Level 2: Post what your remember here...

[troubleshooter]

As I said, silly mistakes happen. FRM gives you way too much time for the exam and you begin to over-think questions. I wrote 16% too initially! Don't worry, I think you should pass

Hey Lanky: Can you check out page 7 of this link under III. Bonds. I think this gives me a bit of hope.
http://www.imf.org/external/pubs/ft/wp/2006/wp06104.pdf

May be we should bring in Dave here...

 

[troubleshooter]

Hey David: Can you please help me out here...

We have a zero coupon bond with Market price of 80,000 with FV of 100,000 maturing in a year. We need to calculate risk neutral PD given riks fre rate of 5% and recovery rate of 0%. Thanks...

 

[LankyLint]

Hey Lanky: Can you check out page 7 of this link under III. Bonds. I think this gives me a bit of hope.
http://www.imf.org/external/pubs/ft/wp/2006/wp06104.pdf

May be we should bring in Dave here...

When I think about it again..I think you could be correct.

If risk-free rate would be 0, the default rate would have to be 20%.

Since the risk-free rate is 5%, we have to compare 80 to 100/(1 + 0.05) which is 95.2 something

80/95 = 84% So, in this case, risk-free default rate and the default rate are the same.

 

[LankyLint]

I still think it is 20%.

Risk neutral mean loss rate = risk neutral probability of default i'm guessing?

http://forum.bionicturtle.com/threads/risk-neutral-mean-loss-rate.1443/

 

[David Harper CFA FRM]

Hi troubleshooter & LankyLint,

It's variant to the compounding frequency, but if annual discounting, I would use a no-arbitrage: MV(1+y)*p = MV(1+Rf), where y= risky yield, Rf = risk-free rate, p = (1-PD);
i.e., MV invested today at expected risky yield must equal certain riskfree yield.

Please note that this [ MV(1+y)*p = MV(1+Rf) ] is identical to your formula above: As Face = MV*(1+y), Face*p = MV(1+Rf) --> MV = Face*p/(1+Rf) = MV.
... so I agree with that calculation, I am not sure why an FRM would necessarily have it memorized but it's the same no-arbitrage idea!

So, on annual no-arbitrage, I would use: (1+y)*p = (1+Rf), or p = (1+Rf)/(1+y) assuming 100% LGD.
As 1/(1+y) = MV/Face, p = (1+Rf)*MV/Face such that PD = 1 - 1.05*80/100 = 16%.

Then I'm always insecure so i test:

• invest 80 at riskfree rate of 5% annual compound rate grows to 80*1.05 = 84.00 certain future value; and this should equal
• invest 80 at risky rate 100/80 - 1 = 25% grows 80*1.25 but 16% default probability so expected future value is 80*1.25%*(1-16%) = 84.00. Okay, passes test.

But it's variant to compound frequency:

• If continuous, I get PD = 15.90% = 1 - exp(5%)*80/100
• if semi-annual, PD = 15.95% = 1 - (1+5%/2)^2*80/100

Hope that's helpful,

 

[LankyLint]

Hi troubleshooter & LankyLint,

It's variant to the compounding frequency, but if annual discounting, I would use a no-arbitrage: MV(1+y)*p = MV(1+Rf), where y= risky yield, Rf = risk-free rate, p = (1-PD);
i.e., MV invested today at expected risky yield must equal certain riskfree yield.

Please note that this [ MV(1+y)*p = MV(1+Rf) ] is identical to your formula above: As Face = MV*(1+y), Face*p = MV(1+Rf) --> MV = Face*p/(1+Rf) = MV.
... so I agree with that calculation, I am not sure why an FRM would necessarily have it memorized but it's the same no-arbitrage idea!

So, on annual no-arbitrage, I would use: (1+y)*p = (1+Rf), or p = (1+Rf)/(1+y) assuming 100% LGD.
As 1/(1+y) = MV/Face, p = (1+Rf)*MV/Face such that PD = 1 - 1.06*80/100 = 16%.

Then I'm always insecure so i test:

• invest 80 at riskfree rate of 5% annual compound rate grows to 80*1.05 = 84.00 certain future value; and this should equal
• invest 80 at risky rate 100/80 - 1 = 25% grows 80*1.25 but 16% default probability so expected future value is 80*1.25%*(1-16%) = 84.00. Okay, passes test.

