Allow me to play devil's advocate for a moment. At the beginning of the test it said that all rates were continuous. Wouldnt this mean that we should instead use 80=100*exp(.05+s) and then say that s = PD*LGD? This would have given us a little more than 17%. Since 16% was the closest I chose it (and it sounds like this was the correct answer!!!), but isnt my way more consistent with the whole continuous rate concept? Thanks, Shannon

Hi Shannon, Interesting, hadn't thought of it. In my humble opinion, that's a fair way to answer, especially in the FRM as you've applied Stulz to infer the spread, then Hull's approximation for the spread; i.e., totally justified by the assignments. And, you make a really interesting point: both of those steps are based on a continuous assumption (Hull's hazard rate). I can find no error with this reasoning, only to say that, per Hull, the resulting PD is an approximation. I think the burden is on the question to be precise (too obvious?). Because when you say continuous application, my continuous solution would be apply the same no-arbitrage idea but continously: 15.90% = 1 - exp(5%)*80/100; i.e., exp(Rf) = exp(y)*(1-PD) Clearly the answer is variant to compound frequency assumption (as always) but I think you've found another way that could only be weakly dismissed as an "approximation." Because your answer also makes use of all of the information.

Does anyone remember the following question: 11) Calculate default rate for 3rd year [(1 - year 2 default rate) * ( 1 - year 3 default rate) = (1 - 0.1051)] Yes. I think I got this one... default intensity = Prob of Default in year 3/probaility of survival for first 2 years = cumulative default for year 3 minus the same for year 2 divided by (1 - cumulative default upto year 2)... I am not sure if I read the question on the test incorrectly, but I think the table of probs given for the question above contained cumulative probs, no?

David, Could you please explain the idea behind this method of discounting. I do not remember seeing this explicit formula for discounting. Maybe I am just fried after the test, but I do not see the logic of this algorithm/formula. Thanks! Shannon

Hi Shannon, As I mentioned above (here), I do not think that formula exactly appears anywhere (I was just keying off it to show it is consistent). I would have gotten to the same place with the no-arbitrage idea: (1+y)*p = (1+Rf), assuming 100% LGD. Or, p = (1+Rf)/(1+y). As 1/(1+y) = MV/Face, p = (1+Rf)*MV/Face such that PD = 1 - 1.05*80/100 = 16%. (annual discounting)

Hi David, I posted this right after the test but I dont think anyone chimed in about it. Do you have any thoughts? Question 4 could have gone two ways. At the beginning of te test it said that unless stated otherwise all interest rates were we continuous. If we said that y=r+spread and spread was PD*LGD it was one answer (this was what the reading said we should use for continuous so this was my answer) but if we used 1-r=(1-PD*LGD)(1+y) we got a different answer. Both answers were possible solutions. VERY VERY VERY frustrating. Thanks! Shannon

Hi, On question 28, I am of the opinion that D is the right choice. The question asked of Funds and not managers. So I think Sharpe Ratio is better placed to assess Funds while IR is for individual managers. Check Andrew Lo on Hedge funds. EIA

When adding a hedge fund to a well diversified portfolio I think we are supposed to use IR so I also went with Nix or whatever the heck it was.

I feel the same. For hedge funds, sharpe ratio has little value because it does not take into account the asymmetric return distribution.

My reasonning was : PV= -80000 FV= 100000 T=1 PMT=0 COMPT Y=25% PD= 1 - (1+5%)/(1+25%) = 16% which gives same result

Hi, On question 3 above, I think if there is a survivor-ship bias according to Andrew Lo The Sharpe ratio will be overstated. IMO performance overstated don't have any meaning. Please check Andrew Lo on Hedge Fund Risk Management. EIA

