taking each individual cash flow and discounting it at the appropriate spot rate for that year뭩 payment. Note that the yield to maturity is the bond뭩 internal rate of return that equates all cash flows to the bond뭩 price. Current spot rates have nothing to do with the bond뭩 yield to maturity

Should be 6.5 for first year then 7^2 for second year and 9.2^3 for third year. Right….???

#2

You can use 0.13 and 0.22 it is just that you will get the answer 0.160538 instead of 16.0538 and you just need to remember to convert this to a percentage. If you simply use percentages (i.e. 13% and 22%) in the first instance you will get an answer that is a percentage.

For the second question, you bolded question at the bottom is right but that correct answer is also right. The discount rates you will use will be 6.5%, 7.0% and 9.2% respectively and you need to obviously discount for the number of periods that will apply (i.e. 1, 2 and 3 years) respectively. B is still the right answer though.

The C answer (which you incorrectly gave) is suggesting that you would multiply 1.065 x 1.07 x 1.092 and then take the cubed root to give a discount rate of 7.56% and then discount all cash flows at this rate. I think you would agree that this is clearly wrong.

Hope this clarifies things for you?

#3

NO. For 1st question, if you use .13 and .22, you would end up with answer A.

ALSO, I wrote ’ Should be 6.5 for first year then 7^2 for second year and 9.2^3 for third year. Right….???’ meaning it should be discounted for number of years. but the answer is clearly wrong here.

HELPPPPPPPPPPPPPPPPP

#4

No, if you use 0.13 and 0.22 and forget to take the square root of it you will get 0.0257724 but if you (correctly) find the square root of this answer, you will get 0.1605378 (which if taken to a percentage will give you 16.05%).

For your second question, I have said that you would need to square and then cube the second and third year discount rates (which is your bolded point), but this doesn’t change the fact that you would use this discount rates which is all that the question is asking.

It is saying, would you (a) just you the 3 year discount rate (b) use the respective discount rate for each cash flow or © take the geometric mean (average) of the 3 years.

Hope we are on the same page?

#5

thankyou =)

#6

wtf all those numbers from question 1 come from? @@

#7

The OP didn’t include all of the information that would normally be in a question, but I extrapolated them from his answer.

The full question would have noted that the first security has an 11% return and a 22% standard deviation and the second asset would have had a 9% return and a 13% standard deviation. Also (as was noted in the OP) the 2 assets had a 0.25 correlation.

Beyond this, his answer is just the calculation you would use for expected return and standard deviation of the 2 assets in the 65%/35% proportion discussed in the OP.

I really hope this makes sense for you now otherwise I would strongly advise a review of the Quant readings prior to Saturday!!!

#8

Thanks, that makes much more sense. Hahah I think I’ll do fine on questions of this type, b/c after all portfolio valuations & risk assessment was one of the best courses I scored during undergrad. The calculations are pretty mechanical.

#9

For the second question: Its most defnitely B.

You are right, you discount the first coupon at 1.065, second at 1.07 (for two periods, hence the squared), and 3rd + principal at 1.092 (for three periods, hence the cube).

Thats excactly what B says.