Sunday, February 20, 2011

Why the duration of a Zero is the years to maturity?

Why the duration for a zero is the same as the maturity in years? I have never figured it out since L2 although I memorized it just for the sake of passing the exam. Here is a simple calculation on a zero coupon of maturity 10 years for $100 par. The discount rate, yield to maturity is the same. The various present values for the respective discount rates are:

4.50% 64.3927682
5.00% 61.39132535
5.50% 58.54305794

Duration = (V- - V+)/(2 * Vo * (Delta Y) )

V- = 64.3927682
V+ = 58.54305794
Vo = 61.39132535
Delta Y = 0.005

Thus, duration = 9.528561611

Hence, this demonstrate that duration of a zero is NOT equal to years. In fact, duration itself has no dimension. How could it be compared with a variable with dimension?

Sunday, February 13, 2011

CFA Level 3 Curriculum Changes (2010-2011)

I would like to share the changes of 2010 and 2011 for CFA Level 3 exams which I found from this link:

Friday, February 4, 2011

Rebalancing the Duration (Reading 28)

This Reading 28 is terrible because the author makes 'sweeping' statements without proof. Nevertheless I guess it is more qualitative than quantitative. So I just have to memorise it.

In the CFA text, rebalancing the fixed income portfolio is done by applying a rebalancing ratio to all securities to maintain the same asset allocation. But in the Schweser notes page 29 of the Reading 28, it also state an additional method called the controlling position method to rebalance the duration. But this second method changes the asset allocation significantly. It is also not in the CFA text. Why does Schweser notes want to add its own material in?