Hi Brave Ones,
Can anyone please help me with this…?
“For a portfolio of non-Treasury securities, spread duration equals portfolio duration.”
What portfolio duration are they talking about, effective duration?
Well, fixed income is simply destroying me and I thought from L1 and L2 that I kind of like this stuff.
many thanks once again
(Level III 2012 Volume 4 Fixed Income and Equity Portfolio Management, 5th Edition. Pearson Learning Solutions p. 32).
for a portfolio I think it would be modified duration … especially since there may be multiple bonds / yields / cash flow patterns etc. So something like a weighted average … which would be the modified duraiton.
CP, but don’t those two types of risk (durations) stem from different sources? How can they mix up those two measures of risk? tks!
wait, im confused here… for NON treasury securities spread duration = port duration? That doesn’t make any sense, you would have a component of duration explained by interest rate risk (duration), and then one composed of the spread over treasury (spread risk), so spread risk could differ from total portfolio duration which would include the treasury curve risk on a non-treasury security, as far as i know… What am i missing here?
Hey its not confusing at all: The section is talking about Spread Duration. Treasuries have 0% spread duration . non-Treasuries have spread duration. So a portfolio comprising of only non treasuries would have a spread duration that is the weighted average of individual spread durations
that’s precisely what I thought at first but they say “equals portfolio duration”…if they meant what you say, question is 100 solved. even more when some lines below they put it clear that you have two components of risk (the spread and interest rate itself)… “The manager can calculate the effect on the portfolio of a change in sector spreads. The effect due to a change in sector spreads is in addition to the effect that is implied by a general increase or decrease in interest rates.”
That is simple too . The risk part is a quadratic term while the spread itself is a linear term . Hence there will be a correlation effect that is non zero . Just think for example that the treasury terms are hedged so we can capture just the spread . However since there are non-linear terms in the risk component you cannot hedge away the interest rate effect.
Yah, the non-treasury portfolio has spread duration, which as you stated is a weighted avg of individual spread durations, but it still has normal interest rate risk (plain duration) on top of that spread duration – thats where the confusion is, according to Tigas, they are saying that spread duration equals portfolio duration, which would be wrong because that would exclude the regular duration component. No?
IMHO duration is a linear term , only applicable in a small region of rate movement. When you put it like that the text is indeed confusing . I think the CFAI authors are not rigorous or indeed even clear. I agree that taken out of context the words do not make sense. However the meaning is clearly that once you go for larger movements such as all treasuries moving by1% , spread duration of the portfolio will not be equal to portfolio duration . However for small spread changes without any visible treasury rate changes , spread duration would adequately describe portfolio duration itself .
Nobody is arguing the fact that treasuries are not subject to spread duration risk, and i think we all get the definitions of duration by now. A freaking corporate bond has spread risk and treasury curve (interest rate) risk, period. You have to make the sweeping assumption that the yield curve is static into perpetuity (or at least until the said corporate bond matures) to make the statement that spread duration = duration. When has this ever occurred?
r-man, where is written or even implied by CFAI that in the text “assuming no change in treasury rate”…??? A portfolio of bonds without treasuries is NOT the a warrant that you will have no change in treasury rate… It is your assumption and it makes sense but…it is a kind of ex-post bias 
t
everyone seems right, but the question does not seem to have been answered. granted spread duration in a portfolio without treasuries is the spread duration from the entire portfolio of bonds, however why give it the all encompassing name of ‘portfolio duration’. surely if you are going to call it portfolio duration you must also have to include the component of interest rate duration? its like saying in portfolio of only corporates and no treasuries, credit risk equals total risk. what about the other risk components?
when you have a portfolio with only treasury securities - there would be no spread duration. (Since the spread would be with respect to the treasury rate itself). However there is Portfolio duration - wt avg of individual security durations.
Spread Duration = 0, Portfolio Duration = p, Total Duration = p + 0 = p = Portfolio Duration Component ONLY.
when you have corporate securities thrown in the mix - there is some spread duration now introduced, there is Portfolio duraiton as before. So both components are present.
Now Spread Duration = s, Portfolio Duration = p’ (to distinguish from p) and Total Duration = p’ + s
the Total Duration is NOT= Portfolio Duration.
if “Portfolio Duration” is the weighted average of individual security durations (which would include both spread and treasury interest rate components), then how can “Total Duration” add “Spread Duration” plus “Portfolio Duration” – this would be double counting both the treasury and spread component.
I think we are getting throwed up in the stupid definitions they use … all i know is that a corporate has spread risk and interest rate (treasury curve) risk, and a treasury has strictly curve risk and no spread risk.
“For a portfolio of non-Treasury securities, spread duration equals portfolio duration.” – this quote from the original start of the thread is just plain wrong, unless the definition of “portfolio duration” is suppose to mean the weighted average of spread durations, which is fucking stupid since any logical person is going to assume that it includes both treasury and spread components, or they EXPLICITLY say to assume that there is zero treasury risk (no yield curve changes).
Has anyone checked errata on this one to see if they changed the wording?
this wording was there last year too::::
checked errata…nothing there.
totally agree with you. bad wording, to say the least…
let’s move on, there’s a lot more to dig