 # quick immunization Q

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) under no circumstances, because risk minimization is the point of immunization. B) 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. C) 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. Your answer: C was incorrect. The correct answer was B) 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. In immunizing a portfolio a manager must consider a trade off between risk minimization and return maximization. Taking on extra risk under the indicated circumstances is appropriate. The probability of not meeting the liabilities can be allowed to decrease a little. There is no strict rule about the return and risk levels remaining “proportional”. -------------------- why is C incorrect? is it simply b/c it would be unrealistic/unexpected for a higher risk/higher return strategy (strategy B) to have a higher chance of meeting liabilities? thank you in advance.

I chose C too , but since we’re talking probabilities and the question does not set a requirement for a minimum probability , I suppose B is correct . The question has a funny wording

higher risk with higher probability of meeting liabilities is kind of impossible. it will have a lower probability if the risk is higher, wouldn’t it.

B has lower probability of meeting the liability but manager can live with it. If manager needs a minimum of 99% he cannot chose B

jan - i see what youre saying. the fact that A has a 99% chance of satisfying liabilities kind of gives it away that B can’t be a higher % cpk - depends how you look at it i guess. if higher risk means higher returns then doesnt that mean you have a higher chance of meeting liabilities

think normal distribution. you are already at 99% (with your current mean and std deviation (risk)) when return increases and your return also increases - the probability will come down. (so equal or lower is a better answer). so long as you meet your liabilities, you are fine. the higher return gives you means to achieve that, you incur higher risk.

if the probability of meeting the liabilities is equal to or higher than that of Strategy A. …i say it is C still!

C is unrealistic. Taking more risk means the probability of not meeting liabilities increases, unless the model has a problem. This is valid since Strategy A meets the liabilities with 99% probability.

i agree its poorly worded but i focused on this if the probability of meeting the liabilities is equal to or higher than that of Strategy A. once u have higher prob of meeting liab and higher returns …ti my simple mind its a no brainer

Higher expected return is not the same as higher probability to meet liabilities. But i agree with you, though. The question is very questionable. its my horse i can flog it all i like C) 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 i still say C note the seconf part it says explicitly there is a higher prob of meeting liability coupled swith higher return…although i am not sure how A>B in probability yet B>A in terms of risk the show ny where did u get this?

I went with B. The way C is worded makes it sound rigid (e.g., “only”). At L3 they don’t seem to like rigid (if A then B) type answers.

in that case why not go with A, not only is it a vowel, its also the 1st letter of the alphabet

The question is not a well-written one, so one can argue until the cows come home. In CFA methodology, you would quantify this type of question and show the trade off: - Risk is measured as stddev of the portfolio. - Trade off is done by comparing some ratio, either with each other or some absolute criteria.In this case, it is more natural to use Sortino since there is a given threshold return. However, it is here the answer is wrong where it says “There is no strict rule about the return and risk levels remaining “proportional””. The ratio assumes proportional trade off: return needs to increase proportionally with risk (stddev) so that the ratio remains constant. Here is one example. threshold return (MAR) = 0.7% A: exp ret = 5%, downward stddev = 1.85% --> 0.009721 chance below MAR if normal distribution. B: 7% and 2.6% but somewhat higher kurtosis --> 0.009815 chance below MAR Sortino ratio prefers B in this scenario, but if you tweaks the assumptions slightly, the Sortino ratio would indicate otherwise. Anyway, it is all an academic discussion splitting hairs. In exam, I think you will get clear numbers to calculate appropriate ratios.

This type of questions looks like is from Stalla or Schweser, it’s too wordy to be from CFAI. Sometimes those providers try too hard to make it difficult and it doesn’t make sense.