But it's variant to compound frequency:

• If continuous, I get PD = 15.90% = 1 - exp(5%)*80/100
• if semi-annual, PD = 15.95% = 1 - (1+5%/2)^2*80/100

Hope that's helpful,

Thought so. Thank you for the clarification, David.

 

[David Harper CFA FRM]

LankyLint - in this context, i interpret "risk-neutral PD" as a correct (perhaps not essential) qualifier that serves to justify the initial no-arbitrage equality. What i mean is, MV = Face*p/(1+Rf) is correct only if you are willing to price (MV) the bond equal to it's discounted expected value. If you are risk-averse, you need compensation for the uncertainty of default/no default, such that risk-aversion would manifest as MV < Face*p/(1+Rf); i.e., yield would need to be higher.

It's similar to risk-neutral in Tuckman's binomial:

• in Tuckman's binomial true context, risk-neutral probabilities are the probabilities that calibrate to equate MV = expected discounted value.
• in this context, it tells us we can infer PD from the "unadjusted" MV as the risk-neutral PD equate MV = expected (average) value.
  
  or, put another way, it justifies discounting (Face*p) by the riskless rate (Rf):
  risk neutral: MV = Face*p/(1+Rf),
  
  if there were risk aversion, the discount would need to be greater as compensation for uncertainty:
  risk averstion: MV less than << 80 = Face*p/(1+Rf + a), where (a) is premium for risk aversion

Thanks,

 

[browniandynamics]

Is there a post for Level 1?

 

[browniandynamics]

Hi David, do you know how the GARP grade the exam? I made a very stupid mistake: I forgot to mark my answers onto the answer sheet till the last 5 minutes! I tickered all of them on the question manual. I managed to mark about 80 onto the answer sheet finally. How much chance do I have to pass it, if I can have 70 of them correct? Thank you!

 

[Ehanif]

I wish you pass.. I believe if a guy can score 70 percent den his chances to pass increases.. BTW u made a big blunder... Wish u all the best..

 

[FRM_Exam]

Hi troubleshooter & LankyLint,

It's variant to the compounding frequency, but if annual discounting, I would use a no-arbitrage: MV(1+y)*p = MV(1+Rf), where y= risky yield, Rf = risk-free rate, p = (1-PD);
i.e., MV invested today at expected risky yield must equal certain riskfree yield.

Please note that this [ MV(1+y)*p = MV(1+Rf) ] is identical to your formula above: As Face = MV*(1+y), Face*p = MV(1+Rf) --> MV = Face*p/(1+Rf) = MV.
... so I agree with that calculation, I am not sure why an FRM would necessarily have it memorized but it's the same no-arbitrage idea!

So, on annual no-arbitrage, I would use: (1+y)*p = (1+Rf), or p = (1+Rf)/(1+y) assuming 100% LGD.
As 1/(1+y) = MV/Face, p = (1+Rf)*MV/Face such that PD = 1 - 1.06*80/100 = 16%.

Then I'm always insecure so i test:

• invest 80 at riskfree rate of 5% annual compound rate grows to 80*1.05 = 84.00 certain future value; and this should equal
• invest 80 at risky rate 100/80 - 1 = 25% grows 80*1.25 but 16% default probability so expected future value is 80*1.25%*(1-16%) = 84.00. Okay, passes test.

But it's variant to compound frequency:

• If continuous, I get PD = 15.90% = 1 - exp(5%)*80/100
• if semi-annual, PD = 15.95% = 1 - (1+5%/2)^2*80/100

Hope that's helpful,

I changed from 16 % to 20 % at the last min - another one bites the dust

 

[hanyongdok]

i have a question for M&A Arbitrage.
what i remeber is A will acquire B
they will exchange B holders who hold 20$ three stocks of B with 58$ A Stock

the answer is simply buying targeted firm and sell acquiring firm?

or considering price convergence 58 =/ 20*3
buy firm A stock and sell B stock

 

[FRM_Exam]

i have a question for M&A Arbitrage.
what i remeber is A will acquire B
they will exchange B holders who hold 20$ three stocks of B with 58$ A Stock

the answer is simply buying targeted firm and sell acquiring firm?

or considering price convergence 58 =/ 20*3
buy firm A stock and sell B stock

As far as I understand - it is always buy targeted firm and sell acquring firm

 

[LankyLint]

As far as I understand - it is always buy targeted firm and sell acquring firm

Precisely.


