 # Quiz Question FI

Bakshi is a Bond Portfolio Manager , who has portfolio of \$40 million under investment which are partly financed by debt of \$17 million. Bakshi had a strong belief over the last few years of a decrease in interest rates and hence also took a long Tbond futures position equivalent to \$8 million of bond contracts. if ED of bonds is 5.1 , the future has ED of 6.2 and debt has ED of .07 calculate ED of overall combined portfolio for 100bps decrease in Interest rates a)5.66 b)6.66 C)10.97 D)11.56

C?

Just eyeballing it I’m pretty sure the answer’s A, but when I’m calculating it out, I’m getting 5.25. You sure that .07 for the debt isn’t a typo?

can someone also come up with the formula plz… not sure how to adjust the bond futures portion?

A?

level3aspirant Wrote: ------------------------------------------------------- > can someone also come up with the formula plz… > not sure how to adjust the bond futures portion? Duration is additive, so you simply add to the portion on the long bonds. Then you subtract the duration of the borrowed funds, but I’m still getting 5.25. OP, you got an answer and an explanation for us?

no way could be A. since you’re using leverage, the duration will always be higher than any individual duration. 5.66 < 6.2, so that’s out. I got C as well. D_mod = (D_port * P + D_future * F - D_borrowed * B) / I where P = amount in portfolio, F = amount of futures, B = amount borrowed, and Durations for each accordingly. I = amount invested, which is portfolio net of leverage. D_mod = (5.1 * 40 + 6.2 * 8 - .07 * 17) / (40 - 17) = 10.97438. C.

never seen using futures and its ED in leverage calculation. This is new to me. Barbosa - answer please

cfaboston28 Wrote: ------------------------------------------------------- > never seen using futures and its ED in leverage > calculation. This is new to me. > > Barbosa - answer please The answer is directly above you. What a stupid I am.

I get C as well.

I’m not sure I follow the logic of incorporating the the duration of the futures in the calculation of the original position duration. My approach was to first calc the leveraged duration based on D_mod = (Dp P - Db B)/E Then taking the weighted average of portfolio and the futures to find the total duration (because duration would be additive) w Dp + w Df = Dtotal Of course it gave me an answer not listed there, so can you point out the section in the curriculum that I now need to review?

I am getting the answer C, but the comment regarding "calculate ED of overall combined portfolio for 100bps decrease in Interest rates " seems to be misleading. Fixed Income portfolios composed of callable/putable bonds, mortgage backed securities, the duration would change but that is not given in the question. Am I reading too much?

This is from R30, L0S a… formula copied from CFAI text: Also for levered P, duration of E >> that of unlevered P, or D(E) = (D(a)A - D(l)L)/E, or Duration of Equity is [Duration of Assets * MV, Assets - Duration of Liab’s * MV, Liab’s] / Equity Wording “… 100 bps decrease in Interest Rates” is meant to confuse us… is true for any duration calculation!

@ mp2438 Wrote: i dont understand the logic of how you adjusted the duration of futures in there? it says “took a long Tbond futures position equivalent to \$8 million of bond contracts” SO why are we not adjusting it in denominator? TKVM

level3aspirant Wrote: ------------------------------------------------------- > @ mp2438 Wrote: > > i dont understand the logic of how you adjusted > the duration of futures in there? it says “took a > long Tbond futures position equivalent to \$8 > million of bond contracts” SO why are we not > adjusting it in denominator? TKVM My guess is that you are not required to put up 8 million in equity in order to gain that kind of exposure through the future. 8 million notional long bond contracts = 80 contracts. I am pretty sure that basic margin on the long bond is \$3,000 per contract, so you could argue that 240,000 should be added to the denominator.

C. Leverage adjusted duration Duration equity (Equity) = Duration assets (assetts) - duration liablilities (liabililities) Duration equity (17MM) = 40MM (5.1) + 8MM(6.2) - 17(.07) solve duration equity = 10.97 for 100 bps = 10.97 Alternatively, you could find the equity duration of the portfolio first, and then factor in the futures. It doesnt matter the order. Of you did it that way: Duration equity (Equity) = Duration assets (assetts) - duration liablilities (liabililities) Duration equity (17MM) = 40MM (5.1) - 17(.07) Solve for equity duration and you get 8.81 Then lever up the futures: Equity (equity duration) + futures notional (futures duration) / equity 23MM x 8.81 + 8MM x 6.2 = 252.33/ 23MM = 10.97…same answer You dont adjust in the denominator for the future (ie value of equity) because the future is assumed to have a negligible equity (small margin amount).

I think I see what I did wrong… I’m not sure I understand 100%, but it sounds like I need to included the Total Portfolio, the Futures, and the Borrowed funds in the denominator, adjusted by the respective durations; and then divide that whole thing by the Equity…?

@ 1morelevel i understood that why it’s fine even if we dont include futures amount in denominator (the margin will be very small) but now i am wondering why you have taken equity as 17 mn. ??? shouldnt it be 40 (assets)-17(liability) = 23 mn equity am i missing something else now?

Rustyrudder - you divide by net equity, assets - liabilities. Typo. How do i fix it? Level3aspirant - its a typo… i was transcribing from sloppy notes. Not sure how to fix it…

Correct answer is C) 10.97 Solution: COV of bonds = -5.1*.01*40000000 COV of debt = -.070*.01*17000000 COV of futures=-6.2*.01*8000000 Total Cov =2040000+11900+496000=2524100 Using \$(delta value)= - ED * .01 * (40000000-17000000)=2524100 Hence ED=10.97