# Bond Portfolio Immunization

Schweser Qbank # 50353

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The manager of a bond portfolio must immunize the portfolio with respect to a given set of liabilities. The manager is choosing between two immunization strategies: Strategy A and Strategy B. Strategy A has a lower return, lower risk, and a 99% probability of providing the required return to meet the given set of liabilities. The manager should choose Strategy B:

A) if that strategy’s higher risk is justified by the higher return, and the probability of meeting the liabilities is equal to or only slightly lower than that of Strategy A.

B) if that strategy’s higher risk is justified by the higher return, and only if the probability of meeting the liabilities is equal to or higher than that of Strategy A.

C) only if the return and risk levels remain proportional.

D) under no circumstances, because risk minimization is the point of immunization.

Your answer: B was incorrect. The correct answer was A) if that strategy’s higher risk is justified by the higher return, and the probability of meeting the liabilities is equal to or only slightly lower than that of Strategy A.

Now, if A is correct… what should be the answer to the following:

Schweser Qbank # 50355

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The manager of a bond fund is assessing several choices in attempting to immunize a portfolio. To meet a predetermined liability, the manager needs a five percent return. Which of the choices below would be the best in pursuit of that goal? An immunized strategy with a target return equal to:

A) 5.0% with a 95% confidence interval at +/- 10 basis points.

B) 6.0% with a 95% confidence interval at +/- 100 basis points.

C) 5.2% with a 95% confidence interval at +/- 20 basis points.

D) 5.6% with a 95% confidence interval at +/- 50 basis points.

Your answer: B was incorrect. The correct answer was D) 5.6% with a 95% confidence interval at +/- 50 basis points.

Here I can understand why D is a better option than A or C. But, what’s wrong with B ? Isn’t B providing a higher return on higher risk with “slightly lower” probability of meeting the liabilities. B has a 2.5% probability of missing the liability and D might have a ~1.5% probability. But, B also has a 50% chance of more than 6% return as opposed to a ~5% chance D has.

how much lower is still “slightly lower” as per the answer to the first question ???

fsa-sucker, CFA

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D seems as the best choice here. From manager standpoint B, C, D, would be appropriate to meet his goal of 5% return even under worst case scenario. However, worst case scenario for D is 5.1% (5.6 - 50 basis points), whereas worst case scenarios for B and C are 5.0%, hence he chooses an alternative that meets his goal of 5% and provides highest potential under worst conditions as compared to two other choices. He doesn’t care much about upside, as long as his goal of 5% is met, so the fact that B has a chance of 6% return is irrelevant here.

I have to admit though, even given volkovv’s comment, there does seem to be an inconsistency. Schweser explicitly mentions upside as a consideration in the first question.

For the second question:

The reason for D could be that even on the downside it is generating a spread of 0.10 bps over the required return of 5% which could be profit for the management after meeting the liability requirement? Just guessing…

It’s a statistical question that slipped something by, tricky little b*stards. The issue is with liabilities, risk of not meeting liabilities usually trumps the chance of extra return.

A is out because there’s a 2.5% chance ( [100-95]/2 ) of having less than 4.9, which isn’t enough to meet liabilities. That’s the worst choice because the chance of not meeting liabilities is larger than 2.5%

B looks plausible because because there’s only a 2.5% chance of not meeting liabilities, but a 50% chance of getting more than 6%, which sounds yummy, but let’s compare other answers first.

C looks plausible too because there is also only a 2.5% chance of not meeting liabilities. Now, you don’t have as yummy an upside return scenario, but if you do have a shortfall, the chances are pretty good that it’s not very large. With B, if you’re in that 2.5% chance of shortfall, it could be substantially larger.

D is the right answer, but why? It’s because there is a 2.5% chance of getting less than 5.1% which is still more than the 5.0% you need. Therefore, the chance of a shortfall is even less than B and C, which is your first consideration.

OK, that’s my explanation after knowing the correct answer. I myself might have been tempted by B, but D definitely would have been given close consideration.

I think the issue with B is that the confidence interval is wider (SD is about 25 bps), so if you have a shortfall, it’s likely to be a lot larger than any of the others. I suppose you could calculate expected excess return divided by shortfall risk as a quasi-sharpe ratio, but unless they give you specific license to do that, you’re probably best doing the conservative thing.

(oops, reread the thread (in AM, can’t sleep), and agree that Schwesser is somewhat inconsistent because they do not specify in the question or the answer what the criterion for “only slightly lower” is). But with calculations, be conservative with risk unless otherwise instructed.

You want a quote? Haven’t I written enough already???

From my experience, Schweser Q bank are not only inconsistant, they suffer from “Frame Dependent” bias. I see your point with the 2nd question. However, I “invent” this “Sharp” ratio. If you use the E(R) of 6%/100bps=0.06, compare to E(R) of 5.6/50bps=.112. We are always tought to go with a higher “risk-award” ration port. Once again, you can call this as “risk-adjusted” return. Therefore, I think they are talking about given both port. can achieve the immunization goal, let’s go with the one that has lower standard deviation (risk)

Yep - If someone asks you the question “Which of the choices below would be the best in pursuit of that goal?” you need to ask what the loss-function is. Here they have this 0-1 loss where there is loss if you don’t meet the goal but all such loss is the same and there is no loss if you meet the goal, but never a gain. That’s a loss function not usually used in portfolio decisions.

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