# stalla mock 2008..key duration, convexity Q

Aurora just borrowed 10 mil from its bank etc etc current market value of the loan is 10 mil. effective duration of the loan is 8 with a 5 year key rate duration of 2 a 10 year key rate duration of 6 and an effective convexity of 0.4. blahblah charles job is to use the proceeds from the loan to make fixed inc investments. blah blah charles constantly calculates the market value of the firms portfolio and compares it to the market value of the liability (loan) Portfolio has an effective duration of 8 and effective convexity of 0.12 assume there is an immediate 100 basis point upward parallel shift in the yield curve which is then followed by a gradual parallel shift downward totaling 200 basis points over the next year. the most likely immediate and one year effects of Aurora’s net worth is IMMEDIATE - DECREASE ONE YEAR- DECREASE Answer: because the durations are equal, parallel shifts in the yield will have the same duration effect. however the portfolio has a convexity of 0.12 which is lower than the convexity of the loan 0.4. the convexity of the firms net worth is 0.12-0.4= -0.28. as a result when rates immediately rise firm net worth will decline because of the convexity effect. similarly when rates fall over the next year, the net worth will not change because of a duration effect but will decline (compared to today’s value) because of the convexity effect. ok i got the duration part i hope, but still do not understand the convexity part…

bump. can you paste the question choices please.

The curve with less convexity would resemble the duration line more, while the curve with more convexity will arc more. Generally speaking, for option free securities, higher convexity implies larger price gains when rates fall, and lower price losses when rates rise.

Immediate One Year a) decrease decrease b) increase decrease c) increase increase d) decrease increase

ok, firstly key rate duration measure would measure the sensitivity to the portfolio due to a parallel shift. So parellel shift up should decrease the net worth after 1 yr, the porfolio value should go up, because of 200 pt down shift if yield curve. Convexity (a positive one here) will only adjust it even more up. so I say answer is d.

i picked d as well but the answer is A which doenst make sense to me at all… as a result when rates immediately rise firm net worth will decline because of the convexity effect. similarly when rates fall over the next year, the net worth will not change because of a duration effect but will decline (compared to today’s value) because of the convexity effect.

that’s duration effect. not convexity effect. Convexity is just an approximation tool that adjusts the duration to be more realistic for a large yield shocks. that’s all. Since duration always under prices the effective shock, convexity adds a little bit, and takes a little bit out, but in the end DURATION defines mostly how much portfolio moves. I am yet to see where convexity effect is greater than the duration effect. just doesn’t make sense.

pepp Wrote: ------------------------------------------------------- > in the end DURATION defines mostly how much > portfolio moves. > this is only true for small rate changes (like 50 Basis points), greater rate changes, the convexity effect takes over. This is why the question said rates changed 100 and 200 basis points, because then its the convexity that is a true measure of changes and not duration.

Ok, that would explain why i didn’t pass FI in L1.

yup had to guess all the FI on L2 last year too. but this year its gonna be different as we only have 3 answers to pick from

are you serious? may be I should not spend time on FI anymore, and move on to other subjects where guessing is less required. errr. Can’t remember which topic that would be. lol.

Just remember that duration is a linear equation that is only accurate for small changes. Also remember that positive convexity is good for the bond holder in all situations (e.g. if rates fall, prices increase at an increasing rate…and when rates increase, prices fall at a decreasing rate). Either one of these scenarios benefits the bond holder. So negative convexity is just the opposite and will have a negative effect when rates rise or decline.

What did you score on the AM section on the Stalla Mock? I took it today and got a 75, took me 4ever to complete tho. It seemed like every question required multi step calcs. The fixed income section killed me, got 4 wrong! I’ll review 2morrow

got 73 % didnt time and it really took me a long time to do this mock. got pretty much everything on fix inc and fsa wrong. did you understand the fix inc explanations? the FSA adjustments were difficult as well…i dont always agree with their answers…in one sections they wanted us to bring goodwill up to its fair value while the CFAI says to remove goodwill together. very confusing…

yea CFAI says to remove goodwill? lol Stalla never said that. Peter Olinto did mention that some analysts remove goodwill altogether but never said that was the standard. The adjustments were def rough. I didn’t watch the explanations yet for the questions, I’ll work on that this afternoon