).Yes. MV = 800,000 FV = 1,000,000
Thanks for the great feedback and input on this thread! On a positive note, it seems like the question samples were well-distributed across the topics? For example, if i read correctly, several Basel III questions, at least three current issues (Allied Irish bank, Irish vs US, Icelandic), implied volatility, even key rates queried, even Eurodollar futures made an appearance!! (I realize not to price, but you see why I included some P1 instruments in my mock?). Some immediate, specific reactions:
1.
@LeeBrittain: In regard to "David- I feel like your notes and questions prepared us well for the exam. One area that I don't think was covered in your notes but was on the exam was the question about the liquidity duration of a portfolio given certain share position sizes and % that could be sold in a day without effecting the price."
Thank you so much! But "liquidity duration" is not a concept anywhere in P2 readings. Of course "liquidity" and of course "duration." I can infer a definition from the comments here, but I'm skeptical that it deserves to be called a "duration." If anyone can cite a source, I'd love to know.
2.
About the DV01 gap (see http://forum.bionicturtle.com/threads/level-2-post-what-your-remember-here.5923/page-2#post-17598)
1. I thought Q.79 (Duration dollar matching qustion) had an issue with the question itself.
Liability Value = 200 M; Modified Duration = 20
Asset Value = 220 M; Modified Duration = 15
What is the gap in DV01.
Answers: 700 M, 1,000 M, 1,100 M, 1200 M
I did 700M but how can DV01 could be so high and 100's of millions.
I see conflicting phrasings of the question. If the question is the difference in DV01 (it is awkward to ask for the "gap" in DV01 [sic]), troubleshooter must be correct, the difference in DV01 implied by this setup is DV01(A) - DV01(L) = (200*20/10000) - (220*15/10000) = 0.07. I would like this question if it asked for the "net DV01" (eg). But if the answer is $700 million, that is NOT DV01, but rather the net dollar duration (aka, net value duration). Or difference/gap in value/dollar duration.
3.
I would be interested to see the full question on implied volatility, I am a little concerned about it, but it's hard to judge. It looks like the question displayed an downward sloping implied volatility skew. Skew would connote downward sloping but sounds like the plot showed anways implied volatility as a decreasing function of strike; i.e., Hull's figure 19.3. In which case:
4.
- If we price the option using the implied volatility given by an ATM option (i.e., compute model price using ATM implied volatility) , clearly BOTH the ITM call and OTM put will be undervalued (i.e., market price > model price). This is the point of crashophobia explanation for the equities implied volatility skew: OTM puts are bid up so their implied volatilities is higher (similar ITM call matches per put-call parity, but the explain starts with OTM puts as expensive catastrophe insurance!). Shannon has expressed this with a statement that I 100% agree with: "If the volatility of the ATM option was used to price the options, but in actuality there was a skew, this means that the ITM calls and OTM puts are both undervalued because the volatility used to price them was lower than the actual volatilities." Yes, true, always true.
- The wording used here is crucial. Here is s statement, from above, that makes does NOT sense: "if the pricing was using implied volatility, then compared to volatility used, which one will be undervalued." It is impossible to "price an option using its own implied volatility" or, by circular definition, you just get the option's traded price. We can say, with validity, for example instead: "the (model) price of OTM put using the implied volatility of an ATM option"
In regard to the negative duration/IO strip, I would be interested to confirm the question is specifically "A manager wants to hedge his fixed income portfolio with an instrument which has negative duration? Is it a) Buy the put option on the zero, b) Buy the put option on IO ..."?
With respect to INSTRUMENTS, a zero coupon bond must have positive duration (i.e., positive Mac duration = maturity); an IO strip must have a negative duration; and, to my thinking, a put on a zero must have a negative duration (rate up --> zero down --> put up); and a put on an IO strip must have positive duration (rate up --> IO strip up --> put down)
This is why the difference between (modified, effective) duration and DOLLAR DURATION matters; it is analogous to percentage Greeks which are sensitivities [~ duration] and POSITION Greeks, which are needed for hedged [~dollar duration]. Start with simple: long a zero-coupon bond is positive duration and positive dollar duration. What is short a zero-coupon bond? The *instrument* remains positive duration, but DOLLAR (aka, value or position) duration is negative as value duration = Price * mod duration. So, short a zero coupon bond = -P * +duration = negative dollar duration; i.e., if rates go UP 1.0 unit, it gives the estimated position GAIN in short position.
So what's a put on an IO strip? I agree with emer: w.r.t IO strip, an increase in rate --> increase in price (i.e., the IO strip is the rare case of negative "instrument" duration). But a long put on an IO strip is an instrument with positive duration, similar to a long bond position: an increase in rate --> decrease in put value. So, long IO put should have positive duration.
HOWEVER, I am concerned the question is imprecise, because if the question is to "hedge interest rate exposure" or "reduce exposure to interest rates," this amounts to DECREASING the absolute value of the position (value) duration (or put another way, it depends on the underlying). For example:
Thanks,
- If the initial (underlying position, eg) is net long T-bonds (long dollar duration), the position is exposed (the risk) is to an increase in rates. Hedges here can include short bond, long IO strip, long IO call, or short IO put (i.e., IO put decreases in price, as rates increase).
- But if the initial exposure is short T-bonds (negative dollar duration), the hedge can include long bond, short IO strip, short IO call, or long IO put
(Answer B could be correct: a long IO put is a derivative on an underlying instrument [IO] with negative instrument duration but positive position duration, and that can reduced the interest rate exposure to an original net short position. Phew.
