# Immunizing a Bond Porfolio by Matching Duration and Convexity of Pension Assets and Liabilities

This post covers part of a Fixed Income March 2014 CIIA exam question that required the calculation of three weights (three unknown weightings) based on modified duration and convexity.

The formula for portfolio duration is needed for equation (2) and the modified durations from the table (highlighted in yellow) as well as the modified duration for the liabilities (given; below the table)

The formula for portfolio convexity is needed for equation (3) and the convexity values from table (highlighted in green) aswell as the convexity given for the liablities (given; below the table).

# Put-Call Parity Theorem – Graphic aswell as Formula

Put-Call Parity Theorem – Graphic aswell as Formula

The graph above is from the CIIA course book; used here for educational purposes.

The above table (put-call parity equation based combinations) shows that we can price a call or a put based on the the instruments that make up its synthetic version.

An example:

Let’s take a 3m American put and a 3m American call on the shares of ABC Corp, each with EUR 40 strike. The current share price is EUR 41.25, the put is priced at EUR 6.25, the call at EUR 4.125. The 3m zero coupon bond is trading at 97.42. Is the put correctly priced vs the call?

Using the above we first find the lower bound of the put and then calculate the lower bound.

The result shows us that the put is correctly priced vs the call.

# A Lower Bound Combination for European Calls / Puts (CIIA Preparation)

Above: Lower Bound Combination for European Calls / Below: Lower Bound Combination for European Puts

Something I found to be important for the exam preparation…

# Active Funds worth the cost (TER) of over 1% – Example Classic Fund

The Classic Fund run by Thomas Braun and Georg von Wyss is an interesting example of an active fund that has beaten its benchmark over the last 10-15 years returning an annulised 10.5%. Although it got clobbered in 2007 and 2008, even vs the benchmark. It has underperformed in 3 of the 7 past years. The fund managers approach worked best in 2000 and 2001, which is probably one of the reasons for the media attention the fund and portfolio managers regularly get, aswell as the very noteworthy performance in 2012 and 2013.

This is a very active fund as can be seen by their portfolio turnover rate of over 130%. With CHF 850m in this particular fund, that turns out to mean their brokers get orders for around CHF 3m every calendar day (so more like CHF 4.4.5m every trading day). This of course makes them a first call for sales and trading departments who in turn feed them what they think or know is the most valuable information.

On a sidenote this fund is also an example of what kind of regulation a fund occurs: They have 2 portfolio managers, 3 analysts, 1 compliance officer, 1 manager, 1 sales/analyst. Thanks to the large size of the fund, all those mouths can be fed without incurring to high of a TER. It is 1.3%. An ETF these days sets you back 0.3% on average I believe.