1. Consider two investment managers, manager A and manager B.
a. Manager A has a portfolio in which she is short short-term debt
(with maturity < 1 yr.) and long long-term debt
(with maturities 5-10 years).
She has matched her short and long positions so that her net
duration
is very close to zero.
b. Manager B has a portfolio in which he is long both short-term and long
- term debt, spanning maturities from 1 month to about 10 years.
The duration of his portfolio is about 6.0.
As part of their risk management duties, these managers will use interest
rate models to generate future rate scenarios, and then will gauge the
distribution of possible gains and shortfalls (i.e. profit and loss) for
their portfolio.
Which manager is in most dire (urgent) need of a multi-factor model (rather
than a 1-factor model) to get even a rudimentary picture of the potential
risk of his/her portfolio?
Bond's return is affected by various factors. Interest rate is just one of
them. In a long-short portfolio with almost zero duration, the interest rate
risk is roughly hedged out, and PM A's performance is mainly due to other
factors. PM B has a long only portfolio, for which a single factor model
based on interest risk should not be too far off from a multifactor model...
thus the conclusion.
Solution:
Manager A is in direr need of a multi-factor model. As she has a duration
of zero, her P&L will not change much under a parallel shift in interest
rates. If long-term rates rise, and short-term rates fall so that long-
maturity bonds fall in value while short-maturity ones increase, her
portfolio will likely suffer a substantial loss. She has a portfolio that
is sensitive to changes in the slope of the yield curve. A one-factor model
is designed to only capture one type of shape-change of the yield curve,
primarily in level.
Although Manager B would probably also benefit from a multi-factor model,
his portfolio is sensitive to changes in the level of the yield curve, as he
is long debt of all maturities, and his portfolio has a large duration.
The most prominent risk in his portfolio (a change in the level of the yield
curve) will be captured by a 1-factor model.
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