Source: CFAI 2018 mock PM session, question no 32
In the contingent immunization,
What is the manager’s expectation regarding the yield curve movement
The answer is Fall
I actually can’t rationalize regarding the explanation.
If you’re fully hedged, the price change of the portfolio should be zero. If you’re underhedged the price change should be in the same direction as the price change of the underlying. If you’re overhedged the price change should be in the opposite direction of the price change of the underlying.
And, of course, you want the price change to be an increase.
Here, the portfolio is underhedged, so, looking for an increase, the manager must want a price increase on the underlying. Bond prices increase when interest rates fall.
Voilà.
Magician is on it. He has a net negative duration gap by underhedging, i.e. the duration of is assets is higher than his liabilities. Think back to %∆P(bond) = -MD*∆%Y (the simplified formula, I know). The duration on his assets is higher than that of his liabilities. The best way for this strategy to work is for his assets to benefit from a rate decrease causing a greater rise to the value of his assets than to those of his liabilities. If rates increased, his net longer duration assets would cause a larger percentage fall in their values than the liabilities, leaving him exposed.
It happens occasionally.
I try not to make it a habit, however; don’t want to get into a rut.
You are underhedged, so you must be expecting that something will work in your favor. Here you would benefit from falling rates (we look at the duration of assets &liabilities), because your assets will rise more than your liabilities. If you were overhedged, you would expect an adverse scenario —> rising rates (because your assets would fall more than your liabilities).
Can someone confirm the answer solution related to B is incorrect on this one.
“B is incorrect because if Ruelas believed rates would rise, he would under-hedge, leaving a net position that would benefit from rising rates.”
Wouldn’t he want to over hedge or fully hedge?
if he underhedges and his duration of assets is lower than the duration of liabilities he will benefit as rates rise because the PVL will fall further than PVA.
But the portfolio is already under hedged, I’m confused
“… has under-hedged, leaving a net position that will benefit from a reduction in interest rates, just as the unhedged position would benefit from a reduction in interest rates. Thus, he must believe interest rates will fall.”
The key here is that you’re underhedged in required nr. of futures which means you’re overhedged on duration.
So overhedged on duration , you expect rates to fall.
sorry man haven’t looked at the whole problem was just responding to the question above. You’d underhedge if you thought rates were increasing to make duration of assets lower than duration of liabilities. If you thought rates were decreasing, you could overhedge to make duration of assets higher than duration of liabilities to benefit from a greater increase from the lower rates. This is all assuming the duration of liabilities is higher than duration of assets before hedging (positive duration gap).
If the case is the opposite (sorry which is the case here) and he’s starting from a higher duration of assets (negative duration gap), underhedging would relate to leaving the duration of assets higher than liabilities and hoping rates fall. If he overhedges then he would make duration of assets lower than liabilities hoping rates rise.
Thanks, that’s what I understood initially.
So, they give a wrong explanation for why B (rise) is incorrect. They say he would under hedge if he expects rates to increase.
That would only be true if he had a positive duration gap (Da < Dl)
Hi magician,
I applied your analysis to example 7 in page 317 but didn’t get to the right answer.
An asset manager is asked to build and manage a portfolio of fixed-income bonds to retire multiple corporate debt liabilities. The debt liabilities have a BPV of GBP 36216, the portfolio of British government bonds have a BPV of GBP 24102. The negative duration gap of GBP 12114 are intentional. The futures BPV is 98.2533. Currently, the asset manager has purchased, or gone long, 160 contracts.
The solution is, the asset manager is over-hedging because the rate view is that 10-year yields will be falling.
Here is how I use your analysis:
The manager should buy 123 contracts to make duration gap 0. Now he has bought 160. He is over-hedging. This means the price change of the portfolio should be in the opposite direction of price change of the fixed income bonds. If we wish the price change of the portfolio to be positive, then the price change of the fixed income bonds should be negative, the interest rate should decrease.
Is there anything wrong with my logic? Thank u.
I see that I wasn’t as clear as I should have been four years ago.
When I used the term “underlying”, I meant “the original (net) underlying position”.
In the example that OP gave, the underlying was a net long position: 91.6k − 59.6k = +32k. The value of a net long position will increase when interest rates fall, and will decrease when interest rates rise. Therefore, underhedging will result in an increase when interest rates fall (same as the underlying (unhedged) position), and a decrease when interest rates rise, while overhedging will result in a decrease when interest rates fall (opposite the underlying position), and an increase when interest rates rise.
In your example, the underlying is a net short position: 24,102 − 36,216 = −12,114. The value of a net short position will decrease when interest rates fall, and will increase when interest rates rise. Therefore, underhedging will result in a decrease when interest rates fall (same as the underlying (unhedged) position), and an increase when interest rates rise, while overhedging will result in an increase when interest rates fall (opposite the underlying position), and a decrease when interest rates rise.
I hope that that helps.
I dint understand this…Pls do explain…