Correction & Exam Answers

Hi Jack. This is Nuno from FTMA1 Class. Look, at the Lesson 6 calculations, when doing the Forward price with dividends paying, you post (T-t) for 10 months = 0.83. I think it's 0,803. Thanks

Interesting. I was actually confused by this since normally (in Dave's calculations) the time (T and t) is given in days. Then it's just a matter of dividing by 360. However this was given in months. So I did (10/12) because there are 12 months in a year (I'm not saying what I did was right though).

What did you do to get 0.803?

Forget it Jack, just did again, and it's 0,83. I made a mistake with the calculator. It's 300/360= 0.8(3).
Thanks anyway.
How are u going with Exam Calculations?

Cheers

Here's what I think so far:

Question 1: Easy - just use Google

Question 2: Easy, just don't get confused about who holds the repo and who holds the reverse repo.

Question 3: I think Dave's notes are incorrect. I'm pretty sure the International Fisher Effect states that the country with a higher interest rate will experience a devaluing of currency. Anyway - double check your answer on this against Google and Dave's notes!

Question 4: Quite tricky. The only two scenarios I could think of are where a credit event occurs and where one doesn't.

Question 5: I think this is a difficult question because I think you need to understand the formula to explain what it's doing. Unless I've missed something?

Question 6: Plugin in the numbers and you're done.

Question 7: Long and lots of different versions of the same formula to use. Be careful with the negative percentage i.e. -(-0.01) is the same as +0.01

Send me ur email, we could cross some results in the calculations.

I'm happy to post my answers on this forum, if you let me know which ones you would like to check. Just because I would rather share any working I have with everyone. Also people can suggest where I have gone wrong!

No problem Jack.

Can you help me with the question 10b...the one about correlation?

For 6b i got DR= 12%, DP=0.988, DDA= 375.
7b) 1- 14.37
2- 9.58
3- 16.43
4- 10.45
5- 12.78
6- 8.85

8b) f= 100.313
Profit= 24.68

Cheers

6B)
Discount Rate: 12%
Discount Price: 0.988125
Dollar Discount Amount: 375



7B)
Share Price 8%, no growth: £14.38
Share Price 12%, no growth: £9.58
Share Price 8%, 1% growth: £16.43
Share Price 12%, 1% growth: £10.45
Share Price 8%, -1% growth: £12.78
Share Price 12%, -1% growth: £8.85



8B)
Forward Price of contract: $100.31
Profit due to Forward Contract: $24.69
Dividend paying security Forward Price: $11.64



9B)
Par bond: $99.86
Discount bond: $975.79
Premium bond: $5147.41

10B)
I'm doing this again.

My Expected Return numbers are the same, but i'm getting big numbers for Company A Standard Deviation and Variance.

I think that 100 value for Possible Return is messing the formulas.

Cause when calculating the Expected Return, the number you get is 10.2,but that's not a percentage.
The numbers in the Final Exam for Probability and Possible Return,are numeric or percentage? I think it's not clear...some confusion with that.

Before jumping into Standard Deviation, why don't you post your numbers for Variance and see how much they differ?

hi! could you explain me the number 7 because i have opposite answers..

Hi,

I will post my full answer and explanation for number 7 when I get home from work this evening if you can hold on until then!

Jack

thank u very much Jack!
Also, for the number 9, how u get price when is semiannual?

Ugh, number 9 sucks because all of Dave's examples are for annual payments. For semi annual you must divide both the coupon rate and discount rate by 2. So the rate per period for the coupon and discount rate is 2% for the first example.

From memory example 1 would be:

Coupon rate = 4/2 (2%)
Discount rate = 4/2 (2%)
Nominal = $100
Paying: Semi-annually

Coupon payments: 100*0.02 = $2

There will be 4 coupon payments that must be discounted to find the present value:

C1 = 2/(1.02^1)
C2 = 2/(1.02^2)
C3 = 2/(1.02^3)
C4 = 2/(1.02^4)

Finally the principle (face value, nominal) must be discounted

DiscountedFaceValue = 100/(1.02^4)

Then just add them all together:

C1 + C2 + C3 + C4 + DiscountedFaceValue

Also, since the Discount Rate and Coupon rate are the same, this will be a par bond.


I don't think semi-annual discounting was covered in the notes - which is extremely unhelpful.