We are SURE that the merger will be complete. On the other hand, the market is not. So, they discount the value of the acquiring firm (because they usually pay premium for the shares) , and increment the value of the firm being targeted (but not completely) to reflect the chance that it will fail.

If it fails, both fall down to earlier price levels (usually even lower).

It can never be that the value of the firm being acquired will be more than theoretical value of the merged firms, so, it is never optimal to buy the firm being targeted.

Hope it makes sense

 

[FRM_Exam]

Precisely.


We are SURE that the merger will be complete. On the other hand, the market is not. So, they discount the value of the acquiring firm (because they usually pay premium for the shares) , and increment the value of the firm being targeted (but not completely) to reflect the chance that it will fail.

If it fails, both fall down to earlier price levels (usually even lower).

It can never be that the value of the firm being acquired will be more than theoretical value of the merged firms, so, it is never optimal to buy the firm being targeted.

Hope it makes sense

i am reallly really sad - as I got the PD wrong for the other question -I selected 16% earlier .. but changed it to 20 % .. same as u did

 

[LankyLint]

i am reallly really sad - as I got the PD wrong for the other question -I selected 16% earlier .. but changed it to 20 % .. same as u did

Don't worry about it. Last time, discussing part 1 on this forum, I figured that I marked 3 answers wrong FOR SURE. I still got top quartile in all sections. I'm guessing that top quartile is 4-5 mistakes per section.

Relax!

 

[FRM_Exam]

Don't worry about it. Last time, discussing part 1 on this forum, I figured that I marked 3 answers wrong FOR SURE. I still got top quartile in all sections. I'm guessing that top quartile is 4-5 mistakes per section.

Relax!

However, I do think this time as the paper was relatively easier - one needs to score atleast 60 / 80 (75%) to pass - so maybe 4 questions wrong each section allowed .. and hence 1st quartile I believe would probably be 1 - 2 mistakes at the max per section.

 

[LankyLint]

However, I do think this time as the paper was relatively easier - one needs to score atleast 60 / 80 (75%) to pass - so maybe 4 questions wrong each section allowed .. and hence 1st quartile I believe would probably be 1 - 2 mistakes at the max per section.

It seems that way because you are talking to people who COME TO A FORUM to discuss the paper immediately after their exam. All of us were over-prepared.

I know people who just study 2-3 days for the exam and expect to pass. 1 person I know left 20 questions. The pass rate will increase marginally, if at all. AND, you will definitely pass. Do not worry.

 

[FRM_Exam]

It seems that way because you are talking to people who COME TO A FORUM to discuss the paper immediately after their exam. All of us were over-prepared.

I know people who just study 2-3 days for the exam and expect to pass. 1 person I know left 20 questions. The pass rate will increase marginally, if at all. AND, you will definitely pass. Do not worry.

Yeah that is true - lot of sweets and chocolates in your mouth - last time I thought I will just pass --- but still got 1st quartitle on all sections - I guess lot of ppl get a huge portion of the paper wrong and ofcourse they are least interested to discuss - ppl over here are serious so I guess .. mistakes here and there should not matter -

I was reading somewhere that a person messed up on current issues section as he did not time to read anything - and u can't get that kind of thing right without reading the case study atleast once

 

[FRM_Exam]

Yeah that is true - lot of sweets and chocolates in your mouth - last time I thought I will just pass --- but still got 1st quartitle on all sections - I guess lot of ppl get a huge portion of the paper wrong and ofcourse they are least interested to discuss - ppl over here are serious so I guess .. mistakes here and there should not matter -

I was reading somewhere that a person messed up on current issues section as he did not time to read anything - and u can't get that kind of thing right without reading the case study atleast once

I think with David experience he should be able to throw some light on what kind of marks (in absolute terms out of 80) do you need to pass with top (1 and 2) quartiles? - when we get an easy paper - from reading over here .. 90% of my answers match other on this forum - but then these ppl as u said are over-prepared