Options question - the wording was confusing. There was a graph of strike vs. IV, with the normal equity frown - meaning the IV of lower strikes was higher than that of higher strikes. It asked something to the effect of, which are over/undervalued relative to the ATM option. For simplicity, let's assume the 40 strike has a vol of 30, the 50 strike (the ATM) has a vol of 20 and the 60 strike has a vol of 10, consistent with the volatility smirk. So, if the OTM puts (or ITM calls) of the 40 strike are trading for the same implied vol as the 50 strike (vol of 20), they are indeed undervalued (or cheap) relative to where they are actually trading in the market. However, if you already had the position where you were long the OTM puts on the 40 strike (say they are valued at where they are trading in the market at a 30 vol) and someone else says they should only be valued at the vol of the ATM (20 vol), then one would say the position in the OTM puts are overvalued. So, you could interpret this question either way, as it is vague. However, since the 4 choices were, OTM put, ITM call, ATM call, and OTM call, the only answer can only be OTM call, as the ITM call and OTM put are the same. So, since you can't have two correct answers, one can conclude that the answer is the OTM call. When they say overvalued, they do not say relative to what. Relative to where they are trading? or relative to the theoretical value if they were trading at the ATM vol. Very confusing. As is this explanation! I think David could re-write this in a more clear way!

Sharpe ratio, for hedge funds, overstates return even when there is no bias. This is because standard deviation is not the appropriate risk measure for most hedge funds. I feel it is overstated performance, simply meaning, the hedge fund industry as a whole seems to return MORE on average.

On the other option question with the 4 barrier options. This was relatively easy if you realized an up and out barrier option plus an up and in barrier option is equal to the option itself. So, up and out plus up and in call is equivalent to a call option Down and out plus down and in put is equivalent to a put option. Additionally, the stock price was given. With call price, put price and stock price, as well as rate and time, the only variable left to solve for is the strike price (K). P + S = Ke(to the -rt) + C or C - P = S - Ke(to the -rt) I believe the answer was 40 and it worked out perfectly.

Hi, This is from Andrew Lo Any quantitative approach to risk management makes use of historical data to some extent. Risk management for hedge funds is no exception, but there is one aspect of hedge-fund data that make this endeavor particularly challenging: survivorship bias. Few hedge-fund databases maintain histories of hedge funds that have shut down, partly for legal reasons,5 and partly because the primary users of these databases are investors seeking to evaluate existing managers they can invest in. In the few cases where databases do contain \dead" as well as active funds, studies have concluded that the impact of survivorship bias can be substantial.6 To see how important survivorship bias can be, consider a collection of n funds with returns R1; : : :; Rn and dene their excess return per unit risk as: Xj = Rj - Rf / Sd j (6) where Rf is the rate of return on the riskless asset and Sd j is the standard deviation of Rj . The Xj's are natural performance statistics that investors might consider in evaluating the funds; observe that the expectation E[Xj ] of these performance statistics is the well-known Sharpe ratio. For simplicity, assume that these performance statistics are independently and identically distributed with distribution function F(X). This is from pg 9 and 10 of Andrew Lo (Hedge Fund Risk Mgt.) EIA

re: the OTM and ITM call. Clearly, from the graph, an OTM put and an ITM call have the same vol. Because of this, and logic pointed out in another post, I think the answer was OTM call. It's a poorly written question because it really is not testing the concept. I can guarantee that most people, if this was not a multiple choice but a fill in the blank test, would put the answer as OTM put (which is the same as ITM call). I logically deduced the OTM call, but I had to spend a few minutes convincing myself of the possible explanation. Do you disagree with my explanation in another post? David Harper, early on in my studying, I believe in looking at the Hull 18 and 24 questions (maybe the chapters have changed), I emailed you a question regarding this same type of thing and you actually explained it to me. I hadn't figured out how to use the forums yet but should have it over email somewhere. Any recollection? The position being overvalued or undervalued is confusing. Clearly, the IV for an OTM call is lower than the IV for an ATM call. If one thinks the ATM vol is the correct vol, then the OTM call is cheap to buy and hence, undervalued. If the option is being marked on your books at the ATM (so not market to market) vol, but is in reality only worth the IV that it is trading at, it will be overvalued (on your books).

Hi jdg123 - I do vaguely recall but I can't find the email/thread. I see your earlier post, i actually AGREE with your suggestion (in the other post) that phrasings are often imprecise. We've had so many threads on here, about IV and IV-based questions (half of the time the setup is confused such that the follow-up goes in circles), that clearly a lot depends on the specific wording of the question and the exact perspective. Without a precise articulation of the exam question asked, I'm not sure i can add value. Sorry,