I started a new topic for question 7: https://fmta.forumotion.com/t20-question-7b

ok, thanks, i did the same calculation for answer number 9! so should be right! :-)

Company A
ErA 0.102
δ2A 0.09

Company B
ErB 0.1175
δ2B 0.250389063

I get a really high value for Standard Deviation.

I get the same values for expected return, but my variance is different.

Expected Return for Company A

Probability * Return

Very weak: 0.1 * -0.04 = -0.004

Weak: 0.2 * -0.01 = -0.002

Steady weak: 0.25 * 0 = 0

Steady strong: 0.2 * 0.01 = 0.002

Strong: 0.15 * 0.04 = 0.006

Very strong: 0.1 * 1 = 0.1

Sum: 0.102
Expected Return 10.2%

Expected Return for Company B

Probability * Return

Very weak: 0.1 * -0.02 = -0.002

Weak: 0.2 * -0.015 = -0.003

Steady weak: 0.25 * -0.01 = -0.0025

Steady strong: 0.2 * 0.1 = 0.02

Strong: 0.15 * 0.4 = 0.06

Very strong: 0.1 * 0.45 = 0.045

Sum: 0.1175
Expected Return 11.75%

Variance for Company A

I have kept everything as a percentage so the numbers don't get too small:

(Return - Expected Return)^2 * Probability
(-4 - 10.2)^2 * 0.1 = 20.164
(-1 - 10.2)^2 * 0.2 = 25.088
(0 - 10.2)^2 * 0.25 = 26.01
(1 - 10.2)^2 * 0.2 = 16.928
(4 - 10.2)^2 * 0.15 = 5.766
(100 - 10.2)^2 * 0.1 = 806.40400

Total: 20.164 + 25.088 + 26.01 + 16.928 + 5.766 + 806.40400
Total = 900.36
Variance = 900.36
Standard Deviation = sqrt(900.36)
Standard Deviation = 30.0059994%

Variance for Company B

I have kept everything as a percentage so the numbers don't get too small:

(Return - Expected Return)^2 * Probability
(-2 - 11.75)^2 * 0.1 = 18.90625
(-1.5 - 11.75)^2 * 0.2 = 35.1125
(-1 - 11.75)^2 * 0.25 = 40.640625
(10 - 11.75)^2 * 0.2 = 0.6125
(40 - 11.75)^2 * 0.15 = 119.709375
(45 - 11.75)^2 * 0.1 = 110.55625

Total: 18.90625 + 35.1125 + 40.640625 + 0.6125 + 119.709375 + 110.55625
Total = 325.5375
Variance = 325.5375
Standard Deviation = sqrt(325.5375)
Standard Deviation = 18.0426578%

Have I done anything wrong here? I think we can agree on the answer for Expected Return for Company A and Company B.

How did you get your value for Variance?

This is just Covariance stuff, so best to ignore this until we can agree on our Variance numbers!

Difference for Company A

(-4 - 10.2) = (-14.2)
(-1 - 10.2) = (-11.2)
(0 - 10.2) = (-10.2)
(1 - 10.2) = (-9.2)
(4 - 10.2) = (-6.2)
(100 - 10.2) = (89.8)

Difference for Company B

(-2) - 11.75 = -13.75
(-1.5) - 11.75 = -13.25
(-1) - 11.75 = -12.75
10 - 11.75 = -1.75
40 - 11.75 = 28.25
45 - 11.75 = 33.25

Product of differences:

(-14.2)*(-13.75) = 195.25
(-11.2)*(-13.25) = 148.4
(-10.2)*(-12.75) = 130.05
(-9.2)*(-1.75) = 16.1
(-6.2)*(28.25) = -175.15
(89.8)*(33.25) = 2985.85

Product*Probability

195.25*0.1 = 19.52500
148.4*0.2 = 29.68
130.05*0.25 = 32.5125
16.1*0.2 = 3.22
-175.15*0.15 = -26.2725
2985.85*0.1= 298.58500

Covariance
19.52500+29.68+32.5125+3.22+(-26.2725)+298.58500 = 357.25

Covariance=357.25

Correlation = 357.25/ (18.0426578 * 30.0059994) = 0.659877969

My last results for Variance and Standard deviation.


Company A
ErA 0.102
δ2A 0.09
δA 30%

Company B
ErB 0.1175
δ2B 0.0326
δB 18%

I did it with the real number, didnt use percentages.
But we have the same values now. I think it's finally correct.

I'll work the covariance and correlation now,i'll post later my results.

Cheers