modified and effective duration and general question

[noalv4]

Hi David,
I have two questions regarding the above:

1. On part 3, Products, modified duration is described as:
Modified Duration = Macaulay Duration / (1 + yield/k) where k = compound periods per year.
In Tuckman Chapter 4, it is as follow:

D=V- - V+/2*(v0)* (delta y)
What is the difference between these two and when we use which?
2. According to the formulla above (Tuckman), the denominator is 2*(v0)* (delta y), and there is an example as such in page 119 (T1.P4.) I solved the example in page 121 according to that formulla:
D=($100.078-$99.9221)/2*100*0.02=3.8975.
Your example shows 7.79 which is 3.8975*2.
can you explain?
3. General question please, I couldn't understand from reading in the forum what is going to be...
Are you going to write practice questions to the chapters in part 4, that don't have practice questions so far? (Allen, Tuckman (Chapter 4 and 6), Narayanan, de servingy, Hull (Chapter 18), Jorion and stress testing?).
Thanks,
Noa

 

[ShaktiRathore]

go to the link:
http://forum.bionicturtle.com/threa...rations-lets-settle-this-now.6012/#post-18668

thanks

 

[David Harper CFA FRM]

Hi Noa,

1. I thank Shakti for linking to the best summary of the technical difference between an effective duration and the modified duration; i.e., both have the same interpretation, only the effective duration is a necessary approximation when the precise modified duration is not available.

2. This is why it helps to understand that the effective duration = -1/P*(dollar duration) = -1/p*slope. The (2) does not need to throw us off if we realize that it is only computing a slope = rise/run. In the p 121 example (Tuckman 5.3) we have:

• price @ 5.01% = 99.9221
• price @ 4.99% = 100.078
• slope = rise/run = (99.9221 - 100.078)/(5.01% - 4.99%) = -799 is the dollar duration such that duration = -1/P*dollar duration = -1/100*-799 = 7.79

The Δy is 0.01%: we are re-pricing at 5.00% +/- 0.01%. Hence the denominator = 0.01%*2. However, in my opinion, it is more robust to realize that we are merely finding a slope between two points (the secant line that is very near the tangent; hence the effective is approximating the modified)

3. This week (tomorrow 3/25) starts a new series on Tuckman, so I do plan to cover Tuckman in T4. A global topic review T4, but I don't plan to write new questions on any other T4. Allen is junk, Hull is misplaced, de Servigny has little worth writing, I don't see Narayanan as fertile (I don't think new questions for these weak readings will be robust over time). After i finish T4, our P1 converage will be very thorough, I'll probably go back and finish off the remaining Miller. Thanks ,

 

[noalv4]

Hi David,
Thank you and Shakti for your reply.

Since my background is not that mathematic, and it is important to me to simplify things as much as possible for the exam (mainly because the time learning is getting shorter), if it is possible, can you provide me a guide line when (for the purpose of the exam) it is appropiate to use each of the following?:

1. Modified Duration = Macaulay Duration / (1 + yield/k) where k = compound periods per year
2. Effective Duration = D=V- - V+/2*(v0)* (delta y)
3. Effective Duration (is it Effective Duration or simply a duration?): dp/dy*-1/p.

Regarding the practice questions, for T1.P4, based on your reply, what is your recomendation to focus on (in the study notes). I did not cover much of Allen chapters, but regarding the other chapters except Tuckman, what is, in your opinion, important to focus on?

Thanks,
Noa.

 

[David Harper CFA FRM]

Hi Noa,

Correction to your (3): the essential building block is modified duration (aka, duration) = dp/dy*-1/p.
(technically, modified duration is the case of duration where price is a function of yield to maturity, YTM, but that is almost always our scenario, so for our purposes: duration = modified duration)

Frankly it is hard to comprehend sufficiently without engaging in the math: i would hope you can at least see how dollar duration is the slope of the tangent line, dP/dy, such that mod duration (aka, duration) is the dollar duration *-1/P.

• In a nutshell, we almost always prefer duration (aka, modified duration) b/c it is the sensitivity and such a near function to dollar duration (the basis for hedging)
• As Macaulay duration is the weighted average maturity, sometimes it is easy/elegant to "reach" the modified duration vis Mac duration
• We use effective duration as an approximation to modified duration when we are forced to; e.g., embedded option, MBS, lack of analytical access ... b/c effective is a brute force finding of the nearby secant's slope

With respect to T4, I think (truly, actually) that GARP bullets are good guides:

• Value-at-Risk (VaR)
  • Applied to stock, currencies, and commodities
  • Applied to linear and non-linear derivatives
  • Applied to fixed income securities with embedded options
  • Structured Monte Carlo, stress testing, and scenario analysis
  • Limitations as a risk measure
  • Coherent risk measures
  • Volatility Models
• Option valuation
  • Pricing options using binomial trees
  • The Black-Scholes-Merton Model
  • The “Greeks”
• Fixed income valuation
  • Discount factors, spot rates, forward rates, and yield to maturity
  • Arbitrage and the Law of One Price
  • One factor measures of price sensitivity
  • Duration, DV01, and convexity
  • Key rate exposures
  • Hedging and immunization
• Country and sovereign risk models and management
  • Fundamental analysis
• External and internal credit ratings
• Expected and unexpected losses
• Operational risk
• Stress testing and scenario analysis

Even the sort order and relative sizing of these topics appear reliable to me. GARP's favorite T4 topic is VaR, then option valuation, then fixed income. So, more important are:

• Hull
• Tuckman
• Dowd (definitely his chapter 2)
• Ong only for the key concepts: EL, UL, correlation, UGD

I hope that helps,

 

[noalv4]

Hi David,
Thank you so much. It helps a lot.
Appreciate your effort.

Noa.